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ANEWSEMIEMPIRICALMETHODFORELECTRONICSTRUCTURE By YA-WENHSIAO ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 1999 Tomydear father, littlesister,Jing-Wen, husband,Magnus, andtothememoryofmydearmother ACKNOWLEDGMENTS Iwouldliketothankmyadvisor,ProfessorMichaelC.Zerner,forbringingthis challengingprojecttomyattention,providinggreathelpduringmyyearsofstudy, andmanyvaluablesuggestionstomythesis. Manythankstothemembersofmycommittee-ProfessorsN.YngveOhrn,John R.Sabin,PhilipJ.Brucat,andNigelG.J.Richards-fortheircommentsonmythesis, whichhavebeenmosthelpful. SpecialthankstoProfessorHendrikJ.Monkhorstforbeingwillingtostandin asexaminerduringbothmyoralandfinaldefenses. I greatly appreciate the daily advice and friendship ofDrs. Marshall Cory, JunqiangSun,andAjithPerera,sinceIjoinedQTP. Immenseappreciationisdedicatedtomyhusband,Magnus,forallhissupport, discussion,andlove. AlsoIthankmyfatherandsisterfortheirconstantencourage- ment,understanding,andcomfort. WithoutthemIsimplycannotfinishanything. TABLEOFCONTENTS page ACKNOWLEDGMENTS iii ABSTRACT vii CHAPTERS 1 INTRODUCTION 1 2 THEORYREVIEW 5 2.1 TheMolecularProblem 5 2.1.1 Time-independentSchrbdingerEquation 5 2.1.2 Born-OppenheimerApproximation 6 2.1.3 VariationalPrinciple 7 2.1.4 TheHartree-FockMethodforMolecules 8 2.1.5 Koopmans’Theorem 13 2.1.6 ElectronCorrelation 15 2.2 SemiempiricalMethods 16 2.2.1 HiickelandExtendedHiickelMethods 17 2.2.2 SemiempiricalSCFMOMethodsoftheZDOType 20 2.2.3 ParameterizationfortheINDOMethod 30 2.2.4 GeneralRemarks 41 3 XINDO 44 3.1 Features 44 3.2 DetailsofBuildingXINDO 46 3.2.1 ComparisonwithPreviousModels 46 3.2.2 IntegralbyIntegral 49 3.2.3 DetailsoftheParameterization 63 3.2.4 SimilarWorkintheField 71 4 PARAMETERSANDOTHERRESULTS 76 IV page 4.1 Parameters 7g 4.2 TestCases 81 4.2.1 GeometryOptimization 81 44..22..32 CO33H3+ ; ; ; 8832 5 CONCLUDINGREMARK 85 REFERENCES 88 BIOGRAPHICALSKETCH 92 V AbstractofDissertation PresentedtotheGraduateSchooloftheUniversityofFlorida inPartialFulfillmentoftheRequirementsforthe DegreeofDoctorofPhilosophy ANEWSEMIEMPIRICALMETHODFORELECTRONICSTRUCTURE By Ya-WenHsiao 1999 Chairman: MichaelC.Zerner MajorDepartment: Chemistry Amodifiedsemiempiricalmolecularorbitalmethod, XINDO, isdevelopedat theINDOlevel. ThecommonlyappliedGoeppert-Mayer-Sklarapproximationisno longer included, and ashort range repulsive term, the effective core potential, is introducedtocompensatethepenetrationeffectwhichcauseserrorsincalculating moleculargeometries. TheXINDOHamiltonianisconstructedovertheSlatertype functions. DuringeachSCFcycle,wesolvethesecularequationwithnon-identity overlapmatrix. Inthisway,weincorporatetheoverlapintotheXINDOmethod.This improvesonthegeometrycalculations, andtheenergydescriptionofantibonding molecularorbitals. Multi-centertermsarealsoadded by both modifyingtheoff- diagonalpart ofthe STO Hamiltonianrepresentation, and indirectlythroughthe SCFprocedure. VI TheXINDOmodelhasbeen implementedforH, C, N, andOwhicharethe mainconstituentsofmostoftheorganicmolecules. Themodelcanbeappliedto calculateelectronicexcitationsandmoleculargeometriesbyusingthesemiempirical two-electronintegralswhichareconventionallyusedonlyforcalculatingspectra. The resultsofthecalculatedgeometriesarequitesatisfactory,andthecalculatedcharge distributionsandinter-atomicanglesareimprovedthroughtheinclusionofmulti- centerintegrals. CHAPTER 1 INTRODUCTION Afterseveral decades, the development ofelectronicstructurecomputational techniqueshasbecomequitemature. Abinitiomethodsprovideaccurateresultsfor smallermolecularsystems,especiallyforgroundstateproperties. However,whenit comestosystemsofbiologicalorpharmacologicalsignificance, abinitiotreatment