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Theoretical Investigation on Organic Magnetic Molecules Thesis Submitted in partial fulfillment of the requirements for the degree of

Doctor of Philosophy by Iqbal Abdul Latif (07403304)

Under the Guidance of Prof. Sambhu N. Datta

Department of Chemistry INDIAN INSTITUTE OF TECHNOLOGY BOMBAY July, 2012


Certificate of course work This is to certify that Mr. Iqbal Abdul Latif was admitted to the Ph.D. program on July 2007. He successfully completed all the courses required for Ph.D. program. The details of the course work are given below.

Sr. No.

Course No.

1

CH 805

2 3 4 5 6 7 8

CH 559 CH 560 CH 821 CH 831 CHS 802 HS 699 PH 801

Course name Stereochemistry and Reactivity of Compounds Solid State Chemistry and its Applications Quantum Chemistry Topics in Chemistry I Advanced Laboratory Techniques Seminar Communication and Presentation Skills Classical Methods of Particles and Fields Total credit

Credit 6.00 6.00 6.00 6.00 8.00 6.00 4.0 (PP) 8.0 (AU) 38.00

AU = Audited

Place: IIT Bombay

Deputy Registrar (Academic)


Contents Chapter 1:

Introduction: Importance of magnetic molecules: Brief history of organic magnetic molecules: Objective

1.1. 1.2. 1.3. 1.4. 1.5 1.6 Chapter 2:

2.2. 2.3. 2.4.

An Overview of Density Functional Theory 2.1.1 Electron Density from Wave Function 2.1.2 Hohenburg-Kohn Theorem 2.1.3 Kohn-Sham Formulation 2.1.4 Exchange-Correlation: With Dirac Exchange 2.1.5 Local Density Approximation 2.1.6 Generalized Gradient Approximation The Broken Symmetry State Methodology References

17 17 17 18 20 21 22 22 25 29

Very strongly ferromagnetically coupled diradicals from mixed radical centres I: nitronyl nitroxide coupled to oxo-verdazyl via polyene spacers

3.1. 3.2. 3.3. 3.4. Chapter 4:

2 2 6 9 11 13

Theoretical background and methodology

2.1.

Chapter 3:

Introduction Why Organic Molecules Brief History of Organic Magnetic Molecules A Qualitative Justification of Molecular Magnetism Objective of This Work References

Introduction Results and Discussion Conclusions Reference

32 35 43 44

Very strongly ferromagnetically coupled diradicals from mixed radical centers. II. Nitronyl nitroxide coupled to Tetrathiafulvalene via spacers

4.1. 4.2. 4.3.

Introduction Calculations Results and Discussion 4.3.1. General Results 4.3.2. Analysis of Results 4.3.3. Test case

48 49 53 53 59 65 i


4.4. 4.5. Chapter 5:

Chapter 6:

Introduction Calculations Results and Discussion Reference

74 78 78 85

Photoswitching and magnetic crossover in organic molecular systems

6.1 6.2 6.3

Introduction Calculations and Analysis Results and Discussion 6.3.1 General trends 6.3.2 Spin alternation 6.3.3 Effect of planarity 6.3.4 Analysis of BS solution 6.3.5 Absorption wavelength 6.3.6 Applicability Conclusions Reference

6.4 6.5

88 91 98 98 100 105 106 110 111 111 113

High magnetic exchange coupling constants: A DFT based study of the almost forgotten Schlenk diradicals

7.1 7.2 7.3 7.4 7.5 Chapter 8:

67 69

Unusually large coupling constants in diradicals obtained from excitation of mixed radical centers: A theoretical study on potential photomagnets

5.1. 5.2. 5.3. 5.4.

Chapter 7:

Conclusions Reference

Introduction Methodology Results and Discussion Conclusions References

116 117 122 125 126

The electronic structure of nitronyl nitroxide radical: An ab-initio relativistic two-component approach

8.1. 8.2.

Introduction Computational Details 8.2.1 Codes 8.2.2 Basis set 8.2.3 Geometry optimization 8.2.4 Nonrelativistic and relativistic treatments

130 131 131 132 133 135 ii


8.3.

8.4. 8.5.

Conclusions

Results and Discussion 8.3.1 Relativistic correction 8.3.2 Correlation energy 8.3.3 Spin density 8.3.4 Charge density 8.3.5 Coupling constant 8.3.6 Spin Interaction Conclusions References

135 135 137 138 142 146 148 150 152

154

Acknowledgment

iii


Chapter 1

Introduction Importance of magnetic molecules: Brief history of organic magnetic molecules: Objective


CHAPTER 1

2

1.1 Introduction Magnetism started with the discovery of ferromagnetism of iron lode in the early stage of human history. It has extensively contributed to human life, starting with the use of a compass and then the process of lifting iron, use of magnets and electromagnets in electrical equipments such as generators, etc. In modern era, magnetic materials have become indispensable for domestic and office purposes as well as in industrial activities. Because of the vast practical use of magnets, especially ferromagnets, magnetism has become one of the most essential issues in parts of basic physics and chemistry where the behavior of magnetic moments in solids is dealt. During the previous few decades, the knowledge gained in the basic science has opened up new trends of magnetism in the development of cutting-edge electronic device applications such as computer memory, magnetic tapes, floppy diskettes, and so on. Organic materials often possess interesting optical properties. This makes it possible to construct devices with new functionality. The study of organic materials in condensed matter physics has recently received a great impulse. This is because of the discovery of conducting polymers, superconducting charge-transfer salts, C60, etc. Conducting polymers, despite their flexibility, can have electrical conductivities as high as conventional metals such as copper. These have been used in the fabrication of polymer transistors and light-emitting-diode devices. Superconducting charge transfer salts can exhibit transition temperatures as high as 15 K. Carbon ‘buckyballs’ C60, a newly discovered allotrope of carbon, when appropriately doped, may exhibit superconductivity1,2 or even unusual magnetic properties. Organic molecular materials have an extraordinarily diverse range of magnetic properties. They can be used as purely organic magnets, the origin of magnetism being one or more unpaired spin. Organic molecules can be used either to mediate the magnetic interactions or to play a role in complexes with magnetic transition metal ions.

1.2 Why Organic Molecules The drive to produce purely organic ferromagnets partly comes from the desire to achieve something that was once thought impossible: making ferromagnetism in materials containing only s and p electrons. Heisenberg’s theory of ferromagnetism,3


CHAPTER 1

3

which was formulated in the 1930s and which introduced the concept of exchange, was thought not to be possible without d and f electrons. Conventional wisdom has it that carbon (containing only s and p electrons) does not have a spontaneous magnetic moment in any of its allotropes. Many organic radicals exist which have unpaired spins, but few were known to be stable enough to be assembled into crystalline structures. Even if the latter becomes possible, making a ferromagnetic alignment is usually impossible. Ferromagnetism is rather rare even among the elements, and it is generally found in elements of the d or f blocks. Molecule-based magnets4 are considered to be promising from several viewpoints. The concept of molecular design works effectively in developing magnetic materials. The various internal degrees of freedom are available for designing functionality in the molecule. Optically active magnets can be built by incorporating the optical function into molecular magnets.5,6 Magnetic sensing probes can be produced by introducing chemical functions into magnetic molecules. Electron-transfer functions can also be added to produce conducting, metallic, or even superconducting magnetic systems.7,8,9 Here, the concerted cooperation of conduction carriers and magnetic moments is expected to give unconventional magnetic features. These features have not been obtained in traditional magnetic materials, where the interaction between conduction carriers and magnetic moments, the so-called s-d interaction, plays an important role in producing strong metal magnets such as ferromagnetic iron. The multifunctionality in magnetic molecules is expected to produce diversified electronic molecular devices. Chemical modifications in molecules or molecular assemblies are advantageous in the design of magnetic materials. Addition of functional groups, substitution of a part of the molecule, modification of the molecular structure, etc. can vary the magnetic feature, chemical activity, and shape of the molecule. Molecules can be in 1-, 2-, and 3dimensional frameworks or in a cluster form. The systems are interesting from the point of view of a systematic and comprehensive investigation of magnetism, and also for applications in magnetic materials. For example, low-dimensional magnetic systems have provided good models to investigate the Haldane quantum spin chain, the spin Peierls transition and spin ladders.10,11,12


CHAPTER 1

4

Organic molecule-based ferromagnetism is also among the perspectives of molecular magnets. The discovery of the first organic ferromagnet, p-NPNN (2-(4nitrophenyl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazolyl-1-oxy-3-oxide),13-15

has

stimulated the race to find organic ferromagnetic materials. The trials for searching highTc organic ferromagnets are expected to bridge the gap between fundamental work and device applications. The study of ferromagnetism in solid-state physics has been traditionally concerned almost exclusively with the study of inorganic elements (for example Fe, Co, Ni), alloys (for example permalloy) and simple compounds (for example transition metal oxides). This field of study has provided numerous rewards based upon the exploitation of such materials. But, always the assumption was that the fundamental researches in physics need to be concentrated on chemically simple materials. This assumption is, of course, oversimplified. Certain organic materials are chemically very complicated. In spite of that some exciting studies in condensed matter physics can be attempted on them. The tunability resulting from the rich structure of carbon chemistry allows many small adjustments to be made to each molecule. In principle, materials can be tailor-made to exhibit desired properties. Of course, the structure–property relations can turn out to be remarkably complex. However there is an obvious advantage: the building blocks of these new organic materials are not atoms but molecules. Thus many of the primary initiatives in this field have come from organic chemistry and coordination chemistry. A selection of molecules forming the basis of the materials is shown in Figure 1.1. The shape of a molecule and its electronic structure play a crucial role in determining the intermolecular interaction in an ensemble and the resulting crystallographic structure and hence the observed physical properties. Intermolecular forces are typically weaker than interatomic forces. In a molecular crystal, they differ markedly from the strong, long range Coulombic forces found in ionic crystals. Molecular crystals are consequently rather soft. Their properties can be tuned by applying pressure. Because of the dominance of intramolecular forces over intermolecular forces, molecular dimensions and vibrational frequencies typically resemble those of the free


CHAPTER 1

5 R

Fullerene

O

O

O

O N

Galvinoxyl

NITR

R1

NO2

CH2 O

CH2

O N

N

N

N

N

N

N

R2

p-NPNN

DMX

R2

Verdazyl

O O

N

O O N

O

O

Tanol suberate

Figure 1.1. Structures of some important magnetic molecules.


CHAPTER 1

6

molecules. The intermolecular interaction, nevertheless, strongly influence properties such as charge transport leading to large correlation effects in the form of enhanced effective mass, superconductivity, and density of states.3

1.3 Brief History of Organic Magnetic Molecules Neutral organic radicals possess one or more unpaired electron and are often highly reactive. They can be stabilized by adding aromatic rings to delocalize the unpaired electron, or protected by introducing bulky substituents. Crystals of neutral organic radicals exhibit paramagnetism at high temperatures, provided dimerization can be prevented. The dimers usually show a very small negative Weiss constant, indicating weak antiferromagnetic interaction. This is to be expected, since the intermolecular overlap of the singly occupied molecular orbitals (SOMO) will tend to lead to a state with the character of a bonding orbital in which one SOMO has a spin up electron and the other has a spin down electron, and vice-versa. Thus the prospect for finding ferromagnetic interaction among organic molecules is limited. But in 1969, ferromagnetic interaction was identified in a crystal of galvinoxyl16 (molecular structure shown in figure 1.1). Magnetic susceptibility measurements gave a positive Weiss constant (19K). The crystal undergoes a phase transition at 85 K to a low temperature phase with strong antiferromagnetic interactions (J ≈ −260 kBK).17,18 In galvinoxyl, the almost planar radicals are arranged in stacks along the c axis. The high temperature susceptibility is well reproduced by a one-dimensional ferromagnetic Heisenberg model with J = 13 ± 1 kBK.19 Although it is difficult to fit the experimental data over the whole low temperature range because of small Χχ PT values, they are consistent with the singlet-triplet (S-T) model with J = −230 ± 20 kBK.19 Another early candidate for organic ferromagnet was tanol suberate (see figure 1.1). It is a biradical with formula (C13H23O2NO)2. The spin density is found to be located on the NO group and almost equally shared between the oxygen and the nitrogen atoms.20 The magnetic susceptibility measured down to liquid helium temperature follows a Curie–Weiss law with a positive Curie temperature (+0.7K). It therefore looked like a candidate for an organic ferromagnet. The specific heat exhibits a λ anomaly21 at 0.38 K


CHAPTER 1

7

which results from ferromagnetic spin alignment.22,23 Tanol suberate was actually found to be an antiferromagnet with a metamagnetic transition in a field of 6 mT. Following these early attempts, genuine organic ferromagnetism was first achieved by using a member of a family of organic radicals called nitronyl nitroxides.24 These have general molecular structure as shown by the molecule labeled NITR in Figure 1.1. Different systems can be obtained by varying the chemical group R, as illustrated by the specific examples shown in the Figure 1.2. Nitronyl nitroxides are extensively used as spin labels to mark biological systems. The unpaired electron in nitronyl nitroxide is mainly distributed over the two NO moieties. Some unpaired spin density is also distributed over the rest of the molecule. The central carbon atom of the O–N–C–N–O moiety is a node of the SOMO. Nitronyl nitroxides are chemically stable. The vast majority of them do not show long range ferromagnetic order. The discovery of long range ferromagnetism in one of the crystal phases (the β phase) of para-nitrophenyl nitronyl nitroxide (C 13H16N3O4, abbreviated to p-NPNN; see Figure 1.1, for molecular structure) was a boost, but the ferromagnetic transition temperature is very low, 0.65 K. Besides, it occurs only in one of its crystal phases.25 In fact, the transition temperatures of all nitroxide based organic radicals that show long range magnetic order are extremely low. NO2 N

N

O

O N

N

O

O N

(a)

N

(b)

O

O N

N

(c)

O

O N

N

(d)

Figure 1.2 Structures of some important magnetic molecules based on nitronyl nitroxide.

Verdazyls provide another family of stable organic radicals (Figure 1.1). Ferromagnetic

intermolecular

interactions

were

first

demonstrated

in

1,3,5-

triphenylverdazyl.26 The compound showed a positive Weiss constant of 1.6 K. Some


CHAPTER 1

8

variants on the structure in the form of oxo-verdazyl and thioxo-verdazyl were also reported.27 Substitutions can be made on several different positions on all these molecules. That might lead to a wide range of magnetic systems. It is particularly worthmentioning that ferromagnetism has been observed with TC = 0.21 K in p-CDpOV, TC = 0.68 K in p-CDTV and TC = 0.67 K in p-MeDpOV.28,29 These transition temperatures are comparable to that of the original p-NPNN nitronyl nitroxide organic ferromagnet. Examples of antiferromagnetism, weak ferromagnetism and spin–Peierls transitions have also been seen in verdazyl systems. The effect of randomly substituted antiferromagnetic and ferromagnetic Heisenberg interactions on a quasi-1D chain to be studied has been possible by alloying between differently substituted oxo-verdazyl radicals.30 Although the number of different verdazyl materials is large, detailed crystal structures have been obtained only in a few cases. Therefore it has not been possible so far to make a detailed study of the structure–property relationships in verdazyls. Very recently, an organic triradical with an open shell doublet ground state has been discovered.31 The material, 5-dehydron-m-xylylene (DMX; see figure 1.1 for molecular structure), is synthesized by reacting a xylene compound with fluorine. Sulfur-based radicals are also emerging as important building blocks for molecular magnets. The recent discovery of spontaneous magnetization below 35 K, associated with noncollinear antiferromagnetism in the β crystal phase of the dithiadiazolylmolecular radical p-NC(C6F4)(CNSSN)32 (see Figure 1.1 for molecular structure) has shown a good route towards higher transition temperatures in comparison to that of the nitroxide based organic radicals described earlier. It was found that TC for the sulfurbased material could be raised still further to 65 K by applying a hydrostatic pressure of 16 kbar.33 A dramatic development in molecular magnetism was provided in 2001 by the report from Makarova et al.34 They reported room temperature ferromagnetism in C60 fullerene polymerized at high temperature and pressure. It has since been reproduced by several other groups.35,36 The maximum permanent magnetization is found for samples polymerized around 800 K, just below the point at which the buckyballs collapse. At these conditions a two-dimensional rhombohedral polymer phase is produced containing layers of covalently bonded C60 molecules. The spontaneous magnetization is stable up to


CHAPTER 1

9

very high temperatures. The estimated Curie temperatures for different samples range from 500 K34 to 820 K35. Using electron microscopy and x-ray diffraction Wood et al

35

showed that the buckyballs are undamaged in the most magnetic phase. It suggests that the radical centers formed by the dangling bonds which are left over following the breaking up of the intermolecular bridging bonds in the polymer leads to the magnetism. The mechanism for the magnetic coupling between these radical centres is not yet wellunderstood. The magnetization is very small and is not uniformly distributed throughout the sample. Nevertheless, it shows that a strong magnetic coupling is possible in a system containing only carbon atoms. This discovery is highly encouraging for the development of molecular ferromagnets with high transition temperatures.

1.4 Qualitative Justification of Molecular Magnetism The behavior of magnetic moments is governed by the competition between thermal agitation and the exchange interaction that couples the magnetic moments. The exchange interaction is described as given in the following equation:

Hˆ  2 JSˆi  Sˆ j ,

(1.1)

where J and S i are the coupling constant of the exchange interaction and the spin operator at site i, respectively. Ferromagnetism is a state in which spins are aligned in parallel. It is stabilized as the temperature is lowered enough to overwhelm the thermal agitation when J is positive, and negative J gives antiferromagnetism with spins arranged anti-parallel to each other. In practice, only ferromagnetism is of interest. Antiferromagnetic materials have no net magnetization. Though they are less important from the viewpoint of applications, they are of theoretical interest. As a qualitative explanation it can be stated that the magnetic moment on the galvinoxyl radical is due to the SOMOs. The next-highest occupied molecular orbital, (NHOMO) for downspin, is higher in energy than the SOMO for upspin because of the large intramolecular exchange. Thus there is a large spin polarization. The intermolecular SOMO–SOMO overlap is very small. A singlet state (antiferromagnetic alignment) is stabilized by resonance with an excited charge transfer configuration involving intermolecular SOMO–SOMO overlap. Because this overlap is small in galvinoxyl, the


CHAPTER 1

10

triplet state (ferromagnetic alignment) is stabilized by resonance with excited charge transfer configurations involving intermolecular interactions between the SOMO on one molecule and the fully occupied molecular orbital on the other.37

up-spin

down-spin

SOMO NLUMO

MO energy, ε e-1/V

NLUMO

SOMO

4-th HOMO

NHOMO

NHOMO

Galvinoxyl

p-NPNN

Figure 1.3. Relative energies of the molecular orbitals in galvinoxyl [38] (left) and p-NPNN (right) [29] (not to scale). NLUMO=next-lowest unoccupied molecular orbital; SOMO=singly occupied molecular orbital; HOMO=highest occupied molecular orbital; NHOMO=next-highest occupied molecular orbital.

Large spin polarization can be achieved from a strong intramolecular exchange. It can be obtained by using electronegative atoms such as oxygen or nitrogen. An extended π system also promotes the SOMO–NHOMO interaction.38


CHAPTER 1

11

The crystal structure must be such that it minimizes the intermolecular SOMO– SOMO overlap. The overlap between the SOMO on one molecule and the NHOMO/NLUMO (NLUMO = next-lowest unoccupied molecular orbital) on the other can be such that the regions of positive spin density on one molecule overlap with regions of negative spin density on the other molecule, thereby leading to ferromagnetic interactions.39 Galvinoxyl fulfills many of the conditions necessary to be an organic ferromagnet above the phase transition at 85 K. The overlaps in all these materials which favour ferromagnetism appear to agree with the McConnell mechanism.39 The McConnell model is given by

H AB   S A  S B  J ijAB iA  Bj ,

(1.2)

ij

SA and SB being the total spin operators for A and B molecules; and ρ iA and ρjB , the πspin densities on atoms i and j of A and B molecules; HAB being the spin Hamiltonian. Due to spin polarization effects positive and negative spin density mostly exist on different parts of each molecule. As a result intramolecular exchange interactions tend to be antiferromagnetic. But in some special case it is quite possible that radicals might sit on top of one another in the crystal lattice such that the atoms of positive spin density are exchange coupled most strongly to atoms of negative spin density in neighboring molecules, thus leading to a ferromagnetic exchange interaction of parallel (total) spin angular momentum on neighboring molecules.

1.5 Objective of This Work The main objective of my work is to predict organic magnetic molecules with very high magnetic coupling constants and also some tunable magnets. This is more related to material science. I have studied magnetic properties of various sets of organic molecules by Computational Quantum Chemistry, mainly density functional theory (DFT), using Gaussian code. To achieve these aims five sets of organic molecules have been investigated by quantum chemical methods. The work is arranged as follows. In Chapter 2, I describe theory and general methodology. In Chapter 3 mixed diradicals that are very strongly ferromagnetically coupled are proposed. These are combinations of monoradical centers


CHAPTER 1

12

nitronyl nitroxide and oxo-verdazyl via polyene spacers. In Chapter 4, another series of very strongly ferromagnetically coupled diradicals are proposed. These diradicals are combinations of monoradical centers nitronyl nitroxide coupled to tetrathiafulvalene via polyene spacers. In both the chapters 4 and 5, diradical nature and percent of ionic character of the broken symmetry solution of all the diradicals are discussed. In Chapter 5, a theoretical study is presented on potential photomagnets with unusually large coupling constants. Chapter 6 gives an illustration of photoswitching magnetic crossover in organic molecular systems. A DFT based study, with high magnetic exchange coupling constants, on almost forgotten Schlenk diradicals has been reported in Chapter 7. In Chapter 8, an examination is performed on whether a DFT calculation using a small basis set can give rise to a reliable estimate of J for a diradical that consists of nitronyl nitroxide mono-radicals and a spacer.


CHAPTER 1

13

1.6 References: 1. Rosseinsky, M. J. J. Mater. Chem. 1995, 5, 1497. 2. Tanigaki. K. and Prassides, K. J. Mater. Chem. 1995, 5 1515. 3. Ishiguro T, Yamaji K and Saito G Organic Superconductors Berlin: Springer 1998. 4. (a) Coronado, E., Delhae`s, P., Gatteschi, D., Miller, J. S., Eds.; Kluwer .Molecular Magnetism: From Molecular Assemblies to the Devices; Academics Publishers: Dordrecht, 1996. (b) Enoki, T.; Yamaura, J.-I.; Miyazaki, A. Bull. Chem. Soc. Jpn. 1997, 70, 2005. (c) Lahti, P. M., Ed.; Magnetic Properties of Organic Materials; Marcel-Dekker: New York, 1999. (d) Molecular Magnetism, New Magnetic Materials; Ito, K., Kinoshita, M., Eds.; Gordon and Breach Science Publishers: Tokyo, 2000. (e) Magnetism: Molecules to Materials; Miller, J. S., Drillon, M., Eds.; Wiley-VCH: Weinheim, Germany, 2001. (f) Magnetism: Molecules to Materials II; Miller, J. S., Drillon, M., Eds.; Wiley-VCH: Weinheim, Germany, 2001. (g) Magnetism: Molecules to Materials III; Miller, J. S., Drillon, M., Eds.; Wiley-VCH: Weinheim, Germany, 2001. (h) Magnetism: Molecules to Materials IV; Miller, J. S., Drillon, M., Eds.; Wiley-VCH: Weinheim, Germany, 2003. (i) Ouahab, L.; Enoki, T. Eur. J. Inorg. Chem. 2004, 933. 5. Decurtins, S.; Gu¨ tlich, P.; Spiering, H.; Hauser, A. Inorg. Chem. 1985, 24, 2174. 6. Sato, O.; Iyoda, T.; Fujishima, A.; Hashimoto, K. Science 1996, 272, 704. 7. Enoki, T.; Yamaura, J.-I.; Miyazaki, A. Bull. Chem. Soc. Jpn. 1997, 70, 2005. 8. Kobayashi, H.; Tomita, H.; Naito, T.; Kobayashi, A.; Sakai, F.; Watanabe, T.; Cassoux, P. J. Am. Chem. Soc. 1996, 118, 368. 9. Coronado, E.; Galan-Mascaros, J. R.; Gimenez-Saiz, C.; Gomez-Garcia, C. J. Proceedings of the NATO Advanced Research Workshop on Magnetism: A Supramolecular Function; Academic Press: New York, 1996. 10. Miller, J. S. and Drillon, M., Ed.; 2001 Magnetism: Molecules to Materials vol 1–3 Weinheim: Wiley–VCH. 11. de Jongh, L. J.; Miedema, A. R. Adv. Phys. 1974, 23, 1. 12. Magnetic Properties of Layered Transition Metal Compounds; de Jongh, L. J., Ed.; Kluwer Academic Publishers: Dordrecht/Boston/London, 1990. 13. Kinoshita, M.; Turek, P.; Tamura, M.; Nozawa, K.; Shimoi, D.; Nakazawa, Y.; Ishikawa, M.; Takahashi, M.; Awaga, K.; Inabe, T.; Maruyama, Y. Chem. Lett. 1991, 1225. 14. Tamura, M.; Nakazawa, Y.; Shimoi, D.; Nozawa, K.; Hosokoshi, Y.; Ishikawa, M.; Takahashi, M.; Kinoshita, M. Chem. Phys. Lett. 1991, 186, 401. 15. Takahashi, M.; Turek, P.; Nakazawa, Y.; Tamura, M.; Nozawa, K.; Shimoi, D.; Ishikawa, M.; Kinoshita, M. Phys. Rev. Lett. 1991, 67, 746.


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14

16. Mukai, K. Bull. Chem. Soc. Japan 1969, 42, 40. 17. Awaga, K.; Sugano, T. and Kinoshita, M. Chem. Phys. Lett. 1986, 128, 587. 18. Awaga, K.; Sugano, T. and Kinoshita, M. J. Chem. Phys. 1986, 85, 1211. 19. Sugano, T. Polyhedron 2001, 20, 1285. 20. Brown, P. J.; Capiomont, A.; Gillon, B. and Schweizer, J. J. Magn. Magn. Mater. 1979, 14, 289. 21. Saint-Paul, M. and Veyret, C. Phys. Lett. A 1973, 45, 362. 22. Benoit, A.; Flouquet, J.; Gillon, B. and Schweizer, J. J. Magn. Magn. Mater 1983, 31–34, 1155. 23. Chouteau, G. and Veyret-Jeandey, C. J. Physique 1981, 42, 1441. 24. Lahti, P. M., Ed; Magnetic Properties of Organic Materials 1999 New York: Dekker. 25. Tamura, M.; Nakazawa, Y.;, Shiomi, D.;, Nozawa, K.;, Hosokoshi, Y.;, Ishikawa, M.;, Takahashi, M. and Kinoshita, M. Chem. Phys. Lett. 1991, 186, 401. 26. Allemand, P-M.; Srdanov, G. and Wudl, F. J. Am. Chem. Soc. 1990, 112, 9391. 27. Neugebauer, F. A.;, Fischer, H. and Krieger, C. J. Chem. Soc. Perkin Trans. 1993, 2, 535. 28. Mukai, K.;, Konishi, K.;, Nedachi, K. and Takeda, K. J. Phys. Chem. 1996, 100, 9658. 29. Itoh, K. and Kinoshita, M., Ed.; 2000 Molecular Magnetism, New Magnetic Materials Tokyo: Kodansha., Amsterdam: Gordon and Breach. p 216 30. Mukai, K.;, Suzuki, K.;, Ohara, K.;, Jamali, J. B. and Achiwa, N. J. Phys. Soc. Japan 1999, 68, 3078. 31. Slipchenko, L. V.;, Munsch, T. E.;, Wenthold, P. G. and Krylov, A. I. Angew. Chem. Int. Edn Engl. 2004, 43, 742. 32. Palacio, F.; Antorrena, G.; Castro, M.; Burriel, R.; Rawson, J.; Smith, J. N. B.; Bricklebank, N.; Novoa, J. and Ritter, C. Phys. Rev. Lett. 1997, 79, 2336. 33. Mito, M.; Kawae, T.; Takeda, K.; Takagi, S.; ,Matsushita, Y.;, Deguchi, H.;, Rawson, J. M. and Palacio, F. Polyhedron 2001, 20, 1509. 34. MakarovaTL, Sundqvist B, HohneR,Esquinazi P,Kopelevich Y, ScharffP,DavydovVA, Kashevarova, L. S. and Rakhmanina, A. V. Nature 2001, 413, 716. 35. Wood R A, Lewis M H, Lees M R, Bennington S M, Cain M G and Kitamura N J. Phys.: Condens. Matter 2002, 14, L385. 36. Narozhnyi V N, M¨uller K-M, Eckert D, Teresiak A, Dunsch L, Davydov V A, Kashevarova L S and Rakhmanina A V Physica B 2003, 329–333, 1217 37. McConnell, H. M. Proc. R. A. Welch Found. Chem. Res. 1967, 11, 144. 38. Awaga, K.;, Sugano, T. and Kinoshita, M. Chem. Phys. Lett. 1987, 141, 540.


CHAPTER 1 39. McConnell, H. M. J. Chem. Phys. 1963, 39, 1910.

15


Chapter 2

Theoretical Background and Methodology An Overview of Density Functional Theory: The Broken Symmetry State: Method of Calculation:


CHAPTER 2.

2.1 2.1.1

17

An Overview of Density Functional Theory Electron Density from Wave Function

The motivation for Density Functional Theory1,2 comes from the fact that the ground state property can be can be found from the ground state electron density only. The electron density can be expressed as a function of wave function as Z ρ(r1 ) = Ψ∗ (r1 , r2 , . . . , rn )Ψ(r1 , r2 , . . . , rn )dr2 , . . . drn .

(2.1)

The advantage of DFT approach over wave functional approach is that for an N electron system number of variable is 3 (or 4 if spin is included) whereas for wave functional approach the number of variable is very high 3N (4N for spin included). The earlier work on the development of DFT started from the work of Thomas and Fermi.3 The the total energy was given by the kinetic energy of a uniform electron gas and the classical electrostatic energy between electrons gas and the nuclei. Dirac extended it by adding exchange energy between electrons themselves.4 But, in spite of that, it gave poor results because of large approximation of kinetic energy. It is the work of Kohn, Hohenberg, and Sham from where the modern density functional theory started. Where the Thomas-Fermy approach involved only electron density, Kohn-Shm reintroduced wave function in between density functional and total energy. The role of wave function is only an intermediate one.

2.1.2

Hohenburg-Kohn Theorem

The main theme of Hohenberg-Kohn theorem1 is that the ground state energy of an electronic system is a unique functional of the electron density. The kinetic energy is unique as the density is unique. Thus the potential energy v(r) is unique for a density ρ(r). Let us assume that there exist another potential energy v 0 (r) which corresponds to the same density ρ(r). Let these two potentials give two Hamiltonian operators H and H 0


CHAPTER 2.

18

that correspond to the ground state density ρ(r) but they have different wave functions Ψ and Ψ0 . Thus HΨ = E0 Ψ and H 0 Ψ = E00 Ψ0 . From variational principle, ˆ 0i E0 < hΨ0 |H|Ψ ˆ 0 |Ψ0 i + hΨ0 |H ˆ −H ˆ 0 |Ψ0 i < hΨ0 |H Z 0 < E0 + ρ(r1 )[v(r1 ) − v 0 (r1 )].

(2.2)

Similarly, ˆ 0 |Ψi E00 < hΨ|H ˆ ˆ 0 − H|Ψi ˆ < hΨ|H|Ψi + hΨ|H Z < E0 − ρ(r1 )[v(r1 ) − v 0 (r1 )].

(2.3)

Adding 2.1 and 2.2 leads to E0 + E00 < E00 + E0 , which is a self contradiction. Thus it can be concluded that two different potential v(r) cannot give rise to the same ρ(r). That is, density is a unique functional of the potential. In turn, the ground state energy is a unique functional of particle density. This is the Hohenburg-Kohn Theorem.

2.1.3

Kohn-Sham Formulation

Just like the Hartree-Fock formulation, the Kohn-Sham formulation centers on mapping the fully interacting system with real potential onto a fictitious non-interacting system where the electron moves within an effective “Kohn-Sham” single particle potential vKS (r).2 The advantage of Kohn-Sham method is that the exchange-correlation energy, incorporated in the Hamiltonian, is taken care of within the single determinantal approach. This is unlike the post-Hartree-Fock approaches, and the reason for Kohn-Sham approache to be computationally less expensive. The variation of total ground state energy with the added constraint

R

n(r)dr − N = 0


CHAPTER 2.

19

multiplied by a Lagrange multiplier looks like Z Z δ[F [n(r)] + vext (r)n(r) − µ( n(r)dr − N )] = 0.

(2.4)

The corresponding Eular Equation would be µ=

δF [n(r)] + vext (r). δn(r)

(2.5)

Removal of one of the major sources of error of Thomas-Fermy Model (TFM), namely, the approximation to kinetic energy, was achieved by Kohn-Sham model by invoking a noninteracting system of electrons. The corresponding wave-function, ΨKS , for this type of system is given by a determinant of single-particle orbitals ψi (ri ), 1 0 ΨKS = √ det[ψ10 (r1 )ψ20 (r2 ) . . . ψN (rN )]. N

(2.6)

The universal functional F [n(r)] written above can be partitioned into three parts. First two parts can be determined almost exactly, and also constitute the major part. The third part, though very small and unknown plays the most important role in DFT. It is known as exchange-correlation energy. F [n(r)] = TS [n(r)] + EH [n(r)] + EXC [n(r)]

(2.7)

TS [n(r)] is the kinetic energy of electron assuming them to be non-interacting gas of density n(r). EH [n(r)] is the electron-electron interaction energy also known as Hartree energy. ZZ n(r)n(r0 ) 1 drdr0 (2.8) EH [n(r)] = 0 2 |r − r | The Eular equation can be rewritten as µ=

δTS [n(r)] + vKS (r), δn(r)

(2.9)

where vKS (r) = vext (r) + vH (r) + vXC (r).

