Basis Sets | Gaussian.com

Most methods require a basis set be specified; if no basis set keyword is included in the route section, then the STO-3G basis will be used. News BenedettaMennucciAwardedERCGrant JapaneseTranslationofExpChem3 Scuseria:AwardfromRSC Caricato:NSFCareerAward JPCTop25Articles GPUs&G16 Products Gaussian16 GaussView6 Linda GMMX ExploringChemistry Support TechnicalSupport Information WhitePapers ContactTechnicalSupport GaussianTutorialVideos CreatingUV/VisiblePlots 中文技术支持 FAQ&Tips AntiferromagneticCoupling GaussianMaintenanceProgram G16ReleaseNotes QST2TransitionStateOptimizations PC/MacProductRegistration G16KeywordList TeachingPhysicalChemistry G16UsersReference ComparingNMRMethods HistoricalDocuments G16IOpsReference VibrationalAnalysisinGaussian G09Citation GaussView6Help ThermochemistryinGaussian VersionsofGaussian LindaManual(gzipped) VisualizingResultsonDifferentMachines G09Keywordpages(gzippedtararchive) InstallationInstructions StudyingChirality GaussView5Reference(zipped) InvestigatingLargeMoleculeswithONIOM OurPeople Orders/Contact ProductPricing ShippingandHandling TermsandConditions OrderForm SalesAgents ContactUs BasisSets DescriptionPurevs.CartesianDensityFitting Description Mostmethodsrequireabasissetbespecified;ifnobasissetkeywordisincludedintheroutesection,thentheSTO-3Gbasiswillbeused.Theexceptionsconsistofafewmethodsforwhichthebasissetisdefinedasanintegralpartofthemethod;theyarelistedbelow: Allsemi-empiricalmethods,includingZIndoforexcitedstates. Allmolecularmechanicsmethods. Compoundmodelchemistries:allGn,CBSandW1methods. BasissetsotherthanthoselistedheremayalsobeinputtotheprogramusingtheExtraBasisandGenkeywords.TheChkBasiskeywordindicatesthatthebasissetistoreadfromthecheckpointfile(definedviathe%Chkcommand).Seetheindividualdescriptionsofthesekeywordsfordetails. ThefollowingbasissetsarestoredinternallyintheGaussian16program(seereferencescitedforfulldescriptions),listedbelowbytheircorrespondingGaussian16keyword(withtwoexceptions): STO-3G[Hehre69,Collins76] 3-21G[Binkley80a,Gordon82,Pietro82,Dobbs86,Dobbs87,Dobbs87a] 6-21G[Binkley80a,Gordon82] 4-31G[Ditchfield71,Hehre72,Hariharan74,Gordon80] 6-31G[Ditchfield71,Hehre72,Hariharan73,Hariharan74,Gordon80,Francl82,Binning90,Blaudeau97,Rassolov98,Rassolov01] 6-31G†:Gaussian16alsoincludesthe6-31G†and6-31G‡basissetsofGeorgePeterssonandcoworkers,definedaspartofvariousCompleteBasisSetmethods[Petersson88,Petersson91].Theseareaccessedviathe6-31G(d')and6-31G(d',p')keywords(respectively).Singleordoublediffusefunctionsmayalsobeadded,ascanffunctions:e.g.,6-31+G(d'f). 