becomesprohibitiveduetothecomputationaldemandsthatarisefromtheincrease inthenumberofelectrons. Moreover,areasonabledescriptionoftheexcitedstates ofmoleculesisstilldifficulttoachieve. However,itispossibletodaytouseabinitio methodstodoexpensivecalculationstoobtainapproximateexcitedstatedescriptions forsmall-sizedmolecules. Nevertheless, abinitiomethodsarestillnotapplicablein practicalstudies involvinglargesystems. Forexample, thestudy ofthe primary electron transfermechanismofbacterialphotosynthesisisanactivesubject. The electronmovesfromthespecialpairtoabacteriopheophytin-6within3psandhence makesexperimentalinvestigationsdifficult. Sincetheentireproteincomplexconsists ofmorethan10,000heavyatoms,itisimpracticaltouseabinitioquantummechanics fortheoreticalpredictions. 1 2 Semiempiricalelectronicstructuremethods,ontheotherhand,offeranalter- nativewayoftreatingtheelectronicstructuresoflargesystemsusingquantumme- chanics. Mostofthelargeproteinsorcomplexcompoundsconsistofsmaller-sized functionalgroupsinwhichindividualmolecularpropertiesareconserved. Basedon thesesmallerorganicmoleculesmanysemiempiricalmethodsareparameterizedtofit theexperimentaldataofthetheseproperties. Thisoffersanadvantagetosemiempir- icalmethodsinthattheyareabletodescribeallclassesofmoleculesaveragelywell forgeneralpurposes. Thedisadvantageofusingthesemiempiricalmethodsisthat calculationsofelectronicspectraarenotavailableinmostofthemethods,andthe methodswhichareabletocalculatespectracannotingeneralbeusedtocalculate moleculargeometry. Therefore,thefewmethodsforcalculatingelectronicexcitations donotgivemeaningfulgroundstatepotentialenergysurfaces,nottomentionexcited statespotentialenergysurfaces. Themotivationofthisthesisistofindasemiempiricalmethodwhichcanyield reasonablemoleculargeometriesaswellaselectronicspectra. Theremayarisetwoquestionstothismotivation. Firstofall,whydowechoose semiempiricalmethods? Becausewewanttohaveamethodwhichcanhelpinour studies on bigmolecularsystems, and as it has been stated previously, ab initio methodsarestillrestrictedtosmallermolecules. Thesecondquestionis: whydo webothertohave amethodwhich ismulti-purposed? The moststraightforward answeristhatsuchamethodismoreconvenientforuserstouseforcalculationsof allproperties,insteadofchangingfrommethodtomethodonlybecausetherange 3 ofapplicabilityofeachmethodsislimited.Anotheradvantageisthatthecalculated propertiesareconsistent. Thegroundstatepotentialenergysurfaceobtainedfrom suchmethodwillbecorrectwithintheaccuracyofthemethod,andtheelectronic excitationswillalsobegood. Thenthenextpossiblestepistocreatetheexcited statepotentialenergysurfacebasedonthegroundstatepotentialsurfaceandthe electronicexcitations. Withsuchamethodonemayimaginethatitbecomespossible tostudytheexcitedstatesofasystemas,e.g., thephotosynthesisreactioncenter mentionedpreviously. Yet, thereareotherproblemsexistinginsemiempiricalmethods, such asthe difficultyinobtainingcorrectconformationalstructures,rotationalbarriers,binding energies,etc.. Thismakesthesemiempiricalmethodsopentofurtherimprovement. Hencewewillattempttodesignthenewmethodtoimprovetheseshortcomingsas theybecomeknown. Manyassumptionshavebeenmadeforsemiempiricalmethodsinorderforthem toyieldfastandcorrectanswerswithlowcost. Inthenewmethod,however,wewill bringbackmoreofthephysicsthathasbeenomittedinearliersemiempiricalmeth- ods. Moreintegralsmayneedtobeadded,butthismustbedonewithgreatcareso thatwewillnotdestroytheadvantageofthesemiempiricalmethods. Wefirstreview themostcommonlyusedsemiempiricalmethods: theZDO(zerodifferentialoverlap) typemethodsandtheEHT (extendedHiickeltheory). Especiallytheassumptions behindthemethodsneedtobeunderstoodandtheinvalidityre-examined. Second,