(2.10)


CHAPTER 2.

20

Comparing 2.7, 2.9, and 2.10 the following two equation can be written: ZZ n(r)n(r0 ) δEH [n(r)] = drdr0 , vH (r) = 0 δn(r) |r â&#x2C6;&#x2019; r |

(2.11)

δEXC [n(r)] . (2.12) δn(r) After some more calculation and writing kinetic energy separately an equation very similar vXC (r) =

to Fock equation appears. This is the Kohn-Sham equation. 1 [â&#x2C6;&#x2019; â&#x2C6;&#x2021;2 + vKS (r)]Ď&#x2C6;i (r) = i Ď&#x2C6;i (r), 2

(2.13)

where i is the Lagrange multipliers corresponding to the orthonormality of the N singleparticle states Ď&#x2C6;i (r). The density of electron is n(r) =

N X

|Ď&#x2C6;i (r)|2 .

(2.14)

i=1

The non-interacting kinetic energy TS [n(r)] looks N Z 1X TS [n(r)] = â&#x2C6;&#x2019; Ď&#x2C6;iâ&#x2C6;&#x2014; (r)â&#x2C6;&#x2021;2 Ď&#x2C6;i (r)d(r). 2 i=1

(2.15)

Thus in Kohn-Sham theory, in order to handle the kinetic energy in an exact manner, N equations have to be solved to obtain the set of Lagrange multipliers {i } whereas in Thomas Fermi model only one equation have to be solved to determine the multiplier Âľ. The main aim of Kohn-Sham theory was to make the unknown contribution to the total energy of the non-interacting system as small as possible. Though the contribution of exchange-correlation energy is very small, still it is an important contribution as the binding energy of many systems is about the same size as EXC [n(r)]. So an accurate description of exchange-correlation energy is very much crucial in DFT.

2.1.4

Exchange-Correlation: With Dirac Exchange

As described in the previous section, the accuracy of the exchange-correlation energy is the central importance in DFT. The history of EXC stem from the addition of exchange


CHAPTER 2.

21

energy term to Thomas-Fermi model by Dirac.4 One of the shortcoming of Thomas-Fermi model is the oversimplified description of electron-electron interaction. Shortly after the introduction of TFM model Dirac develop an approximate expression for exchange interaction based on the homogeneous electron gas. The resulting formula is simple and a local functional of density. This is probably the first step toward addition of exchange-correlation energy term to classical energy Hamiltonian of atoms and molecules.  1/3 Z 3 3 Ex [n(r)] = â&#x2C6;&#x2019; n(r)4/3 dr 4 Ď&#x20AC; Relation 2.16 is written in terms of exchange energy density xc [n(r)] as, Z LDA Exc [n(r)] = n(r)xc [n(r)]dr, where xc [n(r)] can be given in terms of Seitz radius rs ,5  1/3 1 0.4582 3 9 â&#x2030;&#x2C6; â&#x2C6;&#x2019; . xc [n(r)] = â&#x2C6;&#x2019; 4 4Ď&#x20AC; 2 rs rs

(2.16)

(2.17)

(2.18)

Though it was very crude, it was the starting point for adding exchange-correlation potentials.

2.1.5

Local Density Approximation

The simplest approximation is that the exchange-correlation energy at any point of the system can be treated locally and same as that of an uniform electron gas of same density. This approximation holds for a slowly varying density. The exchange correlation energy for a density Ď (r) is given as LDA Exc

Z =

Ď (r)xc (Ď )dr.

(2.19)

where xc (Ď ) is the exchange-correlation energy per particle of an uniform electron gas of density Ď . Thus exchange-correlation potential can be given by LDA vxc [Ď (r)] =

LDA δExc δxc (Ď ) = xc (Ď ) + Ď (r) Î´Ď (r) δĎ

(2.20)


CHAPTER 2.

22

For practical use exchange-correlation energy xc [n(r)] is slitted into exchange and correlation energies xc [n(r)] = x [n(r)] + c [n(r)]. The exchange energy can be given from Dirac functional4 3 xc [Ď (r)] = â&#x2C6;&#x2019; 4

  13 3 Ď (r). 4

(2.21)

Values for c (Ď ) have been determined from Quantum Monte Carlo calculations.6 Thereafter analytic forms for c (Ď ) are created by interpolation.

2.1.6

Generalized Gradient Approximation

In LDA approximation the xc [n(r)] is a function of a local and constant density and does not care about the space-future of the density. It holds good for a system of slowly varying density. But it fails in situations, like in molecules, where the density undergoes a rapid change after certain distance. To improve xc [n(r)] one should include space-future of electron density. Gradient of electron density tells about that future. Thus an improvement is made in GGA (Generalized Gradient Approximation). In it xc [n(r)] is made a function of electron density gradient â&#x2C6;&#x2021;(Ď ) also. Hence the exchange-correlation energy function in GGA looks like xc = xc [Ď (r), â&#x2C6;&#x2021;Ď (r)].

(2.22)

Nowadays a lot of work is going on to get a good analytical form of xc .

2.2

The Broken Symmetry State

A very effective way of estimating J with less computational effort is a DFT formalism established by Noodleman.7 Post HF methods are reliable in computing J value, but they take a lot of computational time. If one can apply DFT, it will be very much cost effective. But the problem with DFT is that it is very difficult to get the energy of a pure spin state. Moreover, in an unrestricted formalism, it is not possible to calculate the diradical singlet.


CHAPTER 2.

23

Noodleman proved that any mixed spin state can be approximated by a weighted average of different spin states. Noodleman’s treatment is as follows. If B corresponds to a mixed state and S to pure spin states then according to Noodleman:7 |ψB i =

X

A(S)|ΨS i

(2.23)

S

Let us consider two interacting centers A and B and the related spatially orthogonal magnetic orbitals ai and bi on A and B, respectively. If there is one unpaired electron in each magnetic orbital a1 and b1 , then the BS determinant can read as |ψB i = (N !)−1/2 M −1/2 det[(a1 + cb1 )αa2 α . . . an α(b1 + ca1 )βb2 β . . . bn β]

(2.24)

where M is the normalization factor. The latter can also be expressed as |ψB i = M −1/2 [φ1 + c(φ2 + φ3 ) + c2 φ4 ].

(2.25)

Let us drop φ4 as it depends on c2 . The other contribution can be written as, φ1 : the purely covalent (A-B)-state, φ2 and φ3 : the charge transfer states for A+−B − and A−−B + . Using Lowdin8 and Nesbet9 spin projection technique it is possible to write φµ =

XX S

S MSOφν .

(2.26)

Ms

If φν be a slater determinant constituted by orthonormal orbitals, we get S MSOφν

= AS (S, MS )[φν +

X

χνµ (S, MS )].

(2.27)

µ

Using the orthoganality theorem for irreducible representations, one obtains 0

0

hSMSOφµ |H|SMSOφν i = hφµ |H|SMSOφν iδSS 0 δM M 0 .

(2.28)


CHAPTER 2.

24

From the above discussion the energy of the BS state comes as, X 1 X [A1 (S)hφ1 |H|φ1 + χ1µ φ1µ i M S µ X + c2 A2 (S)hφ2 |H|φ2 + χ2µ φ2µ i

hψB |H|ψB i =

µ 2

+ c A3 (S)hφ3 |H|φ3 +

X

χ3µ φ3µ i

(2.29)

µ

+ 2cA1 (S)hφ2 |H|φ1 +

X

χ1µ φ1µ i

µ

+ 2cA1 (S)hφ3 |H|φ1 +

X

χ1µ φ1µ i]

µ

where Ai (S) are the vector coupling coefficients of the φi states which can be expressed in terms os S, n and Smax . Now if n be the total number of magnetic electrons on the two centres, then the resulting state φ1 will be

and



n −n

|SA SB i =

2 2

(2.30)

2   n n n −n S; 0 A1 (S) = c 22 2 2

(2.31)

where c(SA SB S; Ma Mb M ) is a Clebsh-Gordan coupling coefficient.1 With the help of some more constraints and after some more derivation one finally gets the energy of the BS state as7

 X 

1

n − S(S + 1)

hψB |H|ψB i = < φ1 |H|φ1 > + A1 (S) × ai b j ai b j n2 r12 i,j S   X n(n + 1) − S(S + 1) + A1 (S) n2 S

   

1

Sa¯2¯b

× 2Sa¯¯b ha1 |h|b1 i + ai bj ai bj + (E2 − E1 ) (2.32) r12 2 X




CHAPTER 2.

25

With some similar calculations one get the energy of a pure spin state as

 X  

1

n − S(S + 1)

× ai b j ai b j hψS |H|ψS i = < φ1 |H|φ1 > + n2 r12 i,j   n(n + 1) − S(S + 1) + n2

   

1

Sa¯2¯b

(E2 − E1 ) (2.33) × 2Sa¯¯b ha1 |h|b1 i + ai bj ai bj + r12 2 From equation 2.32 and 2.33 one can say that the energy of the BS state is a weighted average of the energies of pure spin states and it is also a function of Sa¯¯b , the overlap integral of the magnetic orbitals.

2.3

Methodology

The magnetic exchange interaction between two magnetic sites is normally expressed by the Heisenberg effective Hamiltonian in Eq. (1.1). The eigenfunctions of the Heisenberg Hamiltonian are eigenfunction of S 2 and Sz where S is the total spin angular momentum and directly related to the energy difference between the spin eigenstates. For a diradical, E(S = 1) − E(S = 0) = −2J

(2.34)

One can evaluate J by determining the proper singlet and triplet energy values from a multiconfigurational approach. In literature some MCSCF calculations have been reported on bisverdazyl10 and TME based systems.11 In general, this method faces two major problems. Firstly, it is cumbersome (multiconfigurational) and omits a large amount of correlation corrections (like in CAS [2, 2]). Secondly, a single determinantal wave function gives a poor representation of the ground state singlet, and therefore, an unrestricted approach to yield a proper accounting of this exchange is not feasible. However, Illas et al.12a have


CHAPTER 2.

26

carried out CASSCF calculations for bisverdazyl and discussed the way of effectively introducing dynamical correlation through the CASPT2 method. Within CAS [2, 2], the description of the open-shell singlet is neither single determinantal nor monoconfigurational.12b As broken symmetry method is a reliable alternative way of estimating the energy of pure spin states with much less computational effort, we have used this method for calculating the J values. In the calculations, the spin-polarized, unrestricted density functional method has been used. The BS state is not a pure spin state but an artificial state of mixed ˆ or Sˆ2 . It is an alspin symmetry and lower spatial symmetry. It is not an eigenstate of H most equal mixture of singlet states and triplet states. The coupling constant can be written as J=

(EBS − ET˜ ) 2 1 + Sab

(2.35)

where Sab is the overlap integral between the two magnetically active orbitals a and b. The quantity EBS is the energy of the broken-symmetry solution, and is the energy of triplet state in the unrestricted formalism using the BS orbitals. It is known that there is less spin contamination in the high-spin state in a single-determinantal approach. Hence, ET˜ can be approximated by the triplet state energy which is achieved from a direct computation. The BS state is often found as spin-contaminated. One has to eliminate the effect of spin contamination from the energy of the BS state. To achieve this end, spin-projected methods have been proposed. Equation (2.35) is valid when there is only one pair of magnetically active orbitals. From the same basic methodology, the following three additional spinprojected equations were obtained and these are valid for different general cases:  DF T DF T E − E BS T J GN D = , 2 Smax  DF T EBS − DF T ET B J = , Smax (Smax + 1)  DF T DF T E − E BS T JY = . hS 2 iT − hS 2 iBS

(2.36)

(2.37) (2.38)


CHAPTER 2.

27

These three equations differ in their applicability depending upon the different degree of overlap between the magnetic orbitals. Equation (2.36), (J GN D ), developed by Ginsberg,13 Noodleman et al.,7c,d and Davidson14 (GND), is applicable to the weak overlap limit whereas Eq. (2.37) (J B ) has been proposed by Bencini et al.15 According to Ruiz et al.16 the overlap in Eq. (2.35) is large in binuclear complexes and hence Eq. (2.37) holds. Nevertheless, Illas et al. have explicitly calculated that the overlap is indeed negligibly small. Thus EBS cannot be taken as E(S = 0).12b Equation (2.37) is generally found to be applicable for binuclear transition metal complexes. Equation (2.38), (J Y ), which can be reduced to Eq. (2.36) and Eq. (2.37) in the weak and strong overlap limits respectively, has been derived by Yamaguchi et al.17 Equation (2.38) is equivalent to the proposal by Illas et al. that the BS solution is approximately 50% singlet and 50% triplet.18 In order to avoid a misconception, we put forward a caveat that the strong overlap limit does not hold for practical systems. Therefore, Eq. (2.37) may be overlooked. Borden, Davidson, and Feller19 discussed that the ROHF calculations provide qualitatively correct molecular orbitals but in general fail to produce the correct molecular geometry. They suggested the use of the UHF methodology for a reasonably correct description of triplet (T,S=1) and open-shell singlet, (S, S=0) geometries. We have used spin-polarized unrestricted density functional theory (DFT), more specifically, the UB3LYP method, for both geometry optimization and single point calculation. For diradicals, the ideal BS state corresponds to hS 2 i = 1. Illas et al. found that it is always good to start with correct molecular orbitals for finding the BS solutions.20 Hence, the symmetry breaking in the wave function in the BS calculations has been achieved by using restricted open-shell wave functions for the optimized triplet structure, and then using the corresponding molecular orbitals as an initial guess. All the calculations have been performed by using the Gaussian 03 software.21 Recently, Truhlar et al.22 have proposed the MO6 functional for DFT and found that this functional is about equally as accurate as B3LYP. Range-separated hybrid functionals have


CHAPTER 2.

28

been investigated by Scuseria et al.,23 who have concluded that these functionals provide a significant improvement to B3LYP functional. Nevertheless, much more investigation is required to make the new functionals standard, and therefore, we have opted for the standard hybrids, namely, B3LYP.


CHAPTER 2.

2.4

29

References

1. Hohenberg, P. and Kohn, W. Phys. Rev., 1964, 136, B864. 2. Kohn, W. and Sham, L. J. Phys. Rev., 1965, 140, A1133. 3. (a) Thomas, L. H. Proc. Cambridge Philos. Soc., 1927 23, 542. (b) Fermi, E. Z. Phys., 1928, 48, 73. 4. Dirac, P. A. M. Proc. Cambridge Philos. Soc., 1930, 26, 376. 5. Seitz, F. The modern theory of solids; McGraw-Hill, 1940. 6. Ceperley, D. M. and Alder, B. J. Phys. Rev. Lett., 1980, 45, 566. 7. (a) Noodleman, L. J. Chem. Phys. 1981, 74, 5737. (b) Noodleman, L.; Baerends, E. J. J. Am. Chem. Soc. 1984, 106, 2316. (c) Noodleman, L.; Davidson, E. R. Chem. Phys. 1986, 109, 131. (d) Noodleman, L.; Peng, C. Y.; Case, D. A.; Mouesca, J.-M. Coord. Chem. Rev. 1995, 144, 199. 8. (a) Lowdin, P. O. Phys. Rev. 1955, 97, 1509. (b) Lowdin, P. O. Rev. Mod. Phys. 1962, 34, 80. 9. (a) Nesbet, R. K. Ann. Phys. 1958, 3, 397. (b) Nesbet, R. K. Ann. Phys. 1958, 4, 87. 10. Chung, G.; Lee, D. Chem. Phys. Lett. 2001, 350, 339. 11. (a) Nachtigall, P.; Jordan, K. D. J. Am. Chem. Soc. 1992, 114, 4743. (b) Nachtigall, P.; Jordan, K. D. J. Am. Chem. Soc. 1993, 115, 270. 12. (a) de Graaf, C.; Sousa, C.; Moreira, I. de P. R.; Illas, F. J. Phys. Chem. A 2001, 105, 11371. (b) Moreira, I. de P. R.; Illas, F. Phys. Chem. Chem. Phys. 2006, 8, 1645. 13. Ginsberg, A. P. J. Am. Chem. Soc. 1980, 102, 111. 14. Noodleman, L.; Davidson, E. R. Chem. Phys. 1986, 109, 131. 15. (a) Bencini, A.; Totti, F.; Daul, C. A.; Doclo, K.; Fantucci, P.; Barone, V. Inorg. Chem. 1997, 36, 5022. (b) Bencini, A.; Gatteschi, D.; Totti, F.; Sanz, D. N.; McClevrty, J. A.; Ward, M. D. J. Phys. Chem. A 1998, 102, 10545.


CHAPTER 2.

30

16. Ruiz, E.; Cano. J.; Alvarez, S.; Alemany, P. J. Comput. Chem. 1999, 20, 1391. 17. (a) Yamaguchi, K.; Takahara, Y.; Fueno, T.; Nasu, K. Jpn. J. Appl. Phys. 1987, 26, L1362. (b) Yamaguchi, K.; Jensen, F.; Dorigo, A.; Houk, K. N. Chem. Phys. Lett. 1988, 149, 537. (c) Yamaguchi, K.; Takahara, Y.; Fueno, T.; Houk, K. N. Theo. Chim. Acta 1988, 73, 337. 18. (a) Martin, R. L.; Illas, F. Phys. Rev. Lett. 1997, 79, 1539. (b) Caballol, R.; Castell, O.; Illas, F.; Moreira, I. de P. R.; Malrieu, J. P. J. Phys. Chem. A 1997, 101, 7860. (c) Barone, V.; di Matteo, A.; Mele, F.; Moreira, I. de P. R.; Illas, F. Chem. Phys. Lett. 1999, 302, 240. (d) Illas, F.; Moreira, I. de P. R.; de Graaf, C.; Barone, V. Theor. Chem. Acc. 2000, 104, 265. (e) Illas, F.; Moreira, I. de P. R.; Bofill, J. M.; Filatov, M. Phys. Rev. B 2004, 70, 132414. 19. (a) Borden, W. T.; Davidson, E. R. J. Am. Chem. Soc. 1977, 99, 4587. (b) Borden, W. T.; Davidson, E. R.; Feller, D. Tetrahedron 1982, 38, 737. (c) Feller, D.; Davidson, E. R.; Borden, W. T. Isr. J. Chem. 1983, 23, 105. (d) Kato, S.; Morokuma, K.; Feller, D.; Davidson, E. R.; Borden, W. T. J. Am. Chem. Soc. 1983, 105, 1791. 20. (a) Martin, R. L.; Illas, F. Phys. Rev. Lett. 1997, 79, 1539. (b) Caballol, R.; Castell, O.; Illas, F.; Moreira, I. de P. R.; Malrieu, J. P. J. Phys. Chem. A 1997, 101, 7860. (c) Barone, V.; di Matteo, A.; Mele, F.; Moreira, I. de P. R.; Illas, F. Chem. Phys. Lett. 1999, 302, 240. (d) Illas, F.; Moreira, I. de P. R.; de Graaf, C.; Barone, V. Theor. Chem. Acc. 2000, 104, 265. (e) de Graaf, C.; Sousa, C.; Moreira, I. de P. R.; Illas, F. J. Phys. Chem. A 2001, 105, 11371. (f) Illas, F.; Moreira, I. de P. R.; Bofill, J. M.; Filatov, M. Phys. Rev. B 2004, 70, 132414. 21. M. J. Frisch, et al., GAUSSIAN 03 (Revision E), Gaussian, Inc., Pittsburgh, PA, 2004. 22. Valero, R.; Costa, R.; Moreira, I. de P. R.; Truhlar, D. G.; and Illas, F.; J. Chem. Phys. 2008, 128, 114103. 23. Pablo, R.; Moreira, I. de P. R.; and Illas, F.; Scuseria, G. E.; J. Chem. Phys. 2008, 129, 184110.


Chapter 3 Very strongly ferromagnetically coupled diradicals from mixed radical centres I: nitronyl nitroxide coupled to oxo-verdazyl via polyene spacers Extremely large and positive intramolecular magnetic exchange coupling constants (J) for coupled diradicals constructed from nitronyl-nitroxide and oxo-verdazyl have been predicted. These radicals have the general formula o-VER(N)-nC-NN where nC represents an olefinic spacer with n = 0, 2, 4, 6 and 8. Species like o-VER(C)-nC-NN have negative coupling constants. The atoms in the parenthesis show the point of attachment of the coupler to the moiety. The N-linked and C-linked series have comparable stability. The triplet molecular geometries were optimized by the densityfunctional (UB3LYP) method using 6-311g(d,p) besis set. This was followed by singlepoint UB3LYP calculations using 6-311++g(3df,3pd) basis. To calculate J, single-point broken symmetry computations were performed on the optimized triplet geometries and using the same basis set. The N-linked diradicals coupled through conjugated polyenes are topologically different. These are found to have coupling constants of the order of 1000 cm–1, whereas the C-linked diradicals show coupling constants of the order of –100 cm–1. In general, for both cases, the absolute magnitude of the coupling constants decreases with the increase in the length of the spacer.


CHAPTER 3.

32

3.1 Introduction Synthesis and characterization of nitronyl nitroxide1 and verdazyl2 have already set the benchmark in the field of molecular magnetism. The stability of these species at a relatively high temperature has made them potential systems for possible application as molecular magnets. A lot of efforts have already been made by many investigators to quantify the magnetic behavior of these two important species.3-11 Several nitronyl nitroxide (NN) based diradicals have been experimentally investigated.12 This is because of their exceptional stability, facile method of preparation and ability to generate cooperative magnetic properties.13 The first example of a pure organic ferromagnet is actually based on the ď ˘-phase of p-nitrophenyl-nitronyl nitroxide radical.14 A large variety of imino nitroxides and nitronyl nitroxides have been investigated theoretically. 15 In a recent article, Kiovisto and Hicks have discussed verdazyl (VER) based molecules and the methods of functionalization of such systems. They also have discussed the suitability of VER based systems as magnetic building blocks.16 The first point to consider in designing organic magnets with more than one radical unit connected through spacers is to gain a clear understanding of the intramolecular magnetic exchange coupling constant (J) between the radical fragments prior to their possible use as a novel building blocks in a supramolecular network.17 The role of couplers in molecular magnetism is well known.18 It has also been noticed that the ď °-conjugated linear spacers, as couplers, are stronger than the aromatic ones.6 The magnetic coupling generally arises from spin polarization and spin delocalization.19 The magnetic interaction between two radical centres normally depends upon the nature and length of the coupler. Ali and Datta have discussed the role of different couplers in nitronyl nitroxide diradicals.6 Most of the diradicals constructed solely from verdazyl radicals and a suitable spacer are either antiferromagnetically coupled or very weakly ferromagnetically coupled.2d-e,9,10 The coupling constants of the diradicals constructed solely from nitronyl nitroxide radicals along with polyenic spacers also follow the same trend.1 Recently, Pilkington et al. investigated mixed diradicals constructed from tetrathiafulvalene (TTF) and verdazyl, and obtained moderately high positive coupling constants (J, of the order of 167 cmâ&#x20AC;&#x201C;1) for most of them.20 This finding stimulated our


CHAPTER 3.

33

interest in VER-NN mixed diradicals. The chemical structures of oxo-verdazyl (o-VER), tetrathiafulvalene (TTF), and nitronyl nitroxide (NN) monoradicals are shown in Figure 3.1.

o-VER

NN

TTF Figure 3.1. Structures of oxo-verdazyl (o-VER), nitronyl nitroxide (NN) and tetrathiafulvalene (TTF) cation from which diradicals have been constructed.

The objective of this work is to find molecular magnets with very high ferromagnetic exchange coupling constant. We contend that when VER and VER are magnetically coupled without spacer or with polyenic spacers, the coupling is necessarily antiferromagnetic as per the rule of spin alternation.21 The same situation arises for NNdiradicals. For the VER and TTF combination, however, spin alternation shows the coupling to be necessarily ferromagnetic. As we show in Figure 3.2, this will repeat in the case of diradicals formed from VER and NN fragments. The NN fragments are known to couple more strongly than TTF, as the positive charge on the latter tends to reduce the exchange of electrons.


CHAPTER 3.

34

NN-2C-NN ( Jcalc.= – 350cm–1)

o-VER-oVER ( Jcalc.= – 600cm–1 )

TTF-2C-o-VER ( Jcalc.= 128cm–1)

o-VER(N)-2C-NN ( Jcalc.= 1157cm–1 )

O Me N N

N

O

N N

N

O

Me

o-VER(C)-2C-NN ( Jcalc.= –378cm–1 )

Figure 3.2. Scheme of spin alternation for various diradicals and the calculated J values. See references 7, 10, and 21 for the first three J values. The calculated J values for the fourth and fifth are from this work.


CHAPTER 3.

35

Using density functional treatment (DFT), we show here that diradicals made of VER and NN monoradicals connected through suitable spacers indeed have very high ferromagnetic coupling constants if the oxoverdazyl moieties are linked at the nitrogen atom adjacent to the carbonyl group of it. However, nearly all other verdazyl containing diradicals which have been studied in the context of spin coupling are linked via the substituent at the carbon atom opposite to the carbonyl group of oxoverdazyl. If we consider the C-linkage, the diradicals are found to be antiferromagnetically coupled. This paper is organized as follows: In section 3.2, we briefly discuss the theory involved. The results are discussed in section 3.3, and the concluding remarks are given therein.

3.2 Results and Discussion On the five Ver(N)-NN diradicals and five VER(C)-NN diradicals. The atom in the parenthesis indicates the atom of attachment of the spacer with the verdazyl moiety. The diradicals with N-linkage are (i) o-Ver(N)-0C-NN (ii) o-Ver(N)-2C-NN (with ethylinic spacers) (iii) o-Ver(N)-4C-NN (with butadilinic spacers) (iv) o-Ver(N)-6C-NN (with hexatrilinic spacers) (v) o-Ver(N)-8C-NN (with octatetrilinic spacers). Similarly, the diradicals with C-linkage are (i) o-Ver(C)-0C-NN (ii) o-Ver(C)-2C-NN (with ethylinic spacers) (iii) o-Ver(C)-4C-NN (with butadilinic spacers) (iv) o-Ver(C)-6C-NN (with hexatrilinic spacers) (v) o-Ver(C)-8C-NN (with octatetrilinic spacers). For the triplet geometry optimization we have used 6-311G (d,p) basis set. The optimized geometries for N-linked diradicals are shown in Figure 3.3(a). The same for C-linked diradicals are given in Figure 3.3(b). For the single point calculations we have used 6311++G (3df, 3pd) basis set. For diradicals, the ideal BS state corresponds to  S 2   1 . Illas et al. found that it is always good to start with correct molecular orbitals for finding the BS solutions. 22 Hence, the symmetry breaking in the wave function in the BS calculations has been achieved by using restricted open-shell wave functions for the optimized triplet structure, and then using the corresponding molecular orbitals as an initial guess. All the calculations have been performed by using the Gaussian 03 software.23


CHAPTER 3.

36

o-Ver(N)-0C-NN

o-Ver(N)-2C-NN

o-Ver(N)-4C-NN

o-Ver(N)-6C-NN

o-Ver(N)-8C-NN

Figure 3.3(a). Optimized geometries of oxo-verdazyl (N-linked) nitronyl-nitroxide diradicals from UB3LYP calculations with 6-311G(d,p) basis set.


CHAPTER 3.

37

o-Ver(C)-0C-NN

o-Ver(C)-2C-NN

o-Ver(C)-4C-NN

o-Ver(C)-6C-NN

o-Ver(C)-8C-NN

Figure 3.3(b). Optimized geometries of oxo-verdazyl (C-linked) nitronyl-nitroxide diradicals from UB3LYP calculations with 6-311G(d,p) basis set.


CHAPTER 3.

38

Table 3.1(a). Triplet energy, dihedral angles and  S 2  of oxo-verdazyl(N) nitronylnitroxide diradicals from geometry optimization UB3LYP calculations using 6-311G(d,p) basis set. System

o-VER(N)-0C-NN o-VER(N)-2C-NN o-VER(N)-4C-NN o-VER(N)-6C-NN o-VER(N)-8C-NN

Dihedral anglea (degree)

ET in a.u. (<S2>)

-984.284482 (2.0695) -1061.734273 (2.0960) -1139.162965 (2.1318) -1216.591183 (2.1681) -1294.019432 (2.2047)

o-VER-Coupler

NN-Coupler

69.18

69.18

0.04

0.79

0.00

0.43

0.68

0.25

0.38

0.14

a

This angle is defined with respect to the spacer plane. The dihedral angle for o-VER(N)0C-NN is the angle between the two ring planes.

Table 3.1(b). Triplet energy, dihedral angles and  S 2  of oxo-verdazyl(C) nitronylnitroxide diradicals from geometry optimization UB3LYP calculations using 6-311G(d,p) basis set. System

o-VER(C)-0C-NN o-VER(C)-2C-NN o-VER(C)-4C-NN o-VER(C)-6C-NN o-VER(C)-8C-NN a

Dihedral anglea (degree)

ET in a.u. (<S2>)

-984.355417 (2.0656) -1061.801518 (2.0739) -1139.236720 (2.0871) -1216.671309 (2.0986) -1294.105721 (2.1089)

o-VER-Coupler

NN-Coupler

73.34

73.34

0.42

0.51

0.48

0.24

0.28

0.06

0.09

0..80

This angle is defined with respect to the spacer plane. The dihedral angle for o-VER(C)0C-NN is the angle between the two ring planes.


CHAPTER 3.

39

Table 3.2. Magnetic properties of oxo-verdazyl nitronyl-nitroxid diradicals from single point UB3LYP calculations using 6-311++G(3df,3pd) basis set. We have used 1 a.u. of energy = 27.2114 eV and 1 eV = 8065.54 cmâ&#x20AC;&#x201C;1. The BS calculations have been achieved by using ROHF wave functions for the optimized triplet structure, and then using the corresponding molecular orbitals as an initial guess. System

ET in a.u. (<S2>)

EBS in a.u. (<S2>)

JY (cmâ&#x20AC;&#x201C;1)

o-VER(N)-0C-NN

-984.354192 (2.0695)

-984.353319 (1.0681)

191.3

o-VER(N)-2C-NN

-1061.809859 (2.0955)

-1061.804393 (1.0581)

1157.4

o-VER(N)-4C-NN

-1139.244522 (2.1320)

-1139.239764 (1.0665)

980.1

o-VER(N)-6C-NN

-1216.678935 (2.1686)

-1216.674722 (1.0761)

846.3

o-VER(N)-8C-NN

-1294.113271 (2.2029)

-1294.109779 (1.0876)

752.1


CHAPTER 3.

40

The optimized triplet energies and the dihedral angles for the N-linkage systems have been given in Table 3.1(a). For the C-linkage systems, similar information are given in Table 3.1(b). The single point UB3LYP/6-311++G(3df,3pd) energies of the triplet and brokensymmetry states for the N-linked systems are given in Table 3.2. The average value of the square of spin angular momentum is ideally 2.0 in the triplet state and 1.0 in the BS state. In actual calculations, however, these ideal values were only approximately obtained, showing a small amount of spin deviation. The computed (  S 2 T   S 2  BS ) values deviate somewhat from unity. Therefore, the coupling constants have been calculated using the Yamaguchi expression, Eq. (2.39). The calculated JY values are all large and positive. This shows that all the diradicals are strongly ferromagnetically coupled. The diradical which does not contain any coupler shows a much smaller JY, about 191 cm–1. There is a noticeable jump of the ferromagnetic coupling constant with the addition of a conjugated spacer. This is attributed to a large dihedral angle (of about 69) in the absence of a coupler (Table 3.1(a)), which is basically a stereo-electronic effect. The olefinic spacers make the diradicals almost planar. The dihedral angles are truly small in each case, less than 1º. The high degree of conjugation facilitates the migration of spin waves, and the JY value is of the order of 1000 cm–1. The ethylenic spacer gives a JY of 1157 cm–1. The coupling constant progressively decreases as the chain length increases. For the 8C spacer, we find a JY value of around 752 cm–1 (Table 3.2). In fact, the JY value has been known to similarly decrease in absolute magnitude for nitronyl nitroxide diradicals as the chain length increases.6,24 This happens because of a decreasing strength of spin interaction between the monoradical fragments. Nevertheless, even with the 8C spacer, the calculated exchange coupling constant is very high. The spin density plots for the triplet species are shown in Figure 3.4. These are manifestly in agreement with the spin alternation rule in UHF,21 and the triplet state is undoubtedly the ground state for each species. However, in the case of C-linkage diradicals, calculations show that all the diradicals are strongly antiferromagnetically coupled. See Table 3.3. This is presumably due to the presence of * SOMO’s (singly occupied molecular orbital) nodal plane that passes through the C3 atom of verdazyl group, as discussed by Hicks and Koivisto.16 As


CHAPTER 3.

41

o-Ver(N)-0C-NN

o-Ver(N)-2C-NN

o-Ver(N)-4C-NN

o-Ver(N)-6C-NN

o-Ver(N)-8C-NN

Figure 3.4. Spin density plot of oxo-verdazyl nitronyl-nitroxide triplet diradicals.


CHAPTER 3.

