Variational Monte Carlo and Configurational Interaction Stud

The $C_{60}$ molecule and its fragments are studied using Configuration Interaction (CI) and Variational Monte Carlo (VMC) techniques, within the Hubbard model. Using benzene as a test case, we compare the results of the approximate calculations with exact

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aVARIATIONALMONTECARLOANDCONFIGURATIONINTERACTIONSTUDIESOFC60ANDITSFRAGMENTS1BhargaviSrinivasan2,S.Ramasesha2,4andH.R.Krishnamurthy3,42SolidStateandStructuralChemistryUnitIndianInstituteofScience,Bangalore560012,India3DepartmentofPhysicsIndianInstituteofScience,Bangalore560012,India4JawaharlalNehruCentreforAdvancedScienti cResearchJakkurCampus,Bangalore560064,India

The $C_{60}$ molecule and its fragments are studied using Configuration Interaction (CI) and Variational Monte Carlo (VMC) techniques, within the Hubbard model. Using benzene as a test case, we compare the results of the approximate calculations with exact

Abstract

The $C_{60}$ molecule and its fragments are studied using Configuration Interaction (CI) and Variational Monte Carlo (VMC) techniques, within the Hubbard model. Using benzene as a test case, we compare the results of the approximate calculations with exact

1Introduction

ThediscoveryofC60,anewallotropeofcarbon,byKrotoetal[1]anditsbulksynthesisbyKratschmeretal[2]havebeenamongstthemostexcitingrecentdevelopmentsinchemistryandphysics.C60anditscompoundsshowexoticphysicalandchemicalproperties.AlkalidopedcompoundsofC60aresuperconducting,withRb1.5Cs1.5C60havingasuperconductingtransitiontem-peratureof32K[3].ThecompoundC60 TDAE(TDAE=tetrakisdimethylaminoethylene)isanorganicferromagnetwithafairlylargeCurietempera-tureof16.5K[4,5].

Todevelopmodelsforpersephenomenasuchasthese,itisessentialtohaveareliableunderstandingoftheelectronicstructureofthebasicbuildingblocksofthesesystems.Thecarbonatomsinfullerenesareinanearlysp2hybridcon gurationwithahalf– lledpπ–likeorbitaldirectedradiallyandin-volvedinextendedconjugation.Electronicstructurestudiesonconjugatedor-ganicsystemshavebroughtoutclearlytheimportanceofelectroncorrelationstoaccountformanyoftheobservedspectroscopicandrelatedproperties[6].Explicitlyincludingelectroncorrelationsisaformidablechallengeevenatthelevelofasinglebuckyball.Itisreasonabletohopethataproperstudyofasinglebuckyballanditsfragmentswillshedlightontheesotericelectronicpropertiesofthesesystemsinthebulk.

Itwouldbeinterestingtotryandunderstandthepropertiesofthefullbuckyballintermsofitsfragments.Firstly,forsmallenoughfragments,itis

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The $C_{60}$ molecule and its fragments are studied using Configuration Interaction (CI) and Variational Monte Carlo (VMC) techniques, within the Hubbard model. Using benzene as a test case, we compare the results of the approximate calculations with exact

possibletoperformexactcalculationsthatallowustosystematicallychecktheapproximatemethods.TheelectronicstructuresofthefragmentsareexpectedtobeusefulininterpretingtheelectronicstructureandgeometryofC60.Inthisarticle,westudythegroundstatepropertiessuchasbondorders,charge–chargeandspin–spincorrelationfunctionsofsomefragmentsofC60usingcon gurationinteraction(CI)techniquesandtheVariationalMonteCarlo(VMC)method.WereporttheresultsofourVMCcalculationsonthefullbuckyballwithintheHubbardmodel,withandwithoutbond-alternation.ThesimplestdescriptionoftheelectronicstructureofC60isfoundwithintheframeworkoftheHuckelpicture,whereinanon-zerotransferintegralisin-troducedbetweenthepπ–likeorbitalsonnearest–neighbouratoms(sites).Theresultingmolecularorbitals(MOs)haveahighdegreeofdegeneracyduetotheicosahedralsymmetryofthemolecule.NeutralC60hasa ve-folddegen-eratesetofhighestocccupiedmolecularorbitals(HOMOs)andathree-folddegeneratesetoflowestunoccupiedmolecularorbitals(LUMOs).ThehighdegeneracyoftheMOshasbeenthefocalpointofthediscussionoftheelec-tronicstructureofthesesystems.Forinstance,ina rstapproximation,thedegeneracyoftheLUMOsisconsideredessentialtorationalizetheexistenceofferromagneticexchangebetweentwomonoanionsofC60[7].

TheminimalinteractingdescriptionforC60isgivenbythesinglebandHubbardmodelwhichincorporatesonlyanon-siteelectron–electronrepulsionUbesidestheone-electronpartgivenbytheHuckelpicture.Drastictruncationoftheelectronrepulsiontoanon–siteinteractionisjusti ableinametalwhere

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The $C_{60}$ molecule and its fragments are studied using Configuration Interaction (CI) and Variational Monte Carlo (VMC) techniques, within the Hubbard model. Using benzene as a test case, we compare the results of the approximate calculations with exact

themobileconductionelectronsleadtoshortDebye–Huckelscreeninglengths.Inmoleculesitisstrictlynecessarytoincludeextendedrangeinteractions,atleastatthelevelofthePPPmodel,becauseofine cientscreening.However,obtainingreliableresultsevenforsuchmodelsisdi cultandwestudythesimplerHubbardmodelasa rststepinunderstandingcrucialqualitativee ectsofcorrelationsinmolecularsystemslikeC60anditsfragments.Exactdiagonalizationtechniquesareusefulforsmallsystems(withlessthanabout14sitesatpresent)butareimpracticalforlargesystemsbecauseoftheexplodingdimensionofthebasiswithincreasingsystemsize[8].Therefore,approximateapproachestotheproblemareinescapableforlargersystems.However,exactdiagonalizationprovidesastrongcheckonanynovelapproximationscheme.Amongstapproximatetechniques,perturbationtheorygivesfairlyreliableresultsatlimitingvaluesofthemodelparametersbutbreaksdownforinter-mediatebutrelevantvaluesoftheparameters[9].AnotherequallywidelyusedapproximateapproachhasbeenthevariationalapproachwiththeGutzwillerwavefunction(GWF)asthetrialfunctionofchoiceforHubbardmodels[10].Inthisapproach,avariationalparameterg(0≤g≤1)isintroducedandtheweightofacon gurationinthesiter …… 此处隐藏：17501字，全部文档内容请下载后查看。喜欢就下载吧 ……