6-311G:Specifiesthe6-311Gbasisforfirst-rowatomsandtheMcLean-Chandler(12s,9p)→(621111,52111)basissetsforsecond-rowatoms[McLean80,Raghavachari80b](notethatthebasissetsforP,S,andClarethosecallednegativeionbasissetsbyMcLeanandChandler;theseweredeemedtogivebetterresultsforneutralmoleculesaswell),thebasissetofBlaudeauandcoworkersforCaandK[Blaudeau97],theWachters-Hay[Wachters70,Hay77]allelectronbasissetforthefirsttransitionrow,usingthescalingfactorsofRaghavachariandTrucks[Raghavachari89],andthe6-311GbasissetofMcGrath,Curtissandcoworkersfortheotherelementsinthethirdrow[Binning90,McGrath91,Curtiss95].NotethatRaghavachariandTrucksrecommendbothscalingandincludingdiffusefunctionswhenusingtheWachters-Haybasissetforfirsttransitionrowelements;the6-311+Gformmustbespecifiedtoincludethediffusefunctions.MC-311Gisasynonymfor6-311G. D95V:Dunning/Huzinagavalencedouble-zeta[Dunning77]. D95:Dunning/Huzinagafulldoublezeta[Dunning77]. SHC:D95Vonfirstrow,Goddard/SmedleyECPonsecondrow[Dunning77,Rappe81].AlsoknownasSEC. CEP-4G:Stevens/Basch/KraussECPminimalbasis[Stevens84,Stevens92,Cundari93]. CEP-31G:Stevens/Basch/KraussECPsplitvalance[Stevens84,Stevens92,Cundari93]. CEP-121G:Stevens/Basch/KraussECPtriple-splitbasis[Stevens84,Stevens92,Cundari93].NotethatthereisonlyoneCEPbasissetdefinedbeyondthesecondrow,andallthreekeywordsareequivalentfortheseatoms. LanL2MB:STO-3G[Hehre69,Collins76]onfirstrow,LosAlamosECPplusMBSonNa-La,Hf-Bi[Hay85,Wadt85,Hay85a]. LanL2DZ:D95Vonfirstrow[Dunning77],LosAlamosECPplusDZonNa-La,Hf-Bi[Hay85,Wadt85,Hay85a]. SDD:D95uptoAr[Dunning77]andStuttgart/DresdenECPsontheremainderoftheperiodictable[Fuentealba82,Szentpaly82,Fuentealba83,Stoll84,Fuentealba85,Wedig86,Dolg87,Igel-Mann88,Dolg89,Schwerdtfeger89,Dolg89a,Andrae90,Dolg91,Kaupp91,Kuechle91,Dolg92,Bergner93,Dolg93,Haeussermann93,Dolg93a,Kuechle94,Nicklass95,Leininger96,Cao01,Cao02].TheSDD,SHF,SDF,MHF,MDF,MWBformsmaybeusedtospecifythesebasissets/potentialswithinGenbasisinput.Notethatthenumberofcoreelectronsmustbespecifiedfollowingtheform(e.g.,MDF28fortheMDFpotentialreplacing28coreelectrons).OldSDDrequeststhepreviousdefault. SDDAll:SelectsStuttgartpotentialsforZ>2. cc-pVDZ,cc-pVTZ,cc-pVQZ,cc-pV5Z,cc-pV6Z:Dunning'scorrelationconsistentbasissets[Dunning89,Kendall92,Woon93,Peterson94,Wilson96](double,triple,quadruple,quintuple-zetaandsextuple-zeta,respectively).Thesebasissetshavehadredundantfunctionsremovedandhavebeenrotated[Davidson96]inordertoincreasecomputationalefficiency. Thesebasissetsincludepolarizationfunctionsbydefinition.Thefollowingtableliststhevalencepolarizationfunctionspresentforthevariousatomsincludedinthesebasissets: Atoms   cc-pVDZ   cc-pVTZ   cc-pVQZ   cc-pV5Z   cc-pV6Z H   2s,1p   3s,2p,1d   4s,3p,2d,1f   5s,4p,3d,2f,1g   6s,5p,4d,3f,2g,1h He   2s,1p   3s,2p,1d   4s,3p,2d,1f   5s,4p,3d,2f,1g   notavailable Li-Be   3s,2p,1d   4s,3p,2d,1f   5s,4p,3d,2f,1g   6s,5p,4d,3f,2g,1h   notavailable B-Ne   3s,2p,1d   4s,3p,2d,1f   5s,4p,3d,2f,1g   6s,5p,4d,3f,2g,1h   7s,6p,5d,4f,3g,2h,1i Na-Ar   4s,3p,1d   5s,4p,2d,1f   6s,5p,3d,2f,1g   7s,6p,4d,3f,2g,1h   notavailable Ca   5s,4p,2d   6s,5p,3d,1f   7s,6p,4d,2f,1g   8s,7p,5d,3f,2g,1h   notavailable Sc-Zn   6s,5p,3d,1f   7s,6p,4d,2f,1g   