42

Table 3.3. Magnetic properties of oxo-verdazyl C-linkage nitronyl-nitroxide diradicals from single point UB3LYP calculations using 6-311++G(3df,3pd) basis set. The BS calculations have been achieved by using ROHF wave functions for the optimized triplet structure, and then using the corresponding molecular orbitals as an initial guess. We have used 1 a.u. of energy = 27.2114 eV and 1 eV = 8065.54 cm–1. System

o-VER(C)-0C-NN o-VER(C)-2C-NN o-VER(C)-4C-NN o-VER(C)-6C-NN o-VER(C)-8C-NN

ET in a.u. (<S2>)

EBS in a.u. (<S2>)

-984.355417 (2.0656) -1061.801518 (2.0739) -1139.236720 (2.0871) -1216.671309 (2.0986) -1294.105721 (2.1089)

-984.355798 (1.0736) -1061.803145 (1.1294) -1139.237929 (1.0665) -1216.672274 (1.1616) –1294.106522 (1.1754)

JY (cm–1)

–84.294 –378.068 –282.042 –226.033 -188.799

Table 3.4. Ground state energies of oxo-verdazyl nitronyl nitroxide diradicals (N-C linked and C-C linked, the linkage atom is given in parenthesis) from single point UB3LYP calculations are carried out using 6-311++G(3df,3pd) basis set.

a

System

ET in a.u.

System

Estimated ES in a. u.a

o-VER(N)-0C-NN

-984.354192

o-VER(C)-0C-NN

-984.355801

o-VER(N)-2C-NN

-1061.809859

o-VER(C)-2C-NN

-1061.803244

o-VER(N)-4C-NN

-1139.244522

o-VER(C)-4C-NN

-1139.238005

o-VER(N)-6C-NN

-1216.678935

o-VER(C) -6C-NN

-1216.672339

o-VER(N)-8C-NN

-1294.113271

o-VER(C)-8C-NN

-1294.106579

Estimated from calculation.


CHAPTER 3.

43

a result, there is no spin delocalization on the C3 atom. This atom carries only a small amount of negative spin density via spin polarization. However, in the case of N-linked diradicals the linker nitrogen has a large amount of spin density which results in a facile intramolecular ferromagnetic interaction. We compared the stability of the ground states of the two types of diradicals. See Table 3.4. All the N-linkage diradicals except Ver-0C-NN shows grater stability in comparison to C-linkage radicals. The discrepancy in stability for Ver-0C-NN is due to the large dihedral angles as discussed before.

3.3 Conclusion To conclude, we have examined ten mixed diradicals that can be prepared from oVerdazyl and NN. These have the general formula o-VER-nC-NN where n varies as n=0, 2, 4, 6, 8. The linkages can be either through the N atom on Oxo-Verdazyl, or through C atom. The N-linkage species have more or less the same stability as the C-linkage ones. All N-linkage species are very strongly ferromagnetically coupled. For n=0, a sharp deviation from planarity reduces the coupling constant to about 191 cmâ&#x20AC;&#x201C;1. For the diradicals with spacers, we predict J values of the order of 1000 cmâ&#x20AC;&#x201C;1. If these diradicals can be properly aligned in a crystal, it would be possible to have very strong ferromagnets of organic origin.


CHAPTER 3.

44

3.4 References 1. (a) Awaga, K.; Maruyama, Y. Chem. Phys. Lett. 1989, 158, 556. (b) Awaga, K.; Maruyama, Y. J. Chem. Phys. 1989, 91, 2743. (c) Awaga, K.; Inabe, T.; Nagashima, U.; Maruyama, Y. J. Chem. Soc., Chem. Comm. 1989, 1617. (d) Awaga, K.; Inabe, T.; Nagashima, U.; Maruyama, Y. J. Chem. Soc., Chem. Comm. 1990, 520. (e) Turek, P.; Nozawa, K.; Shiomi, D.; Awaga, K.; Inabe T.; Maruyama, Y.; Kinoshita, M. Chem. Phys. Lett. 1991, 180, 327. (f) Takahashi, M.; Turek, P.; Nakazawa, Y.; Tamura, M.; Nozawa, K.; Shiomi, D.; Ishikawa, M.; Kinoshita, M. Phys. Rev. Lett. 1991, 67, 746. (g) Tamura, M.; Nakazawa, Y.; Shiomi, D.; Nozawa, K.; Hosokoshi, Y.; Ishikawa, M.; Takahashi, M.; Kinoshita, M. Chem. Phys. Lett. 1991, 186, 401. (h) Nakazawa, Y.; Tamura, M.; Shirakawa, N.; Shiomi, D.; Takahashi, M.; Kinoshita, M.; Ishikawa, M. Phys. Rev. B 1992, 46, 8906.

2. (a) Kuhn, R.; Trischmann, H. Angew. Chem., Int. Ed. Engl. 1963, 2, 155. (b) Neugebauer, F. A.; Fischer, H. Angew. Chem., Int. Ed. Engl. 1980, 19, 724. (c) Kopf, P.; Morokuma, K.; Kreilick, R.; J. Chem. Phys. 1971, 54, 105. (d) Gilroy, J. B.; McKinnon, S. D. J.; Kennepohl, P.; Zsombor, M. S.; Ferguson, M. J.; Thompson, L. K.; Hicks, R. G. J. Org. Chem. 2007, 72, 8062. (e) Azuma, N.; Ishizu, K.; Mukai, K. J. Chem. Phys. 1974, 61, 2294. -3

3. Castell, O.; Caballol, R.; Subra, R.; Grand, A. J. Phys. Chem. 1995, 99, 154.-4 4. Barone, V.; Bencini, A.; Matteo, A. di J. Am. Chem. Soc. 1997, 119, 10831.-5 5. Vyas, S.; Ali Md. E.; Hossain E.; Patwardhan, S.; Datta, S. N. J. Phys. Chem. A 2005, 109, 4213.-6

6. Ali, Md. E.; Datta, S. N. J. Phys. Chem. A 2006, 110, 2776.-7 7. Fischer, P. H. H. Tetrahedron 1967, 23, 1939.-8 8. Markovsky, L. N.; Polumbrik, O. M.; Nesterenko, A. M. Int. J. Quantum Chem. 1979, 16, 891.-9

9. Green, M. T.; McCormick, T. A. Inorg. Chem. 1999, 38, 3061.-10 10. Chung, G.; Lee, D. Chem. Phys. Lett. 2001, 350, 339.-11 11. Ciofini, I.; Daul, C. A. Coord. Chem. Rev. 2003, 238,187.-12


CHAPTER 3.

45

12. (a) Takui, T.; Sato, K.; Shiomi, D.; Ito, K.; Nishizawa, M.; Itoh, K. Synth. Met. 1999, 103, 2271. (b) Romero, F. M.; Ziessel, R.; Bonnet, M.; Pontillon, Y.; Ressouche, E.; Schweizer, J.; Delley, B.; Grand, A.; Paulsen, C. J. Am. Chem. Soc. 2000, 122, 1298. (c) Nagashima, H.; Irisawa, M.; Yoshioka, N.; Inoue, H. Mol. Cryst. Liq. Cryst. Sci. Technol. Sect. A 2002, 376, 371. (d) Rajadurai, C.; Ivanova, A.; Enkelmann, V.; Baumgarten, M. J. Org. Chem. 2003, 68, 9907. (e) Wautelet, P.; Le Moigne, J.; Videva, V.; Turek, P. J. Org. Chem. 2003, 68, 8025. (f) Deumal, M.; Robb, M. A.; Novoa, J. J. Polyhedron 2003, 22 (14-17), 1935.-13

13. (a) Ullman, E. F.; Boocock, D. G. B. J. Chem. Soc., Chem. Commun. 1969, 20, 1161. (b) Ullman, E. F.; Osiecki, J. H.; Boocock, D. G. B.; Darcy, R. J. Am. Chem. Soc. 1972, 94, 7049.-14

14. (a) Tamura, M.; Nakazawa, Y.; Shiomi, D.; Nozawa, K.; Hosokoshi, Y.; Ishikawa, M.; Takahashi, M.; Kinoshita, M. Chem. Phys. Lett. 1991, 186, 401. (b) Nakazawa, Y.; Tamura, M.; Shirakawa, N.; Shiomi, D.; Takahashi, M.; Kinoshita, M.; Ishikawa, M. Phys. Rev. B 1992, 46, 8906.-15

15. (a) Shiomi, D.; Ito, K.; Nishizawa, M.; Hase, S.; Sato, K.; Takui, T.; Itoh, K. Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 1999, 334, 99. (b) Romero, F. M.; Ziessel, R.; Bonnet, M.; Pontillon, Y.; Ressouche, E.; Schweizer, J.; Delley, B.; Grand, A.; Paulsen, C. J. Am. Chem. Soc. 2000, 122, 1298. (c) Rajadurai, C.; Ivanova, A.; Enkelmann, V.; Baumgarten, M. J. Org. Chem. 2003, 68, 9907. (d) Ziessel, R.; Stroh, C.; Heise, H.; Kohler, F. H.; Turek, P.; Claiser, N.; Souhassou, M.; Lecomte, C. J. Am. Chem. Soc. 2004, 126, 12604. (e) Takui, T.; Sato, K.; Shiomi, D.; Ito, K.; Nishizawa, M.; Itoh, K. Synth. Met. 1999, 103, 2271.-16

16. Koivisto, B. D.; Hicks, R. G. Coord. Chem. Rev. 2005, 249, 2612.-17 17. Zoppellaro, G.; Ivanova, A.; Enkelmann, V.; Geies, A.; Baumgarten, M. Polyhedron 2003, 22, 2099.-18

18. (a) Lahti, P. M.; Ichimura, A. S. J. Org. Chem. 1991, 56, 3030. (b) Ling, C.; Minato, M.; Lahti, P. M.; van Willigen, H. J. Am. Chem. Soc. 1992, 114, 4, 9959. (c) Minato, M.; Lahti, P. M. J. Am. Chem. Soc. 1997, 119, 2187.-19

19. Dietz, F.; Tyutyulkov, N. Chem. Phys. 2001, 264, 37.-20


CHAPTER 3.

46

20. Polo, V.; Alberola, A.; Andres, J.; Anthony, J.; Pilkington, M. Phys. Chem. Chem. Phys., 2008, 10, 857.-21

21. (a) Trindle, C.; Datta, S. N. Int. J. Quantum Chem. 1996, 57, 781. (b) Trindle, C.; Datta, S. N.; Mallik, B. J. Am. Chem. Soc. 1997, 119, 12947.-22

22. (a) Martin, R. L.; Illas, F. Phys. Rev. Lett. 1997, 79, 1539. (b) Caballol, R.; Castell, O.; Illas, F.; Moreira, I. de P. R.; Malrieu, J. P. J. Phys. Chem. A 1997, 101, 7860. (c) Barone, V.; di Matteo, A.; Mele, F.; Moreira, I. de P. R.; Illas, F. Chem. Phys. Lett. 1999, 302, 240. (d) Illas, F.; Moreira, I. de P. R.; de Graaf, C.; Barone, V. Theor. Chem. Acc. 2000, 104, 265. (e) de Graaf, C.; Sousa, C.; Moreira, I. de P. R.; Illas, F. J. Phys. Chem. A 2001, 105, 11371. (f) Illas, F.; Moreira, I. de P. R.; Bofill, J. M.; Filatov, M. Phys. Rev. B 2004, 70, 132414.-28

23. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision C.02; Gaussian, Inc.: Pittsburgh, PA, 2004.-31

24. (a)Ali, Md. E.; Datta, S. N. J. Phys. Chem. A 2006, 110, 2776. (b) Ali, Md. E.; Datta, S. N. J. Phys. Chem. A 2006, 110, 13232.


Chapter 4 Very strongly ferromagnetically coupled diradicals from mixed radical centers. II. Nitronyl nitroxide coupled to Tetrathiafulvalene via spacers. Large and positive intramolecular magnetic exchange coupling constants (J) have been predicted for coupled diradicals constructed from nitronyl-nitroxide(NN) and tetrathiafulvalene(TTF) monoradical moieties. These diradicals have the general formula TTF-coupler-NN where the couplers are mostly aromatic systems. Unrestricted density functional methodology (UB3LYP) has been used to optimize the molecular geometries of the triplet diradicals using 6-311g(d,p) basis set. This has been followed by single-point UB3LYP calculations for triplet and broken symmetry (BS) states using 6311++g(3df,3pd) basis and the optimized triplet geometries. We find that the species comprising of ethylene (geminal coupling) and pyridine as couplers have singlet ground states whereas the other species have triplet ground states. These findings are in support of spin alternation rule. The largest J value we predict is 648.6 cmâ&#x20AC;&#x201C;1 for the molecule with the spacer pyrrole. We also determine the percent weightings of triplet and singlet components in the BS state, estimate the diradical nature, and calculate the relative weights of different singlet and triplet component functions in the BS solution in each case.


CHAPTER 4.

48

4.1 Introduction A major part of research on molecular magnetism has been on the synthesis and characterization of nitronyl nitroxide1 (NN) and verdazyl radical2 systems. This is because the latter species are stable at a relatively high temperature, are very easy to synthesize, and they have the ability to generate co-operative magnetic properties.3-11 The first example of a pure organic ferromagnet is actually based on the -phase of pnitrophenyl-nitronyl-nitroxide radical.12 A large variety of imino-nitroxides and nitronylnitroxides have been investigated theoretically as well as experimentally. 13,14 Recently, Latif et al. have shown that nitronyl nitroxide (NN) and verdazyl radicals can be used to construct mixed diradicals with different couplers, and these diradicals have very large and positive intramolecular coupling constants.15 Relatively less work has been done on the magnetic properties of a potent candidate, namely, tetrathiafulvalene (TTF) that can be used as a building block for making highly ferromagnetic mixed, (that is, unsymmetrical) diradical systems. Tetrathiafulvalene and its derivatives were originally prepared as strong electron-donor molecules for the development of electrically conducting materials. Its unique electronic properties have drawn attention towards this molecule from various fields of chemistry.16 Research has been carried out on the synthesis of diradicals containing both tetrathiafulvalene and a spin carrier, usually nitrosyl or nitronyl nitroxide group, linked directly or by a p-benzene group, by Sugawara et al.17,18 and Yamaguchi et al.19-20 Pilkington et al.21-22 investigated mixed diradicals constructed from TTF and verdazyl, and found moderately high and positive magnetic exchange coupling constants (J, of the order of 167 cm–1) for most of them.23 This observation gave rise to our interest in TTFNN mixed diradicals. The coupler’s role in molecular magnetism is very well known.24 The role of different couplers in nitronyl nitroxide diradicals has been discussed by Datta et al. 25 It has been noticed that the aromatic moieties are weaker than the corresponding conjugated linear spacers.25c Spin polarization and spin delocalization in general determine the nature of magnetic exchange coupling.26 Also the structure and the length of the coupler determine the magnetic interaction between two radical centers. The diradicals constructed solely from nitronyl nitroxide radicals along with polyenic spacers


CHAPTER 4.

49

have coupling constants which are either antiferromagnetic or very weakly ferromagnetic.1 The aim of this work is to find molecules with very high ferromagnetic exchange coupling constants. From theoretical calculation and experimental observation it has been found that with ethylene (trans) spacer the diradicals formed from coupling of Nitronyl Nitroxide with Nitronyl Nitroxide, Verdazyl (C-linked), and Verdazyl (N-linked) are coupled

antiferromagnetically,

antiferromagnetically,

and

ferromagnetically,

respectively. These observations can be easily rationalized by spin alternation rule. 15,25c The latter rule shows the NN and TTF combinations have necessarily ferromagnetic coupling when the spacers are five-member heterocyclics. However, the exchange coupling constant value for TTF-NN systems are generally expected to be lower than that of Nitronyl Nitroxide-Verdazyl mixed radical systems.15 This is because of the presence of a positive charge on TTF which tends to reduce the exchange of electrons. Using density functional treatment (DFT), we show here that diradicals made of TTF and NN mono-radicals, connected through suitable spacers, indeed have quite high ferromagnetic coupling constants. Our findings are rationalized by defining the diradical nature and estimating the contributions from different component functions to the BS state.

4.2 Calculations We have chosen TTF-coupler-NN type systems with the following couplers: (1) ethylene (geminal connectivity: gem2C), (2) ethylene (trans-connectivity: 2C), (3) pyrrole (Pyrrole), (4) thiophene (Thio), (5) furan (Fur), (6) pyridine (Pyr), (7) m-Benzene (mBenz), and (8) p-Benzene (pBenz). See Figure 4.1. The geometry of the triplet systems are optimized following unrestricted spin polarized density functional methodology, more specifically UB3LYP, using 6-311G(d,p) basis set. The optimized geometries for the eight systems are shown in Figure 4.2. The optimized geometries are more or less planar. This is unlike the verdazyltetrathiafulvalene systems with couplers either linear carbon chains or aromatic molecules, where some of the diradicals adopted non-planar structures.21-23 In the present work, we have very closely followed the same technique described in reference 15. The triplet single point calculations have been performed using the


CHAPTER 4.

50

O N Coupler S

S

N O S

S

NN

TTF

(a) NN-Coupler-TTF H H

H

H

(b) gem2C

(c) 2C

N H

(d) Pyrrole

S

(e) Thio

O

(f) Fur

N

(g) Pyr

(h) mBenz

(i) pBenz

Figure 4.1. (a) General structure of Tetrathiafulvalene Nitronyl nitroxide diradical; (b)-(i) Structures of the couplers.


CHAPTER 4.

(1) TTF-gem2C-NN

(3) TTF-Pyrrole-NN

(5) TTF-Fur-NN

(7) TTF-mBenz-NN

51

(2) TTF-2C-NN

(4) TTF-Thio-NN

(6) TTF-Pyr-NN

(8) TTF-pBenz-NN

Figure 4.2. Optimized triplet geometries of TTF-Coup-NN systems from UB3LYP calculations with the 6-311G(d,p) basis set. The molecular frames are mostly planar.


CHAPTER 4.

52

respective optimized geometries, UB3LYP method and 6-311++G(3df,3pd) basis set. The same geometry, the same methodology and the same basis set have been used for the corresponding BS calculations. The intra-molecular ferromagnetic coupling constant for each species has been determined from Eq. (2.39). For diradicals, the ideal BS state corresponds to <S2>=1. Illas et al. showed that it is always beneficial to start with correct molecular orbitals for finding the BS solutions.27 Hence the symmetry breaking was achieved by using restricted open-shell wave functions for the optimized triplet structure. The corresponding molecular orbitals have been used together as an initial guess. All the calculations have been carried out by using the Gaussian 03 software.28 The spin alternation rule in the unrestricted formalism is a fair description of the ferromagnetic and anti-ferromagnetic pathways.29 It was obtained from a theoretical analysis, although, for the sake of comparison, the energy change was estimated using the parameters from empirical models. It became highly successful when applied to semiempirical calculations and also to unrestricted ab-intio calculations. We notice that spin population alternation derives from the degrees of freedom unavailable to ROHF functions. Furthermore, the UHF singlet wave function occasionally shows spin density alternations. It is a consequence of an energetic advantage of polarization in UHF treatment. Removing the ROHF restrictions is tantamount to mixing of excitations so as to change the spatial part of β spin-orbitals. From a theoretical analysis of the allyl radical and considering only excitations Slβ → S2β, it was shown in ref. 29 that spin polarization will be stabilizing. To establish that the stability indeed arises, Hückel coefficients for the orbitals and the ZDO approximation to the two-electron integrals were used to estimate ∆E. Reference 29 contains a few minor misprints in the expressions for ∆E. In any case, the stabilizing trend propagates through a polarizable medium. Spin polarization needs low-lying excited states of the coupler. To investigate the propagation, one considers the interaction of the polarization emanating from mono-radical centers. Considering 1,1disubstituted ethylene as the coupler, it was discussed that the alternating pattern of α and  spin densities propagates into the coupler. Reference 41 also gives wave functions for the diradical in the simple RHF, UHF, and VB models, and the corresponding energy values.


CHAPTER 4.

53

The molecular shape is basically a stereo-electronic effect. Indeed, bonding is a tug of war between inter-nuclear repulsion plus electron-electron repulsion, and electronnuclear attraction. Unpaired electron delocalization can be accounted for by a careful application of the rule of spin alternation in the unrestricted formalism. This has been successfully demonstrated earlier for radicals containing hetero-nuclear atoms.25 For our systems, we show the spin alternation in Figure 4.3. The triplet state is the ground state for each species with a five-member heterocyclic coupler as well as the para-substituted benzene. Similarity in spin distributions on the atoms coupling the monomers with the spacer causes diradicals with gem2C ethylene, pyridine, and m-benzene couplers to have anti-ferromagnetic tendencies. This is amply supported by our computed results.

4.3 Results and Discussion 4.3.1 General Results The single point UB3LYP/6-311++G (3df,3pd) energies of the triplet states, broken-symmetry states, and the calculated J values are given in Table 4.1. In actual calculations, the <S2> values have been approximately obtained, showing a small amount of spin deviation. Therefore, Eq. (6) has been used in estimating the coupling constants. The calculated JY values show that barring the species with coupler mBenz, all the diradicals have magnetic nature as qualitatively predicted from spin alternation rule (Figure 4.3). The computed spin populations are given in Figure 4.4 for the triplet state of the ferromagnetically coupled diradicals. The spin populations are in agreement with the patterns in Figure 4.3. The only deviation that is observed for the mBenz coupler owes its origin to the two sulfur atoms of the first ring of TTF having nearly equal spin population. For olefinic couplers, it is well-known that the coupling constant progressively decreases with the increase of chain length.25 This is why the higher olefins (that is, 4C, 6C, 8C, etc.) have not been considered here. Heterocyclic five-membered ring couplers have much greater J values (Table 4.1). This may be attributed to the two alternative paths of spin wave propagation. 25 Previously we found diradicals with polyenic couplers and heterocyclic five-membered ring aromatic couplers to have negative J values when the monoradical centers were


CHAPTER 4.

54

Table 4.1 Broken symmetry energies and coupling constants of tetrathiafulvalene nitronyl-nitroxide diradicals from single point UB3LYP calculations using 6311++G(3df,3pd) basis set. We have used 1 a.u. = 219474.6 cm–1. System

ET in a.u. (<S2>)

EBS in a.u. (<S2>)

EBS- ET (cm–1)

JY (cm–1)

TTF-gem2CNN

–2434.547043 (2.0555)

–2434.547135 (1.0558)

–20.2

–20.2

TTF-2C-NN

–2434.567381 (2.0949)

–2434.565377 (0.9812)

439.9

395.0

TTF-PyrroleNN

–2566.198434 (2.0671)

–2566.195460 (1.0604)

652.9

648.6

TTF-Thio-NN

–2909.033340 (2.0794)

–2909.031378 (1.0389)

430.6

413.9

TTF-Fur-NN

–2586.044946 (2.0805)

–2586.042980 (0.9989)

431.5

398.9

TTF-Pyr-NN

–2604.302596 (2.0717)

–2604.302776 (1.0074)

–39.6

–37.2

TTF-mBenzNN

–2588.260128 (2.0645)

–2588.260102 (1.0242)

5.7

5.2

TTF-pBenzNN

–2588.259695 (2.0724)

–2588.259463 (0.9418)

50.0

45.0


CHAPTER 4.

55

O

+

+N N

O

O

S

S

N

S

S

N

S

S

S

S

O

TTF-gem2C-NN

TTF-2C-NN O

O

+N N

N H

S

S

S

S

O

+N

S N

O

TTF-Pyrrole-NN

S

S

S

S

TTF-Thio-NN

O

O

+N

O N

S

S

S

S

O

+N

N N

TTF-Fur-NN

O

S

S

S

S

TTF-Pyr-NN O

O

S

+N

S

+N

S S S

N

O

S

TTF-mBenz-NN

S

N

S O

TTF-pBenz-NN

Figure 4.3. Prediction of ground spin states and nature of the magnetic exchange coupling constant on the basis of spin alternation rule. Notice that the couplers gem2C, Pyr, and mBenz yield AFM coupling by spin alternation rule, whereas actual computations give the coupling in the mBenz species as faintly FM.


CHAPTER 4.

56

0.38 + N

0.111 0.033

0.304

N

-0.075

+

S

S

0.136

-0.022

0.150

-0.142

0.313 -0.237

-0.025

-0.059

0.32 O

O

+

0.081

0.121 0.324

N

-0.027

0.302

N H

0.043

0.105 S

S

0.018

-0.034 0.051

O

0.216

O

0.003

-0.231

-0.018

S

S

N

0.054

0.390

+

0.077 S

S

0.231

0.365

TTF-2C-NN

-0.083

0.342 O +

N

0.308

0.06

0.098 S

-0.022

-0.223

0.375

-0.028 0.136 0.067

-0.029 N

-0.022

TTF-Pyrrole-NN

S

S

0.022

0.085

0.30 O

-0.009

+

S

S

+ -0.023

O

N

-0.082

0.307

0.098

-0.228

O

-0.021

-0.021 0.131 0.067

-0.020

N 0.302 O

0.230

0.381

0.06

S

S

0.027

0.084

-0.017

S

0.229

0.366

TTF-Thio-NN

+

S

TTF-Fur-NN

0.352 0.019 0.350 0.302

+

-0.019

N

+N 0.306

-0.032 0.026 0.186

0.032

N

S

S

-0.041 0.047

-0.242

-0.017

O

-0.032

O

0.311

O 0.320

-0.003

0.049

S 0.215

TTF-mBenz-NN

+

-0.019

0.094

S

-0.019

-0.052 0.057

-0.236

N 0.305

0.030 -0.039 0.068

-0.054 0.043

O

S

0.162

S

0.087

0.043

-0.013

+

S

S 0.221

0.353

TTF-pBenz-NN

Figure 4.4. Atomic spin populations in the triplet states of ferromagnetically coupled diradicals.


CHAPTER 4.

57

0.046

0.035

TTF

NN

TTF

0.059

0.121

0.003

N

TTF

NN

0.034

(2) Ethylene

S

TTF

TTF

NN

20.20

(5) Furan

0.019 0.047

0.038

0.029

O

TTF

(4) Thiophene

0.020 0.037

NN

0.029

0.098

0.021

0.098

0.028

0.082

0.061

0.083

0.067

(3) Pyrrole

NN

0.142

(1) Ethylene (Gem)

0.054

0.136

N

0.046

(6) Pyridine

NN

0.030

0.032

0.032

0.026

0.032

TTF

0.041

TTF 0.039

NN

(7) m-Benzene

Figure 4.5. Atomic spin densities on the atoms of the couplers.

0.043

0.052

0.057 0.054

(8) p-Benzene

NN


CHAPTER 4.

58

same species.25c The reason is that when one considers two electrons that are conjugated and on the heteroatom, the points of contact are antiferromagnetically aligned.25 So, for two similar monoradicals, J tends to be negative. Nevertheless, for (spin-alternationwise) unsymmetric monoradicals such as TTF and NN, J can be positive. Although both paths in a five-membered ring coupler are likely to contribute to the spin wave propagation, the heteroatom route appears to be less efficient as seen from the atomic spin densities on pyridine, pyrrole, furan, and thiophene couplers in Figure 4.5, in spite of this route being shorter. For most of the heterocyclic couplers, the concerned electrons on the heteroatom are in orbitals that are not exactly parallel to the Ď&#x20AC; framework. Pyrrole is an exception. This is why the spin flow is generally less along the heteroatom route, except in pyrrole. It is not surprising that among the species we have investigated. TTF-Pyrrole-NN (3) has the largest J value (Table 4.1). TTF-Thio-NN (4) and TTF-Fur-NN (5) have very similar atomic spin densities on the couplers (Figure 4.5), and these two have nearly equal J values. Another factor that makes the heteroatom route less efficient is that the valence orbital on the heteroatom being low-lying, the corresponding difference from the excited state (Ď&#x20AC;*) energy is greater so that the contribution to spin polarization is less. Nevertheless, an integration of the heteroatom HOMO with the route of conjugation is the major requirement for propagation. Pyridine couples the two mono-radicals anti-ferromagnetically, and J is small and negative. Spin densities on the points of contact are rather small, nearly equal, and of the same sign. A similar situation occurs with m-Benzene as spacer, but calculation here shows the corresponding diradical species to be very faintly ferromagnetically coupled. Thus, the presence of an electronegative heteroatom is a deciding factor for the coupling constant for unsymmtrical diradicals. This indicates another avenue for research on magnetic molecules. We observe a trend in the calculated JY values of the mixed diradicals with heterocyclic aromatic couplers similar to that of the aromaticity of the couplers. Nuclear Independent Chemical Shift (NICS) values given by Schleyer et al.30 are: Pyrrole (13.62) > Thiophene (12.87) > Furan (11.88). The large NICS causes large â&#x2C6;&#x2020;NICS for spacers, leading to a large J value.25


CHAPTER 4.

59

4.3.2 Analysis of Results It is not so simple to obtain percent of ionic and neutral character, and the socalled diradical index and diradical character, for the BS solution. To the best of our knowledge, no one has done it. Using CI with orthogonal, localized orbitals one can get this information from the CI coefficients.31,32 This is not easy either since the CI has to be carried out without symmetry which makes it difficult. Malrieu et al. have used the CI approach several times.31 The other possibility is to use projection techniques. In an extremely localized description where a and b are the magnetic orbitals, the BS determinant is essentially ab

and this is almost a neutral determinant. The ionic

contribution can be deduced from the overlap, and it often comes through the spin contamination.32 Another final possibility is to do CASSCF with only two magnetic orbitals and see the weight of the configurations in the singlet CASSCF function, the triplet being 100% neutral always. This will also give some information on how multiconfigurational or biradical the singlet is. Unfortunately, we are not dealing here with two equivalent mono-radicals. CASSCF and CASPT2 for these systems are doable. Again the lack of symmetry complicates the calculations of diradical index and diradical character. These are interesting questions to raise, but cannot be easily answered, and there is almost no information in the literature.31 We are also using spacers, which complicates the situation further. The charge density is distributed over TTF, Coupler (CO), and NN fragments, the first carrying the largest share of charge in every case. The spin densities are almost equal and opposite in sign in the TTF and NN fragments, the coupler containing only a small amount. See Table 4.2. The total spin in the BS solution is zero in every case, and the spins on the electrons found on the separate sides are coupled to a singlet. Hence the singlet component is neither a pure diradical wave function nor a closed-shell species. It is in the intermediate interaction regime. There is no straight-forward way to estimate the diradical character or the diradical index of the singlet component. It is transparent that the orbital picture is approximate with not enough distinct data except for extremely simple models. In the following, we present an alternative way to analyze most of the quantities.


CHAPTER 4.

60

Table 4.2. Total charge and spin populations on atoms belonging to different fragments on the diradicals in the BS state. The diradical nature, from Eq. (8), is also shown. Charge population a

System

Spin populationa

TTF

Coup

NN

TTF

Coup

NN

Diradical Nature

TTF-gem2CNN TTF-2C-NN

0.9453

0.4500

–0.3954

–0.9840

–0.0334

1.0174

0.984

0.6950

0.5937

–0.2887

–0.8826

–0.0794

0.9619

0.883

TTF-PyrroleNN TTF-ThioNN TTF-Fur-NN

0.9108

0.3558

–0.2666

–0.9300

–0.1080

1.0380

0.930

0.9915

0.3857

–0.3772

–0.9255

–0.1067

1.0322

0.926

1.3413

–0.3467

0.0055

–0.8869

–0.0941

0.9810

0.887

TTF-Pyr-NN

0.8669

0.4940

–0.3609

–0.9316

–0.0618

0.9934

0.927

1.0787 0.3752 –0.4539 –0.9353 TTF-mBenzNN 0.8003 0.6158 –0.4162 –0.8682 TTF-pBenzNN a Mulliken population analysis from Gaussian 03.

–0.0723

1.0076

0.935

–0.0589

0.9270

0.868

Table 4.3. Percent net weight of triplet and singlet components in the computed BS solution. System

Singlet % weight (100m2)

Triplet % weight a (100n2)

TTF-gem2C-NN TTF-2C-NN TTF-Pyrrole-NN TTF-Thio-NN TTF-Fur-NN

47.21 50.94 46.98 48.05 50.05

52.79 49.06 53.02 51.95 49.95

TTF-Pyr-NN 49.63 TTF-mBenz-NN 48.79 TTF-pBenz-NN 52.91 a 2 Using 50* S . Singlet weightage = 100 –Triplet weightage. BS

50.37 51.21 47.09


CHAPTER 4.

61

Singlet and Triplet Weightings Let us consider a general BS state that is an almost equal superposition of Singlet (S) and Triplet (T) states. We write

 BS  m SBS  n TBS where m2  n 2 

1

2

, m2  n 2  1 , and n2  0.5 S 2

(2.1)

BS

so that m2  1  0.5 S 2

BS

. The net

weights of singlet and triplet components in the BS solution are given in Table 4.3. Diradical Nature A diradical is characterized by the spins on the mono-radical centers or groups. In the BS structure,  M 1    M 2 where  is the fragment spin. Fragments are designated as M1, M2, and CO for monomer fragment1, fragment2 and coupler, respectively. In the unrestricted triplet calculation one obtains  M 1   M 2 , both positive, and  M 1 ,  M 2 are more or less equal to their BS counterparts in absolute magnitude. In the BS state  M 1  CO   M 2  0 while in the triplet, the sum equals 2. A measure of the diradical nature of the BS solution would be

1

2



M1

  M 2  . However,

this sum almost always differs from unity, and is sometimes greater. Some spin density is drawn from the monomers M1 and M2 by the coupler CO, which tends to alter the diradical nature. The diradical nature can also be written as

1

2

 

M1

  M 2  , where

 M 1   M 1  1 2 CO and  M 2   M 2  1 2 CO when  M 1 and  CO are of the same sign and  M 2 is necessarily of the opposite sign. This gives the same sum, although  M 1    M 2 . A natural definition evolves by subtracting the contribution of  CO as

N d  1 2   M 1   M 2  CO  .

(2.2)

When  M 1  0 and  CO  0 , N d    M 2 ;  M 1  0 and  CO  0 , N d   M 1 ;  M 2  0 and

 CO  0 , N d    M 1 ;  M 2  0 and  CO  0 , N d   M 2 . When  M 1 and  CO are of the same sign,  M 1 is generally less than 1 while N d   M 1 . This keeps N d as N d  1 .


