PericyclicReactionsand MolecularOrbitalSymmetry
ChapterOutline
1.1ClassificationofPericyclic Reactions2
1.2MolecularOrbitalsof AlkenesandConjugated PolyeneSystems3
1.3MolecularOrbitals ofConjugatedIons orRadicals7
1.4SymmetryPropertiesof p or s-MolecularOrbitals11
1.5AnalysisofPericyclic Reactions 13
1.5.1OrbitalSymmetry CorrelationDiagram Method13
1.5.2FrontierMolecular OrbitalMethod15
1.5.3PerturbationMolecular OrbitalMethod17 FurtherReading19
Inorganicchemistry,alargenumberofchemicalreactionscontainingmultiple bond(s)donotinvolveionicorfreeradicalintermediatesandareremarkably insensitivetothepresenceorabsenceofsolventsandcatalysts.Manyofthese reactionsarecharacterizedbythemakingandbreakingoftwoormorebonds ina singleconcertedstep throughthe cyclictransitionstate,whereinallfirstorderbondingsarechanged.Suchreactionsarenamedaspericyclicreactions byWoodwardandHoffmann.
Theword concerted meansreactantbondsarebrokenandproductbonds areformedsynchronously,thoughnotnecessarilysymmetricallywithoutthe involvementofanintermediate.Theword pericyclic meansthemovementof electrons(p-electronsinmostcases)inacyclicmanneroraroundthecircle (i.e., peri ¼ around, cyclic ¼ circleorring).
Theyareinitiatedbyeither heat (thermalinitiation)or light (photo initiation)andarehighlystereospecificinnature.Themostremarkable observationaboutthesereactionsisthat,veryoften,thermalandphotochemicalprocessesyieldproductswithdifferentstereochemistry.Mostof thesereactionsareequilibriumprocessesinwhichdirectionofequilibrium dependsontheenthalpyandentropyofthereactingspecies.Therefore,in general,threeimportantpointsthatshouldbeconsideredwhilestudyingthe
PericyclicReactions. http://dx.doi.org/10.1016/B978-0-12-803640-2.00001-4
2 PericyclicReactions
pericyclicreactionsare:involvementof p-electrons,typeofactivationenergy required(thermalorlight),andstereochemistryofthereaction.
Thereisacloserelationshipbetweenthemodeofenergysuppliedand stereochemistryforapericyclicreaction,whichcanbeexemplifiedby consideringthesimplerreactionsshownin Scheme1.1.
SCHEME1.1 Stereochemicalchangesinpericyclicreactionsunderthermalandphotochemical conditions.
Whenheatenergyissuppliedtothestartingmaterial,thenitgivesone isomer,whilelightenergyisresponsibleforgeneratingtheotherisomerfrom thesamestartingmaterial.
1.1CLASSIFICATIONOFPERICYCLICREACTIONS
Pericyclicreactionsaremainlyclassifiedintothefourmostcommontypesof reactionsasdepictedin Scheme1.2.
SCHEME1.2 Commontypesofpericyclicreactions.
Inan electrocyclicreaction,acyclicsystem(ringclosure)isformed throughtheformationofa s-bondfromanopen-chainconjugatedpolyene systematthecostofamultiplebondandviceversa(ringopening).These reactionsareunimolecularinnatureastherateofreactionsdependsuponthe
PericyclicReactionsandMolecularOrbitalSymmetry Chapter j 1 3
presenceofonetypeofreactantspecies.Suchreactionsarereversiblein nature,butthedirectionofthereactionismainlycontrolledbythermodynamics.Mostoftheelectrocyclicreactionsarerelatedtoringclosingprocess insteadofringopeningduetoaninteractionbetweentheterminalcarbon atomsforminga s-bond(morestable)atthecostofa p-bond.
Sigmatropicrearrangements aretheunimolecularisomerizationreactions inwhicha s-bondmovesfromonepositiontoanotheroveranunsaturatedsystem. Insuchreactions,rearrangementofthe p-bondstakesplacetoaccommodatethe new s-bond,butthetotalnumberof p-bondsremainsthesame.
In cycloadditionreactions,twoormorecomponentscontaining p-electrons cometogethertoformthecyclicsystem(s)throughtheformationoftwoor morenew s-bondsatthecostofoveralltwoormore p-bonds,respectively,at leastonefromeachcomponent.Amongstthepericyclicreactions,cycloadditionsareknownasthemostabundant,featureful,andvaluableclassofthe chemicalreactions.Thereactionsareknownasintramolecularwhencycloadditionoccurswithinthesamemolecule.Thereversalofcycloadditioninthe samemannerisknownas cycloreversion.Therearesomecycloaddition reactionsthatproceedthroughthestepwiseionicorfreeradicalmechanismand thusarenotconsideredaspericyclicreactions.