8s,7p,5d,3f,2g,1h   9s,8p,6d,4f,3g,2h,1i   notavailable Ga-Kr   5s,4p,2d   6s,5p,3d,1f   7s,6p,4d,2f,1g   8s,7p,5d,3f,2g,1h   notavailable ThesebasissetsmaybeaugmentedwithdiffusefunctionsbyaddingtheAUG-prefixtothebasissetkeyword(ratherthanusingthe+and++notation—seebelow). BasissetsofAhlrichsandcoworkers:theSV,SVP,TZV,TZVPkeywordsrefertotheinitialformationsofthesplitvalenceandtriplezetabasissetsfromthisgroup[Schaefer92,Schaefer94].Thenewerredefinitionsofthesebasissetsin[Weigend05,Weigend06]arerequestedwiththekeywordsDef2SV,Def2SVP,Def2SVPP,Def2TZV,Def2TZVP,Def2TZVPP,Def2QZV,Def2QZVP,Def2QZVPP,andQZVP.NotethatDef2SVPPcorrespondstothe“def2-SV(P)”basissetin[Weigend05];allothernamesfollowthoseinthepaperwiththehyphenremoved. MIDI!ofTruhlarandcoworkers[Easton96].TheMidiXkeywordisusedtorequestthisbasisset. EPR-IIandEPR-III:ThebasissetsofBarone[Barone96a]whichareoptimizedforthecomputationofhyperfinecouplingconstantsbyDFTmethods(particularlyB3LYP).EPR-IIisadoublezetabasissetwithasinglesetofpolarizationfunctionsandanenhancedspart:(6,1)/[4,1]forHand(10,5,1)/[6,2,1]forBtoF.EPR-IIIisatriple-zetabasissetincludingdiffusefunctions,doubled-polarizationsandasinglesetoff-polarizationfunctions.Alsointhiscasethes-partisimprovedtobetterdescribethenuclearregion:(6,2)/[4,2]forHand(11,7,2,1)/[7,4,2,1]forBtoF. UGBS:TheuniversalGaussianbasissetofdeCastro,Jorgeandcoworkers[Silver78,Silver78a,Mohallem86,Mohallem87,daCosta87,daSilva89,Jorge97,Jorge97a,deCastro98].Additionalpolarizationfunctionsmaybeaddedbyincludingasuffixtothiskeyword: UGBSnP|V|O wherenisanintegerindicatingwhethertoadd1,2or3polarizationfunctionsforeachfunctioninthenormalUGBSbasisset.Theseconditemisacodeletterindicatingwhichfunctionshouldbeaugmentedpolarizationfunctions:Paddsthemtoallfunctions,Vaddsthemtoallvalencefunctions,andOrequeststheschemeusedinGaussian03(seebelow).Forexample,theUGBS1Pkeywordrequeststhisbasissetwithoneadditionalpolarizationfunctiontoallorbitals,andUGBS2Vaddstwoadditionalpolarizationfunctiontoallvalenceorbitals. TheOsuffixaddsthesamefunctionsastheUGBSnPkeywordsinGaussian03.UGBS1Oaddsapfunctionforeachs,adfunctionforeachp,andsoon;UGBS2Oaddsapanddfunctionforeachs,adandffunctionforeachp,andUGBS3Oaddsap,dandfforeachs,etc. Diffusefunctionsmaybeaddedasusualwith+or++;thefirstofthesemaybespecifiedas2+toaddtwodiffusefunctionsforheavyatoms. MTSmallofMartinanddeOliveira,definedaspartoftheirW1method(seetheW1Ukeyword)[Martin99]. TheDGDZVP,DGDZVP2andDGTZVPbasissetsusedinDGauss[Godbout92,Sosa92]. CBSB7:Selectsthe6-311G(2d,d,p)basissetusedbyCBS-QB3highaccuracyenergymethod[Montgomery99].Thenotationspecifiestwoadditionaldpolarizationfunctionsonsecondrowsatoms,onedfunctiononfirstrowatomsandapfunctiononhydrogens(notethatthisthree-fieldpolarizationfunctionsyntaxisnotsupportedbyGaussian16). AddingPolarizationandDiffuseFunctions