CHAPTER 4.

62

When  M 1    M 2  1 and  CO  0 , N d  1 and the BS solution is a perfect diradical. If  CO   M 1   M 2 , then  M 1 and  M 2 are necessarily of the same sign,  CO is necessarily of the opposite sign, and N d  0 . This solution, especially for small values of fragment spin populations, represents a non-radical state. In general, N d varies from 0 to 1. Therefore, N d is a measure of the diradical nature. The calculated diradical natures for the BS states are given in Table 4.2. Almost all the species are good diradicals, having N d  86% , whether the coupling is ferromagnetic or not, and regardless of the strength of the coupling ( J value).

Unequal singlet and triplet weights in BS solution The single determinant || TTF  ( 1 )  CO (  2 )  NN (  3 ) || is a linear combination of a singlet and a triplet state with equal weights.

The other combination is

|| TTF  ( 1 )  CO (  2 )  NN ( 3 ) || . It is easy to show that the singlet weightage m2

and

the

triplet

contribution

n2

keep

the

fragment

charges

unaltered:

Qi  Qi   m 2  n 2  Qi  Qi , but change the spin population as  i  i  2mn i . The computed (Mulliken) spin populations 1 ,  2 and 3 correspond to the ingredient determinant || TTF  ( 1 )  CO (  2 )  NN (  3 ) || with  i  i 2mn , etc. As 1   2  3  0 implies 1   2  3  0 , the M S value remains

preserved.

Use of the ingredient

determinant also accounts for the unequal contributions of singlet and triplet to the BS solution. We note that 2mn  1 , the equality being valid only for equal contributions.

Spin components The ingredient structures are not in any canonical form. They can be described as linear superpositions of canonical structures by using at first a spin projection and then a charge projection. The spin projection is achieved by considering four canonical spinonly structures as shown in Figure 4.6. The four structures form an orthonormal set.


CHAPTER 4.

63

TTF

CO

NN

(d)

TTF

CO

NN

(c)

TTF

CO

NN

(b)

TTF

CO

NN

(a)

Figure 4.6. The chosen spin basis. Each up (down) arrow indicates a fragment spin population 1 (â&#x20AC;&#x201C;1).


CHAPTER 4.

64

Table 4.4. Characteristics of the basic determinants. The values within parentheses are fragment spin populations for each of the following canonical structures with different distributions of fragment charge Q. Basic determinants Serial No. (ρ = –1, 0, 1) 1 2 3 4 5 (ρ = –1, 1, 0) 6 7 8 9 (ρ = –1, –1, 2) 10 11 12 13 (ρ = 0, –1, 1) 14 15 16 17

TTF

Fragment Charge CO

NN

1 1 –1 3 1

0 2 2 –2 –2

0 –2 0 0 2

1 1 –1 3

–1 1 1 –1

1 –1 1 –1

1 1 –1 3

–1 1 1 –1

1 –1 1 –1

0 2 2 1

1 –1 1 –2

0 0 –2 2


CHAPTER 4.

65

Only three are needed for a unique solution as there are only three known quantities, namely, 1 ,  2 and 3 . For diradicals that have 3  1 , structure 6(c) is to be chosen in lieu of structure 6(b). Let c1 , c2 , c3 and c4 be the linear combination coefficients for the spin functions 6(a), 6(b), 6(c) and 6(d), respectively. Then TTF    c12  c22  c32  , CO  c22  c32  c42 , and  NN  c12  2c32  c42 .

For c3  0 , we get c12  1   NN  TTF , c22  1   NN and

c42  1  TTF , with the normalization condition c12  c22  c42  1 . For c2  0 , one finds c12  1   CO ,

c32  1   NN

and

c42  1  TTF ,

subject

to

the

normalization

c12  c32  c42  1 .

Charge components We now consider possible charge projections for each canonical spin-only structure by using basic determinants with characteristics shown in Table 4.4. Efforts have been spent on choosing the lowest energy determinants. Comparing with the first basic determinant one finds that determinants 6, 7, 10, 11, 14 and 15 basically add polarity while the rest of the determinants impart a strong ionic character. The highly ionic structures were included to take care of special cases like QTTF  1 and QNN  0 . Three different charge structures with contributions, say, d12 , d 22 and d32 , are selected for each spin-only structure. The normalization of the overall charged structure is kept up by d12  d 22  d32  1 . The values of Mulliken charges on the three fragments uniquely determine the charge structure contributions.

4.3.3 Test case For testing the procedure, the diradical TTF-gem2C-NN is chosen. As

S2

BS

 1.0558 , m2  0.4721 and

n 2  0.5279 . This gives

2mn  0.9984

with

1  0.9855 ,  2  0.0335 , and  3  1.0190 . Because 3  1 , the spin-only structures


CHAPTER 4.

66

Table 4.5. Relative weightage of different basic determinants in the BS solution. The same relative weights describe both the singlet and triplet components. The relative weights are to be multiplied by m2 and n2 to get the net weights of singlet and triplet components.a,b Diradicals from Figure 4.3 1 2 3 4 5 6 7 8 gem2C 2C Pyrrole Thio Furan Pyridine mBenz pBenz (ρ = –1, 0, 1) 1 0.7490 0.5941 0.7331 0.7210 0.7175 0.6966 0.6806 0.5524 2 0.1911 0.1220 0.1189 0.1685 0.1669 0.2105 0.1661 3 0.0264 0.1288 0.0398 0.0038 0.0616 0.0797 4 0.1481 0.0365 5 0.0024 (ρ = –1, 1, 0) 6 0.0077 0.0096 0.0017 0.0137 7 0.0244 0.0062 0.0045 0.0505 8 0.0058 0.0004 0.0071 9 0.0032 (ρ = –1, –1, 2) 10 0.0052 0.0129 0.0101 0.0022 11 0.0132 0.0253 0.0227 0.0054 12 0.0005 0.0018 0.0001 13 0.0003 (ρ = 0, –1, 1) 14 0.0076 0.0765 0.0372 0.0372 0.0119 0.0387 0.0297 0.0782 15 0.0040 0.0238 0.0220 0.0227 0.0173 0.0201 0.0250 16 0.0029 0.0169 0.0091 0.0139 0.0505 0.0123 0.0146 0.0271 17 0.0508 a The fragment charges can be directly calculated from the relative weight. b The spin population values calculated using the relative weights are to be multiplied by a factor of 2mn to get the computed value of (Mulliken) spin population. Basis

Table 4.6. Polar and ionic contributions to the BS solution, compared with the basic determinant 1 taken as the “neutral” structure. Diradicals from Figure 4.3 Total contributions Neutral

1 gem2C

2 2C

3 Pyrrole

4 Thio

5 Furan

6 Pyridine

7 mBenz

8 pBenz

0.7490

0.5941

0.7331

0.7210

0.7175

0.6966

0.6806

0.5524

Polar

0.0300

0.1324

0.0974

0.0927

0.0277

0.0622

0.0574

0.1674

Ionic

0.2209

0.2735

0.1696

0.1863

0.2550

0.2412

0.2619

0.2800


CHAPTER 4.

67

6(a), 6(c), and 6(d) are taken. One obtains c12  0.9666 , c32  0.0190 , c42  0.0145 . The fragment charges are QTTF  0.9453 , QCO  0.4500 , and QNN  0.3954 . These yield, for 6(a),

d12  0.7749 ,

d 22  0.1977

and

d32  0.0273

so that

c12 d12  0.7490 ,

c12 d 22  0.1911 and c12 d 32  0.0264 . In a similar way one obtains, for 6(c), c32 d102  0.0052 , c32 d112  0.0132 and c32 d122  0.0005 , and for 6(d), c42 d142  0.0076 , c42 d152  0.0040 and c42 d162  0.0029 .

Diradicals with Furan and m-Benzene couplers have QTTF  1 . Hence their BS solution has contributions from basic determinants 4, 9, and 13. Furan also has QNN  0 . This can be explained if one includes the mixing of determinants 5 and 17. The spin population on NN is greater than 1 for gem2C, Pyrrole, Thio and mBenz couplers. For the corresponding diradicals, the spin only structure 6(b) (determinants 6-9) is not involved. In stead, structure 6(c) makes its presence felt. The relative weights of the basic determinants for all eight diradicals are exhibited in Table 4.5. These weights yield the exact Mulliken fragment charges and the exact fragment spins (after multiplying by 2mn) for every diradical. The singlet and triplet contributions are in the ratio m2 : n2. The total polar and ionic contributions are given in Table 4.6. The dominance of the ionic character over the polar nature indicates an intermediate to strong interaction.

4.4 Conclusions To conclude, we have examined eight mixed diradicals that can be prepared from TTF and NN. These have general formula TTF-gem2C-NN, TTF-2C-NN, TTF-PyrroleNN, TTF-Thio-NN, TTF-Fur-NN, TTF-Pyr-NN, TTF-mBenz-NN, and TTF-pBenz-NN. The species TTF-2C-NN, TTF-Pyrrole-NN, TTF-Thio-NN, TTF-Fur-NN, TTF-mBenzNN, and TTF-pBenz-NN are ferromagnetically coupled. TTF-2C-NN, and TTF-Pyr-NN are anti-ferromagnetically coupled. Due to dissimilarity in spin positions, diradicals coupled by geminal ethylene and pyridine show anti-ferromagnetic coupling whereas others show ferromagnetic interaction. For a lower basis set, TTF-mBenz-NN is


CHAPTER 4.

68

antiferromagnetically coupled that agrees with spin alternation. Nevertheless, a higher basis shows that the coupling is faintly ferromagnetic. The highly ferromagnetically coupled molecules 3, 4, 2, and 5 can be of immense importance for preparing conducting, semi-conducting or insulating magnetic materials. Knowledge of crystal structure is required for determining the intermolecular coupling constant which can indicate any such possibility of preparing interesting materials. The comparatively high magnetic moment for compounds with the five-membered heterocyclic aromatic couplers may open up newer experimental investigations. The singlet and triplet percentage weights in the BS wave function have been calculated. We have defined the diradical nature and estimated it. Table 4.2 shows that each species has a strong diradical nature. Table 4.5 gives a break-up of the weights of component functions in the BS solution. Table 4.6 exhibits the â&#x20AC;&#x153;neutralâ&#x20AC;?, polar and ionic characters, and shows that all the diradicals are in the intermediately strong regime.


CHAPTER 4.

69

4.5 References 1. (a) Awaga, K.; Maruyama, Y. Chem. Phys. Lett. 1989, 158, 556. (b) Awaga, K.; Maruyama, Y. J. Chem. Phys. 1989, 91, 2743. (c) Awaga, K.; Inabe, T.; Nagashima, U.; Maruyama, Y. J. Chem. Soc., Chem. Comm. 1989, 1617. (d) Awaga, K.; Inabe, T.; Nagashima, U.; Maruyama, Y. J. Chem. Soc., Chem. Comm. 1990, 520. (e) Turek, P.; Nozawa, K.; Shiomi, D.; Awaga, K.; Inabe T.; Maruyama, Y.; Kinoshita, M. Chem. Phys. Lett. 1991, 180, 327. (f) Takahashi, M.; Turek, P.; Nakazawa, Y.; Tamura, M.; Nozawa, K.; Shiomi, D.; Ishikawa, M.; Kinoshita, M. Phys. Rev. Lett. 1991, 67, 746. (g) Tamura, M.; Nakazawa, Y.; Shiomi, D.; Nozawa, K.; Hosokoshi, Y.; Ishikawa, M.; Takahashi, M.; Kinoshita, M. Chem. Phys. Lett. 1991, 186, 401. (h) Nakazawa, Y.; Tamura, M.; Shirakawa, N.; Shiomi, D.; Takahashi, M.; Kinoshita, M.; Ishikawa, M. Phys. Rev. B 1992, 46, 8906. 2. (a) Kuhn, R.; Trischmann, H. Angew. Chem., Int. Ed. Engl. 1963, 2, 155. (b) Neugebauer, F. A.; Fischer, H. Angew. Chem., Int. Ed. Engl. 1980, 19, 724. (c) Kopf, P.; Morokuma, K.; Kreilick, R.; J. Chem. Phys. 1971, 54, 105. (d) Gilroy, J. B.; McKinnon, S. D. J.; Kennepohl, P.; Zsombor, M. S.; Ferguson, M. J.; Thompson, L. K.; Hicks, R. G. J. Org. Chem. 2007, 72, 8062. (e) Azuma, N.; Ishizu, K.; Mukai, K. J. Chem. Phys. 1974, 61, 2294. 3. (a) Ullman, E. F.; Boocock, D. G. B. J. Chem. Soc., Chem. Commun. 1969, 20, 1161. (b) Ullman, E. F.; Osiecki, J. H.; Boocock, D. G. B.; Darcy, R. J. Am. Chem. Soc. 1972, 94, 7049. 4. Castell, O.; Caballol, R.; Subra, R.; Grand, A. J. Phys. Chem. 1995, 99, 154. 5. Barone, V.; Bencini, A.; Matteo, A. di J. Am. Chem. Soc. 1997, 119, 10831. 6. Vyas, S.; Ali Md. E.; Hossain E.; Patwardhan, S.; Datta, S. N. J. Phys. Chem. A 2005, 109, 4213. 7.

Fischer, P. H. H. Tetrahedron 1967, 23, 1939.

8. Markovsky, L. N.; Polumbrik, O. M.; Nesterenko, A. M. Int. J. Quantum Chem. 1979, 16, 891. 9. Green, M. T.; McCormick, T. A. Inorg. Chem. 1999, 38, 3061. 10. Ciofini, I.; Daul, C. A. Coord. Chem. Rev. 2003, 238,187.


CHAPTER 4.

70

11. (a) Takui, T.; Sato, K.; Shiomi, D.; Ito, K.; Nishizawa, M.; Itoh, K. Synth. Met. 1999, 103, 2271. (b) Romero, F. M.; Ziessel, R.; Bonnet, M.; Pontillon, Y.; Ressouche, E.; Schweizer, J.; Delley, B.; Grand, A.; Paulsen, C. J. Am. Chem. Soc. 2000, 122, 1298. (c) Nagashima, H.; Irisawa, M.; Yoshioka, N.; Inoue, H. Mol. Cryst. Liq. Cryst. Sci. Technol. Sect. A 2002, 376, 371. (d) Rajadurai, C.; Ivanova, A.; Enkelmann, V.; Baumgarten, M. J. Org. Chem. 2003, 68, 9907. (e) Wautelet, P.; Le Moigne, J.; Videva, V.; Turek, P. J. Org. Chem. 2003, 68, 8025. (f) Deumal, M.; Robb, M. A.; Novoa, J. J. Polyhedron 2003, 22 (14-17), 1935. (g) Zoppellaro, G.; Ivanova, A.; Enkelmann, V.; Geies, A.; Baumgarten, M. Polyhedron 2003, 22, 2099. 12. (a) Tamura, M.; Nakazawa, Y.; Shiomi, D.; Nozawa, K.; Hosokoshi, Y.; Ishikawa, M.; Takahashi, M.; Kinoshita, M. Chem. Phys. Lett. 1991, 186, 401. (b) Nakazawa, Y.; Tamura, M.; Shirakawa, N.; Shiomi, D.; Takahashi, M.; Kinoshita, M.; Ishikawa, M. Phys. Rev. B 1992, 46, 8906. 13. (a) Shiomi, D.; Ito, K.; Nishizawa, M.; Hase, S.; Sato, K.; Takui, T.; Itoh, K. Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 1999, 334, 99. (b) Romero, F. M.; Ziessel, R.; Bonnet, M.; Pontillon, Y.; Ressouche, E.; Schweizer, J.; Delley, B.; Grand, A.; Paulsen, C. J. Am. Chem. Soc. 2000, 122, 1298. (c) Rajadurai, C.; Ivanova, A.; Enkelmann, V.; Baumgarten, M. J. Org. Chem. 2003, 68, 9907. (d) Ziessel, R.; Stroh, C.; Heise, H.; Kohler, F. H.; Turek, P.; Claiser, N.; Souhassou, M.; Lecomte, C. J. Am. Chem. Soc. 2004, 126, 12604. (e) Takui, T.; Sato, K.; Shiomi, D.; Ito, K.; Nishizawa, M.; Itoh, K. Synth. Met. 1999, 103, 2271. 14. Koivisto, B. D.; Hicks, R. G. Coord. Chem. Rev. 2005, 249, 2612. 15. Latif, I. A.; Panda, A.; Datta, S. N. J. Phys. Chem. A 2009, 113, 1595. 16. Segura, J. L.; and Martin, N. Angew. Chem., Int. Ed., 2001, 40, 1372. 17. Kumai, R.; Matsushita, M. M.; Izuoka, A.; Sugawara, T. J. Am. Chem. Soc., 1994, 116, 4523. 18. Nakazaki, J.; Matsushita, M. M.; Izuoka, A.; Sugawara, T. Tetrahedron Lett., 1999, 40, 5027. 19. Matsuoka, F.; Yamashita,Y.; Kawakami, T.; Kitagawa, Y.; Yoshioka, Y.; Yamaguchi, K. Polyhedron, 2001, 20, 1169.


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71

20. Morita, Y.; Kawai, J.; Haneda, N.; Nishida, S.; Fukui, K.; Nakazawa, S.; Shiomi, D.; Sato, K.; Takui, T.; Kawakami, T.; Yamaguchi, K.; Nakasuji, K. Tetrahedron Lett., 2001, 42, 7991. 21. Chahma, M.; Wang, X. S.; van der Est A.; Pilkington, M. J. Org. Chem., 2006, 71, 2750. 22. Chahma, M.; Macnamara, K.; van der Est A.; Alberola, A.; Polo, V.; Pilkington, M. New J. Chem., 2007, 31, 1973. 23. Polo, V.; Alberola, A.; Andres, J.; Anthony, J.; Pilkington, M. Phys. Chem. Chem. Phys., 2008, 10, 857. 24. (a) Lahti, P. M.; Ichimura, A. S. J. Org. Chem. 1991, 56, 3030. (b) Ling, C.; Minato, M.; Lahti, P. M.; van Willigen, H. J. Am. Chem. Soc. 1992, 114, 4, 9959. (c) Minato, M.; Lahti, P. M. J. Am. Chem. Soc. 1997, 119, 2187. 25. (a) Datta, S. N.; Mukherjee, P.; Jha, P. P. J. Phys. Chem. A 2003, 107, 5049. (b) Ali, Md. E.; Vyas, S.; Datta, S. N. J. Phys. Chem. A 2005, 109, 6272. (c) Ali, Md. E.; Datta, S. N. J. Phys. Chem. A 2006, 110, 2776. (d) Ali, Md. E.; Datta, S. N. J. Phys. Chem. A. 2006, 110, 13232. 26. Dietz, F.; Tyutyulkov, N. Chem. Phys. 2001, 264, 37.--27 27. (a) Martin, R. L.; Illas, F. Phys. Rev. Lett. 1997, 79, 1539. (b) Caballol, R.; Castell, O.; Illas, F.; Moreira, I. de P. R.; Malrieu, J. P. J. Phys. Chem. A 1997, 101, 7860. (c) Barone, V.; di Matteo, A.; Mele, F.; Moreira, I. de P. R.; Illas, F. Chem. Phys. Lett. 1999, 302, 240. (d) Illas, F.; Moreira, I. de P. R.; de Graaf, C.; Barone, V. Theor. Chem. Acc. 2000, 104, 265. (e) Illas, F.; Moreira, I. de P. R.; Bofill, J. M.; Filatov, M. Phys. Rev. B 2004, 70, 132414.--37 28. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J.


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72

J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision C.02; Gaussian, Inc.: Pittsburgh, PA, 2004.---40 29. (a) Trindle, C.; Datta, S. N. Int. J. Quantum Chem. 1996, 57, 781. (b) Trindle, C.; Datta, S. N.; Mallik, B. J. Am. Chem. Soc. 1997, 119, 12947. 30. Chen, Z.; Wannere, C. S.; Corminboeuf, C.; Puchta, R.; Schleyer, P. v. R. Chem. Rev. 2005, 105, 3842. 31. (a) Calzado, C. J.; Cabrero, J.; Malrieu, J. P.; Caballol, R.; J. Chem. Phys. 2002, 116, 3985. (b) Calzado, C. J.; Angelli, C.; Taratiel, D.; Caballol, R.; J.; Malrieu, J. P.; J. Chem. Phys. 2009, 131, 044327. 32. Neese, F.; J. Phys. Chem. of Solids. 2004, 65, 781.


Chapter 5 Unusually large coupling constants in diradicals obtained from excitation of mixed radical centers: A theoretical study on potential photomagnets Three sets of hetero-substituted, inter-convertible, cyclophanediene (CPD) and dihydropyrenes (DDP), and one such set involving dinitrilepyrenes were examined by UB3LYP broken-symmetry methodology with 6-311++g(d,p) bases. Nitronyl nitroxide and oxoverdazyl (with both N and C terminals) are monoradical centers while CPD and DDP moieties serve as couplers.

The photoexcited CPD converts into DDP. The

calculated exchange coupling constant (J) for o-VER(N)-DDP-NN is surprisingly high, 6412 cm1, and much larger than 28.9 cm−1 for the CPD species. But the unsubstituted DDP is known to readily transform into pyrene, with the loss of reversibility. Nevertheless, o-VER(N)-(15,16-dinitrile)DDP-NN also has a large J value, 589.4 cm−1. The corresponding CPD species has J = 53.3 cm−1. We predict that the latter CPD and DDP diradicals are potential molecules to synthesize photomagnetic materials. The oVER(N)-DDP-NN can also be an excellent photomagnetic switch at a considerably low temperature.


CHAPTER 5.

74

5.1 Introduction Perfluorocyclopentene has been widely studied as a photochromic spin coupler. In many nitronyl nitroxide diradicals with perfluorocyclopentene, the intramolecular exchange interaction is extraordinarily weak with the coupling constant J often of the order of hyperfine coupling constants (hfcc). Interest in photomagnetic properties has led to the investigation of photoexcited states of diradicals.1,2 Ali et al. have theoretically predicted photoswitching magnetic properties of four substituted dihydropyrenes and –1

shown that the magnetic exchange coupling constants vary up to 9.44 cm

.3

A

photoinduced antiferromagnetic to ferromagnetic crossover involving the conversion of substituted trans-azobenzene to cis-azobenzene has been investigated by Shil and Misra.4 The substituted pyrene molecule exists in two different forms, namely, cyclophanediene (CPD) and dihydropyrene (DDP), as shown in Figure 5.1. Recently, Latif et al. have shown quite large and positive intramolecular magnetic exchange coupling constants for coupled diradicals constructed from nitronyl nitroxide (NN) and oxoverdazyl (o-VER).5 The present work stems from the natural expectation that the mixed diradical systems coupled via CPD and DDP will result in high positive J values. 4 2 1

13

6

R

15

14

4

5

3

12

10

9

11

CPD

2

h

5

3

R

15

1

8

16

R

h,

7

14

6

7 8

16 R

13 12

10

9

11

DDP

Figure 5.1: Conversion of CPD to DDP.

In this work, we have investigated the ground-states of diradicals containing NN and o-VER. Out of many possible pairs of isomers, we focus our attention only on 3 pairs of hydrogen isomers (R=H) and 1 pair of nitrile isomer (R=CN). These are shown in Figure 5.2. Pairs (a) and (b) with N linkages are chosen in accordance with the rule of spin alternation in the unrestricted formalism,6 so that the resulting diradicals would be ferromagnetically coupled. See Figure 5.S1. The other two pairs (c) and (d) contain Clinkages instead, and are chosen to test the contention of Koivisto and Hicks that there is


CHAPTER 5.

N N

75

O N

H

N N

h,  N

H O

h

N O

NC CN O

o-Ver(N)- (15,16-dihydrogen)DDP-NN , /

N N

h

N O

N

NC N CN

N

N

O

o-Ver(N)- (15,16-dinitrile)CPD-NN

O

o-Ver(N)- (15,16-dinitrile)DDP-NN

(b)

O

O H

N N

N

O N N

N

H

h1//,

h2

//

//

N N

H

N

N N

H

N

O O

O

o-Ver(C)-(15,16-dihydrogen)CPD-NN O N

H H N N

N O

O

h

N

N N

H O

O N

H

O N

N N

o-Ver(N)-(15,16-dihydrogen)CPD-NN (a)

N

N

N O

N N

O

o-Ver(C)-(15,16-dihydrogen)CPD-NN

(c)

o-Ver(C)-(15,16-dihydrogen)DDP-NN O

h1///, h2///

///

N N

N N

H

N

H

N O

O

(d) o-Ver(C)-(15,16-dihydrogen)DDP-NN

Figure 5.2: Photochemical interconversion of (a) o-Ver(N)-CPD-NN and o-Ver(N)DDP-NN, (b) o-Ver(N)-(15,16-dinitrile)CPD-NN and o-Ver(N)-(15,16-dinitrile)DDPNN, (c) o-Ver(C)-CPD-NN (linear) and o-Ver(C)-DDP-NN (linear), and (d) o-Ver(C)CPD-NN (bent) and o-Ver(C)-DDP-NN (bent).


CHAPTER 5.

N N

76

N N

O N

H

N N

H

N O

O

o-VER (N)- CPD-NN

O N

H N

N

H O

o-VER (N)- DDP-NN

(a)

O

O N N

NC

N

N

N

N CN

N

N

O

CN

N O

o-VER (N)-(15,16-dinitrile)CPD-NN

(b)

N O

o-VER (N)-(15,16-dinitrile)DDP-NN

O H

N

NC N

O

N N

N O

O N

O

N N

H

N

N N

H

N

O N N

N

H

O

o-VER(C)-CPD-NN (linear)

O

N

H

N N

O

N

o-VER(C)-DDP-NN (linear)

(c)

O N

H

N

O

N N

O

o-VER(C)-CPD-NN (bent)

N N

H

N

H

N O

O

(d)

o-VER(C)-DDP-NN(bent)

Figure 5.3 Prediction of ground spin states and nature of the magnetic exchange coupling constant on the basis of spin alternation rule.


CHAPTER 5.

o-VER(N)-CPD-NN

o-VER(N)-(15,16 dinitrile)CPD-NN

o-VER(C)-CPD-NN (linear)

o-VER(C)-CPD-NN (bent)

77

o-VER(N)-DDP-NN

o-VER(N)-(15,16 dinitrile)DDP-NN

o-VER(C)-DDP-NN (linear)

o-VER(C)-DDP-NN (bent)

Figure 5.4: Optimized triplet geometries of o-VER-Coup-NN systems from UB3LYP calculations with the 6-311G(d,p) basis set.


CHAPTER 5.

78

not any spin delocalization and very small spin polarization on the carbon joining a substituent (in the present case, the coupler), thereby leading to only a few percent of spin population on the same carbon atom.7

5.2 Calculations We have used spin-polarized unrestricted density functional theory (DFT), (more specifically, the UB3LYP method), at first with 6-31G bases and finally with 6-311G (d,p) basis set for the optimization of geometry of the triplet diradicals. We then carried out single-point runs using 6-311G++(d, p) basis. Single-point broken symmetry (BS) calculations were based on the final triplet geometries and the latter basis set. The optimized geometries for the N-linked, C-linked and the 15,16-dinitrile diradicals are illustrated in Figure 5.S3. The relatively greater planarity of o-VER(N)-DDP-NN indicates a high positive J value and a potential organic ferromagnet. The optimized triplet energies, the mean dihedral angles and C15-C16 (see Figure 5.1) distances for the systems are also given in Supplementary Information. All the computations were performed using GAUSSIAN 03 software.9 The average value of the square of spin angular momentum is ideally 2.0 in the triplet (T) state and 1.0 in the BS state. In actual calculations, however, these ideal values are approximately obtained, showing spin deviation. Therefore, the coupling constant has been calculated using the Yamaguchi expression10 Y

J 

( DFT EBS  DFT ET ) .  S 2T  S 2  BS

(1)

5.3 Results and Discussion The single-point UB3LYP/6-311++G (d, p) energies of the triplet and BS states for the o-VER-Coup-NN systems are given in Table 5.1. With the N-linkage systems we can see a large change in J value as the species undergoes conversion from open ring to closed ring isomer (from 29cm−1 to 6412.1cm−1 for the 15,16-dihydrogen species and from 53.3cm−1 to 589.4cm−1 for the 15,16-dinitrile species).


CHAPTER 5.

79

Table 5.1: Properties of the studied diradicals calculated from single-point UB3LYP calculations using 6-311++G(d,p) basis set.a System

ET in a.u. (<S2>)

EBS in a.u. (<S2>)

JY (cm–1)

o-VER(N)-CPD-NN

−1600.10256 (2.08548) −1600.13631 (2.19630) −1784.62141 (2.09587) −1784.63857 (2.21659) −1600.10728 (2.08379)

−1600.10242 (1.07971) −1600.10710 (1.00171) −1784.62117 (1.08651) −1784.63550 (1.07524) −1600.10735 (1.08839)

28.9

−1600.13858 (2.08870) −1600.10159 (2.08516) −1600.13103 (2.14194)

−1600.13954 (1.18009) −1600.10156 (1.08296) −1600.13069 (1.10430)

o-VER(N)-DDP-NN o-VER (N)-(15,16dinitrile)CPD-NN o-VER (N)-(15,16dinitrile)DDP-NN o-VER(C)- CPD -NN (linear) o-VER(C)- DDP-NN (linear) o-VER(C)-CPD-NN (bent) o-VER(C)- DDP-NN (bent) a

6412.1 53.3 589.4 −15.4 −219.4 5.1 71.4

The BS calculation has been achieved by using ROHF wave functions for the optimized triplet structure and then using the corresponding molecular orbitals as an initial guess. We have used 1 a.u. of energy = 27.2114 eV and 1 eV = 8065.54 cm–1.


CHAPTER 5.

80

Table 5.2: Triplet energy, mean dihedral angles, C15-C16 distances and <S2> of oVER(N/C)-(CPD/DDP)-NN diradicals from geometry optimization by UB3LYP calculations using the 6-311G (d,p) basis set.

System

ET in a.u. 2

(<S >)

Mean Dihedral angle(deg) o-VER-Coupler

NN-Coupler

C15-C16 distance(Å)

o-VER(N)-CPD-NN

−1600.0800 (2.0889)

26.3

4.3

2.58

o-VER(N)-DDP-NN

−1600.1144 (2.2044)

19.9

9.7

1.52

−1784.5956 (2.0998)

16.6

3.5

2.71

dinitrile)DDP-NN

−1784.6134 (2.2251)

16.8

2.4

1.55

o-VER(C)- CPD -NN (linear)

−1600.0850 (2.0872)

2.6

4.0

2.59

o-VER(C)- DDP-NN (linear)

−1600.1167 (2.0933)

2.0

11.5

1.52

o-VER(C)-CPD-NN

−1600.0790 (2.0885)

32.1

7.7

2.60

o-VER(C)- DDP-NN

−1600.1089 (2.1505)

32.3

4.1

1.52

o-VER (N)-(15,16dinitrile)CPD-NN o-VER (N)-(15,16-


CHAPTER 5.

81

The dihedral angle between DDP coupler and two magnetic centers is somewhat smaller and C15-C16 distance in the DDP diradical is much less than that in CPD species, owing to the near-planarity of the DDP coupler. See Table 5.2. The high degree of conjugation facilitates the migration of spin waves, and the JY value is very large. For the C-linkage systems, the J values are comparatively small for both open and closed ring isomers. It is mainly due to the much less planarity of the diradical. In 5.2(d), the o-VER moiety is joined through the 14th carbon of the coupler and due to steric interaction with hydrogen attached to carbon 11, goes out of the ring plane and subtends a mean angle of 32.30. The numbering of carbon atoms is taken from Williams et al.11 A similar situation does not exist with 5.2(c) in which the coupling is linear. There is a large change of J values (−15.4 cm−1 to −219.4 cm−1) in 5.2(c). The systems are antiferromagnetically coupled. The systems 5.2(d) are ferromagnetically coupled. This phenomenon can be explained by the generalized spin alternation rule due to Ali et al.12 When there are more than one nonbonded electron in  orbitals of heteroatoms like N, O, S, etc. and the bonding of these atoms is otherwise satisfied, all the nonbonded  electrons should be considered in the spin alternation rule. That is, nitrogen atom in sp2 hybridization offers two electrons for spin alternation. The spin alternation has been illustrated in Figure 5.3, and it correctly predicts the nature of the coupling – ferromagnetic or antiferromagnetic.  Koivisto and Hicks7 concluded that the odd electron in verdazyl resides in a 

singly occupied molecular orbital (SOMO) that spans the four nitrogen atoms of the ring. Because of the orbital symmetry, there is no spin delocalization on the carbon atoms, and spin polarization effects lead to a small spin density on the carbon atom. If the substituent is aromatic, the spin population on the carbon atom is about 1% or less, and there is also vanishingly small spin on the opposite carbon atom. While their discussion is of some qualitative merit, our calculations show the following Mulliken spin populations on the oVER carbon that is coupled to the spacer. In the triplet states, spin population on this carbon atom are −0.1767 and −0.1753 for 5.2(d) CPD and 5.2(d) DDP, respectively. For 2(c) species, spin population on this carbon in BS state are −0.1778 in CPD and 0.1850 in DDP. These numbers are not negligibly small, and arranging spin alternation by assuming almost zero spin on this carbon atom would be wrong. The spin population on


CHAPTER 5.