Thesereactionsarefurtherextendedtocheletropicand1,3-dipolar reactions,whichshallbediscussedindetailinChapter5.
Grouptransferreactions involvethetransferofoneormoreatomsor groupsfromonecomponenttoanotherinaconcertedmanner.Inthese reactions,twocomponentsjointogethertoformasinglemoleculethroughthe formationofa s-bond.
Itisveryimportanttonotethatinstudyingthepericyclicreactions,thecurved arrowscanbedrawninclockwiseoranticlockwisedirection(Scheme1.3).The directionofarrowsdoesnotindicatetheflowofelectronsfromonecomponentor sitetoanotherasinthecaseofionicreactions;rather,itindicateswheretodraw thenewbonds.
SCHEME1.3 Clockwiseandanticlockwisedirectionofthecurvedarrowsinpericyclic reactions.
1.2MOLECULARORBITALSOFALKENESAND CONJUGATEDPOLYENESYSTEMS
Inordertounderstandandexplaintheresultsofthevariouspericyclicreactionsonthebasisofdifferenttheoreticalmodels,abasicunderstandingof themolecularorbitalsofthemolecules,particularlythoseofalkenesand conjugatedpolyenesystemsandtheirsymmetryproperties,isrequired.
Accordingtothemolecularorbitaltheory,molecularorbitals(MOs)are formedbythelinearcombinationofatomicorbitals(LCAO)andthenfilled bytheelectronpairs.InLCAOwhentwoatomicorbitalsofequivalent energyinteract,theyalwaysyieldtw omolecularorbitals,abondinganda correspondingantibondingorbital.Thebondingorbitalpossesseslower energyandmorestabilitywhileantibondingpossesseshigherenergyandless stabilityascomparedtoanisolatedatomicorbital.Letusconsiderthe simplestexampleofH2 moleculeformedbythecombinationof1satomic orbitals( Figure1.1).
Thebondingmolecularorbitalisaresultofpositive(constructive)overlap, andhenceelectrondensityliesintheregionbetweentwonuclei.However,an antibondingmolecularorbitalisformedasaresultofnegative(destructive) overlapand,therefore,exhibitsanodalplaneintheregionbetweenthetwo nuclei.Thebondingandantibondingmolecularorbitalsexhibitunequal splittingpatternwithrespecttotheatomicorbitalsbecauseafullyfilled molecularorbitalhashigherenergyduetointerelectronicrepulsion.
Wenowconsidermolecularorbitaltheorywithreferencetothesimplest p-molecularsystem,ethene.Asalreadydiscussed,thenumberofmolecular orbitalsformedisalwaysequaltothenumberofatomicorbitalscombining together.Similarly,inthecaseofanethenemolecule,sidewaysinteraction between p-orbitalsofthetwoindividualcarbonatomsresultsintheformation ofthenew p bondingand p*antibondingmolecularorbitalsthatdifferin energy(Figure1.2).Inthebondingorbitalofethene,thereisaconstructive overlapoftwosimilarlobesof p-orbitalsinthebondingregionbetweenthe nuclei.However,inthecaseofanantibondingorbital,thereisdestructive overlapoftwooppositelobesinthebondingregion.Each p-orbitalconsistsof twolobeswithoppositephasesofthewavefunction.
Weignore s-bondskeletoninthistreatmentassigmamolecularorbitals remainunaffectedduringthecourseofapericyclicreaction.
Theconjugatedpolyenesconstituteanimportantclassoforganic compoundsexhibitingavarietyofpericyclicreactions.Onthebasisofthe
(σ) bonding
FIGURE1.1 FormationofmolecularorbitalsinthecaseofanH2 molecule.
numberof p-electrons,suchcompoundsareclassifiedintotwocategories bearing4nor(4n þ 2) p-electronsystems.Inordertoconstructthemolecular orbitalsforsuchpolyenesystems,letusconsiderbuta-1,3-dieneasthe simplestexample.
