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P1:GQT/GAMP2:GLMFinalPages Qu:00,00,00,00 EncyclopediaofPhysicalScienceandTechnologyEN013C-606July26,200117:34 PotentialEnergySurfaces DonaldG.Truhlar UniversityofMinnesota I.Introduction II.QuantumMechanicalBasisforAdiabatic PotentialEnergySurfaces III.TopologyofAdiabaticPotentialEnergySurfaces IV.BreakdownoftheAdiabaticApproximation V.ShapesofPotentialEnergySurfaces GLOSSARY Adiabaticrepresentation Representationinwhichthe electronicwavefunctionsarecalculatedforÞxed (i.e.,nonmoving)nuclei. Avoidedintersection Caseinwhichtwopotentialenergy surfacescometogetherbutdonotintersect. Conicalintersection Caseinwhichtwopotentialen- ergysurfacesintersectsuchthattheirseparation decreasestozerolinearlyintherelevantnuclear coordinates.Diabaticrepresentation Representationinwhichthe electronicwavefunctionisnotadiabatic. Dunhamexpansion Taylorseriesexpansionofapoten- tialenergycurveinthevicinityofitsminimum. ElectronafÞnity Bindingenergyofanelectrontoaneu- tralatomormolecule. EquilibriumconÞguration GeometryofamoleculeÕs nuclearframeworkcorrespondingtotheminimumadi- abaticenergy. ForceÞeld Thegradientofthepotentialenergy surface. Glancingintersection Caseinwhichtwopotentialen- ergysurfacesintersectsuchthattheirseparationde- creasestozeroquadraticallyintherelevantnuclear coordinates.Ionizationenergy Energyrequiredtoremoveanelectron fromanatomormolecule. APOTENTIALENERGYSURFACE isaneffectivepo- tentialfunctionformolecularvibrationalmotionoratomic andmolecularcollisionsasafunctionofinternuclearco- ordinates.Theconceptofapotentialenergysurfaceis basictothequantummechanicalandsemiclassicalde- scriptionofmolecularenergystatesanddynamicalpro- cesses.Itarisesfromthegreatmassdisparitybetween nucleiandelectrons(afactorof1838ormore)andmay beunderstoodbyconsideringelectronicmotionstobe muchfasterthannuclearmotions.(Whenwesaynuclear motionsandnucleardegreesoffreedominthisarticle,we refertomotionsofthenucleiconsideredaswholes,i.e., toatomicmotions.)Thisdifferenceintimescalesleads totheso-calledelectronicadiabaticapproximationandto 9
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