82

-0.02 0.42

-0.17

0.15N

N

-0.03

0.08 H

-0.06 0.04

O

-0.01

0.13 -0.13

O

0.26

-0.03 0.06

H

-0.07

0.04

0.40 0.16 N

0.03

-0.05

N

0.36

0.01

N

-0.19

-0.06

-0.15 0.35

O

0.02

0.14 -0.04

o-VER(N)-CPD-NN 0.02 -0.17

N

0.40

0.12 N

N

0.16 N

0.07

0.44

-0.03

N

O

0.14 -0.15

0.26

0.37

0.02 -0.03 -0.02

0.43N

0.02

-0.02

0.03

0.03 -0.05

N

0.28

O

0.38

-0.14

O

-0.17 0.03

O

0.14

O

-0.13

0.28

0.38

O

0.26 -0.19

0.08 H

-0.09

0.26

-0.01

0.01

0.09

H

-0.09 0.06

0.17

-0.04

0.07

-0.08

0.09

0.27 N -0.19 N

-0.09

0.27

-0.18

0.44 N N

0.37

-0.1

-0.08

0.07

O

N

0.17 -0.13

o-VER(N)-(15,16 dinitrile)DDP-NN

N

0.16

-0.20

CN

0.13 -0.14

0.07

O 0.36

0.27 N

0.17

-0.05

0.36

N

0.39

NC

-0.03

O

N 0.43

N

-0.04

-0.06 H

-0.01

-0.18

0.17

0.03 -0.05

H

0.02

0.03

O

0.12 N

0.14 N

o-VER(N)-(15,16 dinitrile)CPD-NN -0.01

N

0.14 -0.12

0.17 -0.14

0.13 -0.15

0.40

N

0.26 N

0.04 -0.06

0.02 -0.02

0.02

N

0.36

-0.19

-0.08 0.06

-0.05 CN

0.07

-0.17

0.15

-0.13

0.12

O

0.05 -0.06

0.08

-0.03 H

0.37

-0.04

-0.07

N

o-VER(N)-DDP-NN

-0.02 NC

0.28

0.16 -0.12

0.13 -0.12

O

0.36

O 0.38

H

-0.15 0.01

N

0.14 N

-0.13

0.13

N

N

0.26 N

-0.04 0.06

0.38

N

N

-0.09 O

0.37

0.43

0.16

O

o-VER(C)-CPD-NN (bent)

o-VER(C)-DDP-NN (bent)

Figure 5.5: Spin population of the ferromagnetically coupled diradicals in their triplet states. The slight deviation from spin alternation at the site of C1 coupled to N of o-VER and C8 coupled to C of NN suppresses the FM coupling in o-VER(N)-CPD-NN.


CHAPTER 5.

83

the coupling C atom of o-VER is substantially large, which indeed agrees with spin alternation rule. The spin populations on all atoms of ferromagnetically coupled species are given as Figure 5.5. In passing, we note that the spin alternation shown for the o-VER(C) containing diradicals in ref. 6 has been somewhat incorrect. The spin alternation rule in Figure 5.5 shows a slight deviation from spin alternation on atoms 1 and 8 in CPD of 5.2(a). This indicates a reduced FM interaction, accompanied by J value much smaller than that of the DDP isomers. The extremely large change in J value of 5.2(a) upon photoexcitation is a good indication of applicability of such systems as good photomaterials. But there is a problem of thermal instability. Though the DDP form can be kept intact indefinitely in degassed cyclohexane at 0 oC, at higher temperature and in the presence of air it undergoes a rapid conversion to pyrene.11 This disqualifies the criteria of reversibility that is a fundamental requirement of photomagnetic coupler.

H H

2537 Å

H H

h or O2 (fast)

FIGURE 5.6: Dehydrogenation of unsubstituated DDP.

When R is H (Figure 5.1), the CPD form is expected to have a restricted life time as hydrogen cannot pose enough hindrance to the rapid conversion to DDP. Thus to have a pragmatic application as molecular switches, R should be so chosen that the activation barrier for CPD→DDP conversion is high. Proper substitutions can increase the activation barrier to hinder the thermal conversion. Indeed, Williams et al.12 have found that when R is CN, the activation barrier is maximum (E#= 25.3 Kcal mol–1) among the related species. Hence we have taken 15,16-dinitrile pyrene as coupler, and found a sufficiently high positive J value for the closed ring dimer (J= 589.4 cm−1) whereas in the CPD form the J value is small (53.3 cm−1). So we predict o-VER (N)-(15,16dinitrile)DDP-NN as a potential photomagnet. At room temperature, J/KBT ~ 0.25 for the


CHAPTER 5.

84

CPD species that would behave as a paramagnet, while J/KBT ~ 3 for the DDP species that can behave ferromagnetically if properly aligned. These molecules have not been synthesized so far, but a suggestion can be made. The synthesis of 1,5-dimethyl-6-oxoverdazyls typically proceeds through the reaction of methyl hydrazine with phosgene to form a bis-hydrazide, followed by condensation with an aldehyde to form a tetrazene and subsequent oxidation to give the verdazyl (Scheme 1 of ref. 13). Nitronyl nitroxide is routinely synthesized starting from aliphatic aldehydes and 2,3-dimethyl-2,3-bis(hydroxylamino)-butane. Direct treatment of the reaction mixture with sodium perchlorate or lead dioxide forms a nitronyl nitroxide derivative. 14 Mitchell et al. have discussed the synthesis of dinitrile CPD (Scheme 1 in ref. 15). Mitchell and Bockelheide11 prescribed the method of synthesizing CPD derivatives with hydrogen atoms at position 15 and 16 (Figure 5.1). One has to now attach o-Ver to positions 1 or 14 and NN to position 8 of CPD. It may not be easy. The CPD diradical may turn out to be quite unstable, but the preparation of a.derivative may be feasible. If the derivative contains an electron withdrawing group, it is likely to have a decreased absolute value of J, while an electron donating group can lead to a larger J value. The real utility of the systems as photomagnetic materials requires fitting oVER(N)-(15,16-dihydrogen)DDP-NN

and

o-VER(N)-(15,16-dinitrile)DDP-NN

suitable 5.geometric patterns in a matrix, the former at a low temperature.

in


CHAPTER 5.

85

5.4 References 1. Teki, Y.; Toichi, T.; Nakajima, S. Chem. Eur. J. 2006, 12, 2329. 2. Huai, P.; Shimoi, Y.; Abe, S. Phys. Rev. B 2005, 72, 094413. 3. Ali, Md. Ehesan and Datta, Sambhu N. J. Phys. Chem. A, 2006, 110, 10525. 4. Shil, S. and Misra, A. J. Phys. Chem. A 2010, 114, 2022. 5. Latif, I. A.; Panda, A.; Datta, S. N. J. Phys. Chem. A 2009, 113, 1595. 6. (a) Trindle, C.; Datta, S. N. Int. J. Quantum Chem. 1996, 57, 781. (b) Trindle, C.; Datta, S. N.; Mallik, B. J. Am. Chem. Soc. 1997, 119, 12947. 7. Koivisto, B. D.; Hicks, R. G. Coord. Chem. Rev. 2005, 249, 2612. 8. (a) Borden, W. T.; Davidson, E. R. J. Am. Chem. Soc. 1977, 99, 4587. (b) Borden, W. T.; Davidson, E. R.; Feller, D. Tetrahedron 1982, 38, 737. (c) Feller, D.; Davidson, E. R.; Borden, W. T. Isr. J. Chem. 1983, 23, 105. (d) Kato, S.; Morokuma, K.; Feller, D.; Davidson, E. R.; Borden, W. T. J. Am. Chem. Soc. 1983, 105, 1791. 9. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.;

Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.;

Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision C.02; Gaussian, Inc.: Pittsburgh, PA, 2004. 10. (a) Yamaguchi, K.; Takahara, Y.; Fueno, T.; Nasu, K. Jpn. J. Appl. Phys. 1987, 26, L1362. (b) Yamaguchi, K.; Jensen, F.; Dorigo, A.; Houk, K. N. Chem. Phys. Lett.


CHAPTER 5.

86

1988, 149, 537. (c) Yamaguchi, K.; Takahara, Y.; Fueno, T.; Houk, K. N. Theo. Chim. Acta 1988, 73, 337. 11. Mitchell, R. H.; Boekelheide, V. J. Am. Chem. Soc. 1974, 96, 1547. 12. Williams, R. V.; Edwards, W. D.; Mitchell, R. H.; Robinson, S. G. J. Am. Chem. Soc. 2005, 127, 16207. 13. Pare, E. C.; Brook, D. J. R.; Brieger, A.; Badik, M.; Schinke, M. Org. Biomol. Chem., 2005, 3 , 4258. 14. Ullman, E.F.; Osiechi, J.H.; Boocock, D.G.B.; Darcy, R. J. Am. Chem. Soc. 1972, 94, 7049. 15. Ayub, K.; Zhang, R.; Robinson, S. G.; Twamley, B.; Williams, R. V.; Mitchell, R. H. J. Org. Chem. 2008, 73, 451.


Chapter 6 Photoswitching and magnetic crossover in organic molecular systems Efficient photomagnetic diradicals has theoretically been designed using both substituted and unsubstituted cyclophanediene (CPD) and dihydropyrenes (DHP) as spacers. Nitronyl nitroxide (NN), oxoverdazyl (o-VER), and tetrathiafulvalene (TTF) are chosen as monoradical centers. Molecular geometries have been optimized by the density functional method UB3LYP using 6-311G(d,p) basis set. Final single point calculations have been done with 6-311++G(d,p) basis. Absorption wavelengths have been estimated from time-dependent density functional treatment using restricted spin-polarized density functionals (RB3LYP) and 6-31G basis. Both the substituted and unsubstituted CPD species with mixed monoradical centers are found to be antiferromagnetically coupled. Diradicals with the same centers but with DHP coupler exhibit strong ferromagnetic coupling. Also, photoexcitations of the diradicals are generally red-shifted by only a few nanometers from those of the 15,16-dimethyl pyrenes. This indicates that on photoexcitation a consistent magnetic crossover from an antiferromagnetic to a ferromagnetic regime is possible. The accompanying change in magnetic exchange coupling constant Î&#x201D;J is very large, varying from 445 cmâ&#x2C6;&#x2019;1 to 1003 cmâ&#x2C6;&#x2019;1. As far as organic molecular magnetism is concerned, this observation is entirely new and likely to be of technological significance.


CHAPTER 6.

88

6.1 Introduction

The 180o reorientation of the magnetization vector from its original direction

represents â&#x20AC;&#x153;magnetization reversalâ&#x20AC;?. It is one of the most crucial processes in magnetism and is linked to magnetic data storage such as that in hard disk drives. 1 Reversal of magnetization by photoinduction is an easy process that can find diverse applications.2a Thirion et al. 2b have discussed the importance of materials with magnetization reversal for application in spintronics. A magnetization crossover involves the conversion of an antiferromagnetic alignment to a ferromagnetic one and vice-versa within a molecule. In the material, this molecular process can lead to a conversion from diamagnetism to ferromagnetism (or even to diamagnetism depending on the intermolecular orientation in lattice) at a lower temperature, and to paramagnetism at a higher temperature. This is important for modifying the physical properties of materials. A reversible photochemical conversion of a chemical species is called photochromism. A photochromic molecule, when connected between two magnetic units as a spin coupler, changes magnetic behavior of the integrated species upon exposure to radiation of a particular wave length. Matsuda and co-workers have isolated and examined various photochromic spin couplers like diarylethene, azobenzene and so on.3 Huge interest in photomagnetic properties has resulted in the investigation of excited states of diradicals.4,5 Photoactive diradicals constructed from nitronyl nitroxide (NN) and imino nitroxide (IN) coupled through substituted pyrene molecule have been studied by Ali and Datta.6

Shil and Misra7 have claimed to show a photoinduced

antiferromagnetic to ferromagnetic crossover involving the conversion of substituted trans-azobenzene to cis-azobenzene. Meanwhile, Latif et al.8 have conceptually fabricated magnetic molecules using mixed diradicals of NN, tetrathiafulvalene (TTF) and oxo-verdazyl (o-VER) with a variety of spacers and predicted very high J values for these species. Other authors have used TTF as a monoradical center.9 In most of these investigations, the J value does not change sign,

6

or even if the sign is changed, Î&#x201D;J is

quite small.7 Substituted

pyrene

molecule

exists

in

two

different

forms,

namely,

cyclophanediene (CPD) and dihydropyrene (DHP), as shown in Figure 6.1.10(a) The numbering of carbon atoms is taken from Williams et al.10(b)


CHAPTER 6.

89 4

2

4

5 6

3

2

7

R

1

15

8

16 R

14

10

13 11

12

CPD

9

h 1 ,  h 2

1

5 6

3 15

14

7

R

8

16 R

13

10

9

11

12

DHP

Figure 6.1: Conversion of CPD to DHP. The work of Latif et al.8c indicated that the mixed diradical systems involving NN and o-VER, and coupled through CPD and DHP, can have a large variation of the coupling constant. No crossover was evidenced. Because TTF carries a positive charge, the concerned unpaired electron is somewhat localized. There exists two routes of conjugation from the point of contact with the coupler to the lone electron. A structural change such as the change of the dihedral angle between the coupler and TTF planes can favor a specific route over the other, thereby changing the nature of coupling and making crossover possible. Therefore, in the present work, we computationally investigate the ground-state photomagnetic properties of NN-TTF and o-VER-TTF diradicals using both substituted and unsubstituted pyrene molecules as spacers. The four pairs of diradicals are illustrated in Figure 6.2. The molecules investigated are (1) NN-substituted couplerTTF, (2) NN-coupler-TTF, (3) o-VER-substituted coupler-TTF, (4) o-VER-coupler-TTF. The substituted coupler has two nitrile groups in place of two middle hydrogen atoms. We find a large photoinduced magnetization crossover for every pair. We also rationalize the magnetic nature of every species by using the spin alternation rule11 as well as the computed atomic spin densities. Besides, we examine the composition of the broken symmetry state and the effect of planarity of the molecule in considerable detail. Finally, the absorption frequencies are estimated from TDDFT calculations on each species to show that they are in the range of observed frequencies for the dimethyl substituted pyrenes. This reveals the possible technological importance of the systems investigated here.


CHAPTER 6.

90

O

O

N

N

CN

S

S

h 1 , 

N

S

S

h 2

N

NC

O

(1)

H H

S S

S

h 3 , 

N

H

S

h 4

N

H

O

(2)

(a)

S CN

S

S S

h 5 ,  h 6

N N N N

H

Me

S

S

S

S

(b)

Me

S S

S

S

(a)

o-VER-(15,16-dihydrogen)CPD-TTF Figure 6.2:

S

o-VER-(15,16-dinitrile)DHP-TTF

Me

N N

CN

Me

o-VER-(15,16-dinitrile)CPD-TTF

H

S

CN

O

(3)

(a)

O

S

Me

CN

O

S

NN-(15,16-dihydrogen)DHP-TTF

Me

N N

S

(b)

NN-(15, 16-dihydrogen)CPD-TTF

Me

S

O

O

N N

S

NN-(15,16-dinitrile)DHP-TTF

O

N N

S

(b)

NN-(15,16-dinitrile)CPD-TTF

N

CN

O

(a)

N

NC

h 7 ,  h 8

N N

H

N N

H

O Me

(4)

S

S

S

S

(b)

o-VER-(15,16-dihydrogen)DHP-TTF

Photochemical interconversion of (1) NN-(15,16-dinitrile)CPD-TTF and NN(15,16-dinitrile)DHP-TTF; (2) NN-(15, 16-dihydrogen)CPD-TTF and NN-(15,16dihydrogen)DHP-TTF; (3) o-VER-(15,16-dinitrile)CPD-TTF and o-VER-(15,16-dinitrile)DHPTTF; and (4) o-VER-(15,16-dihydrogen)CPD-TTF and o-VER-(15,16-dihydrogen)DHP-TTF.


CHAPTER 6.

91

6.2 Calculation and Analysis All calculations reported here have been carried out with Gaussian 03 software.12 Molecular geometries of the triplet diradical have been optimized by the unrestricted spin polarized density functional methodology UB3LYP using 6-311G(d,p) basis set. The triplet single point calculations have been performed using the respective optimized molecular geometry, UB3LYP method and 6-311++G(d,p) basis set. The same geometry, the same methodology and the same basis set have been used for the corresponding BS calculation. The intra-molecular ferromagnetic coupling constant for each species has been determined from Eq. (2.39). Computed energy values, S 2

and J Y are given in

Table 6.1. Following the analysis given in ref. 8(b), we determine the diradical nature

N d  1 2   M 1   M 2  CO

(6.1)

where  M 1 ,  M 2 and  CO are the net spin densities on monoradical 1 (M1), monoradical 2 (M2) and coupler (CO), respectively. The calculated N d values are shown in Table 6.2. The broken symmetry wave function can be written as

 BS  m SBS  n TBS

(6.2)

where  SBS and  TBS are singlet and triplet component functions. Furthermore, m2  n 2 

1

2

and normalization of  BS stipulates m2  n 2  1 . Also, n2 =0.5 S 2

that m2 = 1− 0.5 S 2

BS

BS

so

. The percent net weight of triplet and singlet components in the

computed BS solution are given in Table 6.3. The BS solution can be written as

 BS  M 1 q1 , 1  CO  q2 ,  2  M 2  q3 , 3 

(6.3)

where q1 etc. are the computed Mulliken charges and 1 etc. are the computed spin densities.

The

corresponding

ingredient

determinant

is

M 1 q1 , 1  CO  q 2 ,  2  M 2  q 3 , 3  that can be used to construct the singlet and triplet wave functions,


CHAPTER 6.

92

Table 6.1. Broken symmetry energies and coupling constants of NN-TTF and o-VERTTF diradicals from single point UB3LYP calculations using 6-311++G(d,p) basis set. The BS calculation has been achieved by finding ROHF wave functions for the optimized triplet structure and then using the corresponding molecular orbitals as an initial guess. a

a

System

ET in a.u. (<S2>)

EBS in a.u. (<S2>)

EBS- ET (cm–1)

JY (cm–1)

1a. NN(15,16dinitrile)CPDTTF 1b. NN(15,16dinitrile)DHPTTF 2a. NN-CPD TTF

−3157.3611291 (2.079154)

−3157.3625326 (0.886741)

−308.0

−258.3

−3157.3809176 (2.14157)

−3157.3783627 (1.104239)

560.7

540.6

−2972.8483677 (2.068416)

−2972.8495325 (0.858698)

−255.6

−211.3

2b. NN-DHPTTF

−2972.8901059 (2.120127)

−2972.8863355 (1.075278)

827.5

792.0

3a. o-VER(15,16dinitrile)CPDTTF 3b. o-VER(15,16dinitrile)DHPTTF

−3073.7420224 (2.029511)

−3073.7432179 (0.883334)

−262.4

−228.9

−3073.7623587 (2.057372)

−3073.7613285 (1.01267)

225.9

216.3

4a. o-VERCPD-TTF

−2889.2295402 (2.028481)

−2889.2303737 (0.878007)

−182.9

−159.0

4b. o-VER– DHP-TTF

−2889.2716158 (2.055954)

−2889.2700082 (1.025251)

352.8

342.3

We have used 1 a.u. of energy = 27.2114 eV and 1 eV = 8065.54 cm–1.


CHAPTER 6.

93

Table 6.2. Total charge and spin population on atoms belonging to different fragments of the diradical in the BS state. The diradical nature is also shown.

1a

Charge population a NN CO TTF (o-VER) 0.1812 0.2829 0.5359

Spin population a NN CO TTF (o-VER) 0.8821 −0.0546 −0.8274

1b

0.2246

0.2650

0.5105

1.0933

−0.1990

−0.8942

0.8942

2a

0.2544

0.2301

0.5155

0.8539

−0.0712

−0.7827

0.7827

2b

0.2579

0.3651

0.3770

1.0720

−0.3378

−0.7342

0.7343

3a

0.3099

0.1247

0.5654

0.8703

−0.0139

−0.8565

0.8565

3b

0.3316

0.1773

0.4911

1.0005

−0.1349

−0.8656

0.8676

4a

0.3533

0.1208

0.5260

0.8589

−0.0405

−0.8184

0.8065

4b

0.2518

0.4786

0.2695

1.0075

−0.2924

−0.7152

0.7152

System

a

Diradical Nature 0.8274

Mulliken population analysis from Gaussian 03.

Table 6.3. Percent net weight of singlet and triplet components in the computed BS solution. System

Singlet % Weightage Triplet % Weightage (100m2) (100n2)a 1a. NN-CN(Open)-TTF 55.67 44.34 1b. NN-CN(Close)-TTF 44.79 55.21 2a. NN-H(Open)-TTF 57.07 42.93 2b. NN-H(Close)-TTF 46.24 53.76 3a. o-VER-CN(Open)-TTF 55.83 44.17 3b. o-VER-CN(Close)-TTF 49.37 50.63 4a. o-VER-H(Open)-TTF 56.10 43.90 4b. o-VER-H(Close)-TTF 48.74 51.26 a 2 Using 50* S . Singlet weightage = 100 –Triplet weightage. BS


CHAPTER 6.

94

 S  N   M1 q1 , 1  CO  q 2 ,  2  M2  q 3 ,  3   M1 q1 ,  1  CO  q 2 ,   2  M2  q3 ,  3  

and

(6.4)

 T  N   M1 q1 , 1  CO  q 2 ,  2  M2  q 3 , 3   M1 q1 ,  1  CO  q 2 ,   2  M2  q 3 ,  3   N

where

N

and  12

N    2(1  )

are  12

, N    2(1  ) 

overall

normalization

constants,

,  being the overlap of two involved determinants

in (5). Because of (3), one can write

 BS  2

1

2

[ mN   nN   M1 q1 , 1  CO  q 2 ,  2  M2  q 3 , 3  

 mN   nN  

(6.5)

M1 q1 ,  1  CO  q 2 ,   2  M2  q 3 ,  3  ].

This gives qi  2  m 2 N 2  n 2 N 2  q i while  i  4mnN  N  i . In the two electron twoorbital model,      N |  / N 2

2 1

 2 where  and  / are the spatial parts of spin

orbitals of α and β spins respectively, so that   1 . This leads to N   N  

1

2

, and

gives qi  q i and  i  2mn i . It would be useful to know the BS solution as a linear combination of wave functions representing the “neutral”, “polar” and “ionic” structures with different spin distributions over M1, M2 and CO. This is done as follows. The fragment M1 is NN- or o-VER while M2 is TTF. In the first step, four spin structures are considered. These are abbreviated as (  M 1 ,  CO ,  M 2 ). One is the ground state spin structure, (1, 0, –1). The other three differ by 1 on two of the three fragments: (0, 1, –1), (2, –1, –1) and (1, –1, 0). The chosen spin-only basis sets are illustrated in Figure 6.3. The corresponding linear combination coefficients c1, c2 , c3 and c4 are determined from a comparison with the computed spin population in Table 6.2 divided by 2mn. c12  c22  c32  c42  1 .

The normalization condition is


CHAPTER 6.

95

M1

CO

TTF

(d)

M1

CO

TTF

(c)

M1

CO

TTF

(b)

M1

CO

TTF

(a)

Figure 6.3. The chosen spin basis. Each up (down) arrow indicates a fragment spin population 1 (â&#x20AC;&#x201C;1); (M1 = NN or o-VER).

2

M1

M1

M1

M1

CO

TTF

M1

CO

2

TTF

M1

CO

(1)

(2)

(3)

Neutral

Ionic

Ionic

CO

TTF

M1

CO

M1

TTF

CO

(4)

(5)

(6)

Polar

Polar

Ionic

CO

TTF

M1

CO

TTF

M1

CO

(7)

(8)

(9)

Polar

Polar

Ionic

CO

TTF

2

M1

CO

TTF

M1

2

CO

(10)

(11)

(12)

Polar

Polar

Ionic

TTF

TTF

TTF

TTF

Figure 6.4. Canonical structures with different distributions of fragment charge Q for each set of fragment spin population; (M1 = NN or o-VER).


CHAPTER 6.

96

Table 6.4. Characteristics of the basic determinants. The values within parentheses are fragment spin populations for the canonical structures with different distributions of fragment charge. Basic determinant Serial No. (ρ = 1, 0, –1) 1 2 3 (ρ = 0, 1, –1) 4 5 6 (ρ = 2, –1, –1) 7 8 9 (ρ = 1, –1, 0) 10 11 12

Fragment Charge NN (o-VER)

CO

TTF

0 0 2

0 2 0

1 –1 –1

–1 1 1

1 –1 1

1 1 –1

–1 1 1

1 –1 1

1 1 –1

0 0 2

1 –1 –1

0 2 0


CHAPTER 6.

97

Table 6.5. Relative weightage of different basic determinants in the BS solution. The same relative weights describe both the singlet and triplet components. The relative weights are to be multiplied by m2 and n2 to get the net weights of singlet and triplet components.a,b Diradicals from Figure 6.2 Basis 1a 1b 2a 2b 3a 3b 4a 4b (ρ = 1, 0, –1) 1 0.5534 0.6049 0.4950 0.4552 0.5782 0.6450 0.5264 0.4491 2 0.1019 0.1061 0.0752 0.1207 0.0461 0.0767 0.0417 0.1693 3 0.0653 0.0899 0.0831 0.0853 0.1145 0.1434 0.1219 0.0891 (ρ = 0, 1, –1) 4 0.0459 0.0512 0.0427 0.0435 5 0.0402 0.0529 0.0543 0.0592 6 0.0260 0.0332 0.0269 0.0319 (ρ = 2, –1, –1) 7 0.0362 0.0279 0.0002 0.0029 8 0.0343 0.0238 0.0002 0.0020 9 0.0229 0.0233 0.0001 0.0029 (ρ = 1, –1, 0) 10 0.1072 0.0669 0.1288 0.1800 0.0774 0.0791 0.0983 0.2104 11 0.0448 0.0270 0.0540 0.0497 0.0389 0.0330 0.0461 0.0384 12 0.0151 0.0118 0.0266 0.0340 0.0213 0.0223 0.0310 0.0358 a The fragment charges can be directly calculated from the relative weight. b The spin population values calculated using the relative weights are to be multiplied by a factor of 2mn to get the computed value of (Mulliken) spin population.

Table 6.6. Polar and ionic contributions to the BS solution, compared with the basic determinant 1 taken as the “neutral” structure.

Total contributions

Diradicals from Figure 6.4

Neutral

1a 0.5534

1b 0.6049

2a 0.4950

2b 0.4552

3a 0.5782

3b 0.6450

4a 0.5264

4b 0.4491

Polar

0.2381

0.1644

0.2869

0.2814

0.2133

0.1125

0.2471

0.2537

Ionic

0.2083

0.2307

0.2181

0.2633

0.2088

0.2425

0.2265

0.2971


CHAPTER 6.

98

It is possible to write down canonical structures with different distributions of the fragment charge for each spin-only structure. The lowest charge bearing sets are shown in Table 6.4 and Figure 6.4. The first basic determinant (designated 1) is considered neutral. Comparing the rest with this structure, one finds 4, 5, 7, 8, 10 and 11 to be polar in character and the remaining ones to be largely ionic. Linear combination coefficients for different charge structures for each spin-only structure have been determined by comparison with the charge population in Table 6.2. These yields the coefficients d1 ,..., d12

subject to normalization conditions

d12  d 22  d32  1 ,

d 4 2  d52  d 62  1 ,

d7 2  d82  d92  1 and d10 2  d112  d122  1 . Finally, the relative weight of the basic

determinants (like c 22 d 6 2 for the 6th canonical structure) has been determined for all eight diradicals. These are given in Table 6.5. The total polar and ionic contributions are listed in Table 6.6. To predict the wavelength of light for photo-conversion in each pair of molecules, we carried out TDDFT calculation by following restricted spin polarized density functional methodology (RB3LYP) using 6-31G basis set.

6.3 Results and discussion 6.3.1 General trends Table 6.1 shows that all the open ring isomers (1a, 2a, 3a, 4a) are antiferromagnetically coupled while the corresponding close ring isomers (1b, 2b, 3b, 4b) are ferromagnetically coupled. The dihedral angle between DHP coupler and two magnetic units and also the C15-C16 distances (Table 6.7 of supporting information) are consistently less than those in CPD species. This enables the DHP containing diradical to have a nearly planar structure, and is largely responsible for the high degree of conjugation that facilitates the migration of spin waves. A superposition of spin waves migrating from one atom to the next in two opposite directions leads to the formation of a standing wave that appears as spin alternation, much like the superposition of plane waves giving rise to sine or cosine waves. The spin alternation from one atom to the next is a manifestation of spin polarization, the latter being a stabilizing influence,11(a) and the Y

extent of spin alternation increases with conjugation. In consequence, the J value


CHAPTER 6.

99

Table 6.7: Triplet energy, mean dihedral angles, C15-C16 distances and <S2> of NN(CPD/DHP)-TTF and o-VER-(CPD/DHP)-TTF diradicals from geometry optimization by UB3LYP calculations using the 6-311G (d,p) basis set.

System 1a. NN-(15,16dinitrile)CPD-TTF 1b. NN-(15,16dinitrile)DHP-TTF 2a. NN-CPD -TTF 2b. NN-DHP-TTF 3a. o-VER-(15,16dinitrile)CPD-TTF 3b. o-VER-(15,16dinitrile)DHP-TTF 4a. o-VER-CPDTTF 4b. o-VER–DHPTTF

Eopt in a.u. (<S2>) −3156.3078297 (2.085598) −3157.3570682 (2.14533) −2972.8274195 (2.070658) −2972.8698508 (2.122994) −3073.7186961 (2.029539) −3073.739496 (2.051735) −2889.2098087 (2.028396) −2889.2522994 (2.053704)

Dihedral angle (deg) NN or o-VERTTFCoupler Coupler

C15-C16 Distance (Å)

3.61

29.38

2.68

3.33

18.94

1.54

4.25

34.52

2.54

0.27

14.28

1.52

3.01

41.77

2.7

2.46

25.17

1.54

1.61

34.15

2.55

0.48

15.97

1.52


CHAPTER 6.

100

becomes very large for the DHP species. A detailed discussion on spin dynamics will be published elsewhere. For each pair of CPD and DHP species, there is not only a change in the sign of J but also a consistently large variation in its absolute magnitude. For instance, the coupling constant changes from â&#x2C6;&#x2019;211 cmâ&#x2C6;&#x2019;1 for NN-CPD-TTF to 792 cmâ&#x2C6;&#x2019;1 for NN-DHPTTF. The dinitrile systems are better diradicals than the unsubstituted ones, as can be seen from the diradical nature in Table 6.2. One may compare 1a versus 2a, 1b versus 2b, 3a versus 4a, and 3b versus 4b. This is because the nitrile substitution generally increases the absolute magnitude of spin density on NN (o-VER) and TTF, but decreases the spin density on the spacer, thereby giving the molecule a greater appearance as a diradical and a less amount of spin delocalization. The spin densities on the first monomer (NN, o-VER) are highly accentuated by closure, for both substituted and unsubstituted molecules, and this tends to increase the (negative) spin density on the coupler. The (negative) spin density on the second monomer (TTF) decreases by closure for the dihydrogen systems and increases for the dinitrile species, accompanied by a further rise in the (negative) spin density of the coupler in the first case and a lowering in the second situation (Table 6.2). The net effect is that for dinitrile systems, the closed (DHP) form has a higher diradical nature than the open (CPD) form (1b > 1a, 3b > 3a) while the open form has a higher diradical nature for the dihydrogen systems (2a > 2b, 4a > 4b) as evidenced from Table 6.2.

6.3.2 Spin alternation We compare spin alternation in triplet and that in BS solution to decide which solution would be more stable. This indicates the sign of J, and the relative stability of triplet and the two-configuration singlet, E(T)<E(BS)<E(S2) or E(T)>E(BS)>E(S2). The singlet states of CPD isomers (1a, 2a, 3a, 4a) are more sTable 6.than the triplet states as can be seen from an application of spin alternation rule11 (Figure 6.5 of supporting information). When there is more than one nonbonding electron in the pz orbital of a heteroatom like N, O, S, etc. and the bonding of these atoms is otherwise satisfied, all the nonbonding pz electrons should be considered in the spin alternation rule. That is,


CHAPTER 6.

101

O

O

N

NC

N CN

S

S

S

S

S

S

S

S

NC N

N

CN

O

O

NN-(15,16-dinitrile)CPD-TTF

NN-(15,16-dinitrile)DHP-TTF

O

O

N

H

N H

S

S

S

S

S

S

S

S

S

S

S

S

H N

N O

H O

NN-CPD-TTF

NN-DHP-TTF

Me

Me N

N

CN

N S

N

CN

S

O

O N

N

CN

N S

Me

N

CN

S Me

o-VER-(15,16-dinitrile)CPD-TTF

o-VER-(15,16-dinitrile)DHP-TTF

Me

Me N

N

H

N S

O

N

H

S

S

S

S

S

O N

N

Me

o-VER-CPD-TTF

H

N S

N

H

S Me

o-VER-DHP-TTF

Figure 6.5: Prediction of ground spin states and nature of the magnetic exchange coupling constant on the basis of spin alternation rule.


CHAPTER 6.

102

-0.005

O 0.219 N 0.212

-0.047

0.008 -0.005

0.02

0.02

-0.133

CN

-0.002 0.437

-0.162

-0.006

-0.003

-0.05

S

-0.041

O 0.321

0.032

-0.062

-0.019

-0.002

-0.070

0.006

-0.005

-0.027

-0.023

NC N 0.226

-0.133

S

0.003

-0.095 -0.028

S

S

-0.132

-0.128

NN-(15,16-dinitrile)CPD- TTF 0.00

O 0.319

0.00

-0.04

N 0.227

0.00

-0.021

H

-0.010 0.00

-0.018

0.032 -0.052

-0.156

-0.012

-0.03

0.01

-0.118

S

-0.051 -0.002

0.019

-0.092

-0.09

S

-0.001

-0.023

S

-0.122

-0.130

O 0.267

-0.025

0.004

H N 0.202

-0.120 S

0.006

NN-CPD-TTF Me 0.156 0.347

N

-0.016

N

0.00

-0.147

O

-0.03

0.012

0.02 CN -0.03

0.002

0.016

-0.138 S

0.003

-0.007

-0.024

-0.138

S

-0.02

-0.06 -0.99

N

-0.01

N

-0.015

0.367

0.018 CN

0.002

-0.019

-0.070

Me -0.003

0.001

S

S

-0.133

-0.133

-0.03

o-VER-(15,16-dinitrile)CPD-TTF

Me 0.159

0.337

N

N -0.149

O

0.00

N 0.147

N

0.342

-0.01

0.003 -0.01

0.01 H -0.031 0.02 H

0.003

-0.02

0.003

-0.01 0.001

-0.125 S

-0.132

S

-0.011 -0.052

0.012

-0.098

S

-0.137

Me

-0.027

-0.099

S

-0.024

-0.127

o-VER-CPD-TTF Figure 6.6: Spin population of the antiferromagnetically coupled diradicals in their BS states.