Inthemoleculeofbuta-1,3-diene,therearefour p-orbitalslocatedonfour adjacentcarbonatomsandhencethisgeneratesfournew p-molecularorbitals onoverlapping.Thewaytogetthesenew p-molecularorbitalsisthelinear combinationoftwo p-molecularorbitalsofetheneaccordingtothe perturbationmolecularorbital (PMO) theory.Likethecombinationofatomic orbitals,overlappingofthebonding(s or p)orantibondingmolecularorbitals (s*or p*)ofthereactants(here,ethene)resultsintheformationofthenew molecularorbitalsthataredesignatedas J1, J2,etc.intheproduct(here, buta-1,3-diene).
AccordingtoPMOtheory,linearcombinationalwaystakesplacebetween thetwoorbitals(twomolecularorbitalsortwoatomicorbitals,oroneatomic andonemolecularorbital)havingminimumenergydifference.Thus,herewe needtoconsider p p and p* p*interactions(constructiveordestructive) insteadofinteractionsbetween p and p*orbitals(Figure1.3).Inbuta1,3-diene,4p-electronsareaccommodatedinthefirsttwo p-molecularorbitals,andtheremainingtwohigherenergy p-molecularorbitalswillremain unoccupiedinthegroundstateofthemolecule.
Thelowestenergyorbital(representedaswavefunction J1)ofbuta1,3-dienedoesnothaveanynodeandisthemoststableduetothepresenceof threebondinginteractions.However,thesecondmolecularorbital J2 possessesonenode,twobondingandoneantibondinginteractions,andwould belessstablethan J1.The J3 hastwonodesandonebondinginteraction. Duetothetwoantibondinginteractions, J3 possessesoverallantibonding characterandthusenergyofthisorbitalismorethantheenergyof J2.The J4 orbitalisformedbytheinteractionbetween p*and p*oftwoethenemolecules.Itbearsthreenodesandthehighestenergy.
Similarly,inthecaseoflongerconjugatedsystemslikeahexa-1,3,5-triene system,therearesix p-orbitalsonsixadjacentcarbonatoms,whichcan
FIGURE1.2 Formationoftwomolecularorbitals(p and
3 nodes, 0 bonding interaction
2 nodes, 1 bonding interaction
1 node, 2 bonding interactions
most stable, 0 node, 3 bonding interactions
generatesixnew p-molecularorbitals(Figure1.4).Inhexa-1,3,5-triene,6pelectronsareaccommodatedinthefirstthreebonding p-molecularorbitals (J1, J2, J3)andtheremainingthreehigherenergyantibonding p-molecular orbitals(J4, J5, J6)willremainunoccupiedinthegroundstate.
Onthebasisofmolecularorbitaldiagramsofethene,buta-1,3-diene,and hexa-1,3,5-triene,thefollowingpointsshouldbeconsideredwhileconstructingthemolecularorbitalsoftheconjugatedpolyenes:
1. Consideronly p-molecularorbitalsandignore s-bondskeletonassigma molecularorbitalsremainunaffectedduringthecourseofapericyclic reaction.
2. Forasystemcontainingn p-electrons(n ¼ even),interactionof p-orbitals leadstotheformationofn/2 p-bondingandn/2 p-antibondingmolecular orbitals.
3. Thebondingmolecularorbitalsarefilledbytheelectrons,whileantibondingorbitalsremainvacantinthegroundstateofthemolecule.
4. Thelowestenergymolecularorbital(forexample, J1 inthecaseofbuta1,3-diene)alwayshasnonode,however,thenexthigherhasonenodeand thesecondhigherhastwonodesandsoon.Thus,thenthmolecularorbital willhaven 1nodes.
HOMO
Buta-1,3-diene
FIGURE1.3 Formationof p-molecularorbitalsinbuta-1,3-diene.
PericyclicReactionsandMolecularOrbitalSymmetry
4 nodes, 1 bonding interaction
3 nodes, 2 bonding interactions
2 nodes, 3 bonding interactions
5 nodes, 0 bonding interaction bonding
1 node, 4 bonding interactions Hexa-1,3,5-triene
most stable, 0 node, 5 bonding interactions
FIGURE1.4 p-Molecularorbitalsinahexa-1,3,5-trienesystem.
5. Itisimportanttonotethatthenodesarefoundatthemostsymmetricpoints inamolecularorbital.Forexample,inthecaseof J2 ofbuta-1,3-diene,a nodeispresentatthecenterofC2 C3 bond,however,itwillbeincorrectif thenodeispresentatthecenterofaC1 C2 bondorC3 C4 bond.
