Basis set (chemistry) - Wikipedia

Dozens of Gaussian-type orbital basis sets have been published in the literature. ... Basis sets typically come in hierarchies of increasing size, giving a ... Basisset(chemistry) FromWikipedia,thefreeencyclopedia Jumptonavigation Jumptosearch Abasissetintheoreticalandcomputationalchemistryisasetoffunctions(calledbasisfunctions)thatisusedtorepresenttheelectronicwavefunctionintheHartree–Fockmethodordensity-functionaltheoryinordertoturnthepartialdifferentialequationsofthemodelintoalgebraicequationssuitableforefficientimplementationonacomputer. Theuseofbasissetsisequivalenttotheuseofanapproximateresolutionoftheidentity:theorbitals | ψ i ⟩ {\displaystyle|\psi_{i}\rangle} areexpandedwithinthebasissetasalinearcombinationofthebasisfunctions | ψ i ⟩ ≈ ∑ μ c μ i | μ ⟩ {\textstyle|\psi_{i}\rangle\approx\sum_{\mu}c_{\mui}|\mu\rangle} ,wheretheexpansioncoefficients c i k {\displaystylec_{ik}} aregivenby c μ i = ∑ ν ⟨ μ | ν ⟩ − 1 ⟨ ν | k ⟩ {\textstylec_{\mui}=\sum_{\nu}\langle\mu|\nu\rangle^{-1}\langle\nu|k\rangle} . Thebasissetcaneitherbecomposedofatomicorbitals(yieldingthelinearcombinationofatomicorbitalsapproach),whichistheusualchoicewithinthequantumchemistrycommunity;planewaveswhicharetypicallyusedwithinthesolidstatecommunity,orreal-spaceapproaches.Severaltypesofatomicorbitalscanbeused:Gaussian-typeorbitals,Slater-typeorbitals,ornumericalatomicorbitals.[1]Outofthethree,Gaussian-typeorbitalsarebyfarthemostoftenused,astheyallowefficientimplementationsofPost-Hartree–Fockmethods. Contents 1Introduction 2STOhierarchy 3Split-valencebasissets 3.1Poplebasissets 4Correlation-consistentbasissets 5Polarization-consistentbasissets 6Karlsruhebasissets 7Completeness-optimizedbasissets 8Even-temperedbasissets 9Plane-wavebasissets 10Real-spacebasissets 11Seealso 12References 13Externallinks Introduction[edit] Inmoderncomputationalchemistry,quantumchemicalcalculationsareperformedusingafinitesetofbasisfunctions.Whenthefinitebasisisexpandedtowardsan(infinite)completesetoffunctions,calculationsusingsuchabasissetaresaidtoapproachthecompletebasisset(CBS)limit.Inthiscontext,basisfunctionandatomicorbitalaresometimesusedinterchangeably,althoughthebasisfunctionsareusuallynottrueatomicorbitals. Withinthebasisset,thewavefunctionisrepresentedasavector,thecomponentsofwhichcorrespondtocoefficientsofthebasisfunctionsinthelinearexpansion.Insuchabasis,one-electronoperatorscorrespondtomatrices(a.k.a.ranktwotensors),whereastwo-electronoperatorsarerankfourtensors. Whenmolecularcalculationsareperformed,itiscommontouseabasiscomposedofatomicorbitals,centeredateachnucleuswithinthemolecule(linearcombinationofatomicorbitalsansatz).ThephysicallybestmotivatedbasissetareSlater-typeorbitals(STOs), whicharesolutionstotheSchrödingerequationofhydrogen-likeatoms,anddecayexponentiallyfarawayfromthenucleus.ItcanbeshownthatthemolecularorbitalsofHartree-Fockanddensity-functionaltheoryalsoexhibitexponentialdecay.Furthermore,S-typeSTOsalsosatisfyKato'scuspconditionatthenucleus,meaningthattheyareabletoaccuratelydescribeelectrondensitynearthenucleus.However,hydrogen-likeatomslackmany-electroninteractions,thustheorbitalsdonotaccuratelydescribeelectronstatecorrelations. Unfortunately,calculatingintegralswithSTOsiscomputationallydifficultanditwaslaterrealizedbyFrankBoysthatSTOscouldbeapproximatedaslinearcombinationsofGaussian-typeorbitals(GTOs)instead.BecausetheproductoftwoGTOscanbewrittenasalinearcombinationofGTOs,integralswithGaussianbasisfunctionscanbewritteninclosedform,whichleadstohugecomputationalsavings(seeJohnPople). DozensofGaussian-typeorbitalbasissetshavebeenpublishedintheliterature.