CHAPTER 6.

103

O 0.405

-0.079

0.086

-0.065 -0.105 0.063 NC 0.093 0.122 0.013 S -0.022 0.007 0.041 -0.059 0.137 -0.007 -0.168 0.037 N 0.264 CN 0.035 0.113 -0.052 0.116 -0.098 S 0.152 O 0.403 0.053 0.003 N 0.262

0.108 S

0.025

0.095 S

0.020

0.115

NN-(15,16-dinitrile)DHP-TTF

0.404 -0.063

O

0.085

-0.035 -0.108 H 0.032 0.060 0.077 0.128 -0.010 S S -0.035 0.018 0.003 0.162 -0.006 -0.172 -0.014 0.006 0.079 0.010 0.014 N 0.268 H 0.013 -0.097 0.136 0.020 0.139 S S 0.139 0.084 O 0.033 -0.061 0.403 N

0.226

NN-DHP-TTF

-0.052 0.002 Me

-0.028 0.198 0.417 0.080 0.021 N N CN 0.105 -0.056 0.122 -0.030 S S -0.008 0.022 0.034 O 0.019 0.098 0.006 -0.0169 0.006 0.101 0.042 0.046 N CN 0.198 N -0.046 0.127 -0.063 0.101 0.026 0.041 S S Me 0.116 0.157 0.075 -0.056

o-VER-(15,16-dinitrile)DHP-TTF

-0.041

0.018

Me

0.192 0.424 -0.064 0.028 N H 0.005 0.097 0.007 -0.016 -0.173 -0.008 -0.033 O -0.013 0.024 0.131 N N0.423 H 0.025 -0.075 0.113 -0.019 0.153 0.193 Me -0.047 0.079 N

0.070 S

S

0.010 S

0.085

0.146

0.014

0.085 0.019 S

0.085

o-VER-DHP-TTF Figure 6.7: Spin population of the ferromagnetically coupled diradicals in their triplet states.


CHAPTER 6.

104

NN-(15,16-dinitrile)CPD-TTF

(a)

NN-CPD-TTF

(b)

o-VER-(15,16-dinitrile)CPD-TTF

o-VER-CPD-TTF

NN-(15,16-dinitrile)DHP-TTF

NN-DHP-TTF

(c) o-VER-(15,16-dinitrile)DHP-TTF

(d)

o-VER-DHP-TTF

Figure 6.8: Spin-density plots of optimized triplet geometries of NN-coupler-TTF and oVER-Coup-TTF systems from UB3LYP calculations with the 6-311G(d,p) basis set.


CHAPTER 6.

105

nitrogen atom in sp2 hybridization with three ligands offers two electrons for spin alternation. The spin wave propagation is likely to have two routes in the first ring of TTF, through S and through C–S, while approaching from the coupler side. The first route is more efficient in open ring isomers as seen from the greater atomic spin density of S compared to the carbon atom of C–S in the BS state (Figure 6.6), thereby favoring antiferromagnetic coupling. The spin density values inherit the opposite trend in case of all DHP isomers in their triplet state (Figure 6.7), and spin propagation occurs mainly through C–S, thereby giving rise to ferromagnetic coupling. The antiferromagnetic to ferromagnetic crossover is mainly due to the variation of the exchange pathway (Figure 6.5). The atom-atom overlaps change with structural changes. In fact, TTF-coupler dihedral angle drastically decreases on ring closure (Table 6.5). With a large dihedral angle of about 35o, one nonbonding orbital of each sulfur atom becomes parallel to (while the carbon pz orbitals of TTF deviate from) the carbon pz orbitals of the coupler. This directly favors the shorter S-path because the delocalization is more feasible here. A smaller dihedral angle favors extensive delocalization of the carbon atom pz orbitals although the sulfur nonbonding orbitals are no longer parallel to the coupler π system. Then the longer route, the C-S path, becomes more favorable as it involves a greater spin alternation (greater antiferromagnetic exchange or greater bonding in the valence-bond sense) that enhances stability. The spin density plot of each species in its triplet state is given in Figure 6.8. Polarization of spin on the pyrene coupler is greatly reduced in the high spin states of open isomers (1a, 2a, 3a, 4a). The exchange between unpaired electrons on radical sites through the coupler is quite sluggish in the CPD form in its triplet state. This is in support of the open species having a low spin ground state while the closed isomers have high spin ground states.

6.3.3 Effect of planarity The J value of the closed, ferromagnetically coupled isomers is greater for the unsubstituted pyrene molecule than the substituted species as coupler. The dihedral angles follow the order 1b > 2b and 3b > 4b while the C15-C16 distance remains more or


CHAPTER 6.

106

less the same from the substituted to the unsubstituted DHP species (Table 6.S1). The trend in J is 2b>1b and 4b>3b. The average dihedral angle shows the trend 2a > 1a with C15-C16 distance decreasing by 0.14 Å from 1a to 2a. Although the average dihedral angle follows the trend 3a > 4a, the C15-C16 distance decreases by 0.15 Å from 3a to 4a. Thus the change in C15-C16 distance plays the dominant role here in determining J (1a>2a, 3a>4a). In short, a decrease in dihedral angle in the closed isomer and an increase in C15C16 distance in the open species tend to enhance planarity. It is observed that NN-TTF diradicals are much more strongly coupled than oVER-TTF diradicals. It is due to the difference in the first monoradical (NN versus oVER) as well as a lesser amount of planarity of the o-VER-TTF diradical. The planarity follows the order 1a > 3a, 1b > 3b and 2b > 4b – a consequence of increasing dihedral angle of the second species – while the C15-C16 distance remains more or less unchanged, and the J value follows the same order (Table 6.1). Species 2a and 4a have comparable dihedral angles and comparable C15-C16 distances. The somewhat larger |J| for 2a is purely the consequence of NN being the monoradical center instead of o-VER.

6.3.4 Analysis of BS solution The original equation due to Noodleman13 contains the overlap of magnetically active orbitals. These orbitals are directly related to the broken-symmetry solution. Neese14 made an analysis of the broken-symmetry state and showed that the “diradical character” in the BS approach can be related to the overlap integral between the BS magnetic orbitals. The latter can be unambiguously obtained from a corresponding orbital transformation (COT) due to Amos and Hall.15 The COT leaves the BS determinant unchanged and orders the BS spin orbitals into pairs of orbitals of maximum similarity. The group of MOs with spatial overlap half way between zero and unity form valence bond-like overlapping magnetic pairs14. An analysis of the BS solution is important in this context. The diradical character introduced by Neese14 is zero if n  0 and 100% when

n 2  0.50 . This is somewhat misleading because whenever the distance between the two


CHAPTER 6.

107

unpaired electrons is large enough, that is, they are localized on two distinct molecular fragments like NN and TTF, the species can be considered as a diradical regardless of the spin state. Also, from calculation, we have often found n 2  0.50 . Therefore, we introduced a different definition and called the property as “diradical nature”. 8(b) From Table 6.2, it is observed that all the species except 2a, 2b and 4b have diradical nature above 80% in the BS state. Even 4b has diradical nature greater than 70%. Therefore, all the eight species are good diradicals. This implies that they possess a robust magnetic nature. But, being radicals, their reactivities also increase. This would make it difficult to keep them in store. For the ferromagnetic species (all close ring isomers), the triplet weightage is greater than the singlet weightage in the BS solution and for the antiferromagnetic species (all open ring isomers), the singlet weightage is greater. This can be seen from Table 6.3. That is, the computed BS solution shows a tendency to be closer in composition to the more sTable 6.state. This is an artifact of the calculational method. In fact, Dai and Whangbo16 have shown that for a diradical, the reverse Clebsch-Gordon coefficients for the pure BS state are m  2

 12

, n2

 12

.

The relative weights of different basic determinants in the BS solutions are given in Table 6.5. A canonical structure and the corresponding structure with reversed spins together form the singlet and triplet component wave functions. Therefore, the same relative weights describe both singlet and triplet components. The relative weights are to be multiplied by m2 and n2 to get the net weights of the singlet and triplet components. The fragment charges can be directly calculated from the relative weights using Table 6.4 and Figure 6.4. The spin population values calculated using the relative weights are to be multiplied by a factor of 2mn to get the computed Mulliken spin densities on M1, M2 and coupler. In Table 6.6, we find that the contribution of the so-called “neutral” structure (basic determinant 1 and its spin reversed form) is quite high (around 50%) in the BS state of all diradicals. The rest is accounted for by the contribution from the polar and ionic

structures. The latter contributions vary from one diradical to another. The polar

character


CHAPTER 6.

108

Table 6.8. Prominent absorption wavelengths (nm) and oscillator strengths (in parentheses) for 15,16 dimethyl substituted CPD molecule and radical substituted CPD molecules from TDDFT calculation using 6-31G basis set.

2 CH3 Substituents

o-VER, 2H,TTF

o-VER, 2CN,TTF

263.6 (0.589) 271.6 (0.133)

NN, 2H,TTF

NN, 2CN,TTF

269.5 (0.209) 274.0 (0.458) 279.5 (0.133)

UV

281.3 (0.005) 282.3 (0.197)

288.1 (0.215)

Near UV

284.3 (0.083) 285.3 (0.060) 290.7 (0.574) 291.4 (0.402) 292.2 (0.156)

284.5 (0.167)

290.3 (0.104)

292.5 (0.368)

293.2 (0.059) 295.8 (0.627) 296.0 (0.289)

294.6 (0.477) 296.9 (0.131)

298.5 (0.004)

297.8 (0.074)

310.9 (0.022) 314.3 (0.011)

304.9 (0.054) 311.0 (0.011) 314.5 (0.020)

282.2 (0.078)

310.9 (0.016) 316.1 (0.006)

292.6 (0.060)

301.9 (0.023) 309.1 (0.042) 314.0 (0.073)


CHAPTER 6.

109

Table 6.9. Prominent absorption wavelengths (nm) and oscillator strengths (in parentheses) for 15,16 dimethyl substituted DHP molecule and radical substituted DHP molecules from TDDFT calculation using 6-31G basis set.

Substituents

Near UV

2CH3

o-VER, 2H,TTF

370.3 (0.0264) 375.1 (0.134) 379.3 (0.075)

o-VER, 2CN,TTF

NN, 2CN,TTF

365.8 (0.012)

359.5 (0.023)

385.8 (0.029) 390.6 (0.108)

380.5 (0.083) 388.4 (0.048)

414.0 (0.008) 425.8 (0.037)

421.9 (0.015)

369.9 (0.015) 374.2 (0.180)

388.4 (0.044) 408.0 (0.045)

Visible

NN, 2H,TTF

445.5 (0.057)

440.1 (0.030)

525.3 (0.203)

515.3 (0.226) 534.4 (0.018) 549.7 (0.295)

481.4 (0.018)

534.2 (0.002)

501.4 (0.038)

548.7 (0.17)

565.3 (0.269)

533.3 (0.118) 550.53 (0.074) 562.7 (0.413)

577.9 (0.04) 584.6 (0.386)


CHAPTER 6.

110

always dominates the antiferromagnetically coupled species whereas the ionic nature is generally more prominent in the ferromagnetically coupled ones (except 2b). The magnetic interaction is intermediately strong in each diradical.

6.3.5 Absorption wavelength The CPD molecules absorb in the UV region (位<313 nm) to convert to the corresponding DHP forms and the DHP molecules absorb in the visible region (位>365 nm) to convert to the corresponding CDP forms.19 We have carried out TDDFT calculations on both the 15,16 dimethyl substituted CPD and DHP molecules, and on the unsubstituted and dinitrile substituted CPD and DHP diradicals. Table 6.8 and Table 6.9 show the calculated most prominent absorption peak frequencies and corresponding oscillator strengths in the region necessary for photo-conversions. A total of around thirty lowest-energy transitions have been considered for each species. Results for the dimethyl derivatives are in close agreement with the experimental values measured by Mitchell.17 Table 6.8 shows that in near UV region dimethyl substituted CPD molecule does not show any appreciable absorption. Ligand substituted CPD molecules show faint absorptions in the same region, which can be attributed to the weak absorptions in the ligand moieties. In the UV region, the dimethyl substituted CPD molecule shows only two absorptions while the CPD diradicals show several absorptions with highly increased oscillator strength. For the species under investigation, the original CPD states become mixed with the substituent and radical states, are more prominent and up to 10 nm red shifted. These transitions would be responsible for conversion to the DHP forms. A few new transitions also appear. Another noticeable point is that when the 15,16 positions are unsubstituted, (that is, occupied by H atoms), they show a large number of relatively prominent absorptions. Conversely, with dinitrile derivatives, one finds a reduced number of prominent transitions. This occurs due to the mixing of the transitions of the subtituents. The dihydrogen species also show two new transitions at lower wavelengths. Table 6.9 shows that in the initial range (near UV) dimethyl substituted DHP molecule has only one faint absorption. Ligand substituted DHP molecules show similarly faint and at least one prominent absorptions in this region. These are approximately 5-20 nm red shifted. In the visible region, dimethyl substituted DHP


CHAPTER 6.

111

molecule shows only two absorptions whereas ligand substituted DHP molecules show several absorptions in this region, some with much greater oscillator strength. A few of the latter are blue-shifted, the rest being red-shifted. This indicates that conversion of ligand substituted DHP molecules to the corresponding CPD molecules would be more extensive. The large number of transitions (see Supporting Information) adds to the width of the absorption spectrum. The experimental spectrum on dimethyl CPD and DHP are extensively broad.10(a). It is obvious that the absorption spectra of the molecules under investigation will be quite similar to the spectrum of the dimethyl substituted pyrenes, aside from the effects of ligand participation and red shifts by a few nanometers.

6.3.6 Applicability The DHP form can be preserved in degassed cyclohexane at 0°C. Although thermochromic compounds are useful for certain applications, a big limitation of them as molecular switches is the restricted lifetime of the colorless CPDs which undergo facile thermal return to corresponding colored DHPs. A substituent R should be chosen in such a way that the activation barrier for CPD→DHP is high enough to hinder the thermal conversion. This can be achieved when R is CN,10(b) the activation barrier for the dinitrile system being maximum (25.31 kcal/mol) among the related species. The NN-TTF diradical with 15,16-dinitrile pyrene as coupler (DHP form) has a sufficiently high and positive J value (540.6 cm−1). At room temperature, 2J / kBT ~ –2.6 for the CPD form while 2J / kBT ~ 5.4 for the DHP species. If the molecules are properly aligned in a lattice, the CPD species would behave as an antiferromagnet whereas the DHP chains would be ferromagnetic. A lowering of temperature will make the magnetization reversal even sharper. The o-VER-TTF diradical chain with the same couplers (with dinitrile substituents) can also show a distinct AFM → FM transition.

6.4 Conclusion Photoinduced magnetic crossover of organic systems is very important in the field of photomagnetic switches, optical data storage, spintronics applications, optical sensing, spin valves, optical information processing devices, conducting and semi-conducting


CHAPTER 6.

112

magnetic materials etc. In this work, we have investigated eight different mixed diradicals made from NN, o-VER and TTF with both substituted and unsubstituted pyrene couplers by UB3LYP computations using 6-311++G(d, p) basis set. From the computed total energy values, we predict a large antiferromagnetic to ferromagnetic crossover and the reverse process for each pair of open and close ring isomers upon exposure to light of a specific wavelength. The nature of coupling in each species can be predicted from spin alternation rule, and properly accounted for by the computed spin densities. The increase in |J| as an effect of increased planarity is evidenced. Substituted as well as unsubstituted CPD and DHP diradical species have excitations red shifted by only a few nanometers, and the DHPâ&#x2020;&#x2019;CPD and CPDâ&#x2020;&#x2019;DHP conversions are generally more extensive than the conversion of the dimethyl derivatives without NN, o-VER and TTF. We have determined total charge and spin population on different fragments of each species in their BS solution and showed that all the eight molecules have good diradical nature and the magnetic interaction is intermediately strong. A detailed analysis of the BS solution indicates that the open species that are antiferromagnetically coupled have an appreciably large polar character while the closed species generally have an enhanced ionicity. The large change in J value accompanied by a change in sign for each pair (on going from open to close ring isomer) makes these molecules ideal for materials of magnetic crossover.


CHAPTER 6.

113

6.5 References: 1. J. Stohr, H. C. Siegmann, Magnetism: From fundamentals to Nanoscale Dynamics (Springer-Verlag, Berlin, 2006). 2. (a) Sato, O.; Iyoda, T.; Fujishima, A.; Hashimoto, K. Science 1996, 272, 704. (b) Thirion, C.; Wernsdorfer, W.; Mailly, D. Nat. Mater. 2003, 2, 524. 3. (a) Tanifuji, N.; Matsuda, K.; Irie, M. Polyhedron 2005, 24, 2484. (b) Matsuda, K.; Irie, M. Polyhedron 2005, 24, 2477. (c) Matsuda, K. Bull. Chem. Soc. Jpn. 2005, 78, 383. (d) Tanifuji, N.; Irie, M.; Matsuda, K. J. Am. Chem. Soc. 2005, 127, 13344. (e) Tanifuji, N.; Matsuda, K.; Irie, M. Org. Lett. 2005, 7, 3777. (f) Matsuda, K.; Irie, M. J. Photochem. Photobiol.C: Photochem. Rev. 2004, 5, 69. (g) Matsuda, K.; Matsuo, M.; Irie, M. J. Org. Chem. 2001, 66, 8799. 4. Teki, Y.; Toichi, T.; Nakajima, S. Chem. Eur. J. 2006, 12, 2329. 5. Huai, P.; Shimoi, Y.; Abe, S. Phys. Rev. B 2005, 72, 094413. 6. Ali, Md. E.; Datta, S. N. J. Phys. Chem. A 2006, 110, 10525. 7. Shil, S. and Misra, A. J. Phys. Chem. A 2010, 114, 2022. 8. (a) Latif, I. A.; Panda, A.; Datta, S. N. J. Phys. Chem. A 2009, 113, 1595. (b) Latif, I. A.; Singh, V. P.; Bhattacharjee, U.; Panda, A.; Datta, S. N. J. Phys. Chem. A 2010, 114, 6648-6656. (c) Bhattacharjee, U.; Panda, A.; Latif, I. A.; Datta, S. N. J. Phys. Chem. A 2010, 114, 6701-6704. 9. Polo, V.; Alberola, A.; Andres, J.; Anthony, J.; Pilkington, M. Phys. Chem. Chem. Phys., 2008, 10, 857-864. 10. (a) Mitchell, R. H.; Ward, T. R.; Chen, Y.; Wang, Y.; Weerawarna, S. A.; Dibble, P. W.; Marsella, M. J.; Almutairi, A.; Wang, Z.-Q. J. Am. Chem. Soc. 2003, 125, 2974. (b) Williams, R. V.; Edwards, W. D.; Mitchell, R. H.; Robinson, S. G. J. Am. Chem. Soc. 2005, 127, 16207. 11. (a) Trindle, C.; Datta, S. N. Int. J. Quantum Chem. 1996, 57, 781. (b) Trindle, C.; Datta, S. N.; Mallik, B. J. Am. Chem. Soc. 1997, 119, 12947. 12. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda,


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R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03W, revision D.01; Gaussian, Inc.: Wallingford, CT, 2004. 13. (a) Noodleman, L. J. Chem. Phys. 1981, 74, 5737. (b) Noodleman, L.; Baerends, E. J. J. Am. Chem. Soc. 1984, 106, 2316. (c) Noodleman, L.; Davidson, E. R. Chem. Phys. 1986, 109, 131. (d) Noodleman, L.; Peng, C. Y.; Case, D. A.; Mouesca, J.-M. Coord. Chem. Rev. 1995, 144, 199. 14. Neese F. J. Phys. Chem. Solids. 2004, 65, 781. 15. (a) Amos, A. T.; Hall G.G. Proc. R. Soc. Ser. A. 1961, 263, 483. (b) King, H. F.; Stanton, R. E.; Kim, H.; Wyatt, R. E.; Parr, R. G. J. Chem. Phys. 1967, 47, 1936. 16. Dai D.; Whangbo M. J. Chem. Phys. 2003, 118, 417. 17. Mitchell, R. H. Eur. J. Org. Chem. 1999, 102, 2695.


Chapter 7 High magnetic exchange coupling constants: A DFT based study of the almost forgotten Schlenk diradicals

Schlenk diradical is known since 1915. After a brief work by Rajca, its magnetic nature has remained more or less unexplored. We have investigated the nature of magnetic coupling in several substituted Schlenk diradicals by quantum chemical calculations. Substitution has been considered at the fifth carbon atom of the meta-phenylene moiety. The UB3LYP method has been used to study a total of twelve diradicals. The 6-311G(d,p) basis set has been employed for optimization of molecular geometry in both singlet and triplet states for each species. In two cases where almost pure singlet energies have been found, the calculated S-T energy gaps are very large, indicating that the singledeterminant singlet state lies much higher in energy. As the outcome of a calculated move, the singlet optimization led to the optimization of the broken-symmetry structure for ten species including the unsubstituted one. This hoped for development made it possible to carry out further broken symmetry calculations in two ways. The 6311++G(d,p) basis set has been used for a single run on the optimized triplet geometry, and the broken symmetry calculations using the optimized geometries of both triplet and broken symmetry states. We find that a direct optimization of the broken symmetry geometry always leads to a better estimate of the magnetic exchange coupling constant (J ). The calculated J for the unsubstituted Schlenk diradical is 511 cm–1 that is of the order of the value 455 cm–1 estimated by Rajca. In general, the coupling constants are large and positive, in the range of 411-525 cm–1. Introduction of ortho-para directing groups decreases the J compared to that of the unsubstituted Schlenk diradical, while the meta directing groups at the same position increases the J value.


CHAPTER 7.

116

7.1 Introduction There has been a large number of theoretical and experimental investigations on high-spin organic diradicals based on the m-phenylene moiety.1-16 The latter group has been extensively used as an effective ferromagnetic coupler. When connected between radical sites such as carbon-centered1,8,17 and nitrogen-centered18 spin carriers, carbenes19 and nitrenes,20 the resulting diradical almost invariably has a triplet ground state. In some of the m-phenylene based diradicals, E(S)–E(T) is much greater than thermal energy (RT) at an ambient temperature.21,22 There are only a few reports of a singlet ground state.23, 24 Meta-phenylene is generally very unsTable 7.owing to a facile dimerization and reaction with oxygen.25 Nevertheless, many substituted derivatives of m-phenylene have been successfully synthesized.7-12 One of the most famous example is the sterically crowded Schlenk diradical (Figure 7.1). It was first synthesized in 1915.7 Various substituted Schlenk diradicals have been studied by Rajca et al.9 The latter authors synthesized different alkyl and halogen substituted Schlenk diradicals and showed that most of them have triplet ground states. Zhang et al.25 have studied the substitution at the 4th and 6th positions in m-phenylene that is attached to two (substituted) methylene radical centers at positions 1 and 3, and calculated the magnetic exchange coupling constants (J) by UB3LYP method using 6-31G(D) basis set. To the best of our knowledge, the magnetic nature of the substituted Schlenk diradicals has remained largely unexplored. Molecules

R 5 6

4

1

3 2

1 2 3 4 5 6 7 8 9 10 11 12

Substituent (R) −H −NMe2 −OH −OMe −Me −F −Br −CN −CHO −CF3 −COOH −NO2

Figure 7.1: Molecules under investigations (5-substituted Schlenk diradicals).


CHAPTER 7.

117

In this work, we have considered eleven different substitutions at the 5th position of m-phenylene group in Schlenk diradical (Figure 7.1). Substitution has been done with ortho-para directing groups, meta directing groups and groups with −I effect. To obtain good values of J, we devise a strategy for optimizing the geometry of the broken symmetry state. It is shown that the exchange coupling constants are generally large and positive, in the range of 411 to 530 cm–1. It is also demonstrated that electron pushing groups at the 5th position lowers the J value compared to that of the parent unsubstituted Schlenk diradical whereas introduction of electron withdrawing groups at the same position enhances the J value.

7.2 Methodology The interaction between two magnetic sites is expressed by the well known Heisenberg effective spin Hamiltonian. Hˆ  2 JSˆ1  Sˆ2 ,

(71)

J being the magnetic exchange coupling constant. A determination of the magnetic nature of the ground state of the coupled system and the strength of the magnetic nature requires the knowledge of J. In particular we note

E (S  1)  E (S  0)  2 J .

(7.2)

Therefore, one needs to compare the singlet and triplet ground state energies for a diradical, but the task is far from simple. Borden, Davidson, and Feller26 demonstrated that restricted quantum chemical methods can easily give qualitatively correct wave functions but fail to give a correct molecular geometry unless the basis set is very large, whereas the unrestricted methods easily yield reasonably correct energy and optimized molecular geometry. Therefore, it becomes very difficult to determine a reliable S−T energy difference for a diradical. The latter quantity varies with different correlation methodologies and with basis sets. This has been well-documented by the early investigations of Nachtigall and Jordan27, Cramer and Smith28, and Mitani et al.29 To avoid this difficulty we relied on the well known broken symmetry (BS) approach proposed by Noodleman. 30 In this approach, a BS solution with <S2> = 1 is sought. The BS wave function is an approximately equal


CHAPTER 7.

118

mixture of the singlet and triplet wave functions. Noodleman established the following expression for the magnetic exchange coupling constant, (E J

E) T 2 1 S ab BS

(7.3)

where EBS is the total energy corresponding to the BS wave function and Sab is the overlap integral between the two magnetically active orbitals a and b. The quantity EŤ stands for the energy of the triplet formed from the BS orbitals. Because of the very less spin contamination in the triplet, EŤ can be approximated to ET, the computed energy for the triplet wave function. The BS method has several advantages. Built in the framework of density functional theory (DFT), it can account for exchange and correlation energies with relative ease and requires very less computing time. It avoids the computational difficulties associated with a two-determinant (singlet) state, as the BS wave function is a single determinant. While calculating the singlet ground state for a diradical, it is quite possible that the calculation would lead to a BS solution when the two-determinant singlet is higher lying but the single-determinant singlet is still higher in energy, as we shall shortly see. A number of Broken Symmetry formulas for J are available. We have found that the most useful is the one put forward by Yamaguchi et al.31 JY 

( DFT EBS  DFT ET ) .  S 2 T  S 2  BS

(7.4)

As usual, we have relied on unrestricted Becke 3-parameter exchange Lee, Yang, and Parr correlation hybrid density functional methodology (UB3LYP) for both geometry optimization and single point calculation. The BS calculation requires a good initial guess for <S2>. Therefore, we used ROHF wave function of the molecules as the initial guess, and carried out a single-point calculation on the BS state using a larger basis set and the optimized geometry of the triplet or even of the BS state. All calculations have been performed using Gaussian 03 (G03) software.32


CHAPTER 7.

119

Table 7.1. Computed total energies of single-determinant singlet and triplet wavefunctions. The molecular geometry has been optimized in every case by UB3LYP method using 6-311G (d, p) basis set. We have used 1 a.u. = 219474.6 cm–1.a ES− ET Substituents ET in a.u. ES in a.u. 2 2 (<S >) (<S >) (cm–1)b −F −1333.371226 −1333.345895 5559.5 (2.057578) (0.000002) −Br −3807.649115 −3807.623572 5606.0 (2.057543) (0.000010) a

Singlet state not found for the rest of the diradicals. Computed  and  orbital energy values are same in Singlet. Thus the Singlet calculation has reduced to a restricted calculation. b

Table 7.2. Computed total energies of single-determinant BS and triplet wave functions. The molecular geometry has been optimized in every case by UB3LYP method using 6311G(d,p) basis set. We have used 1 a.u. = 219474.6 cm–1.a Substituents

−H

−NMe2 −OH −OMeb −Me

ET in a.u. (<S2>)

EBS in a.u. (<S2>)

−1234.106693 −1234.104318 (2.056844) (1.040921) Otho-para position directing groups −1368.107139 −1368.105147 (2.05695) (1.041119) −1309.349887 −1309.347627 (2.057834) (1.038729) −1348.659734 − (2.057605) − −1273.4340586 −1273.431735 (2.058712) (1.040002)

EBS− ET (cm–1)

JY (cm–1)

521.3

513.1c

437.2

430.4

496.0

486.7

510.0

500.6

534.1

522.8

519.5

509.4

533.1

520.9

536.8

525.8

540.8

530.1

Meta position directing groups −CHO −COOH −CN −CF3 −NO2 a

−1347.460732 (2.061173) −1422.736836 (2.059816) −1326.371283 (2.060417) −1571.246014 (2.059169) −1438.662629 (2.059900)

−1347.458294 (1.039541) −1422.734458 (1.040044) −1326.368854 (1.036954) −1571.243568 (1.038296) −1438.660165 (1.039788)

Singlet molecular geometry optimization has reduced to a BS solution. Convergence failure for BS calculation. c Estimated J = 455 cm–1, ref. 33. b


CHAPTER 7.

120

H 0.120 -0.007

-0.113

-0.008

-0.015 -0.162

0.247

0.247

0.120 0.637

-0.064

-0.008

-0.008

0.124 -0.007

-0.065

-0.140

0.126 0.645

-0.107 0.117

-0.065

-0.063

-0.111

-0.063

-0.111 -0.160

-0.065

0.244

0.230

0.118 0.638

0.120 -0.111

-0.161

-0.066

0.130

-0.065

-0.065

0.122 0.647

0.127

0.125

-0.063

-0.066 0.130

0.125 CH3

-0.065 0.119

0.239

-0.109 -0.158

-0.064

0.122 0.643

-0.063

-0.067

0.130

0.128

0.125

-0.065

-0.063

-0.110

0.128 -0.067

0.244

0.263

0.125

0.124

-0.113 0.123

-0.063

-0.062

-0.065

0.127

0.131

0.131

-0.067

-0.063

F

-0.112 -0.161

-0.109

-0.063

-0.117

-0.064

-0.103 0.118

0.126 0.637

0.641 0.121

-0.113

0.128

0.120

-0.160

0.253

0.124

-0.064

-0.065

0.125

0.130

-0.003

-0.135 0.240

0.115

0.639 0.116

0.248

0.126

0.129

-0.061

0.153 -0.109

-0.115 0.127

0.127

-0.063

-0.066

0.130

0.128

-0.063

-0.112 0.222

0.121 0.251 -0.111 -0.160

-0.114

-0.066

-0.063

-0.067 0.128

0.642 0.121

0.254 -0.110 0.126

0.127

0.124

0.122

-0.006OMe

-0.102 0.115

-0.070

0.130

-0.008 OH -0.062

-0.119

0.136

0.634 0.131

0.225

0.131

0.125

0.130

-0.148

0.127

0.125

0.130

0.129

0.227

0.220

-0.110

-0.068 -0.111

-0.066

-0.115 0.138

0.132

0.637 0.120

0.253

-0.063

-0.007

-0.113

-0.162

-0.111 0.125

0.124

-0.007 NMe2

0.120

-0.126

0.243

0.117

-0.161 -0.112 0.637

0.125

-0.063

0.118

-0.113

0.122 -0.064

0.123 -0.065

0.126

Br 0.000 -0.064 0.119

0.026

-0.118 0.248 0.248

-0.112 -0.163

-0.063

0.118 0.638

0.261

0.122

-0.112 0.125

-0.062

-0.065

0.127

-0.163

-0.064 0.119 -0.112

0.126 -0.063

0.638 0.118 -0.122

0.125

-0.065

0.122 -0.062

0.127

Figure 7.2. Mulliken atomic spin density distribution in the triplet state of diradicals from calculations using 6-311++G(d,p) basis set: ortho-para position directing groups.


CHAPTER 7.

121

0.018

CHO

-0.067

0.120

0.128

0.262

0.643

0.120

-0.064

-0.133 0.231

-0.162

-0.109

-0.065

0.009

0.118 -0.110

-0.156

0.639

0.264 -0.114

-0.067 0.126

0.129

-0.063

-0.066

0.126

-0.061

-0.065

0.126

-0.066

0.127

-0.160

0.644

0.122

0.256

0.126

-0.115 0.126

0.126

-0.062

-0.065

0.125 -0.063

-0.111 -0.158

0.118 0.637

0.125

-0.062

-0.066

0.126

-0.063

-0.064

-0.066

-0.062

CF3

0.246 -0.151

-0.109 0.120 0.638

-0.110

0.125

0.126

0.126

-0.066

-0.144

0.119

0.637 0.118

-0.111 0.122

0.126

-0.111

-0.158

0.234

0.127

0.118

0.251

-0.113

-0.065

-0.066

-0.065

-0.065 0.120

0.128

0.000

-0.140 0.251

-0.108

0.645

0.127

-0.032 CN

0.118

0.247

0.126

-0.062

-0.062

-0.065

0.128

-0.109

0.640

0.127

-0.065

0.120

-0.110

-0.109 0.121

0.119

-0.152

0.259

0.122

0.127

0.127

0.120

-0.152

0.124

0.128

-0.065

0.241

0.247

-0.109

0.120

-0.065

-0.140

0.121

-0.110

0.125

COOH

0.125

-0.065

0.124 0.125

0.127

0.008 NO2

-0.062

0.128

0.256

-0.119 - 0.173

-0.062

0.119 0.646

0.115

-0.059

-0.115 0.256

0.121

-0.173

-0.60

-0.059

0.122

-0.116

0.122 -0.059

0.646 0.114

0.270 -0.116 0.115

0.114

-0.118 0.119

-0.062

0.121 0.062

0.128

Figure 7.3. Mulliken atomic spin density distribution in the triplet state of diradicals from calculations using 6-311++G(d,p) basis set: meta position directing groups.