1.3MOLECULARORBITALSOFCONJUGATEDIONSOR RADICALS
Theconstructionofmolecularorbitalsinthecaseofconjugated p-systems havinganoddnumberofcarbonscanbemadeinasimilarmanner.Some importantexamplesofthisclassincludecationoranionorfreeradicalof
propenyl-,pentadienyl-,andheptatrienyl-likesystems.Suchsystems,in additiontobondingandantibondingorbitals,possessanonbondingmolecular orbitalinwhichnodalplanespassthroughthecarbonatoms.
Letusfirstconsiderthecaseofanallylicsystembearingcationoranionor freeradicalcharacter.Inanallylicsystem,threenewmolecularorbitalscanbe generatedbyalinearcombinationofonemolecularorbitalofethene componentandanisolated p-orbitalofthecarbonatom.AsperPMOtheory, intheallylicsystemlinearcombinationtakesplacebetweenoneethenemolecularorbitalandone p-orbital,andthusweneedtoconsidertheresultsof p p and p* p orbitalinteractionsonly.Thelinearcombinationof p with p-orbitalinabondingmanner(withthesignsofthewavefunctionofthetwo adjacentatomicorbitalsmatching)yieldsanewmolecularorbitalhavingleast energy,i.e., J1,whileinantibondingmanner(withthesignsofthewave functionofthetwoadjacentatomicorbitalsunmatched)thisgivesanothernew molecularorbitalhavingmoreenergyi.e., J20 Inasimilarway,interactionof p*with p-orbitalinabondingaswellasantibondingmanneryieldstwonew molecularorbitals,onehavinglowenergy,i.e., J200 ,andanotherhavinghigher energy,i.e., J3 (Figure1.5).
FIGURE1.5 Mixingof p-orbitalwithmolecularorbitalsofetheneinanallylicsystem.
However,wecannotgetfourorbitalsbyusingthreeorbitals.Infact,wedo notgettwoseparateorbitals J20 and J200 butsomethinginbetween,namely J2.Theorbital J2 canbecreatedbyadding J20 and J200 sothattheycancel eachotheronC 2andreinforceeachotheronC 1andC 3.Thus J2 canbe consideredasacombinationof J20 and J200 ,whichisformedbymixingthe p-orbitalinanantibondingmannerandwiththe p*-orbitalinabonding
PericyclicReactionsandMolecularOrbitalSymmetry Chapter j 1 9
manner.Incaseof J2,anonbondingmolecularorbital,anodeisalways presentatthecentralcarbonofthesystem.Thismeansthatthereisno p-electrondensityatthecentralcarbonatom.Moreover,theenergyofa nonbondingmolecularorbitalisthesameasthecontributingatomicorbitals. Hence,thereisnonetstabilizationasaresult(Figure1.6).
antibonding M. O.
FIGURE1.6 Mixingof p-orbitalwithmolecularorbitalsofetheneinanallylicsystem continued.
Asillustratedin Figure1.6,thefollowingpointsneedtobeconsidered whileconstructingthemolecularorbitaldiagramofaconjugatedopen-chain systemhavinganoddnumberofcarbonatoms.
1. Incaseofconjugated p-systemshavinganoddnumberof n carbonatoms, n numberofmolecularorbitalsarepresent.
2. Thesystemwillhave(n 1)/2bonding,(n 1)/2antibonding,andone nonbondingmolecularorbital.
3. Thenonbondingmolecularorbitalwillbe(n þ 1)/2ndorbitalandalways liesbetweenthebondingandantibondingmolecularorbitals.
4. Allnodalplanes(n 1)passthroughthecarbonatom(s)ofthe nonbondingmolecularorbitals(Jn).
5. Allnodalplanespassbetweentwocarbonnucleiincaseofodd Jn (J1, J3, J5,soon)whileonenodalplanepassesthroughthecentralcarbon atomandremainingnodalplanespassbetweentwocarbonatomsincaseof even Jn (J2, J4, J6,soon).
Themolecularorbitaldiagramsforpropenylandpentadienylsystemsare illustratedin Figure1.7 inwhichthemolecularorbitalsfortheircorresponding
Pentadienyl system
FIGURE1.7 Molecularorbitalsofpropenylandpentadienylsystems.
cationoranionorcarbonfreeradicalremainthesame.Thecationoranionor freeradicalspeciesdifferinnumberofelectrons(electronoccupancy)thatare filledaccordingtoAufbau’sruleintheirgroundstateasshownin Figure1.8. Also,Hund’sruleandthePauliexclusionprincipleshouldbefollowed.
