First-principles calculations of the structural, e

arXiv:cond-mat/0301189v1[cond-mat.mtrl-sci]13Jan2003First-principlescalculationsofthestructural,electronic,vibrationalandmagneticpropertiesofC60andC48N12:acomparativestudyRui-HuaXieandGarnettW.BryantAtomicPhysicsDivision,NationalInstituteofStandardsandTechnology,Gaithersburg,MD20899-8423LasseJensenTheoreticalChemistry,MaterialScienceCentre,RijksuniversiteitGroningen,Nijenborgh4,9747AGGroningen,TheNetherlandsJijunZhaoDepartmentofPhysicsandAstronomy,UniversityofNorthCarolinaatChapelHill,ChapelHill,NC27599VedeneH.Smith,Jr.DepartmentofChemistry,Queen’sUniversity,Kingston,ONK7L3N6,Canada(February2,2008)Weperformfirst-principlescalculationsofthestructural,electronic,vibrationalandmagneticpropertiesoftheC48N12azafullereneandC60.FullgeometricaloptimizationshowsthatC48N12ischaracterizedbyseveraldistinguishingfeatures:onlyonenitrogenatomperpentagon,twonitrogenatomspreferentiallysittinginonehexagon,S6symmetry,6uniquenitrogen-carbonand9uniquecarbon-carbonbondlengths.TheMullikenchargeanalysisindicatesthatthedopednitrogenatomsinC48N12existaselectronacceptorsandthree-fourthsofthecarbonatomsaselectrondonors.Elec-tronicstructurecalculationsofC48N12showthatthehighestoccupiedmolecularorbital(HOMO)isadoublydegeneratelevelofagsymmetryandthelowestunoccupiedmolecularorbital(LUMO)isanondegeneratelevelofausymmetry.ThecalculatedbindingenergyperatomandHOMO-LUMOenergygapofC48N12areabout1eVsmallerthanthoseofC60.ForbothC48N12andC60,thetotalenergiescalculatedwithSTO-3G,3-21Gand6-31Gbasissetsdifferfromthe6-31G*basissetresultsbyabout1.5%,0.6%and0.05%,respectively.Becauseofelectroncorrelations,theHOMO-LUMOgapdecreasesabout5eVandthebindingenergyperatomincreasesabout2eV.OurvibrationalfrequencyanalysispredictsthatC48N12hasintotal116vibrationalmodes:58modesareinfrared-active(29doubly-degenerateand29non-degeneratemodes)and58modesareRaman-active(29doubly-degenerateunpolarizedand29non-degeneratepolarized).ItisfoundthatC48N12exhibitseight13Candtwo15NNMR(nuclearmagneticresonance)spectralsignals.Incomparisontoiso-latedcarbonornitrogenatoms,anenhancementinthedipolepolarizabilityisfoundduetothedelocalizedπelectronsinC48N12andC60.Theaveragesecond-orderhyperpolarizabilityofC48N12isabout55%largerthanthatofC60.Inaddition,theeffectsofbasissetsarediscussedindetail,andthedifferentmethodsforcalculatingnuclearmagneticshieldingtensorsarecompared.OurdetailedstudyofC60revealstheimportanceofelectroncorrelationsandthechoiceofbasissetsinthefirst-principlescalculations.Ourbest-calculatedresultsforC60withtheB3LYPhybriddensityfunctionaltheoryareinexcellentagreementwithexperimentanddemonstratethedesiredefficiencyandaccuracyneededforobtainingquantitativeinformationonthestructural,electronicandvibra-tionalpropertiesofthesemolecules.OurresultssuggestthatC48N12haspotentialapplicationsassemiconductorcomponents,nonlinearopticalmaterials,andpossiblebuildingblocksformolecularelectronicsandphotonicdevices.I.INTRODUCTIONGraphiteisastableandabundantsolidformofpurecarbon[1].Inthisform,threevalenceelectronsofeachcarbonatomformthreestrongsp2trigonalbondstothreenearestneighborswithanequaldistanceof0.142nm,whilethefourthvalenceelectronfromdifferentcar-bonatomsinteractsbyweakπbondsperpendiculartosuccessivesheetswithaninter-planedistanceof0.34nm[2].Diamondisanotherslightlylessstableandlessabun-dantcrystallographicformofpurecarbon[1],whereeachcarbonatomiscovalentlybondedtofourneighborsviasp3hybridizationattheapexesofaregulartetrahedron.In1985,afascinatingmolecule,namedC60(atruncatedicosahedronwith20hexagonaland12pentagonalfaces,and60vertices,eachofwhichisattheintersectionoftwohexagonalandonepentagonalfaces)wasdiscoveredbyKrotoetal.[3],andanewformofpurecarbon,namedfullerenes[4],wasborn.Fullerenescancrystallizeinavarietyofthree-dimensionalstructures[5,6],beingmadefromanevennumberofthree-coordinatedsp2carbonatomsthatar-rangethemselvesinto12pentagonalfacesandanynum-ber(1)ofhexagonalfaces[4].Themacroscopicsyn-1thesisofsoot[5],whichcontainsC60andotherfullerenesinlargecompounds,plusthestraightforwardpurificationtechniquesofthesootwhichmakethepurefullerenema-terialsavailable,haveledtoextensivestudiesoffullerenes[7–10,12].Dopedfullereneshavealsoattractedagreatdealofinterestduetotheirremarkablestructural,electronic,opticalandmagneticproperties[7–10,12].Forexample,thedopedfullerenescanexhibitlargethird-orderopti-calnonlinearities[9,10]andbeidealcandidatesaspho-tonicdevicesincludingall-opticalswitching,datapro-cessing,andeyeandsensorprotection[9,10].Anotherexampleisalkali-dopedC60crystals,whichcanbecomesuperconducting[13,14],forexample,atacriticaltem-peratureTc=30K[13].Inadditiontotheendohedraldoping(insidefullerenes)andexohedraldoping(outsidefullerenes),thereisanothertypeofdoping,namedsub-stitutionaldoping,whereoneormorecarbonatomsoffullerenearesubstitutedbyotheratoms[7–12],duetotheuniquestructuralandelectronicpropertiesoffullerenes.Becauseboronandnitrogenbracketcarboninthepe-riodictable,muchattentionhasbeenpaidtoalternateboron-and/ornitrogen-dopedcompounds[7–12].Overthepast10years,boronandnitrogenatomshaveb