CHAPTER 8.
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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