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1、Chapter2ElectronicStructureTheoryofCoordinationCompoundFocusonTransitionmetalcoordinationchemistryTheatomicstructureSymmetryinChemistry–GroupTheoryGroupTheoryisoneofthemostpowerfulmathematicaltoolsusedinQuantumChemistryandSpectroscopy.Itallowstheusertopredi
2、ct,interpret,rationalize,andoftensimplifycomplextheoryanddata. AtitsheartisthefactthattheSetofOperationsassociatedwiththeSymmetryElementsofamoleculeconstituteamathematicalsetcalledaGroup.Thisallowstheapplicationofthemathematicaltheoremsassociatedwithsuchgr
3、oupstotheSymmetryOperations.AllSymmetryOperationsassociatedwithisolatedmoleculescanbecharacterizedasRotations:(a)ProperRotations:Cnk;k=1,......,n Whenk=n,Cnk=E,theIdentityOperation nindicatesarotationof360/nwheren=1,....(b)ImproperRotations:Snk,k=1,.....,
4、n Whenk=1,n=1Snk=s,ReflectionOperation Whenk=1,n=2Snk=i,InversionOperationIngeneralpracticewedistinguishFivetypesofoperation:(i)E,IdentityOperation(ii)Cnk,ProperRotationaboutanaxis(iii)s,Reflectionthroughaplane(iv)i,Inversionthroughacenter(v)Snk,Rotationa
5、boutanaxisfollowedbyreflectionthroughaplaneperpendiculartothataxis.EachoftheseSymmetryOperationsisassociatedwitha SymmetryElement whichisapoint,aline,oraplaneaboutwhichtheoperationisperformedsuchthatthemolecule'sorientationandpositionbeforeandaftertheoperat
6、ionareindistinguishable.TheSymmetryElementsassociatedwithamoleculeare:(i)AProperAxisofRotation:Cnwheren=1,.... Thisimpliesn-foldrotationalsymmetryabouttheaxis.(ii)APlaneofReflection:sThisimpliesbilateralsymmetryabouttheplane. Theseplanesarefurtherclassifi
7、edas:sh-HorizontalPlanewhichisperpendiculartothePrincipalAxisofRotation(i.e.Axiswithhighestvalueofn).Ifnoprincipalaxisexistsshisdefinedasthemolecularplane.svorsd-VerticalPlanewhichcontainsthePrincipalAxisofRotationandisperpendiculartoashplane,ifitexists.Whe
8、nbothsvandsdplanesarepresent,thesvplanescontainthegreaternumberofatoms,thesdplanescontainbondanglebisectors.Ifonlyonetypeofverticalplaneispresent,svorsdmaybeuseddependingonthetotalsymmetryofthemolecule
