1、Wave FunctionAb initio(MRCI,CIS)Semiempirical(Zindo/1,INDO/S,CNDO/S)DFT TDDFT,MC-DFT,DFT+CI222(,)(,)82hihr tVr tmt Separation of variables()()rr B-O Approximation(,)()(,)()()eleceleceffelecnuclnucleffr RRr RRR Molecular orbitals1122()()().()nnrrrr 111121211122121222222222112()(1)()(1)()(1)()(1).()(1
2、)()(1)()(2)()(2)()(2)()(2).()(2)()(2)1()()()()()()(!nnnniiirrrrrrrrrrrrrririrn 222112222112222)()().()()()()()()()()()()()().()()()()()()()()()()()().()()()()ininijjjjnjnjnnnnnnnniriririrjrjrjrjrjrjrnrnrnrnrnrn Configuration interaction Full CI:000SSsbb Mller-Plesset Perturbation Theory 0V Limited C
3、I:*properties:well-defined,size-consistent,variational,very expensive and impractical for all but the very smallest systemsCIS,CISD,CISDT,QCI,QCISD,QCISD(T)HFLimitSchdinger EquationFull CI HF MP2 MP3 MP4 QCISD(T)Electron CorrelationBasis Set TypeMinimalSplit-valencePolarizedDiffuseHigh ang.momentum
4、Current DFT methods partition the electronic energy into several terms:VJXC VJ corresponds to the classical energy of the charge distribution XCaccounts for the remaining terms in the energy*the exchange energy arising from the antisymmetry of the quantum mechanical wavefunction.*dynamic correlation
5、 in the motions of the individual electrons SCF methodsExcitation energy in the HF/SCF model:Eorbital(ELUMO-EHOMO,etc.)Whats left?Electronic correlation energy Multiconfigurational description of the transitions Single-configuration methods:*CIS(CI-Singles)*Response methods:RPA,SOPPA*Coupled-cluster
6、 Methods:EOM-CCSD(T),CC3,SAC-CIMulti-configuration methods:*Multireference CI:MRCI,MR-SC2CI*Multireference perturbation:MR-PT(CASPT2,.)*Multireference Coupled-cluster:MRCC Reference:HF-SCF,yielding MOs Excited states:linear combination of singly-excited determinants Applicability:near closed-shell g
7、roung-state geometry,singlets and triplets,nondegenerated situations,analytic gradients Performance:very poor,errors1-3ev Reference:HF-SCF,yielding MOs Excited states:energies and intensities from polarizabilities Applicability:near closed-shell ground-state geometry,singlets and triplets,nondegener
8、ated situation,analytic gradients Performance:qualitatively correct near ground-state equilibrium geom.,0.5-2ev Linear,quadratic,response methods Based on single,double,replacements No wave functions obtained Limited precision,especially in doubly-excited or multiconfigurational states Reference:HF-
9、SCF,yielding MOs Excited states:energies and intensities Applicability:near closed-shell ground-state geometry,singlets and triplets,nondegenerated situations,analytic gradients(CCSD,SAC-CI)Performance:very accurate near in singly-reference cases 0.1-0.3ev when including triple excitationsCoupled-cl
10、uster methods:solved by linear response EOM-CCSD,EOM-CCSD(T)CC2,CC3:approximated expansions SAC(Single Adapted Cluster)-C1:EOM-CCSD-like Problems:very expensive,large errors in multiconfigurational situations,problems with degenerated situations000.iiisisiDiDiiicccc Classification:Singles,doubles,tr
11、iplesCI excitations:MRCI(SDT),Non size-extensive method(Davidson correction+Q,SC2CI)Only applicable to very small systems(otherwise the errors reach several eVs)Coupled-cluster excitations CC with triples:MRCC(SDT)Very expensive methods still under development (avoid the errors of CCSD(T)Only applic
12、able to small systems Mller-Plesset Perturbations MRMP:CASPT2,CASPT3,etc Generality and precission in medium-large-size systems Problems in the selection of the reference (size,intruder states,etc)Non-orthogonality of the statesMR methods Applicability:no restrictions,except limitations in the selec
13、tion of the reference TD Kohn-Sham method 212iSitVttit 2iiitnt212(2,)()()()SNXCexttV tVdVtVtrTime DependentExternal PerturbationReference:HF-SCF,yielding MOsExcited states:energies and intensities from linear responseApplicability:near closed-shell ground-state geometry,singlets and triplets,nondege
14、nerated situations,analytic gradients(new)Performance:qualitatively correct near ground-state equilibrium geom.,0.31ev better performance than methods of comparable effort.like RPAAdvantages:black-box behavior for a large number of states extension to larger systemsDisadvantages:well-known and sometimes erratic failuresSummary?How to choose the method according to different systems 210.2050.100.semiempiricalCISMCSCFTD-DFT,CCSD-LRTMRCIFCI