[2]Basissetstypicallycomeinhierarchiesofincreasingsize,givingacontrolledwaytoobtainmoreaccuratesolutions,howeveratahighercost. Thesmallestbasissetsarecalledminimalbasissets.Aminimalbasissetisoneinwhich,oneachatominthemolecule,asinglebasisfunctionisusedforeachorbitalinaHartree–Fockcalculationonthefreeatom.Foratomssuchaslithium,basisfunctionsofptypearealsoaddedtothebasisfunctionsthatcorrespondtothe1sand2sorbitalsofthefreeatom,becauselithiumalsohasa1s2pboundstate.Forexample,eachatominthesecondperiodoftheperiodicsystem(Li-Ne)wouldhaveabasissetoffivefunctions(twosfunctionsandthreepfunctions). Ad-polarizationfunctionaddedtoaporbital[3] Aminimalbasissetmayalreadybeexactforthegas-phaseatomattheself-consistentfieldleveloftheory.Inthenextlevel,additionalfunctionsareaddedtodescribepolarizationoftheelectrondensityoftheatominmolecules.Thesearecalledpolarizationfunctions.Forexample,whiletheminimalbasissetforhydrogenisonefunctionapproximatingthe1satomicorbital,asimplepolarizedbasissettypicallyhastwos-andonep-function(whichconsistsofthreebasisfunctions:px,pyandpz).Thisaddsflexibilitytothebasisset,effectivelyallowingmolecularorbitalsinvolvingthehydrogenatomtobemoreasymmetricaboutthehydrogennucleus.Thisisveryimportantformodelingchemicalbonding,becausethebondsareoftenpolarized.Similarly,d-typefunctionscanbeaddedtoabasissetwithvalenceporbitals,andf-functionstoabasissetwithd-typeorbitals,andsoon. Anothercommonadditiontobasissetsistheadditionofdiffusefunctions.TheseareextendedGaussianbasisfunctionswithasmallexponent,whichgiveflexibilitytothe"tail"portionoftheatomicorbitals,farawayfromthenucleus.Diffusebasisfunctionsareimportantfordescribinganionsordipolemoments,buttheycanalsobeimportantforaccuratemodelingofintra-andinter-molecularbonding. STOhierarchy[edit] ThemostcommonminimalbasissetisSTO-nG,wherenisaninteger.TheSTO-nGbasissetsarederivedfromaminimalSlater-typeorbitalbasisset,withnrepresentingthenumberofGaussianprimitivefunctionsusedtorepresenteachSlater-typeorbital.Minimalbasissetstypicallygiveroughresultsthatareinsufficientforresearch-qualitypublication,butaremuchcheaperthantheirlargercounterparts.Commonlyusedminimalbasissetsofthistypeare: STO-3G STO-4G STO-6G STO-3G*-PolarizedversionofSTO-3G ThereareseveralotherminimumbasissetsthathavebeenusedsuchastheMidiXbasissets. Split-valencebasissets[edit] Duringmostmolecularbonding,itisthevalenceelectronswhichprincipallytakepartinthebonding.Inrecognitionofthisfact,itiscommontorepresentvalenceorbitalsbymorethanonebasisfunction(eachofwhichcaninturnbecomposedofafixedlinearcombinationofprimitiveGaussianfunctions).Basissetsinwhichtherearemultiplebasisfunctionscorrespondingtoeachvalenceatomicorbitalarecalledvalencedouble,triple,quadruple-zeta,andsoon,basissets(zeta,ζ,wascommonlyusedtorepresenttheexponentofanSTObasisfunction[4]).Sincethedifferentorbitalsofthesplithavedifferentspatialextents,thecombinationallowstheelectrondensitytoadjustitsspatialextentappropriatetotheparticularmolecularenvironment.Incontrast,minimalbasissetslacktheflexibilitytoadjusttodifferentmolecularenvironments. Poplebasissets[edit] Thenotationforthesplit-valencebasissetsarisingfromthegroupofJohnPopleistypicallyX-YZg.