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1、Chapter8ElectronicCorrelationMethodsHartree-Fork方法用平均相互作用描述電子－電子相互作用HF~99%ofthetotalenergy~1%veryimportantforchemicalphenomenaElectronicCorrelationEnergy=DifferencebetweenHFandthelowestpossibleenergyinagivenbasisset電子相關(guān)相同軌道的兩個電子（自旋相反）~20kcal/mol不同軌道的兩個電子（自旋
2、相反，相同）~1kcal/molCoulomb相關(guān)：不同自旋電子Fermi相關(guān)：相同自旋電子Coulomb相關(guān)largestcontribution!Startingpoint:HFwavefunctionΨ=a0ΦHF+∑aiΦii=1ExcitedSlaterDeterminantsN電子M基函數(shù)體系：占據(jù)軌道：N/2個，空軌道M-N/2ReplacingoccupiedMOswithvirtualMOs?GeneralExcitedSlaterDeterminants1:singly2:doubly3:
3、triply4:quardruply…Accuracy?chemicalaccuracy~1kcal/molonlyforsmallsystems!?relativeenergiesconstanterrors!thecoreorbitalsandthevalenceorbitalsfrozencoreapproximationThreemainmethodsConfigurationInteraction(CI)ManyBodyPerturbationTheory(MBPT)CoupledClusters(
4、CC)Notation:level/basislevel2/basis2//level1/basis1ConfigurationInteraction(組態(tài)相互作用)ΨCI=a0ΦSCF+∑aSΦS+∑aDΦD+∑aTΦTL=∑aiΦiSDTi=0L=ΨHΨ?λ[ΨΨ?1]CICICICI2ΨCIHΨCI=∑∑ΨiHΨjI=∑a0Ei+∑∑aiajΨiHΨjIij==00i=0ii=≠0j22ΨCIΨCI=∑∑aiajΨiΨj=∑aiΨiΨi=∑aii0==0ji=0i=0?L=2∑ajΦiHΦj?2λai=
5、0?aijai(ΦiHΦj?λ)+∑ajΦiHΦj=0j≠iai(Ei?λ)+∑ajΦiHΦj=0j≠i?H00?EH01LH0jL??a0??0????????H10H11?ELH1jL??a1??0?(H?EI)a=0?LLLLL??L?=?L?Ha=Ea???????Hj0LLHjj?EL??aj??0????????LLLLL??L??L?本征值問題CIMatrixElementsH=ΦHΦijijH=0ijIfФi與Фj具有不同的自旋，<α
6、β>=0aΦHΦ=φhφ+∑(φφφφ?φφφφ0iiai
7、jajijjajabΦHΦ=φφφφ?φφφφ0ijijabijbaφhφ+∑(φφφφ?φφφφ=φFφiaijajijjaiaj將MO表示為AO的線性組合MMφihφj=∑∑cαicβjχαhχβαβMMMMφiφjφkφl=∑∑∑∑cαicβjcγkcδlχαχβχγχδ~M8αβγδφiφjφkφl=∑∑cαi(∑cβj(cγk(∑cδlχαχβχγχδ~M5αγβδSizeoftheCImatrixHOwith6-31G(d)210電子，38自旋軌道?10??28??????=n個電子激發(fā)到空軌道?
8、????n??n?10????102838!總數(shù)∑?????????=n?n??n?10!(38?10)!減少個數(shù)：自旋考慮,對稱性考慮7536400FullCI(完全CI)包括所有的組態(tài)(行列式)包括所有電子相關(guān)N電子，M基函數(shù)組態(tài)個數(shù)：M!(M+1)!NumberofCSFs=?N??N??N??N???!?+1??M??!?M?+1?!?2??2??2??2?對HO6-31G~30×106(N=10,M=19)26-311G(2d,2p)~106×109(N=10,M=41)對HO2FullCI應(yīng)用：f
9、orDZP24基函數(shù)451681246行列式實驗值相比：~0.2a.u(~125kcal/mol)FullCI:沒有實際應(yīng)用意義，標(biāo)志性！TruncatedCImethodsCIS:包含所有單重激發(fā)態(tài)行列式aΦFΦ=0Brillouins定理0i基態(tài)：E＝ECISHFCID：包含所有雙重激發(fā)CISD：包含所有單雙重激發(fā)~M6CISDT：S,D,T~M8CISDTQ:S,D,T,Q~M10E≈ECIS