FIGURE1.8 Electronoccupancydiagramofpropenyl,pentadienyl,andheptatrienesystems.
PericyclicReactionsandMolecularOrbitalSymmetry Chapter j 1 11
1.4SYMMETRYPROPERTIESOF p OR s-MOLECULAR ORBITALS
Therearetwoindependentsymmetryelements,viz.,mirrorplane, m,and twofoldaxis, C2,thatareusedtocharacterizevariousmolecularorbitalsof alkenesorconjugatedpolyenesystems.
1. Symmetryaboutamirrorplane(m)bisectsthemolecularorbitalinsucha waythatlobesofthesamecolororsignarereflected,and,therefore, reflectionsoneithersideoftheplaneareidentical.Itisperpendiculartothe planeoftheatoms.
2. Symmetryaboutatwofoldaxis(C2)passingatrightanglesinthesameplane, andthroughthecenteroftheframeworkoftheatomsformingthemolecular orbitalissaidtobepresentiftherotationofthemoleculearoundtheaxisby 180 (360 /2)resultsinamolecularorbitalidenticalwiththeoriginal.
Letusexaminesymmetrypropertiesof p-orbitalsofetheneintheground stateandalsointheexcitedstate.Thegroundstate(p)orbitalissymmetric (S)withrespecttothemirrorplane, m,andantisymmetric(A)withrespectto rotationaxis, C2.Ontheotherhand,theantibondingorbital(p*)ofetheneis antisymmetricwithrespectto m andsymmetricwithrespecttothe C2 axis. However,thesigmaorbitalofaC Ccovalentbondhasamirrorplanesymmetry, andsincearotationof180 throughitsmidpointregeneratesthesamesigma orbital,italsohas C2 symmetry.A s*orbitalisantisymmetricwithrespectto both m and C2.ThesymmetrypropertiesoftheseMOs(bondingorantibonding) areshownin Figures1.9and1.10,andaresummarizedin Table1.1
FIGURE1.9 Twofoldaxis(C2)symmetricandantisymmetricmolecularorbitals. m symmetric orbitals
antisymmetric orbitals
FIGURE1.10 Mirrorplane(m)symmetricandantisymmetricmolecularorbitals.
TABLE1.1 Symmetrypropertiesofthe s and p-molecular orbitals; A ¼ antisymmetric,S ¼ symmetric.
Orbitals mC2
Orbitals mC2
p SA s SS
p*AS s*AA
Ψ6 (m-A; C2-S)
Ψ4 (m-A; C2-S)
Ψ5 (m-S; C2-A)
Ψ3 (m-S; C2-A)
Ψ4 (m-A; C2-S)
Ψ2 (m-A; C2-S)
Ψ3 (m-S; C2-A)
Ψ2 (m-A; C2-S)
Ψ1 (m-S; C2-A)
Ψ1 (m-S; C2-A)
FIGURE1.11 Symmetrypropertiesofthemolecularorbitalsofbutadieneandhexatrienesystems.
Hexatriene
Butadiene
PericyclicReactionsandMolecularOrbitalSymmetry Chapter j 1 13
Asimilarconsiderationleadstothefollowingsymmetrypropertiesforthe four p-molecularorbitalsofbutadieneandsix p-molecularorbitalsofhexatrieneandaresummarizedin Figure1.11.
Inconclusion,foralinearconjugated p-system,thewavefunction Jn will haven 1nodes.Whenn 1iszerooraneveninteger, Jn willbe symmetricwithrespecttomirrorplane(m)andantisymmetricwithrespectto C2.Whenn 1isanoddinteger, Jn willhavethesymmetryexactlyreversed (Table1.2).