Singlefirstpolarizationfunctionscanalsoberequestedusingtheusual*or**notation.Notethat(d,p)and**aresynonymous—6-31G**isequivalentto6-31G(d,p),forexample—andthatthe3-21G*basissethaspolarizationfunctionsonsecondrowatomsonly.The+and++diffusefunctions[Clark83]areavailablewithsomebasissets,asaremultiplepolarizationfunctions[Frisch84].Thekeywordsyntaxisbestillustratedbyexample:6-31+G(3df,2p)designatesthe6-31Gbasissetsupplementedbydiffusefunctions,3setsofdfunctionsandonesetofffunctionsonheavyatoms,andsupplementedby2setsofpfunctionsonhydrogens. WhentheAUG-prefixisusedtoadddiffusefunctionstothecc-pV*Zbasissets,onediffusefunctionofeachfunctiontypeinuseforagivenatomisadded[Kendall92,Woon93].Forexample,theAUG-cc-pVTZbasisplacesones,oned,andonepdiffusefunctionsonhydrogenatoms,andoned,onep,oned,andonefdiffusefunctionsonBthroughNeandAlthroughAr. Thereareseveraloptionsforaugmentingthecc-pV*Zbasissetswithdiffusefunctions: spAug-cc-pV*Zaugmentswithsandpfunctionsonly,includingsfunctionsonHandHe. dAug-cc-pV*Zaugmentswithwith2shellsofeachangularmomentuminsteadofone. Truhlar’s“calendar”basissetvariations[Papajak11]areavailable.Thenamingofthisseriesofbasissetscomesfromthefactthatthecc-pV*ZbasissetswithaddedpolarizationfunctionsareknownastheAug-cc-pV*Z.Truhlarnotedthat“Aug”isalsoanabbreviationforthemonthofAugustinEnglish,soheproposednewaugmentationschemesforthecc-pV*Zbasissets,alsonamedaftermonthsoftheyear.TheyareconstructedbyremovingdiffusefunctionsfromtheAugbasissets.Forexample,theJul-cc-pV*ZbasissetsremovethediffusefunctionfromHandHefromAug-cc-pV*Z.Jun-cc-pV*Zalsoremovesthehighestangularmomentumdiffusefunctionfromallotheratoms,May-cc-pV*Zremovesthetwohighestangularmomentumfunctions,andApr-cc-pV*Zremovesthethreehighestangularmomentumfunctions.  Nevertheless,bydefault,atleastsandpdiffusefunctionsarealwaysincludedinthesebasissets.Thisservestoavoidsomeinherentinconsistencies,butitdiffersfromTruhlarandcoworkers'originaldefinitions.UsetheformsTJul,TJun,andsoontospecifytheoriginalversionswherethelimitisappliedunconditionally:e.g.,TMay-cc-ppVDZincludesonlyadiffusesfunctiononClbutbothdiffusesandpfunctionsonFeandBr,whileMay-cc-ppVDZhasdiffusesandpfunctionsonalloftheseatoms. Addingasinglepolarizationfunctionto6-311G(i.e.6-311G(d))willresultinonedfunctionforfirstandsecondrowatomsandoneffunctionforfirsttransitionrowatoms,sincedfunctionsarealreadypresentforthevalenceelectronsinthelatter.Similarly,addingadiffusefunctiontothe6-311Gbasissetwillproduceones,onep,andoneddiffusefunctionsforthird-rowatoms. WhenafrozencorecalculationisdoneusingtheD95basis,boththeoccupiedcoreorbitalsandthecorrespondingvirtualorbitalsarefrozen.ThuswhileaD95**calculationonwaterhas26basisfunctions,anda6-31G**calculationonthesamesystemhas25functions,therewillbe24orbitalsusedinafrozencorepost-SCFcalculationinvolvingeitherbasisset. Thefollowingtablelistspolarizationanddiffusefunctionavailabilityandtherangeofapplicabilityforeachbuilt-inbasissetinGaussian16: BasisSet   Appliesto   