量子化学与群论基础1

《量子化学与群论基础1》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

1、6Grouptheory6.1IntroductionGroupTheoryisoneofthemostpowerfulmathematicaltoolsusedinQuantumChemistryandSpectroscopy.Itallowstheusertopredict,interpret,rationalize,andoftensimplifycomplextheoryanddata.Grouptheorycanbeconsideredthestudyofsymmetry.Grouptheoryisabasicstructureofmodernalgebra,consistingo

2、fasetofelementsandanoperation.Grouptheoryisthesubjectofintensestudywithinmathematics,andisusedinmanyscientificfields.e.g.,groupsareusedinchemistrytodescribethesymmetriesofmolecules,andtheLorentzgroupisacentralpartofspecialrelativity.Also,thetheoryofgroupsplaysacentralroleinparticlephysics,whereitha

3、sledtothediscoveryofnewelementaryparticles.CurlKrotoSmalley1985Fullerenes1990,KratcshmerTheinvolvementofsymmetryinchemistryhasalonghistory;in540BCthesocietyofPythagorasheldthattheearthhadbeenproducedfromthecube,firefromthetetrahedron,airfromtheoctahedron,waterfromtheicosahedron,andtheheavenlysphere

4、fromtheregulardodecahedron.Symmetryexistsallaroundusandmanypeopleseeitasbeingathingofbeauty.Symmetry,isrelatedtoequivalence,mutuallycorrespondingarrangementofvariouspartsofabody,producingaproportionate,balancedform.AtitsheartisthefactthattheSetofOperationsassociatedwiththeSymmetryElementsofamolecul

5、econstituteamathematicalsetcalledaGroup.ThisallowstheapplicationofthemathematicaltheoremsassociatedwithsuchgroupstotheSymmetryOperations.6.2SymmetryelementsandoperationsSymmetryoperationsAsymmetryoperationisdefinedas:"movementofamoleculetoaneworientationinwhicheverypointinthemoleculeiscoincidentwit

6、hanequivalentpoint(orthesamepoint)ofthemoleculeinitsoriginalorientation."SymmetryElementsAsymmetryelementisageometricalentity(aline,planeorpoint)withrespecttowhichoneormoresymmetryoperationsmaybecarriedout.SymmetryelementsandoperationsSymmetryElementSymmetryOperationSymboln-FoldsymmetryaxisMirrorPl

7、aneCenterofInversionn-FoldImproperRotationAxisIdentityRotationby(2/n)radiansReflectionInversionRotationby(2/n)radiansfollowedbyreflectionperpendiculartorotationaxisECniSn1.Typesofsymmetryoperation(a)Inve