多参考态微扰理论大小一致性的数值研究(英文).docx

多参考态微扰理论大小一致性的数值研究(英文)
NumericalStudyofConsistencybetweenDifferentOrdersofPerturbationTheoryinMulti-ReferenceConfigurationInteractionCalculations
Introduction:
Incomputationalchemistry,themulti-referenceconfigurationinteraction(MRCI)methodisacommonlyusedmethodtocalculatetheelectronicstructureofmolecules.Itisespeciallyusefulformoleculeswithopen-shellelectronicconfigurationsorinthepresenceofstrongcorrelationeffects.However,MRCIcalculationsbecomecomputationallyexpensiveasthesizeofthesystemincreases,anditisnotalwaysfeasibletoperformcalculationsatthehighestleveloftheory.Toaddressthisproblem,perturbationtheory(PT)canbeusedtoextrapolateenergiesfromlowertohigherlevelsoftheory.Thisapproachisknownasmulti-referencePT(MRPT).Inthispaper,weinvestigatetheconsistencybetweendifferentordersofPTinMRCIcalculations.
Theory:
TheMRPTmethodcanbedescribedasfollows.Thetotalenergyofasystemcanbeexpandedintermsofapowerseriesinaperturbationparameter,λ:
E(λ)=E^{(0)}+λE^{(1)}+λ^2E^{(2)}+λ^3E^{(3)}+...
whereE^{(k)}isthek-thorderPTcorrectiontotheenergy.Foramulti-configurationalreferencewavefunction,thezerothordertermE^{(0)}isthesumoftheenergiesofthereferenceconfigurations.ThefirstordercorrectionE^{(1)}istheenergydifferencebetweenthereferenceconfigurationsandthesinglyexcitedconfigurations.ThesecondordercorrectionE^{(2)}istheenergydifferencebetweenthesinglyexcitedanddoublyexcitedconfigurations,andsoon.
ThedifferentordersofPThavedifferentlevelsofcomplexityandcomputationalcost.ThezerothordertermE^{(0)}isobtainedfromasimpleenergycalculationusingthereferencewavefunction.ThefirstordercorrectionE^{(1)}canbecalculatedusingthelinearresponsemethod,whichinvolvessolvingasetoflinearequations.ThesecondordercorrectionE^{(2)}requiressolvinganon-linearequation,whichismorecomputationallyexpensive.HigherordersofPTbecomeincreasinglydifficultandcomputationallyexpensivetocalculate.
InMRCIcalculations,thesize-consistencyproblemariseswhentheenergiesoftwonon-interactingsystemsarecombined.Thisproblemcanbeaddressedbyintroducin