CHAPTER 7.

122

7.3 Results and discussion The molecular geometries of all the twelve molecules in both singlet and triplet states were optimized by UB3LYP method using 6-311g(d,p) basis set. A curious thing indeed turned out during the singlet optimization. Singlet optimized geometries were obtained only for two species, those with substituents fluorine and bromine. For the rest of the diradicals, the optimization process led to broken symmetry solutions with <S2> nearly equal to 1. These results are given in Table 7.1 and Table 7.2 respectively. Nevertheless, it is possible that other authors might have noticed a similar happening, but to our knowledge no one has put forward a reason for it or a discussion on this topic. The reason is very simple: this can happen when the BS solution is the lowestenergy single determinant with multiplicity 1. The large singlet-triplet energy difference in Table 7.1 is understandable as the singlet is a single determinant wave function with much higher energy. Table 7.2, however, gives us results for broken symmetry solution with optimized geometry, which is rarely achieved. Thus the magnetic exchange coupling constant (J) calculated here should be close to the experimental values. Indeed, we obtain JY = 513 cm−1 for the unsubstituted Schlenk diradical. This is very close to the value of 455 cm−1 estimated by Rajca et al.33 The intramolecular magnetic coupling in these diradicals is always ferromagnetic, and this is compatible with the spin alternation rule.34 There are two possible paths of spin wave propagation here: either through carbon-2 (shorter route) or through carbon-5 (longer route). Both the paths significantly contribute as can be seen from the spin density distribution in Figures 2 and 3. Table 7.2 also reveals that the strongly activating ortho-para directing groups lower the J value. This is a consequence of increasing electron density in 2,4,6 positions. As a result, the net spin population decreases on each atom of the central ring (spacer). See Figure 7.2. This effect gives rise to a less strong coupling between the monoradical centers. The opposite trend is observed for the meta directing groups (Figure 7.3). Table 7.3 shows the single-point triplet and broken symmetry energy values obtained from the optimized triplet geometries, and the calculated J for each molecule. The BS calculation here is based on the optimized triplet geometry. Molecule 1 is the parent unsubstituted Schlenk diradical, and as per the present calculation, it has the J value of 601.8 cm−1. In fact, all the calculated J values are about 100 cm−1 larger, showing


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Table 7.3. Broken symmetry energies and coupling constants of substituted Schlenk diradicals from single point UB3LYP calculations using optimized geometry of the triplet and the 6-311++G(d,p) basis set. We have used 1 a.u. = 219474.6 cm–1. Substituents

ET in a.u. (<S2>)

EBS in a.u. (<S2>)

EBS− ET (cm–1)

JY (cm–1)

614.5

601.8a

527.1

516.8

594.0

581.1

590.2

577.8

−1273.445780 −1273.443062 596.9 (2.057970) (1.036938) Weakly deactivatimg −F −1333.387424 −1333.384548 631.2 (2.057731) (1.033745) −Br −3807.661126 −3807.658255 629.9 (2.058682) (1.034404) Meta position directing groups Moderately Deactivating −CHO −1347.475978 −1347.473090 632.1 (2.060460) (1.035665) −COOH −1422.754634 −1422.751806 621.1 (2.059500) (1.036310) Strongly deactivating −CN −1326.384962 −1326.382076 633.4 (2.060211) (1.033833) −CF3 −1571.268384 −1571.265513 630.2 (2.058680) (1.034390) a Estimated J = 455 cm–1, ref. 33. b BS calculation on NO2-substituted diradical was not successful.

584.7

−H

−NMe2 −OH −OMe

−Me

−1234.118434 −1234.115634 (2.057800) (1.036781) Otho-para position directing groupssb Strongly Activating −1368.120476 −1368.118074 (2.056412) (1.037170) −1309.365808 −1309.363101 (2.057332) (1.035098) −1348.674376 −1348.671687 (2.057183) (1.035803) Weakly Activating

616.4 615.0

616.8 607.0

617.1 615.2


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Table 7.4. Broken symmetry energy from optimized BS geometry, triplet energy from optimized triplet geometry, and estimated coupling constant of substituted Schlenk diradicals from single point UB3LYP calculations using 6-311++G(d,p) basis set. We have used 1 a.u. = 219474.6 cm–1. Substituents

−H

−NMe2 −OH

−Me

ET in a.u. (<S2>)

EBS in a.u. (<S2>)

EBS− ET (cm–1)

−1234.118434 −1234.116061 520.8 (2.057800) Otho-para position directing groupssb Strongly Activating −1368.120476 −1368.118505 532.6 (2.056412) (1.040211) −1309.365808 −1309.3635202 502.1 (2.057332) (1.038063) Weakly Activating

JY (cm–1) 511.8a

411.0 492.6

−1273.445780 −1273.443381 526.5 517.3 (2.057970) (1.040064) Meta position directing groups Moderately Deactivating −CHO −1347.475978 −1347.473562 530.3 519.4 (2.060460) (1.038885) −COOH −1422.754634 −1422.752274 578.0 507.8 (2.059500) (1.039542) Strongly deactivating −CN −1326.384962 −1326.382528 534.2 522.0 (2.060211) (1.036809) −CF3 −1571.268384 −1571.265940 536.4 525.3 (2.058680) (1.037556) a –1 Estimated J = 455 cm , ref. 33. b BS calculations on NO2-, F- and Br- substituted diradicals were not successful.


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the hidden drawback of the traditional BS calculation based on the optimized triplet geometries. This is rectified in Table 7.4 where the BS results are obtained from calculations involving the BS optimized geometries. This has caused improvements over the J values given in Table 7.2. The BS calculations with substitution of weakly activating groups (F and Br) did not succeed. These kept up producing local maxima for the BS energy, indicating that somehow the higher-lying single-determinant singlet function had been getting mixed with the BS wave function. The dihedral angles between m-phenylene and substituted phenyl groups have almost identical values (varying from 32.8˚ to 34.1˚) in all the twelve molecules. This structural feature has limited the width of variation of the coupling constant.

7.4 Conclusion Density functional UB3LYP calculations with BS approach have been done on various substituted Schlenk diradicals to investigate the variations of J value with substitution at 5th position. It has been demonstrated here that a singlet geometry optimization can lead to the optimized geometry of broken symmetry structure when the two-determinant singlet lies higher in energy than the triplet and the single-determinant singlet is still higher in energy. Detailed analysis shows that electron-pushing substituents decrease the J value and electron-withdrawing substituents increase the J value. An important observation is that optimization of the molecular geometry in the BS state gives excellent J values, whereas the traditional way of carrying out BS calculation on optimized triplet geometry has led to coupling constants that are larger by about 100 cm−1.


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References: 1. Wenthold, P. G.; Kim, J. B.; Lineberger, W. C. J. Am. Chem. Soc. 1997, 119, 1354. 2. Silverman, S. K.; Dougherty, D. A. J. Phys. Chem. 1993, 97, 13273. 3. Kato, S.; Morokuma, K.; Feller, D.; Davidson, E. R.; Borden, W. T. J. Am. Chem. Soc. 1983, 105, 1791. 4. Fort, R. C., Jr.; Getty, S. J.; Hrovat, D. A.; Lahti, P. M.; Borden, W. T. J. Am. Chem. Soc. 1992, 114, 7549. 5. Hrovat, D. A.; Murcko, M. A.; Lahti, P. M.; Borden, W. T. J. Chem. Soc., Perkin Trans. 2 1998, 1037. 6. Iwase, K.; Inagaki, S. Bull. Chem. Soc. Jpn, 1996, 69, 2781. 7. Schlenk, W.; Brauns, M. Ber. Dtsch. Chem. Ges. 1915, 48, 661. 8. Kothe, G.; Denkel, K. H.; Summermann, W. Angew. Chem. Int. Ed. Engl. 1970, 9, 906. 9. (a) Rajca, A.; Utamapanya, S.; Xu, J. J. Am. Chem. Soc. 1991, 113, 9235–9241. (b) Utamapanya, S.; Rajca, A. J. Am. Chem. Soc. 1991, 113, 9242-9251. (c) Rajca, A.; Utamapanya, S. J. Org. Chem. 1992, 57, 1760–1767. (d) Rajca, A.; Utamapanya, S. J. Am. Chem. Soc. 1993, 115, 2396. 11. Veciana, J.; Rovira, C.; Crespo, M. I.; Armet, O.; Domingo, V. M.; Palacio, F. J. Am. Chem. Soc. 1991, 113, 2552. 12. Gajewski, J. J.; Gitendra, C. P. Tetrahedron Lett. 1998, 39, 351. 13. Mitani, M.; Mori, H.; Takano, Y.; Yamaki, D.; Yoshioka, Y.; Yamaguchi, K. J. Chem. Phys. 2000, 113, 4035. 14. Mitani, M.; Yamaki, D.; Takano, Y.; Kitagawa, Y.; Yoshioka, Y.; Yamaguchi, K. J. Chem. Phys. 2000, 113, 10486. 15. Mitani,M.; Takano, Y.; Yoshioka, Y.; Yamaguchi, K. J. Chem. Phys. 1999, 111, 1309. 16. Mitani, M.; Yamaki, D.; Yoshioka, Y.; Yamaguchi, K. J. Chem. Phys. 1999, 111, 2283. 17. Migirdicyan, E.; Bauder, J. J. Am. Chem. Soc. 1975, 97, 7400. 18. Wasserman, E.; Murray, R. W.; Yager, W. A.; Trozzolo, A. M.; Smolinsky, G. J. J. Am. Chem. Soc. 1967, 89, 5076. 19. Itoh, K. Chem. Phys. Lett. 1967, 1, 235.


CHAPTER 7.

127

20. Haider, K.; Soundararajan, N.; Shaffer, M.; Platz, M. S. Tetrahedron Lett. 1989, 30, 1225. (b) Fukuzawa, T. A.; Sato, K.; Ichimura, A. S.; Kinoshita, T.; Takui, T.; Itoh, K.; Lahti, P. M. Mol. Cryst. Liq. Cryst. 1996, 278, 253. 21. Amiri , S.; Schreiner, P. R. J. Phys. Chem. A 2009, 113, 11750. 22. Rajca , A.; Shiraishi , K.; Pink, M.; Rajca, S. J. Am. Chem. Soc. 2007, 129, 7232. 23. (a) Dvolaitzky, M.; Chiarelli, R.; Rassat, A. Angew. Chem., Int. Ed. Engl. 1992, 31, 180. (b) Kanno, F.; Inoue, K.; Koga, N.; Iwamura, H. J. Am. Chem. Soc. 1993, 115, 847. (c) Fujita, J.; Tanaka, M.; Suemune, H.; Koga, N.; Matsuda, K.; Iwamura, H. J. Am. Chem. Soc. 1996, 118, 9347. 24. (a) Okada, K.; Imakura, T.; Oda, M.; Murai, H. J. Am. Chem. Soc.1996, 118, 3047. (b) Okada, K.; Imakura, T.; Oda, M.; Kajiwara, A.; Kamachi, M.; Yamaguchi, M. J. Am. Chem. Soc. 1997, 119, 5740. 25. (a) Zhang, G.; Li, S.; Jiang, Y. J. Phys. Chem. A 2003, 107, 5573-5582. (b) Zhang, G.; Li, S.; Jiang, Y. Tetrahedron 2003, 59, 3499. 26. (a) Borden, W. T.; Davidson, E. R. J. Am. Chem. Soc. 1977, 99, 4587. (b) Borden, W. T.; Davidson, E. R.; Feller, D. Tetrahedron 1982, 38, 737. (c) Feller, D.; Davidson, E. R.; Borden, W. T. Isr. J. Chem. 1983, 23, 105. (d) Kato, S.; Morokuma, K.; Feller, D.; Davidson, E. R.; Borden, W. T. J. Am. Chem. Soc. 1983, 105, 1791. 27. (a) Nachtigall, P.; Jordan, K. D. J. Am. Chem. Soc. 1992, 114, 4743. (b) Nachtigall, P.; Jordan, K. D. J. Am. Chem. Soc. 1993, 115, 270. 28. Cramer, C. J.; Smith, B. A. J. Phys. Chem. 1996, 100, 9664.29. (a) Mitani, M.; Mori, H.; Takano, Y.; Yamaki, D.; Yoshioka, Y.; Yamaguchi, K. J. Chem. Phys. 2000, 113, 4035. (b) Mitani, M.; Yamaki, D.; Takano, Y.; Kitagawa, Y.; Yoshioka, Y.; Yamaguchi, K. J. Chem. Phys. 2000, 113, 10486. 30. (a) Noodleman, L. J. Chem. Phys. 1981, 74, 5737. (b) Noodleman, L.; Baerends, E. J. J. Am. Chem. Soc. 1984, 106, 2316. (c) Noodleman, L.; Davidson, E. R. Chem. Phys. 1986, 109, 131. (d) Noodleman, L.; Peng, C. Y.; Case, D. A.; Mouesca, J.-M. Coord. Chem. Rev. 1995, 144, 199. 31. (a) Yamaguchi, K.; Takahara, Y.; Fueno, T.; Nasu, K. Jpn. J. Appl. Phys. 1987, 26, L1362. (b) Yamaguchi, K.; Jensen, F.; Dorigo, A.; Houk, K. N. Chem. Phys. Lett. 1988, 149, 537. (c) Yamaguchi, K.; Takahara, Y.; Fueno, T.; Houk, K. N. Theo. Chim. Acta 1988, 73, 337.


CHAPTER 7.

128

32. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision C.02; Gaussian, Inc.: Pittsburgh, PA, 2004. 33. Rajca, A. Chem. Rev. 1994, 94, 871. 34. (a) Trindle, C.; Datta, S. N. Int. J. Quantum Chem. 1996, 57, 781. (b) Trindle, C.; Datta, S. N.; Mallik, B. J. Am. Chem. Soc. 1997, 119, 12947.


Chapter 8 The electronic structure of nitronyl nitroxide radical: Effect of basis size on diradical calculation In this work we show that a density functional (DF) calculation using the 6-31G* basis set that is quite popular in literature gives an unreliable estimate of the intra-molecular magnetic exchange coupling constant J for a diradical consisting of nitronyl nitroxide (NN) monoradicals and a spacer. First, we have carried out quantum chemical calculations on NN following different Hartree-Fock (HF), correlation and DF methodologies with 6-31G* and larger basis sets. Atomic charge and spin densities have been obtained from self-consistent-field calculations (HF and DF). Among the correlation methodologies (CI, CC, CASSCF and CASPT2), only the CASSCF calculations yield charge and spin densities. CASSCF(13,13) calculations with correlation-consistent basis set provides a reasonably good platform for comparing the charge and spin densities that are obtained from other types of calculations. Different basis sets give rise to smoothly changing spin densities from DF treatments, but a reasonably correct description evolves only when a large basis set is used. A pronounced spin density alternation for all the bases indicates NN to be a strong monoradical. The variation of atomic spin densities in NN with basis size is rather slow, and incapable of explaining any large variation of J in a diradical containing NN. The Mulliken atomic charges show a lack of regularity, and are less informative. Next, because the spin effect is accommodated in Dirac theory in a natural way, we have also performed relativistic calculations on NN. As the molecule has no heavy atom, relativistic correction to the total energy is quite small and almost atom-wise additive. The calculated spin densities more or less reflect those from the nonrelativistic calculations using restricted methodologies. Finally, from the analysis of two diradicals, NN-C2H2-NN and NN-pm-NN, we find that the basis size strongly affects the spacer-mediated coupling between the two monoradicals. Larger basis sets almost fully reproduce the isolated monoradical spin densities on the radical centers of the diradical, while a basis set like 6-31G* gives extremely reduced spin densities on the monoradical fragments. The interaction energy becomes progressively more accurate with an increasingly large basis, and the coupling constant J approaches the experimental value. This is why the 6-31G* basis set gives highly inflated J values and is not reliable.


CHAPTER 8.

130

8.1 Introduction Quantum chemical calculations that have been carried out on a large number of atoms, molecules, radicals and clusters during the last few decades have become powerful tools for supporting experimental observations and sometimes even predicting the outcome of an experiment. Quantum chemical results provide important information about the internal structure, energy and property of a system of molecular dimension, and generate an in-depth picture of electron dynamics inside a molecule. Nitronyl nitroxide, C7H13N2O2 (NN), is an organic radical, a part of p-nitrophenyl nitronyl nitroxide (p-NPNN) radical that is known to be a molecular magnet in the crystal form.1 The NN radical contains a five-member ring that consists of two nitrogen and three carbon atoms with an unpaired electron remaining on the oxygen and nitrogen atoms. See Figure 8.1. Though the radical has not yet been synthesized, several of its 6O

6O 4N H

4N 2 H

1 5N 7O

2

1

3

5N

3

7O

Figure 8.1. The nitronyl nitroxide monoradical. derivatives are known to be stable. We have carried out extensive quantum chemical calculations on NN-containing diradicals to study their magnetic properties, mostly by unrestricted density functional methods.2 The basic mono-radical NN is truly important in organic magnetism. In organic systems, magnetism originates from electron spin, unlike in transition metal complexes where both orbital angular momentum and spin contribute. In many or most cases the orbital angular momentum of metal atoms in complexes is quenched. Of late, the 6-31G* basis set has become very popular in the investigation of magnetism in organic molecules by density functional (DF) treatment. Our present work stems from a desire to inspect whether this basis set gives rise to an acceptable spin distribution in the versatile monoradical NN. It is well known that for a diradical, the spin


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131

density distribution is a major influence on the magnitude of the magnetic exchange coupling constant (J). In this work, we have carried out quantum chemical calculations on NN following different Hartree-Fock, correlation and DF methodologies with 6-31G* and larger basis sets. A major conclusion is that the DF calculations lead to somewhat improper spin density distributions in NN as compared to the CASSCF/CASPT2 calculations. A smooth trend is observed while varying the basis size, and a reasonably correct description of spin density evolves only when a large basis set is used and the molecular geometry is optimized. As spin effect is accommodated in Dirac theory in a natural way while a nonrelativistic treatment incorporates it in an ad hoc manner, we have also performed relativistic calculations on NN. Since the molecule has no heavy atom, relativistic effects are quite small and the calculated spin densities more or less reflect those from the nonrelativistic restricted calculations. Finally, we have investigated two diradicals, NN-C2H2-NN and NN-pm-NN. The first one is known to have large antiferromagnetic coupling. The second one is ferromagnetically coupled with a small J value. We show that the 6-31G* basis yields inflated J values. A large basis leads to a more realistic J, which cannot be accounted for by the rather small change of atomic spin densities in the isolated monoradical. The real explanation is that a large basis generates a more accurate spin density distribution in the radical centers of the diradical, and a more accurate energy for the spacer-mediated interaction between the monoradicals.

8.2 Computational Details 8.2.1 Codes Quantum chemical calculations following restricted open-shell Hartree-Fock (ROHF), unrestricted Hartree-Fock (UHF), density functional (DF), unrestricted configuration interaction with single and double excitations (UCISD), unrestricted fourthorder Møller-Plesset perturbation (UMP4), complete active space self-consistent field (CASSCF) and unrestricted coupled cluster UCCSD, UCCSD(T) methodologies have been done using Gaussian09 (G09) code.3 The DF methodology is based on the Becke 3-


CHAPTER 8.

132

parameter exchange and Lee, Yang and Parr correlation hybrid functional model – both restricted and unrestricted versions (ROB3LYP and UB3LYP). While B3LYP is a natural choice in this work, there are many alternatives, especially including those with longrange and dispersion corrections like generalized gradient approximation (GGA) type, double-hybrid density functionals, etc. We have used MOLCAS version 7.6 code4 to carry out calculations by ROHF and its relativistic version, namely, two-component Dirac-Hartree-Fock (DHF/DKH2), CASSCF and its relativistic counterpart (CASSCF/DKH2) approaches. The twocomponent calculations have been based on the second-order Douglas, Kroll and Hess (DKH2) transformation.5-6 The short-range electron-electron interaction effect, that is, the dynamic correlation has been studied in both nonrelativistic and relativistic sets of calculation by using complete active space second-order perturbation theory (CASPT2) program module. Both G09 and MOLCAS 7.6 softwares have been used for calculations involving contracted basis sets. The DIRAC10 code7 has been employed for Lévy-Leblond and two-component DHF calculations using uncontracted bases. The DHF calculations here have involved infinite-order scalar and spin-orbit terms from Barysz, Sadlej and Snijders (BSS) transformation,8-10 and mean-field spin-same-orbit treatment (MFSSO) with atomic mean-field integrals (AMFI).11 The Lévy-Leblond method12 is the nonrelativistic mode (c → ∞ limit where c is the speed of light) in DHF calculation.

8.2.2 Basis set The basis sets employed are as follows. In most cases we have adopted 6-31G* basis in order to have a proper comparison. Correlation energy and relativistic corrections have also been determined from ROHF, DHF/DKH2, CASSCF, CASSCF/DKH2, CASPT2 and CASPT2/DKH2 calculations involving Dunning’s13 correlation-consistent basis set cc-pvDZ using the MOLCAS 7.6 software. The 6-311+G(d) basis has been used in the UB3LYP, UMP4, UCCSD and UCCSD(T) methods. The UB3LYP calculations have also been carried out using 6-31G*, 6-311++G(d, p) and 6-311++G(3df, 3pd) basis sets. See Table 8.1 and Table 8.2. In all the post-Hartree-Fock calculations, 11 core


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133

orbitals have been by default taken as frozen, (36 orbitals remaining inactive in CASSCF).

8.2.3 Geometry optimization Molecular geometry has been optimized at ROHF and UHF levels using 6-31G* basis set. These optimized geometries have been adopted for single point calculations by other restricted and unrestricted methodologies, respectively, except in the UB3LYP calculations. G09 allows CISD, MP4 and CCSD(T) calculation only in the unrestricted mode, and hence the correlation corrections correspond to the UHF/6-311+G(d) optimized geometry. Molecular geometry has again been optimized in UB3LYP calculations using 6-31G*, 6-311+G(d) and 6-311++G(d,p) bases. The single-point UB3LYP/6-311++G(3df, 3pd) calculation has used the optimized geometry for 6311++G(d,p) basis. See Table 8.1. All calculations using DIRAC10 and MOLCAS 7.6 have been based on C2 point group symmetry. The ROHF/6-31G* optimized geometry is shown in Figure 8.2.

Figure 8.2. The optimized geometry of nitronyl nitroxide from ROHF calculation using 6-31G* basis set.


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134

Table 8.1. Computed nonrelativistic and relativistic ground state energy of nitronyl nitroxide radical by different methods

a

Geometryb Basis type

Method

Basis set

ROHF

6-31G*

Opt1

contracted

UHF

6-31G*

Opt2

contracted

UHF

6-311+G(d)

Opt3

contracted

Lévy-Leblondb

6-31G*

Sp1

uncontracted

Two-component DFc

6-31G*

Sp1

uncontracted

CASSCF (13, 13)

6-31G*

Sp1

contracted

R(O)B3LYP

6-31G*

Sp1

contracted

UB3LYP

6-31G*

Opt4

contracted

UB3LYP

6-311+G(d)

Opt5

contracted

UB3LYP

6-311++G(d, p)

Opt6

contracted

UB3LYP

6-311++G(3df, 3pd)

Sp6

contracted

UCISD

6-31G*

Sp2

contracted

Energy (a.u.) (<S2>) −531.083654 (0.7500) −531.123143 (1.1696) −531.246376 (1.1634) −531.101755 (0.7500) −531.363528 (0.7500) −531.268264 (0.7500) −534.385441 (0.7500) −534.394883 (0.7984) −534.534444 (0.7963) −534.552257 (0.7964) −534.589274 (0.7964) −531.252172

UCISD

6-311+G(d)

Sp3

contracted

−532.522563

UMP4

6-311+G(d)

Sp3

contracted

−533.087802

UCCSD

6-311+G(d)

Sp3

contracted

−533.017681

UCCSD(T)

6-311+G(d)

Sp3

contracted

−533.091488

Optimization calculation (Optn), single point calculation on nth optimization (Spn). b Nonrelativistic mode in Dirac-Fock calculation. c Infinite order scalar and spin-orbit terms using BSS transformation, mean-field spinsame-orbit. (MFSSO) treatment and atomic mean-field integral (AMFI) code.


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135

8.2.4 Nonrelativistic and relativistic treatments In the nonrelativistic case, we have taken 191 basis functions (360 primitives) for ROHF treatment using contracted 6-31G* basis set, whereas the uncontracted set has been used to carry out Lévy-Leblond calculation that results in an additional stability of about 0.2 hartree. The Lévy-Leblond results have been compared with the corresponding DHF results from DIRAC10 in the next section. In order to study the spin density distribution in the radical, a static correlation treatment CASSCF(13,13) has been carried out using the contracted 6-31G* basis set as well as Dunning’s correlation-consistent basis cc-pvDZ. The latter basis set has been chosen especially for the correlation treatment by CASSCF and CASPT2 approaches using MOLCAS 7.6. The steps followed are ROHF, then CASPT2 to determine the active space, then CASSCF and the final CASPT2. The 13 active orbitals mostly involve valence p-orbitals of carbon, nitrogen and oxygen atoms. The orbitals have been optimized using super-CI method.14 These are occupied by 13 electrons. The number of determinants involved has been 1472528 from which 644231 configuration state functions have been generated. The CASSCF wave function has been calculated for the 2A ground state. In the dynamic correlation treatment, the same active space has been adopted. Eleven orbitals have been kept frozen, 25 have been kept inactive and 77 have been used in the secondary subspace. Similarly, relativistic calculations have been performed with 382 two-component spinors corresponding to 191 orbitals. The square-root parametrization6 has been followed in the two-component calculation.

8.3 Results and Discussion The ground state energy values and <S 2> calculated using G09 and DIRAC10 softwares are given in Table 8.1. Energy values calculated by MOLCAS 7.6 using the correlation-consistent cc-pvDZ basis set are listed in Table 8.2.

8.3.1 Relativistic correction The Breit interaction has been included in relativistic calculations. The difference in energy between relativistic (DHF) and nonrelativistic (Lévy-Leblond) calculations is about −0.2618 hartree (Table 8.1). This can be compared with the sum of the individual


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136

Table 8.2. Nonrelativistic and relativistica energy of the ground state of nitronyl nitroxide radical using contracted cc-pvDZ basis set. All calculations have been done with ROHF (opt1) molecular geometry. All energy values are in atomic units.

Method

a

Active Space/Electrons

Energy

Relativistic corrections

Static correlation energy

Dynamic correlation energy (CASPT2 − CASSCF) -

ROHF

1/1

−531.125533

-

(CASSCF − HF) -

CASSCF

13/13

−531.317470

-

−0.191937

-

CASPT2 DHF/DKH2 CASSCF/DKH2 CASPT2/DKH2

13/13 1/1 13/13 13/13

−532.203534 −531.373754 −531.565883 −532.451953

−0.248254 −0.248415 −0.248419

−0.192129 -

−0.886064 −0.886070

Energy is free from spin-orbit coupling.


CHAPTER 8.

137

relativistic corrections for all atoms, −0.2649 hartree, calculated for the same basis set. Thus only 0.0031 hartree accounts for relativistic correction to total binding energy. Relativistic correction to total energy turns out to be −0.2483, −0.2484 and −0.2484 hartree at HF, CASSCF and CASPT2 levels using cc-pvDZ basis set (Table 8.2). The sum for all atoms using the same basis set is −0.2486 hartree, so that the correction to binding energy turns out to be negligibly small here. Interestingly, numerical calculations due to Fischer (nonrelativistic HF) and Desclaux (DHF) show that the total relativistic correction for all atoms of NN is −0.2440 hartree in Hartree-Fock limit.15

8.3.2 Correlation energy Electron correlation effects have been studied in different ways. UCISD calculation with 6-31G* basis set and 50 active orbitals (Table 8.1) gives a total correlation energy of −0.1290 hartee. With a larger basis, namely, 6-311+G(d), UCISD, UMP4, UCCSD and UCCSD(T) yield much improved correlation energy values, −1.2762 hartee, −1.8414 hartee, −1.7713 hartree and −1.8451 hartree, respectively. The UCCSD results are comparable to UMP4 and UCCSD(T) results. The CAS(13,13) calculations using cc-pvDZ basis set are more illustrative. They yield −0.1919 hartree and −0.1921 hartree as the static correlation energy at nonrelativistic and relativistic levels (CASSCF – HF), and a dynamic correlation energy of −0.8861 hartree (CASPT2 – CASSCF) at both levels of theory. Thus the total correlation energy calculated by CAS(13,13) method is about −1.078 hartree (both relativistic and nonrelativistic). See Table 8.2. As the molecule is small and consists of light atoms, relativistic corrections to total energy for the molecule and correlation energy for the molecule are practically additive to each other as illustrated in Table 8.2. Thus the sum of relativistic correction and correlation energy from ROHF level in Table 8.2 is −1.3263 hartree and the difference of CASPT2/DKH2 and ROHF energies is −1.3264 hartree. As expected, no significant difference is found between the nonrelativistic and relativistic valence or virtual orbital energy (see Supporting Information).


CHAPTER 8.

138

It would be interesting to compare the results from UCISD/6-31G* with those from UB3LYP/6-31G*. The B3LYP scheme has 20% HF exchange and 80% Slater exchange with 72% correction to Slater exchange as inducted by Becke. 16 It would be reasonable to assume that a UB3LYP level calculation gives a small deviation from UHF exchange energy. The DF method projects a huge additional exchange (DF–UHF) plus correlation energy, −3.2717 hartree, over the UHF energy. This is a quantity certainly different from the correlation energies calculated by post-Hartree-Fock methodologies. Nevertheless, because the additional exchange is estimated to be small, a comparison with the correlation energy values can reveal the nuances of DF modeling.

The

correlation energy calculated by the CI method is −0.1290 hartree. The rather large energy difference is partly due to the additional exchange and correlation in the DF calculation and in part due to the new geometry optimization at UB3LYP level. Both the factors depend upon the DF modeling of hybrid functionals. With the 6-311+G(d) basis set, the calculated additional exchange plus correlation energy is −3.2881 hartree (UB3LYP), and the correlation energies are −1.2762 (UCISD), −1.7713 (UCCSD), −1.8414 (UMP4) and −1.8451 [UCCSD(T)] in hartree. All differences are measured from the UHF value. At the new (UB3LYP-optimized) geometry, the UHF energy is greater than the optimized UHF value. The UHF exchange energy is generally negative. Therefore, one can only conclude that the UB3LYP model overestimates the exchangecorrelation energy. This would affect the population distribution and the spin density.

8.3.3 Spin density The atomic spin densities from different levels of calculation are given in Table 8.3. Some of the calculations give spin densities for the correspondingly optimized geometries, while other spin densities are from single point calculations. As mentioned earlier, a single-point run was carried out by UB3LYP method with 6-311++G(3df,3pd) basis set using 6-311++G(d,p) optimized geometry. This has been done because many of our earlier investigations of magnetic molecules were based on the same procedure.2 The CASSCF(13,13) calculation using cc-pvDZ basis set is the most extensive one among the calculations that yield spin densities here. Therefore, these spin densities


CHAPTER 8.

