激發(fā)態(tài)理論研究方法課件

TheoreticalmethodforexcitedstatesTheoreticalmethodforexcitedMethodclassifications

WaveFunctionAbinitio(MRCI,CIS…)Semiempirical(Zindo/1,INDO/S,CNDO/S…)DFT

TDDFT,MC-DFT,DFT+CI…MethodclassificationsWaveFuAbinitiomethodSeparationofvariablesB-OApproximationAbinitiomethodSeparationofHartree-FockTheoryMolecularorbitalsHartree-FockTheoryMolecularoElectroncorrelationmethods?Configurationinteraction

FullCI:?M?ller-PlessetPerturbationTheory

LimitedCI:*properties:well-defined,size-consistent,variational,veryexpensiveandimpracticalforallbuttheverysmallestsystemsCIS,CISD,CISDT,QCI,QCISD,QCISD(T)Electroncorrelationmethods?CHFLimitSch?dingerEquationFullCI………………………………HFMP2MP3MP4QCISD(T)ElectronCorrelation→BasisSetTypeMinimalSplit-valencePolarizedDiffuseHighang.momentum…∞HFSch?dingerEquationFullCI……DensityFunctionalTheoryCurrentDFTmethodspartitiontheelectronicenergyintoseveralterms:

correspondstotheclassicalenergyofthechargedistribution

accountsfortheremainingtermsintheenergy*theexchangeenergyarisingfromtheantisymmetryofthequantummechanicalwavefunction.*dynamiccorrelationinthemotionsoftheindividualelectronsDensityFunctionalTheoryCurreAbinitiomethodsforexcitedstatesΔSCFmethodsExcitationenergyintheHF/SCFmodel:ΔEorbital(ELUMO-EHOMO,etc.)What’sleft??Electroniccorrelationenergy?MulticonfigurationaldescriptionofthetransitionsAbinitiomethodsforexcitedSingle-configurationmethods:*CIS(CI-Singles)*Responsemethods:RPA,SOPPA*Coupled-clusterMethods:EOM-CCSD(T),CC3,SAC-CIMulti-configurationmethods:

*MultireferenceCI:MRCI,MR-SC2CI*Multireferenceperturbation:MR-PT(CASPT2,..)*MultireferenceCoupled-cluster:MRCCSingle-configurationmethods:Single-referencemethods:CI-SinglesReference:HF-SCF,yieldingMOsExcitedstates:linearcombinationofsingly-exciteddeterminantsApplicability:nearclosed-shellgroung-stategeometry,singletsandtriplets,nondegeneratedsituations,analyticgradientsPerformance:verypoor,errors±1-3evSingle-referencemethods:CI-SSingle-referencemethods:Propagator

ApproachReference:HF-SCF,yieldingMOsExcitedstates:energiesandintensitiesfrompolarizabilitiesApplicability:nearclosed-shellground-stategeometry,singletsandtriplets,nondegeneratedsituation,analyticgradientsPerformance:qualitativelycorrectnearground-stateequilibriumgeom.,±0.5-2evSingle-referencemethods:PropPropagatorapproaches:RPA,SOPPA,ADC,Green’sfunctionsLinear,quadratic,…responsemethodsBasedonsingle,double,…replacementsNowavefunctionsobtainedLimitedprecision,especiallyindoubly-excitedormulticonfigurationalstatesPropagatorapproaches:RPA,SOSingle-referencemethods:Coupled-ClusterReference:HF-SCF,yieldingMOsExcitedstates:energiesandintensitiesApplicability:nearclosed-shellground-stategeometry,singletsandtriplets,nondegeneratedsituations,analyticgradients(CCSD,SAC-CI)Performance:veryaccuratenearinsingly-referencecases±0.1-0.3evwhenincludingtripleexcitationsSingle-referencemethods:CoupCoupled-clustermethods:solvedbylinearresponseEOM-CCSD,EOM-CCSD(T)CC2,CC3:approximatedexpansionsSAC(SingleAdaptedCluster)-C1:EOM-CCSD-like

Problems:veryexpensive,largeerrorsinmulticonfigurationalsituations,problemswithdegeneratedsituationsCoupled-clustermethods:solvedMulti-referencemethods:Classification:Singles,doubles,triples…CIexcitations:MRCI(SDT),…?Nonsize-extensivemethod(Davidsoncorrection+Q,SC2CI)?Onlyapplicabletoverysmallsystems(otherwisetheerrorsreachseveraleVs)

Multi-referencemethods:ClassiCoupled-clusterexcitationsCCwithtriples:MRCC(SDT)…?Veryexpensivemethodsstillunderdevelopment(avoidtheerrorsofCCSD(T))?OnlyapplicabletosmallsystemsM?ller-PlessetPerturbationsMRMP:CASPT2,CASPT3,etc?Generalityandprecissioninmedium-large-sizesystems?Problemsintheselectionofthereference(size,intruderstates,etc)?Non-orthogonalityofthestatesMRmethods’Applicability:norestrictions,exceptlimitationsintheselectionofthereference

Coupled-clusterexcitationsCCTime-DependentDensityFunctionalTheory

TD-DFTTDKohn-ShammethodTimeDependentExternalPerturbationTime-DependentDensityFunctioTD-DFTmethod’spropertiesReference:HF-SCF,yieldingMOsExcitedstates:energiesandintensitiesfromlinearresponseApplicability:

nearclosed-shellground-stategeometry,singletsandtriplets,nondegeneratedsituations,analyticgradients(new)TD-DFTmethod’spropertiesRefePerformance:

qualitativelycorrectnearground-stateequilibriumgeom.,±0.3~1evbetterperformancethanmethodsofcomparableeffort.likeRPAAdvantages:

black-boxbehaviorforalargenumberofstatesextensiontolargersystemsDisadvan