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1、Chapter6StructureTheory6.1TheStructureHypothesisThemolecularconcepthasbecomesocentralinchemistrythatunderstandingofchemicaleventsiscommonlyassumedtoconsistofrelatingexperimentalobservationstomicroeventsatthemolecularlevel,whichmeanschangesinmolecularstructure.Inthissensemolecularst
2、ructureisafundamentaltheoreticalconceptinchemistry.Asthemicrochangesareinvariablytrig-geredbyelectrontransfer,thecorrecttheoryatthemolecularlevelmustbequantummechanics.Itisthereforesurprisingthataquantumtheoryofmolecularstructurehasneverdeveloped.Thisfailurestemsfromthefactthatphys
3、icsandchemistryoperateatdifferentlevelsandthatgraftingthemodelsofphysicsontochemistryproducesanincompletepicture.Althoughthephysicsmodelmaygiveareasonablequalitativeaccountofchemicalconcepts,suchaschemicalcohesion,itfailsatthequantitativelevel,becauseessentialfactorsareignored.Themo
4、stimportantfactoristheenvironment.Thefreeatomofphysicsrepresentsauniverse,completelyempty,exceptforasolitaryatom.Suchanatomcanneverexplainchemicaleffects,whichoccurbecauseoftheinteractionofanatomwithitsenviron-ment.Whenthetotalenvironmentistakenintoaccountonedealswiththefamiliarclas
5、sicalmacroworld.Betweenthetwoextremesischemistryanditisimportanttoknowwhethertodescribechemicalentities,likemolecules,inclassicalornon-classicalterms.Thisproblemrelatestothequestionofwheretheso-calledclassical/quantumlimitoccurs.IthasalreadybeenshownthatSchr¨odinger’sequation:∂Ψ~
6、22i~=∇+VΨ(6.1)∂t2mseparatesintospacecoordinates,xandtimecoordinates,t,onassuming203204CHAPTER6.STRUCTURETHEORYΨ(x,t)=f(t)·ψ(x).Substitutionof∂Ψ∂f(t)∂2Ψ∂2ψ(x)=·ψ(x);=f(t)∂t∂t∂x2∂x2into6.1gives:1df(t)~21d2ψ(x)i~=+V(x)f(t)dt2mψ(x)dx2Theleft-handsideisafunctionoftimeonlyandther.h.s.ofc
7、oordinatesonly.Thisisonlypossiblewhenbothsidesareequaltothesameseparationconstant,E.Thusdf(t)iE=dtf(t)~OnIntegration:lnf(t)=iEt/~+Af(t)=Aexp(iEt/~)=Aexp(iS/~)wheretheproductEt=Sisknownastheactionofthesytem.Whenthissolutionissubstitutedinto(6.1),therealpartoftheequationrearrangesto:
8、1~2∇2A∂S2(∇S)+V−+=02m2mA∂t