[5]Inthiscase,XrepresentsthenumberofprimitiveGaussianscomprisingeachcoreatomicorbitalbasisfunction.TheYandZindicatethatthevalenceorbitalsarecomposedoftwobasisfunctionseach,thefirstonecomposedofalinearcombinationofYprimitiveGaussianfunctions,theothercomposedofalinearcombinationofZprimitiveGaussianfunctions.Inthiscase,thepresenceoftwonumbersafterthehyphensimpliesthatthisbasissetisasplit-valencedouble-zetabasisset.Split-valencetriple-andquadruple-zetabasissetsarealsoused,denotedasX-YZWg,X-YZWVg,etc.Hereisalistofcommonlyusedsplit-valencebasissetsofthistype: 3-21G 3-21G*-Polarizationfunctionsonheavyatoms 3-21G**-Polarizationfunctionsonheavyatomsandhydrogen 3-21+G-Diffusefunctionsonheavyatoms 3-21++G-Diffusefunctionsonheavyatomsandhydrogen 3-21+G*-Polarizationanddiffusefunctionsonheavyatoms 3-21+G**-Polarizationfunctionsonheavyatomsandhydrogen,aswellasdiffusefunctionsonheavyatoms 4-21G 4-31G 6-21G 6-31G 6-31G* 6-31+G* 6-31G(3df,3pd) 6-311G 6-311G* 6-311+G* The6-31G*basisset(definedfortheatomsHthroughZn)isavalencedouble-zetapolarizedbasissetthataddstothe6-31Gsetfived-typeCartesian-GaussianpolarizationfunctionsoneachoftheatomsLithroughCaandtenf-typeCartesianGaussianpolarizationfunctionsoneachoftheatomsScthroughZn. AscomparedtoPoplebasissets,correlation-consistentorpolarization-consistentbasissetsaremoreappropriateforcorrelatedwavefunctioncalculations.[6] ForHartree-Fockordensityfunctionaltheory,however,Poplebasissetsaremoreefficient(perunitbasisfunction)ascomparedtootheralternatives,providedthattheelectronicstructureprogramcantakeadvantageofcombinedspshells. Correlation-consistentbasissets[edit] SomeofthemostwidelyusedbasissetsarethosedevelopedbyDunningandcoworkers,[7]sincetheyaredesignedforconvergingPost-Hartree–Fockcalculationssystematicallytothecompletebasissetlimitusingempiricalextrapolationtechniques. Forfirst-andsecond-rowatoms,thebasissetsarecc-pVNZwhereN=D,T,Q,5,6,...(D=double,T=triples,etc.).The'cc-p',standsfor'correlation-consistentpolarized'andthe'V'indicatestheyarevalence-onlybasissets.Theyincludesuccessivelylargershellsofpolarization(correlating)functions(d,f,g,etc.).Morerecentlythese'correlation-consistentpolarized'basissetshavebecomewidelyusedandarethecurrentstateoftheartforcorrelatedorpost-Hartree–Fockcalculations.Examplesoftheseare: cc-pVDZ-Double-zeta cc-pVTZ-Triple-zeta cc-pVQZ-Quadruple-zeta cc-pV5Z-Quintuple-zeta,etc. aug-cc-pVDZ,etc.