同核双原子分子的电子结构B

ForB,CandNatoms,theirs-andp-orbitalsarecloseinenergyandhenon-negligiblesp-orbitalinteraction.Accordingly,hybridizationofs-andp-orbitalsshouldbeconsideredwhentheseatomsareinvolvedinchemicalbonds.Hybridization/Mixingofs-andp-orbitals

Whendoesspmixingoccur?B,C,andNallhe

1/2filled2porbitalsO,FandNeallhe

1/2filled2porbitals.Hing>1/2filled2porbitalsraisestheenergiesoftheseorbitalsduetoincreasede–-e–repulsion.Iftwoelectronsareforcedtobeinthesameorbital,theirenergiesgoup.spmixingoccurswhenthesandpatomicorbitalsarecloseinenergy(

1/2filled2porbitals),whichallowsthes(p)AOofoneatomtointeractstronglywithnotonlythesAO,butalsothepAO,ofanotheratom.MOdiagramwithsp-mixing(forB2,C2,N2etc)Nosp-mixingsp-mixing1

g(2s)1

u(2s)2

g(2p)2

u(2p)2

u(2sp)2

g(2sp)1

g(2sp)1

u(2sp)Howdoessp-mixingoccur?sp-mixing=sp-hybridizationEnergy2s2s1g1u2p2p2g2u1u1gHOMOLUMON2:KK(1

g)2(1

u)2(1

u)4(2

g)2sp-hybridizationofAO’ssp-mixingofMO’sEnergydiagramforX2:(a)withand(b)without2s-2pzhybridization(mixing).The1satomicorbitalsareleftout.(a)(b)1

g1

u*1

g1

u*2

g2

u*1

u1

g*1

u2

g1

g*2

u*EEachatomhastwoequivalentsp-HO’s.Enhancethebondingandantibondingnatureof1

gand2u*,respectivelyWeakenthebondingandantibondingnatureof2

g,1u*,respectively.Stabilize1

g,1u*.Destabilize2

g,2u*.Effectsofspz-mixingN2:KK(1

g)2(1

u)2(1

u)4(2

g)2BEnergyBB22s2s1g1*u2p2p2*u1u1*g(px,py)pzHOMOLUMOTheeffectofinteractionsbetween2sand2p.AtthestartofthesecondrowLi-N,wehemixingof2sand2p.Theresultisthat1

u*ispusheddowninenergywhereas2

gisraised.B2:KK(1

g)2(1

u)2(1

u)22gMoleculeLi2Be2B2C2N2O2F2Ne2BondOrder10123210BondLength(Å)2.67n/a1.591.241.011.211.42n/aBondEnergy(kJ/mol)105n/a289609941494155n/aDiamagnetic(d)/Paramagnetic(p)dn/apddpdn/a2s-2pzmixingParamagnetic:unpairedelectron(s)EPR-activeDiamagnetic:allelectronsarepaired!Schrödingerequation:Wefunction:Hamiltonoperator:One-electronwefunctionsandeigenequation:§2Molecularorbitaltheoryanddiatomicmolecules1.Molecularorbital(MO)theory

IndependentElectronModel:Everyelectroninamoleculeissupposedtomoveinaneragepotentialfieldexertedbythenucleiandotherelectrons.(IndependentElectronApproximation)!MeanfieldexertedoneiSummaryLCAO-MO:

AtomicorbitaloverlapandbondingInteractionbetweenatomicorbitalsleadstoformationofcovalentbondsonlyiftheorbitals:1)areofthesamesymmetry;2)canoverlapwell;3)areofsimilarenergy(lessthan10-15eVdifference).AnytwoorbitalsyAandyBcanbecharacterizedbytheoverlapintegral,Dependingonthesymmetryandthedistancebetweentwoorbitals,theoverlapintegralSmaybepositive(bonding),negative(antibonding)orzero(non-bondinginteraction).TheoverlapintegralSmaybepositive(bonding),negative(antibonding)orzero(non-bondinginteraction).MOdiagramforF2FFF22s2s2g2*u2p2p3g3*u1u1*g(px,py)pzEnergyBEnergyBB22s2s2g2*u2p2p3g3*u1u1*g(px,py)pzMOdiagramforB2sp-mixingElectronicconfigurations2s-2pzmixing3su1p*g3sg1pu2s*u2sgHomogeneousdiatomicmoleculesMoleculeLi2Be2B2C2N2O2F2Ne2BondOrder10123210BondLength(Å)2.67n/a1.591.241.011.211.42n/aBondEnergy(kJ/mol)105n/a289609941494155n/aDiamagnetic(d)/Paramagnetic(p)dn/apddpdn/a2s-2pzmixingParamagnetic:unpairedelectron(s)EPR-activeDiamagnetic:allelectronsarepaired!3.Thestructureofhomonucleardiatomicmoleculesc.Themolecularspectroscopy–spectraltermParity:g×g=gg×u=uu×u=ge.g.,(1

u)2=(1+1)1(1-1)1

LTz=+1-1=0,ST=1,u×u=gAclosed-shellmolecularconfigurationhasbothSand

equaltozeroandgivesrisetotheterm.Thespectraltermsofmoleculeswithopenshell(s)aredeterminedbytheelectronsintheopenshell(s).Excitedstates+1-1ForEquivalentelectronsinanopenshell(e.g.,)Pauliexclusionprinciple&Hund’sruleshouldbefulfilledtodetermineitsground-stateterm.ForEquivalentelectronsinanopenshell(e.g.,),Pauliexclusionprinciple&Hund’sruleshouldbefulfilledtodetermineitsground-stateterm,forwhichML=0(=0)andMs=

(3/2).Thespinfactorofitswefunctionism+1-1whichissymmetricuponpermutation.Therefore,thespatialfactorshouldbeantisymmetricuponpermutation,i.e.,Thisfunctionarefoundtoheeigenvalueof-1withrespecttoreflectionofelectroniccoordinatesinthe(xz)symmetryplane;thesuperscript–referstotheeigenvalue.or+1-1Similarly,forthecaseof=0(ML=0)andS=0(Ms=0),m+1-1Thespinfactorisantisymmetricuponpermutation,i.e.,Thisfunctionarefoundtoheeigenvalueof1withrespecttoreflectionofelectroniccoordinatesinth