TABLE1.2 Symmetryelementsintheorbital Jn ofalinearconjugated p-system. WavefunctionsNodes(n 1) mC2 Jodd 0orEvenintegerS A Jeven Oddinteger A S
1.5ANALYSISOFPERICYCLICREACTIONS
Pericyclicreactionshavebeenknownforalongtime,butitwasin1965when WoodwardandHoffmannofferedareasonableexplanationforthembasedon theprincipleofthe“ConservationofOrbitalSymmetry.”Theprinciplestates thatorbitalsymmetryisconservedintheconcertedreactions.Molecular orbitalsinthereactantcanonlytransformintothoseorbitalsintheproducts thathavethesame symmetryproperties withrespecttotheelementsof symmetrypreservedinthereaction.Evenifsymmetryisslightlydisturbedina reactantbyatrivialsubstituentorbyasymmetryofthemolecule,aconcerted reactionmaystillbeanalyzedbymixingtheinteractingorbitalsaccordingto quantummechanicalprinciplesandfollowingthemthroughthereaction.The energyofthetransitionstateofasymmetryallowedprocesswillnecessarily belowerthanthatofthealternativesymmetryforbiddenpath,andevenwhen thisdifferenceissmall,aconcertedreactionwilltakethepathofleastresistance,i.e.,thesymmetryallowedpath,ifthatpathisavailable.
AnotherexplanationhasbeenproposedbyK.Fukuiionthebasisof frontiermolecularorbitals(HOMO LUMO)ofthesubstrates;thismethodis knownasthefrontiermolecularorbitals(FMO)method.Alternatively,the PMOtheorybasedontheWoodward HoffmannruleandHu ¨ ckel-Mo ¨ bius methodisalsousedtoexplaintheresultsofpericyclicreactions.
1.5.1OrbitalSymmetryCorrelationDiagramMethod
TheorbitalsymmetrycorrelationdiagrammethodwasdevelopedbyWoodwardandHoffmannandextendedbyLonguet-HigginsandAbrahamson.
Themostimportantobservationinthestudyofpericyclicreactionsisthe existenceofconservationofmolecularorbitalsymmetrythroughoutthe transformation,meaningtherebythatthesymmetricorbitalsareconvertedinto symmetricorbitalswhereasantisymmetricorbitalsareconvertedintoantisymmetricorbitals.Inthisapproach,symmetrypropertiesofvariousmolecularorbitalsofthebondsthatareinvolvedinthebondbreakingandformation processduringthereactionareconsideredandidentifiedwithrespectto C2 and m elementsofsymmetry.Thesepropertiesremainpreservedthroughout thecourseofreaction.Thenacorrelationdiagramisdrawninwhichthe molecularorbitallevelsoflikesymmetryofthereactantarerelatedtothatof theproductbydrawinglines.
Inthegroundstate,ifthesymmetryofMOsofthereactantmatchesthatof theproductsthatarenearestinenergies,thenreactionis thermallyallowed. However,ifthesymmetryofMOsofthereactantmatchesthatoftheproduct inthefirstexcitedstatebutnotinthegroundstate,thenthereactionis photochemicallyallowed (Figure1.12).Whensymmetriesofthereactantand productmolecularorbitalsdiffer,thereactiondoesnotoccurina concerted manner.Itmustbenotedthatasymmetryelementbecomesirrelevantwhen orbitalsinvolvedinthereactionareallsymmetricorantisymmetric.In conclusion,wecansaythatinpericyclictransformations,symmetryproperties ofthereactantsandproductsremainconserved.
FIGURE1.12 CorrelationbetweenreactantandproductMOsunderthermalandphotochemical conditions.
Whiledrawingtheorbitalcorrelationdiagramforanysystem,the followingpointsmustbeconsidered:
1. Eachreactantmoleculemustbeconvertedintosimpleranaloguebyremoving thesubstituentsattached,ifany,becausesubstituentaffectsonlytheenergy levelsofMOsandnotthesymmetrypropertiesofthe p-system.Letus considertheDiels Alderreaction,a[4 þ 2] p-system(Scheme1.4).
SCHEME1.4 Conversionofthereactantmoleculesintosimpleranalogue.
PericyclicReactionsandMolecularOrbitalSymmetry Chapter j 1 15
2. Differentprocessesmustbetreatedseparatelyeveniftheyoccurwithinthe samemoleculebecausesimultaneousconsiderationmayleadtoerroneous outcome.Forexample,hypotheticaltwo[2 þ 2]cycloadditionreactionsin cyclooctatetraenehavetobeconsideredseparately.Similarly,inhexa2,4-diene,conrotatoryanddisrotatoryelectrocyclizationprocesseshaveto betreatedseparatelywhilemakingtheorbitaldiagram(Scheme1.5).
3. Drawandidentifytheorbitalsundergoingchange.
4. Arrangetheorbitalsinorderoftheirincreasingenergies,anddrawthem forreactantonleftandforproductontherightside.
5. Symmetrypropertiesofthevariousmolecularorbitalsofthebondsbeing involvedinbreakingandformationprocessduringthereactionare consideredandidentifiedwithrespecttoelementsofsymmetry(C2 and s) thatarepreservedthroughoutthereaction.