PolarizationFunctions   DiffuseFunctions 3-21G   H-Xe     + 6-21G   H-Cl   *or**   4-31G   H-Ne   *or**   6-31G   H-Kr   through(3df,3pd)   +,++ 6-311G   H-Kr   through(3df,3pd)   +,++ D95   H-ClexceptNaandMg   through(3df,3pd)   +,++ D95V   H-Ne   (d)or(d,p)   +,++ SHC   H-Cl   *   CEP-4G   H-Rn   *(Li-Aronly)   CEP-31G   H-Rn   *(Li-Aronly)   CEP-121G   H-Rn   *(Li-Aronly)   LanL2MB   H-La,Hf-Bi     LanL2DZ   H,Li-La,Hf-Bi     SDD,SDDAll   allbutFrandRa     cc-pVDZ   H-Ar,Ca-Kr   includedindefinition   addedviaAUG-prefix(H-Ar,Sc-Kr) cc-pVTZ   H-Ar,Ca-Kr   includedindefinition   addedviaAUG-prefix(H-Ar,Sc-Kr) cc-pVQZ   H-Ar,Ca-Kr   includedindefinition   addedviaAUG-prefix(H-Ar,Sc-Kr) cc-pV5Z   H-Ar,Ca-Kr   includedindefinition   addedviaAUG-prefix(H-Na,Al-ArSc-Kr) cc-pV6Z   H,B-Ne   includedindefinition   addedviaAUG-prefix(H,B-O) SV   H-Kr     SVP   H-Kr   includedindefinition   TZVandTZVP   H-Kr   includedindefinition   QZVPandDef2   H-La,Hf-Rn   includedindefinition   MidiX   H,C-F,S-Cl,I,Br   includedindefinition   EPR-II,EPR-III   H,B,C,N,O,F   includedindefinition   UGBS   H-Lr   UGBS(1,2,3)P   +,++,2+,2++ MTSmall   H-Ar     DGDZVP   H-Xe     DGDZVP2   H-F,Al-Ar,Sc-Zn     DGTZVP   H,C-F,Al-Ar     CBSB7   H-Kr   includedindefinition   +,++ STO-3Gand3-21Gaccepta*suffix,butthisdoesnotactuallyaddanypolarizationfunctions. Purevs.Cartesian Thefollowingadditionalkeywordsareusefulinconjunctionwiththesebasissetkeywords: 5Dand6D:Use5or6dfunctions(purevs.Cartesiandfunctions),respectively. 7Fand10F:Use7or10ffunctions(purevs.Cartesianffunctions),respectively.Thesekeywordsalsoapplytoallhigherfunctions(gandbeyond). IssuesArisingfromPurevs.CartesianBasisFunctions Gaussianusersshouldbeawareofthefollowingpointsconcerningpurevs.Cartesianbasisfunctions: Allofthebuilt-inbasissetsusepureffunctions.Mostalsousepuredfunctions;theexceptionsare3-21G,6-21G,4-31G,6-31G,6-31G†,6-31G‡,CEP-31G,D95andD95V.Theprecedingkeywordsmaybeusedtooverridethedefaultpure/Cartesiansetting.Notethatbasisfunctionsaregenerallyconvertedtotheothertypeautomaticallywhennecessary,forexample,whenawavefunctionisreadfromthecheckpointfileforuseinacalculationusingabasisconsistingoftheothertype[Schlegel95a]. Withinajob,alldfunctionsmustbe5Dor6D,andallfandhigherfunctionsmustbepureorCartesian. WhenusingtheExtraBasis,GenandGenECPkeywords,thebasissetexplicitlyspecifiedintheroutesectionalwaysdeterminesthedefaultformofthebasisfunctions(forGen,theseare5Dand7F).Forexample,ifyouuseageneralbasissettakingsomefunctionsfromthe3-21Gand6-31Gbasissets,purefunctionswillbeusedunlessyouexplicitlyspecify6DintheroutesectioninadditiontoGen.Similarly,ifyouaddbasisfunctionsforatransitionmetalfromthe6-311G(d)basissetviaExtraBasistoajobthatspecifiesthe6-31G(d)basissetintheroutesection,Cartesiandfunctionswillbeused.Likewise,ifyouwanttoaddbasisfunctionsforXefromthe3-21Gbasissettothe6-311basissetviatheExtraBasiskeyword,theXebasisfunctionswillbepurefunctions. DensityFitting