139

Table 8.3. Computed atomic spin densities in the ground state of nitronyl nitroxide Atom

ROHF

UHF

UHF

LévyLeblond (a,b) 6-31G*

DHF (a,b,c)

CASSCF (b)

ROB3LYP (b)

UB3LYP

UB3LYP

UB3LYP

6-31G*

6-31G*

6-31G*

6-31G*

6-311+G*

0.0097

0.0099

−0.0750

0.0066

−0.2446

−0.2463

6-311++ G(d, p) −0.2448

UB3LYP (b) 6-311++ G(3df,3p d) −0.2731

6-31G*

6-31G*

1C

0.0098

−0.8358

6-311+ G* −0.8552

2C

0.0044

−0.0520

−0.0163

0.0000

0.0050

−0.0065

0.0046

−0.0147

−0.0160

−0.0174

−0.0215

3C

0.0044

−0.0520

−0.0163

0.0091

0.0050

−0.0065

0.0046

−0.0147

−0.0160

−0.0174

−0.0215

4N

0.2498

0.4711

0.4787

0.2508

0.2509

0.1904

0.1957

0.2616

0.2752

0.2763

0.2930

5N

0.2498

0.4711

0.4787

0.2508

0.2509

0.1904

0.1957

0.2616

0.2752

0.2763

0.2930

6O

0.2291

0.4420

0.4452

0.2273

0.2272

0.3479

0.2791

0.3515

0.3440

0.3435

0.3367

7O

0.2291

0.4420

0.4452

0.2273

0.2272

0.3479

0.2791

0.3515

0.3440

0.3435

0.3367

8C

0.0082

0.0257

0.0125

0.0012

0.0012

0.0008

0.0118

0.0162

0.0191

0.0180

0.0118

9H

0.0006

0.0001

0.0005

0.0002

0.0002

0.0002

0.0010

0.0006

0.0010

0.0009

0.0012

10H

0.0000

−0.0013

−0.0017

0.0000

0.0000

−0.0000

0.0000

−0.0006

−0.0009

−0.0003

0.0007

11H

0.0001

−0.0033

−0.0032

0.0001

0.0001

−0.0001

0.0002

−0.0013

−0.0011

−0.0003

0.0012

12C

0.0023

0.0115

−0.0177

0.0082

0.0083

0.0001

0.0036

0.0048

−0.0033

−0.0038

0.0115

13H

0.0002

−0.0023

−0.0024

0.0001

0.0001

0.0001

0.0002

−0.0006

−0.0005

−0.0001

0.0001

14H

0.0000

−0.0015

−0.0017

0.0000

0.0000

−0.0000

0.0000

−0.0008

−0.0007

−0.0017

−0.0015

15H

0.0003

−0.0008

−0.0020

0.0006

0.0006

0.0001

0.0004

0.0001

−0.0003

−0.0003

−0.0004

16C

0.0023

0.0115

−0.0177

0.0082

0.0083

0.0048

0.0036

0.0048

−0.0033

−0.0038

0.0115

17H

0.0002

−0.0023

−0.0024

0.0001

0.0001

0.0001

0.0002

−0.0006

−0.0005

−0.0001

0.0001

18H

0.0000

−0.0015

−0.0017

0.0001

0.0001

0.0000

0.0000

−0.0008

−0.0007

−0.0017

−0.0015

19H

0.0003

−0.0008

−0.0020

0.0006

0.0006

0.0001

0.0004

0.0001

−0.0003

−0.0003

−0.0004

20C

0.0082

0.0257

0.0125

0.0001

0.0012

0.0008

0.0118

0.0162

0.0191

0.0180

0.0118

21H

0.0001

−0.0033

−0.0032

0.0002

0.0000

−0.0001

0.0002

−0.0013

−0.0011

−0.0003

0.0012

22H

0.0006

0.0001

0.0005

0.0002

0.0002

0.0002

0.0010

0.0006

0.0010

0.0009

0.0012

23H 24H

0.0000 0.0002

−0.0013 0.0575

−0.0017 0.0710

0.0000 0.0001

0.0000 0.0001

0.0000 0.0001

0.0000 0.0003

−0.0006 0.0111

−0.0009 0.0134

−0.0003 0.0151

0.0007 0.0072

a

Uncontracted form of the basis set is used. Single-point calculations. c The spin densities are obtained from one electron distributed over two-spinor calculation. b


CHAPTER 8.

140

Table 8.4. Nonrelativistic and relativistica atomic spin densities of the ground state of nitronyl nitroxide using cc-pvDZ basis set. All are single-point calculations using ROHF/6-31G* optimized geometry.

0.0172

DHFb 0.0172

CASSCFc −0.1783

CASSCF/DKH2b, c −0.1783

2C 3C

0.0061 0.0061

0.0061 0.0061

0.0066 0.0066

0.0066 0.0066

4N 5N 6O 7O 8C 9H 10H 11H 12C 13H 14H 15H 16C 17H 18H 19H 20C 21H 22H 23H 24H

0.2443 0.2443 0.2296 0.2296 0.0080 0.0007 0.0000 0.0002 0.0021 0.0002

0.2444 0.2444 0.2294 0.2294 0.0080 0.0007 0.0000 0.0002 0.0021 0.0002

0.2765 0.2765 0.3017 0.3017 0.0043 0.0003 0.0001

0.2766 0.2766 0.3017 0.3017 0.0043 0.0003 0.0001

−0.0002

−0.0002

0.0006

0.0006

−0.0000

−0.0000

−0.0000

−0.0000

−0.0001

−0.0001

0.0002 0.0021 0.0002

0.0002 0.0021 0.0002

−0.0001

−0.0001

0.0006

0.0006

−0.0000

−0.0000

−0.0000

−0.0000

−0.0001

−0.0001

0.0002 0.0080 0.0002 0.0007 0.0000 0.0002

0.0002 0.0080 0.0002 0.0007 0.0000 0.0002

−0.0001

−0.0001

0.0043

0.0043

−0.0002

−0.0002

0.0003 0.0001

0.0003 0.0001

−0.0012

−0.0012

Atoms

R(O)HF

1C

a

Relativistic calculation in the so-called “spin-free” representation. Second-order Douglas-Kroll-Hess transformed version. c CASSCF(13,13). b


CHAPTER 8.

141

are taken as reference. See Table 8.4. The reference results show that the electronic spin is distributed mainly on five atoms, 1C (−0.178), 4N and 5N (0.276 on each), and 6O and 7O (0.302 on each). The CASSCF(13,13) results given in Table 8.3 are not taken as standard because the basis set used is small, 6-31G(d), and not correlation-consistent. R(O)HF and DHF calculations with cc-pvDZ basis set give smaller spin densities on the nitrogen atoms (0.244) and still smaller spin densities on the oxygen atoms (0.230), and leave a small positive spin density on 1C (0.017). See Table 8.4. The ROHF, Lévy-Leblond and DHF calculations using 6-31G* basis set gives similar results (0.250 on each nitrogen and around 0.228 on each oxygen) except for leaving only a residual spin density (0.010) on 1C (Table 8.3). As expected, there is hardly any difference in spin densities calculated from the corresponding nonrelativistic and relativistic treatments. The ROHF method cannot generate beta spin density. The unrestricted and restricted HF calculations give a very different account of the spin distribution. The UHF method piles up a huge negative spin density on 1C. In consequence, spin density significantly increases on nitrogen as well as oxygen atoms. Also, the nitrogen spin density becomes manifestly greater than the oxygen spin density. In short, UHF gives an extremely bad spin density distribution. The CASSCF(13,13)/6-31G* and ROB3LYP/6-31G* calculations give a vastly reduced spin density on nitrogen and a small positive density on 1C. Considering the consistency with CAS calculations, the unrestricted DF method UB3LYP appears to exhibit the right trend, a negative spin density on 1C that is somewhat large, an almost correct spin density on nitrogen atoms, and a somewhat inflated spin density on the oxygen atoms. Comparing the CASSCF(13,13) results in Table 8.4, we find that the deviation of the spin densities on nitrogen and oxygen atoms follow the order 6-31G* > 6-311+G* > 6-311++G(d,p). The 1C spin density is about −0.245 in all these three cases as compared to −0.178 obtained from the reference calculations. The UB3LYP/6-311++G(d,p) calculation gives nitrogen atomic spin density practically at par with CASSCF(13,13)/cc-pvDZ results. The oxygen atom spin density from UB3LYP/6-311++G(d,p) level is closest to that from CASSCF level. The single point calculation with 6-311++G(3df,3pd) basis set increases spin density on 1C and the


CHAPTER 8.

142

nitrogen atoms, though a slightly better spin density (comparing CASSCF as reference) evolves on each oxygen atom. Typical spin density plots are given in Figure 8.3. In short, the unrestricted DF calculations produce qualitatively correct spin densities on the five important atoms 1C, 4N, 5N, 6O and 7O. These are systematically improved with basis size. However, the magnitude of the change in spin density in the NN radical is not large enough to rationalize any large change of the calculated J for a diradical with an increasingly large basis. The presence of the coupler causes a great variation of spin densities in the radical fragments with change in basis size when the basis set is small. It is interesting to note that Yamaguchi et al.17 calculated the spin densities of para-nitrophenyl,

meta-nitrophenyl,

para-dimethylaminophenyl

and

meta-

dimethylaminophenyl derivatives of nitronyl nitroxide. Their results are not very informative for our purpose, because the calculations were done by the semi-empirical INDO method. Besides, the presence of the phenyl group greatly influences the spin distribution in the NN moiety, bringing in a large negative spin density on 1C. The only noticeable effect is that the oxygen atoms have greater spin density than the nitrogen atoms.

8.3.4 Charge density The trend of Mulliken atomic charges is given in Table 8.5 and Table 8.6. A pattern exists for charges on the five important atoms that have been obtained from the calculations ROHF, DHF, CASSCF and CASSCF/DKH2 using cc-pvDZ basis. Table 8.6 shows that the correlation-consistent basis set gives rise to a charge of around 0.35 on 1C, charges around –0.24 on 2C and 3C, around –0.02 on 4N and 5N, around – 0.42 on 6O and 7O and a charge around 0.09 on 8C. These atomic charges, except for that on 8C, are best matched by CASSCF/6-31G* charges in Table 8.5. ROHF, LévyLeblond and DHF calculations, using 6-31G* basis, give atomic charges that are qualitatively comparable to the CASSCF/6-31G* charges. The trend continues to UHF/631G* calculation and even to ROB3LYP/6-31G* and UB3LYP/6-31G* calculations.


CHAPTER 8.

UB3LYP/6-31G(d)

UHF/6-31G(d)

143

UB3LYP/6-311++G(d,p)

ROHF/6-31G(d)

Figure 8.3. The spin density contours of nitronyl nitroxide radical at different levels of calculation. Spin alternation is evident in the unrestricted methodologies. There is substantial alternation in the DF calculations, accompanied by a reduction of spin density on 1C. Atomic spin densities systematically change from 6-31G* to 6-311++G** bases in DF calculations, but the variation is slow.


CHAPTER 8.

144

Table 8.5. Computed atomic charges in the ground state of nitronyl nitroxide Atom

ROHF

UHF

UHF

LévyLeblond (a,b) 6-31G*

DHF (a,b,c)

CASSCF (b)

ROB3LYP (b)

UB3LYP

UB3LYP

UB3LYP

6-31G*

6-31G*

6-31G*

6-31G*

6-311+G*

0.3530

0.3524

0.2357

0.2490

0.2503

0.0873

6-311++ G(d, p) 0.2726

UB3LYP (b) 6-311++ G(3df,3p d) 0.7426

6-31G*

6-31G*

1C

0.2972

0.2806

6-311+ G* 0.0481

2C

0.1045

0.1156

0.6105

0.1202

0.1204

0.0883

0.1360

0.1461

0.2012

−0.0668

0.0805

3C

0.1045

0.1156

0.6105

0.1202

0.1204

0.0883

0.1360

0.1461

0.2012

−0.0668

0.0805

4N

−0.0309

−0.0708

−0.1123

0.0191

0.0190

−0.0254

0.0354

0.0057

−0.0145

−0.1707

−0.2245

5N

−0.0309

−0.0708

−0.1123

0.0191

0.0190

−0.0254

0.0354

0.0057

−0.0145

−0.1707

−0.2245

6O

−0.5633

−0.5033

−0.0404

−0.6387

−0.6384

−0.4901

−0.4994

−0.4758

−0.0562

−0.0065

−0.4495

7O

−0.5633

−0.5033

−0.0404

−0.6387

−0.6384

−0.4901

−0.4994

−0.4758

−0.0562

−0.0065

−0.4495

8C

−0.4740

−0.4752

−1.0945

−0.4999

−0.5001

−0.4743

−0.4492

−0.4501

−0.8957

−0.3756

0.0487

9H

0.1777

0.1763

0.2818

0.1928

0.1928

0.1746

0.1580

0.1572

0.2724

0.1509

0.0239

10H

0.1815

0.1817

0.2876

0.1761

0.1761

0.1810

0.1607

0.1613

0.2776

0.1732

0.0267

11H

0.2150

0.2076

0.3030

0.2201

0.2201

0.2071

0.1838

0.1820

0.2940

0.2001

0.0405

12C

−0.4724

−0.4740

−1.2659

−0.4995

−0.4997

−0.4741

−0.4534

−0.4553

−1.0901

−0.6775

0.0115

13H

0.1697

0.1682

0.2745

0.2199

0.2199

0.1682

0.1524

0.1516

0.2656

0.1653

0.0172

14H

0.2153

0.2098

0.3020

0.1835

0.1835

0.2090

0.1851

0.1860

0.2956

0.1975

0.0338

15H

0.1875

0.1875

0.2913

0.1871

0.1871

0.1853

0.1635

0.1626

0.2796

0.1600

0.0211

16C

−0.4724

−0.4740

−1.2659

−0.4995

−0.4997

−0.4741

−0.4534

−0.4553

−1.0901

−0.6775

0.0115

17H

0.1697

0.1682

0.2745

0.2199

0.2199

0.1682

0.1524

0.1516

0.2656

0.1653

0.0172

18H

0.2153

0.2098

0.3020

0.1835

0.1835

0.2090

0.1851

0.1860

0.2956

0.1975

0.0338

19H

0.1875

0.1875

0.2913

0.1871

0.1871

0.1853

0.1635

0.1626

0.2796

0.1600

0.0211

20C

−0.4740

−0.4752

−1.0945

−0.4999

−0.5001

−0.4743

−0.4492

−0.4501

−0.8957

−0.3756

0.0487

21H

0.2150

0.2076

0.3030

0.2201

0.2201

0.2071

0.1838

0.1820

0.2940

0.2001

0.0405

22H

0.1777

0.1763

0.2818

0.1928

0.1928

0.1746

0.1580

0.1572

0.2724

0.1509

0.0239

23H 24H

0.1815 0.2816

0.1817 0.2727

0.2876 0.2768

0.1761 0.2855

0.1761 0.2855

0.1810 0.2649

0.1607 0.2050

0.1613 0.2071

0.2776 0.2539

0.1732 0.2277

0.0267 −0.0027

a

Uncontracted form of the basis set is used Single-point calculations. c The atomic charges are obtained from one electron distributed over two-spinor calculation. b


CHAPTER 8.

145

Table 8.6. Nonrelativistic and relativistica atomic charges of the ground state of nitronyl nitroxide using cc-pvDZ basis set. All are single-point calculations using ROHF/6-31G* optimized geometry.

a

CASSCFc

CASSCF/DKH2b, c

0.3730

DHFb 0.3751

0.3464

0.3485

2C 3C 4N 5N

−0.2443 −0.2443 −0.0137 −0.0137

−0.2418 −0.2418 −0.0132 −0.0132

−0.2417 −0.2417 −0.0209 −0.0209

−0.2391 −0.2391 −0.0203 −0.0203

6O 7O 8C 9H 10H 11H 12C 13H 14H 15H 16C 17H 18H 19H 20C 21H 22H 23H 24H

−0.4554 −0.4554 0.0945 0.0383 0.0403 0.0672 0.1012 0.0357 0.0666 0.0421 0.1012 0.0357 0.0666 0.0421 0.0945 0.0672 0.0383 0.0403 0.0824

−0.4581 −0.4581 0.0922 0.0388 0.0408 0.0678 0.0985 0.0362 0.0671 0.0427 0.0985 0.0362 0.0671 0.0427 0.0922 0.0672 0.0383 0.0408 0.0830

−0.4164 −0.4164 0.0926 0.0366 0.0395 0.0635 0.0996 0.0345 0.0636 0.0402 0.0996 0.0345 0.0636 0.0402 0.0926 0.0635 0.0366 0.0395 0.0713

−0.4192 −0.4192 0.0903 0.0372 0.0401 0.0640 0.0969 0.0351 0.0641 0.0408 0.0969 0.0351 0.0641 0.0408 0.0903 0.0640 0.0372 0.0401 0.0719

Atoms

R(O)HF

1C

Relativistic calculation in the so-called “spin-free” representation. Second-order Douglas-Kroll-Hess transformed version. c CASSCF(13,13). b


CHAPTER 8.

146

However, the systematic trend exhibited by spin densities from the DF calculations is not observed for the atomic charges. The results are mostly inconclusive (Table 8.5). In the DF geometry optimization with a progressively large basis set, the

electron density increases on the nitrogen atoms and decreases on the oxygen atoms, thereby slowly taking the atomic charge distribution away from the CASSCF/DKH2/ccpvDZ results. Some sort of balance is achieved from the single point DF calculation using 6-311++G(3df,3pd) basis while we find that the atomic charges on oxygen atoms improve and the 8C charge dwindles to 0.05. Typical electronic density plots are shown in Figure 8.4. But no major insight is gained here, which points out that some other factor must be responsible for the variation of J for a diradical with basis size.

8.3.5 Coupling constant From the previous section we find that DF calculations in general produce bad atomic spin densities in the isolated monoradical NN. However, these spin densities become progressively better as the basis size increases while the molecular geometry is optimized for each basis set. It is expected that the same conclusion would hold for other molecules. What is important here is that NN, along with a coupler and other monoradicals including itself, form diradicals. The intra-molecular exchange coupling constant J estimated from DF based broken symmetry calculations on the diradicals is generally quite sensitive to the choice of basis set. To illustrate this point, we have considered two examples, NN-C2H2-NN that has

(a) NN-C2H2-NN

(b) NN-pm-NN

Figure 8.5. Nitronyl nitroxide diradicals with (a) ethylene (b) 2,2â&#x20AC;˛-(1,2-ethynediyldi-4,1 3,1-phenylene)bis[4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazole-1-oxyl-3-oxide] (pm) couplers.


CHAPTER 8.

UB3LYP/6-31G(d)

UHF/6-31G(d)

147

UB3LYP/6-311++G(d,p)

ROHF/6-31G(d)

Figure 8.4. Total electronic density contour plots for nitronyl nitroxide monoradical at different levels of calculation. This diagram is less informative, but it shows that DF calculations lead to a more compact electronic distribution.


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148

a large negative J and NN-pm-NN with a small positive J. See Figure 8.5. The calculated J values are given in Table 8.7. The observed J for NN-C2H2-NN is –350 cm–1.18 Thus the larger basis sets give rise to a limiting value, but the one calculated using 6-31G* basis set is too large by a factor greater than 2. In fact, for NN-pm-NN species too, the 631G* basis gives a value that is more than 2.5 times the limiting J value.

8.3.6 Spin Interaction The spin density distributions in the monoradical NN, obtained from different basis sets, are inadequate to explain why the calculated J in Table 8.7 is largely inconsistent for 6-31G* or other small basis sets. Atomic charge densities are not directly informative. The coupling constant J equals the coupler-mediated interaction energy Eint between the two monomer fragments A and B. The nature of interaction depends upon the monoradical structures and the point of attachment of the monoradicals with the spacer. These two points are covered by the so-called spin alternation rule in unrestricted formalism.19 There should be sufficient spin density alternation in the monoradicals as well as the conjugated chain(s) of atoms in the spacer. This is discussed in the subsequent paragraphs and illustrated by Figure 8.6. As our DF calculations show, all the basis sets generate a marked spin alternation from 1C to the two NO fragments in the monoradical NN. When attached to the monoradicals, the spacer would also exhibit spin alternation but the atomic spin densities in the spacer tend to decrease with the spacer size. The interaction energy is given by Eint = ½ [E(S)–E(T)] = [E(BS)–E(T)] where S, BS and T refer to singlet, broken symmetry and triplet states with ideal values of <S 2 > (0, 1 and 2). Its magnitude depends on two factors, namely, spacer size and basis size. In our earlier investigations2 we have repeatedly shown that J decreases rather drastically with increase in spacer size. This would explain the large magnitude of J for diradical 5(a) and the small magnitude for 5(b). We observe that the exchange-correlation energy in DF varies very slowly with basis size. For NN, it is about -3.2717 for 6-31G* and -3.2881 for 6-311+G*. Therefore, the change in total energy of the diradical and the change in total energy difference between two states are basically a mean-field effect. As the basis size increases, an


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149

Table 8.7. Magnetic exchange coupling constants from UB3LYP calculations on triplet and broken symmetry states. Molecule

Basis Sets

ET in a.u. (<S2>T)

EBS in a.u. (<S2>BS)

EBS–ET (cm–1)

J a (cm–1)

6-31G* b

–1145.023180 (2.1033) –1145.309621 (2.0660) –1145.080898 (2.0620) –1145.327150 (2.0629) –1145.327357 (2.0629)

–1145.026737 (1.2249) –1145.311387 (1.1392) –1145.082295 (1.1273) –1145.328747 (1.1286) –1145.328953 (1.1285)

– 780.7

– 888.7

– 387.5

– 418.1

– 350.6

– 375.1

– 350.6

– 375.2

–1605.862573 (2.0822) –1606.226202 (2.0806) –1605.909924 (2.0843) –1605.961397 (2.0768)

–1605.862539 (1.0784) –1606.226171 (1.0771) –1605.909907 (1.0822) –1605.961384 (1.0758)

6-311G**

NN-C2H2-NN

e

c,d c

6-31+G** 6-311+G**

c,d

6-311++G** 6-31G*

NN-pm-NN

f

6-311G* 6-31G** 6-31+G**

c

– 350.4

– 375.0

7.37

7.34

6.78

6.76

3.76

3.75

2.78

2.78

Yamaguchi formula, J = [E(lowspin) – E(highspin)]/ [<S2>hs - <S2>ls]; ref. 16. Optimized triplet geometry. The BS calculation is a single point calculation using the triplet geometry. c From ref. 2(b). Triplet geometry optimized at 6-311G** level. d From ref. 2(e). Triplet geometry optimized at 6-311G** level. e Observed J = – 350.0 cm–1 , ref. 17. f Total energy and <S2> are from ref. 2(c). a

b


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150

increasingly greater number of basis functions are mixed to form the valence orbitals. The bonding levels are stabilized. This leads to a weakening of interaction energy, a reduced difference [E(BS)–E(T)], and a reduction in the calculated J value. This is exactly what is evidenced in Table 8.7.

8.4 Conclusion The quality of interaction can also be gauged by comparing the atomic spin densities in the diradical with those in the monoradical. These densities for the important atoms in NN-C2H2-NN are shown in Figure 8.6. It is manifest that for the larger basis sets with diffused functions, the average spin densities on the nitrogen and oxygen atoms of the radical centers in diradical 5(a) are in good agreement with those in the isolated

0.4

Average Spin Density

0.3 0.2 0.1 0

SC

CC

N

O

-0.1 -0.2 -0.3

--

Figure 8.6. Average atomic spin density in NN-C2H2-NN: 6-31G* (▬), 6-311G** ( ), 6-31+G** (▪▪▪), 6-311+G** (──), 6-311++G** (∙∙∙). Points are for the isolated monoradical NN: 6-31G* (□), 6-311++G** (○). SC is the spacer carbon atom and CC is the connecting carbon atom.


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monoradical NN. The spin density on the connecting atom is somewhat reduced from its monoradical value, which is expected. In comparison, the 6-31G* basis reproduces extremely reduced spin densities on these three sets of atoms. This happens because of the erroneously stronger interaction of the monoradical fragment with the coupler, achieved with this basis set. One can also draw two minor conclusions from this work. First, because NN is a small molecule of light atoms, relativistic corrections to binding energy and spin densities are negligibly small. Correlation energy and relativistic correction to total energy are effectively additive here, indicating that the molecular orbitals remain almost unchanged by relativity. Relativistic corrections to valence and virtual orbital energy are negligibly small (See Supporting Information). Second, the ad-hoc spin scheme in UHF leads to a wrong estimate of total energy and quite wrong spin densities. The latter features enter into the unrestricted DF methodology. The calculation of J survives as it is done as the difference of energy of two similar states differing only in <S 2> and <Sz>. Thus the sign of J depends on the monoradical structure and points of contact with the coupler, and is independent of the nature and size of the basis set. But the absolute magnitude of the calculated J is sensitive to the smallness of the basis size.


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8.5 References 1. (a) Takahashi, M.; Turek, P.; Nakazawa, Y.; Tamura, M.; Nozawa, K.; Shiomi, D.; Ishikawa, M.; Kinoshta, M. Phys. Rev. Letts. 1991, 67, 746. (b) Tamura, M.; Nakazawa,Y.; Shiomi, D.; Nozawa, K.; Hosokoshi, Y.; Ishikawa, M.; Takahashi, Kinoshta, M. Chem. Phys. Letts. 1991, 186, 401. 2. (a) Ali, Md. E.; S. Datta, N. J. Phys. Chem. A 2006, 110, 2776. (b) Ali, Md. E.; Datta, S. N. J. Phys. Chem. A 2006, 110, 13232. (c) Datta, S. N.; Mukherjee, P.; Jha, P. P. J. Phys. Chem. A 2003, 107, 5049. (d) Ali, Md. E.; Vyas, S.; Datta, S. N. J. Phys. Chem. A 2005, 109, 6272. (e) Ali, Md. E.; Datta, S. N. J. Phys. Chem. A 2006, 110, 2776. (f) Ali, Md. E.; Datta, S. N. J. Phys. Chem. A 2006, 110, 1323. (g) Latif, I. A.; Panda, A.; Datta, S. N. J. Phys. Chem. A 2009, 113, 1595. (h) Latif, I. A.; Singh, V. P.; Bhattacharjee, U.; Panda A.; Datta, S. N. J. Phys. Chem. A 2010, 114, 6648. (i) Bhattacharjee, U.; Panda, A.; Latif , I. A.; Datta, S. N. J. Phys. Chem. A 2010, 114, 6701. 3. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R;. Scalmani, G.; V. Barone, Mennucci, B.; Petersson, G. A.; Nakatsuji,; Caricato, H. M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Toyota, M. K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda,; Kitao, Y. O.; Nakai, H.; Vreven, T.; Montgomery, Jr., J. A.; Peralta, J. E.;

Ogliaro, F.; Bearpark, M.; Heyd, J. J.; E. Brothers, K.; Kudin, N.;

Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth,

G. A.; Salvador, P.; Dannenberg, J. J.;

Dapprich, S.; Daniels, A. D.; Farkas, O.; Foresman, J. B.; Ortiz, Cioslowski, J. V; D. Fox, J. Gaussian, Inc., Wallingford CT (2009). 4. Andersson, K.; Aquilante, F.; Barysz, M.; Bernhardsson, A.; Blomberg, M. R. A.; Carissan, Y.; Cooper, D. L.; Cossi, M.; DeVico, L.; Ferré, N.; Fülscher, M. P.; Gaenko, A.; Gagliardi, L.; Ghigo, G.; Graaf, C. de; Gusarov, S.; Hess, B. A.; Hagberg, D.; Holt, A.; Karlström, G.; Lindh, R.; Malmqvist, P.-Å.; Nakajima, T.; P.; Olsen,

J.;

Pedersen, T.;

Pitonak,

M.; Raab,

J.; Reiher,

Neogrády,

M.;

Roos,


CHAPTER 8.

B. O.; Ryde, U.; Schimmelpfennig,

153

B.; Schütz, M.; Seijo,

L.; Serrano-Andrés,

L.;

Siegbahn, P. E. M.; Stålring, J.; Thorsteinsson, T.; Veryazov, V.; Widmark. P.O. MOLCAS Version 7.6. Department of Theoretical Chemistry, Chemical Centre, University of Lund, Sweden, (2011).

5. Douglas M.; Kroll, N. M. Ann. Phys. (NY) 1974, 82, 89. 6. Hess, B. A. Phys. Rev. A 1986, 33, 3742. 7. Saue T.; Visscher, L.; Jensen, H. J. Aa.; Bast, R.; Dyall, K. G.; Ekström, U.; Eliav, E.; Enevoldsen, T.; Fleig, T.; Gomes, A. S. P.; Henriksson, J.; Ilias, M.; Jacob, C. R.; Knecht, S.; Lee, Y. S.; Nataraj, H.; Norman, P.; Olsen, J.; Park, Y. C.; Pernpointner, M.; Ruud, K.; Schimmelpfennig, B.; Sikkema, J.; Thorvaldsen, A.; Thyssen, J.; Villaume, S.; and Yamamoto, S. A relativistic ab initio electronic structure program, Release DIRAC10, (2010). Available from: http://dirac.chem.sdu.dk. 8. Barysz, M.; Sadlej, A. J.; Snijders, J. G. Int. J. Quantum Chem. 1997, 65, 225. 9. Barysz M.; Sadlej, A. J. J. Mol. Struct. (Theochem.) 2001, 573, 181. 10. Barysz, M.; Sadlej, A. J. J. Chem. Phys. 2002, 116, 2696. 11. (a) Hess, B. A.; Marian, C. M.; Wahlgren, U.; Gropen, O. Chem. Phys. Lett. 1996, 251, 365. (b) Ilias, M.; Kello, V.; Visscher, L.; Schimmelpfennig, B. J. Chem. Phys. 2001, 115, 9667. 12. Lévy-Leblond, J.-M. Commun. Math. Phys. 1967, 6, 286. 13. Dunning, T. H. Jr. J. Chem. Phys. 1989, 90, 1007. 14. Roos, B. O. Int. J. Quantum Chem. 1980, S14, 175. 15. (a)Fischer, C. F., Comput. Phys. Commun. 1972, 4, 107. (b) Desclaux, J. P. Atom. Data Nucl. Data Tables 1973, 12, 311. 16. Becke, A. D. Phys. Rev. A 1988, 38, 3098. 17. Yamaguchi, K; Okumura, M.; Nakamo, M. Chem. Phys. Lett. 1992, 191, 237. 18. Ziessel, R.; Stroh, C.; Heise, H.; Koehler, F. K.; Turek, P.; Claiser, N.; Souhassou, M.; Lecomte, C. J. Am. Chem. Soc. 2004, 126, 12604. 19. (a) Trindle, C.; Datta, S. N. Int. J. Quantum Chem. 1996, 57, 781. (b) Trindle, C.; Datta, S. N.; Mallik, B. J. Am. Chem. Soc. 1997, 119, 12947.


154

Conclusions The main aim of all the calculations was to find J, which might help in identifying the applicability of new molecules in material science. The magnetic exchange coupling constant (J) is half of the difference between the energy of singlet (E ) and triplet (E ) S

T

states. It has been theoretically found for a number of molecules, of which some are even photomagnetic. All the calculations are based on the density functional theory using broken symmetry formalism. The broken symmetry calculations are easy to perform even on a large molecule using moderate computational facilities. Calculations on a total 79 molecules are presented in this thesis. Each species is investigated in two different spin states by a number of methodologies and using different basis sets. The result of all these calculation can be realized by synthesizing the same diradicals. I have investigated five sets of organic molecules by quantum chemical methods. The first two sets involve strongly ferromagnetically coupled molecules, as crystals of the latter can serve as molecular magnets. The next two sets consist of photomagnetic molecules that can show crossover from paramagnetism to ferromagnetism and antiferromagnetism to ferromagnetism, respectively. The fifth set is again on strongly ferromagnetically coupled, almost forgotten Schlenk diradicals. Detailed analysis shows that electron-pushing substituents decrease the J value and electron-withdrawing substituents increase it. In the final part, we see that the coupler-mediated interaction energy becomes progressively more accurate with an increasingly large basis. In short, the above work will be more fruitful if at least some of the molecules are synthesized, and their properties are checked. It is really very difficult to predict if in the near future it will be computationally cost-effective to do post Hertree-Fock calculations in detail. Till then DFT is the way in the investigation of organic molecules of high spin. Also, optimized wave function and the spin density analysis can be of great importance as regards the magnetic nature of a species.


Acknowledgment

I express my deep sense of gratitude, respect and admiration to my guide Prof. S. N. Datta for his constant support and guidance. I am greatly indebted to him for his priceless help, genial behavior, moral boost, good wishes, ebullience, criticism, enormous patience, useful suggestions and keen interest throughout the continuation of my work. His thorough approach to scientific problems and affirmative outlook has always enlivened me. I am grateful to Council of Scientific and Industrial Research for fellowship. I also acknowledge Department of Science and Technology (DST) grants “Theoretical investigation of magnetism in molecules, molecular magnets and magnetic materials (SR/S1/PC-19/2010)” and “Theoretical and computational investigation of molecular magnets and extended systems as candidates of exotic nanomaterials with usefull properties (DST/INT/Spain/P42/2012)” for computing facilities. I convey my deepest gratitude and respect to Prof. R. B. Sunoj and Prof. Arindam Chowdhury for painstakingly evaluating my annual progress reports and bestowing their valuable suggestions and comments throughout the PhD program. I would also like to thank my co-workers and friends Saumik Sen, Dr Soumendra Roy, Shekhar Hansda, Arun Pal, Tumpa Sadhukhan, Dr. Nital Mehta, Dr. Anirban Panda, Pritam Jana, Suranjan Shil, Ved Prakash Singh, Ujjal Bhattechjee, and Srikant V. Raghavan.

Iqbal Abdul Latif


List of Publications Publications: 1. Theoretical investigation of magnetic and conducting properties of substituted silicon chains. I. Hydrogen and oxo-Verdazyl ligands: Shekhar Hansda, Iqbal A. Latif and Sambhu N. Datta; J. Phys. Chem. C 2012, 116, 12725. 2. On the photomagnetism of nitronyl nitroxide, imino nitroxide and verdazyl substituted azobenzene: Sambhu N. Datta, Arun K. Pal, Shekhar Hansda and Iqbal A. Latif; J. Phys. Chem. A 2012, 116, 3304. 3. Photoswitching Magnetic Crossover in Organic Molecular Systems: Arjun Saha, Iqbal A. Latif, and Sambhu N. Datta; J. Phys. Chem. A 2011, 115, 1371. 4. Unusually large coupling constants in diradicals obtained from excitation of mixed radical centers: A theoretical study on potential photomagnets: Ujjal Bhattacharjee, Anirban Panda, Iqbal A. Latif, and Sambhu N. Datta; J. Phys. Chem. A 2010, 114, 6701. 5. Very strongly ferromagnetically coupled diradicals from mixed radical centres. II. Nitronyl nitroxide coupled to Tetrathiafulvalene via spacers: Iqbal A. Latif, Ved Prakash Singh, Ujjal Bhattacharjee, Anirban Panda, and Sambhu N. Datta; J. Phys. Chem. A 2010, 114, 6648. 6. Very strongly ferromagnetically coupled diradicals from mixed radical centres: nitronyl nitroxide coupled to oxo-verdazyl via polyene spacers: Iqbal A. Latif, Anirban Panda, and Sambhu N. Datta; J. Phys. Chem. A 2009, 113, 1595.

Manuscript submitted or under preparation: 1. High magnetic exchange coupling constants: A DFT based study of the almost forgotten Schlenk diradicals: Iqbal A. Latif, Shekhar Hasnda and Sambhu N. Datta. 2. The electronic structure of nitronyl nitroxide radical: Effect of basis size on diradical calculation: Iqbal A. Latif, S. K. Roy and Sambhu N. Datta.


MyThesis