6. Orbitalsofsamesymmetrydonotcrossinthecorrelationdiagramasper non-crossrule.
7. Afterassigningthesymmetryelementtoeachorbital,constructanorbital correlationdiagrambyconnectingtheorbitalsofstartingmaterialstothose oftheproductnearestinenergyandhavingsamesymmetry.
8. Ifheteroatomsarepresentinanalkenecomponent,theyhavetobe replacedbycarbonanalogues.Interactionsinsuchsystemsshouldbe consideredcarefullyastheymaygeneratethepossibilitiesofnewreaction eitherbynonbondingelectronsorbyavailabilityoflowenergyLUMO.
1.5.2FrontierMolecularOrbitalMethod
Althoughitismorefruitfultoconstructacorrelationdiagramforthedetailed analysisofapericyclicreaction,thereis,nevertheless,analternativemethod thatalsoenablesustoreachsimilarconclusions.Itisaneasyandextremely simpleapproachthatisbasedontheinteractionofthefrontierorbitals,i.e., the highestoccupiedmolecularorbital (HOMO)and thelowestunoccupiedmolecularorbital (LUMO)ofthecomponentsthatareinvolvedinapericyclic reaction.
Asshownin Figure1.13,irradiationofanalkeneorconjugatedpolyene systempromotesanelectronfromitsgroundstateHOMOtothegroundstate LUMO,whichthenbecomesthehighestoccupiedmolecularorbitalinthe excitedstate,forexample, J3 ofbutadienebecomesHOMOuponexcitation ofanelectronfrom J2 to J3 onirradiation.
SCHEME1.5 Independentprocessesoccurringinthesamemolecule.
Theexplanationforthisalternativeapproachisbasedonthefactthat overlappingofwavefunctionsofthesamesignisessentialforthebondformation.Whentwosystemscomeclosetoeachother,thentheirunperturbed molecularorbitalsstarttointeractandthosethatarecloseinenergyinteract morestronglythanotherorbitals.Itiswellknownthatinteractionoftwofilled MOsdoesnotleadtothenetenergystabilizationofthesystembutitisthe interactionbetweenonefilledandothervacantMOthatleadstonetenergy stabilization.ThisexplainswhyinteractionbetweenHOMOandLUMOis consideredinthisapproach(Figure1.14).Ifinteractionbetweenthesetwo MOsisofbondingtype(overlappingofsamesignedwavefunctions)inthe groundstate,thenreactionis thermallyallowed.However,ifitisofantibondingtype(overlappingofoppositesignedwavefunctions)thenitisa thermallyforbidden reaction.Ontheotherhand,ifinteractionbetween HOMO LUMOisofbondingtypeintheexcitedstate,thenreactionis photochemicallyallowed.However,itisaphotochemicallyforbiddenreaction whenitisofantibondingtype.
InordertoapplytheFMOapproachinunimolecularpericyclicreactions likeelectrocyclicreactionsandsigmatropicrearrangements,wehavetotreata singlemoleculeashavingseparatecomponents.Insuchacase,onlyHOMOof thecomponenthastobeconsideredtopredictthefeasibilityofthereaction undergivenconditions.Furthermore,thistheorydoesnottellwhytheenergy barriertoforbiddenreactionsissohigh.
FIGURE1.13
FIGURE1.14
PericyclicReactionsandMolecularOrbitalSymmetry
1.5.3PerturbationMolecularOrbitalMethod
Thereisyetanotherqualitativemolecularorbitalapproach,developedby M.J.S.Dewar,thatyieldssimplemnemonicstopredictthesamestereochemicalvariationsinpericyclicreactionsasdotheothermethods.Inthe PMOmethod,aromaticorantiaromaticcharacterofthecyclictransitionstate isexplainedbyconsideringtheHuckel-Mobiusconceptofaromaticity.Ina Hu ¨ ckel-typesystem,acyclicarrayofalltheinteracting p-orbitalssharesa commonnodalplane.AHuckelsystemisaromatic(stabilizedbycyclic delocalization)when(4n þ 2) p-electronsarepresent,andantiaromatic (destabilizedbycyclicdelocalization)when4n p-electronsarepresent. However,inaMobius-typesystemanextranodeispresent,introducedby twistingthesetoforbitalssothateachoneformsanangle,theta,withits neighbors.InaMobius-typesystem,themoleculesandtransitionstatesrequire 4n p-electronsforaromaticityandareantiaromaticwiththeusual(4n þ 2) pelectrons. Itcanbegeneralizedandshownthatacyclicarrayoforbitalswith zerooranevennumberofsigninversionsbelongstotheHu¨ckelsystem,and thosewithanoddnumberofsigninversionsbelongtotheMobiussystem . Applicationofthismethodtopericyclicreactionsledtothegeneralization thatthermalreactionstakeplacevia aromaticorstabletransitionstates whereasphotochemicalreactionsproceedvia antiaromaticorunstabletransitionstates.Thisisthecasebecauseacontrollingfactorinphotochemical processesisconversionofexcitedstatereactantsintogroundstateproducts. Thus,thephotochemicalreactionsconvertthereactantsintotheantiaromatic transitionstatesthatcorrespondtoforbiddenthermalpericyclicreactionsand soleadtocorrespondingproducts.