Gaussian16providesthedensityfittingapproximationforpureDFTcalculations[Dunlap83,Dunlap00].Thisapproachexpandsthedensityinasetofatom-centeredfunctionswhencomputingtheCoulombinteractioninsteadofcomputingallofthetwo-electronintegrals.ItprovidessignificantperformancegainsforpureDFTcalculationsonmediumsizedsystemstoosmalltotakeadvantageofthelinearscalingalgorithmswithoutasignificantdegradationintheaccuracyofpredictedstructures,relativeenergiesandmolecularproperties.Gaussian16cangenerateanappropriatefittingbasisautomaticallyfromtheAObasis,oryoumayselectoneofthebuilt-infittingsets. Thedesiredfittingbasissetisspecifiedasathirdcomponentofthemodelchemistry,asinthisexample: #BLYP/TZVP/TZVPFit Notethatslashesmustbeusedastheseparatorcharactersbetweenthemethod,basisset,andfittingsetwhenadensityfittingbasissetisspecified. ThefollowingfittingsetskeywordsareavailableinGaussian16: DGA1andDGA2[Godbout92,Sosa92].DGA1isavailableforHthroughXe,andDGA2isavailableforH,HeandBthroughNe. SVPFit[Eichkorn95,Eichkorn97]correspondingtotheSVPbasisset. TZVPFit[Eichkorn95,Eichkorn97]correspondingtotheTZVPbasisset. TheW06fittingsetofAhlrichsandcoworkers[Weigend05,Weigend06],designedforusewiththeSVP,TZV,andQZVPbasissets. Fit:Selectthefittingsetcorrespondingtothespecifiedbasisset.Ifthereisnosuchfittingset,theresultwillproduceanerror. NoFit:Turnofffittingsetuseforthiscalculation.ThiskeywordisusedtooverridetheDensityFitkeywordpresentwithintheDefault.Routefile. Auto:Generateafittingsetautomatically(seebelow). DensityfittingsetscanbegeneratedautomaticallyfromtheAOprimitiveswithinthebasisset.ThisisrequestedusingtheAutofittingsetkeyword.Theprogramautomaticallytruncatesthesetatareasonableangularmomentum:thedefaultisMax(MaxTyp+1,2*MaxVal),whereMaxTypisthehighestangularmomentumintheAObasis,andMaxValisthehighestvalenceangularmomentum.YoucanrequestthatallgeneratedfunctionsbeusedwithAuto=All,orrequestthoseuptoacertainlevelwithAuto=N,whereNisthemaximumangularmomentumretainedinthefittingfunctions.Finally,thePAutoformgeneratesallproductsofAOfunctionsononecenterinsteadofjustsquaresoftheAOprimitives,butthisistypicallymorefunctionsthanareneeded. Bydefault,nofittingsetisused.DensityfittingbasissetsmaybeaugmentedwiththeExtraDensityBasiskeyword,definedinfullwiththeGenkeyword,andoptionallyretrievedfromthecheckpointfile(useChkBasistodoso).TheoptionstotheDensityFitkeywordcanbeusedtocontrolsomeaspectsofthefittingsetusedwithincalculations. DensityfittingcanbemadethedefaultforjobsusingpureDFTfunctionalsbyaddingtheDensityFitkeywordtotheroutesection(-#-)lineintheDefault.Routefile.FittingisfasterthandoingtheCoulombtermexactlyforsystemsuptoseveralhundredatoms(dependingonbasisset),butisslowerthanexactCoulombusinglinearscalingtechniques(whichareturnedonautomaticallywithexactCoulomb)forverylargesystems. Lastupdatedon:17May2021.[G16Rev.C.01] QuickLinks @gaussian