Inthisapproach,wehaveonlytoconsideracyclicarrayofinteracting atomicorbitals,representingthoseorbitalsthatundergochangeinthetransitionstatewithoutconsideringthesymmetrypropertiesandassignsignsto thewavefunctionsinthebestmannerforoverlap.Finally,thenumberof nodesinthearrayandthenumberofelectronsinvolvedarecounted.Itshould benotedthatwhilecountingthenumberofnodesweignoresigninversions withinanyofthebasisorbitals(forexample,aswithina p-orbital).The followingexamplesillustratetheconstructionoforbitalinteractiondiagrams forthe[2 þ 2]and[4 þ 2]cycloadditionsbysupra supraandsupra antara modes.(Foradetaileddescriptionoftheseterms,refertoChapter4).Whether, thereactionsareallowedornotarepredictedasfollows.Inthecaseof [p 2 s þ p2s]cycloaddition(4n p-electronsystem),asupra supramodeof additionleadstoaHu ¨ ckelarray,whichisantiaromaticwith4n p-electrons (Figure1.15).Therefore,thesupra supramodeofreactionisthermally forbidden.However,asupra antaramodeofadditionusesaMobiusarray, whichisaromaticwith4n p-electrons.Therefore,thereactionisthermally allowedinthismode.Similarly,wecananalyzethe[p 4 s þ p2s]cycloaddition having(4n þ 2) p-electrons(Figure1.15).Inthiscase,asupra supramodeof additionleadstoaHuckelarray,whichisaromaticwith(4n þ 2) p-electrons. Therefore,[p 4 s þ p2s]cycloadditionreactionnowbecomesthermally
allowed.However,a[p 4 s þ p2a]cycloadditionusesaMo ¨ biusarray,whichis antiaromaticwith(4n þ 2) p-electrons.Therefore,thereactionisthermally forbiddeninthismode.
T. S. for [π2s + π2s] cycloaddition, Hückel system, 0 node, 4 electrons, antiaromatic, hv allowed
T. S. for [π2s + π2a] cycloaddition, Möbius system,1 node, 4 electrons, aromatic, Δ allowed
T. S. for [π4s + π2s] cycloaddition, Hückel system, 0 node, 6 electrons, aromatic, Δ allowed
T. S. for [π4s + π2a] cycloaddition, Möbius system,1 node, 6 electrons, antiaromatic, hv allowed
FIGURE1.15 PMOapproachfor[2 þ 2]and[4 þ 2]cycloadditions.
Woodward Hoffmannrulesbasedontheperturbationmolecularorbital methodaresummarizedin Table1.3.
TABLE1.3 Woodward Hoffmann rulesbasedontheperturbation molecularorbitalmethod.
No.of electrons
4n þ 2
No.of nodes T.State typeAromaticityFeasibility
0orEvenHu ¨ ckelAromatic D allowed, hv forbidden
4n 0orEvenHu ¨ ckelAntiaromatic D forbidden, hv allowed
4n þ 2
OddMobiusAntiaromatic D forbidden, hv allowed
4n OddMobiusAromatic D allowed, hv forbidden
PericyclicReactionsandMolecularOrbitalSymmetry
Therefore,thepredictionofreactionfeasibilityunderthermalorphotochemicalconditiondependsupontheextentofstabilizationofacyclictransitionstateascomparedtoanopen-chainsystem.Thestabilizationor destabilizationdependsuponthearomaticorantiaromaticcharacterofacyclic transitionstateinthegroundstate.
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