-Augmentedversionsoftheprecedingbasissetswithaddeddiffusefunctions. cc-pCVDZ-Double-zetawithcorecorrelation Forperiod-3atoms(Al-Ar),additionalfunctionshaveturnedouttobenecessary;thesearethecc-pV(N+d)Zbasissets.Evenlargeratomsmayemploypseudopotentialbasissets,cc-pVNZ-PP,orrelativistic-contractedDouglas-Krollbasissets,cc-pVNZ-DK. WhiletheusualDunningbasissetsareforvalence-onlycalculations,thesetscanbeaugmentedwithfurtherfunctionsthatdescribecoreelectroncorrelation.Thesecore-valencesets(cc-pCVXZ)canbeusedtoapproachtheexactsolutiontotheall-electronproblem,andtheyarenecessaryforaccurategeometricandnuclearpropertycalculations. Weightedcore-valencesets(cc-pwCVXZ)havealsobeenrecentlysuggested.Theweightedsetsaimtocapturecore-valencecorrelation,whileneglectingmostofcore-corecorrelation,inordertoyieldaccurategeometrieswithsmallercostthanthecc-pCVXZsets. Diffusefunctionscanalsobeaddedfordescribinganionsandlong-rangeinteractionssuchasVanderWaalsforces,ortoperformelectronicexcited-statecalculations,electricfieldpropertycalculations.Arecipeforconstructingadditionalaugmentedfunctionsexists;asmanyasfiveaugmentedfunctionshavebeenusedinsecondhyperpolarizabilitycalculationsintheliterature.Becauseoftherigorousconstructionofthesebasissets,extrapolationcanbedoneforalmostanyenergeticproperty.However,caremustbetakenwhenextrapolatingenergydifferencesastheindividualenergycomponentsconvergeatdifferentrates:theHartree-Fockenergyconvergesexponentially,whereasthecorrelationenergyconvergesonlypolynomially. H-He Li-Ne Na-Ar cc-pVDZ [2s1p]→5func. [3s2p1d]→14func. [4s3p1d]→18func. cc-pVTZ [3s2p1d]→14func. [4s3p2d1f]→30func. [5s4p2d1f]→34func. cc-pVQZ [4s3p2d1f]→30func. [5s4p3d2f1g]→55func. [6s5p3d2f1g]→59func. aug-cc-pVDZ [3s2p]→9func. [4s3p2d]→23func. [5s4p2d]→27func. aug-cc-pVTZ [4s3p2d]→23func. [5s4p3d2f]→46func. [6s5p3d2f]→50func. aug-cc-pVQZ [5s4p3d2f]→46func. [6s5p4d3f2g]→80func. [7s6p4d3f2g]→84func. Tounderstandhowtogetthenumberoffunctionstakethecc-pVDZbasissetforH: Therearetwos(L=0)orbitalsandonep(L=1)orbitalthathas3componentsalongthez-axis(mL=-1,0,1)correspondingtopx,pyandpz.Thus,fivespatialorbitalsintotal.Notethateachorbitalcanholdtwoelectronsofoppositespin. Forexample,Ar[1s,2s,2p,3s,3p]has3sorbitals(L=0)and2setsofporbitals(L=1).Usingcc-pVDZ,orbitalsare[1s,2s,2p,3s,3s,3p,3p,3d'](where'representstheaddedinpolarisationorbitals),with4sorbitals(4basisfunctions),3setsofporbitals(3×3=9basisfunctions),and1setofdorbitals(5basisfunctions).Addingupthebasisfunctionsgivesatotalof18functionsforArwiththecc-pVDZbasis-set. Polarization-consistentbasissets[edit] Density-functionaltheoryhasrecentlybecomewidelyusedincomputationalchemistry.However,thecorrelation-consistentbasissetsdescribedabovearesuboptimalfordensity-functionaltheory,becausethecorrelation-consistentsetshavebeendesignedforPost-Hartree–Fock,whiledensity-functionaltheoryexhibitsmuchmorerapidbasissetconvergencethanwavefunctionmethods. Adoptingasimilarmethodologytothecorrelation-consistentseries,FrankJensenintroducedpolarization-consistent(pc-n)basissetsasawaytoquicklyconvergedensityfunctionaltheorycalculationstothecompletebasissetlimit.[8]LiketheDunningsets,thepc-nsetscanbecombinedwithbasissetextrapolationtechniquestoobtainCBSvalues. Thepc-nsetscanbeaugmentedwithdiffusefunctionstoobtainaugpc-nsets. Karlsruhebasissets[edit] SomeofthevariousvalenceadaptationsofKarlsruhebasissetsare def2-SV(P)-Splitvalencewithpolarizationfunctionsonheavyatoms(nothydrogen) def2-SVP-Splitvalencepolarization def2-SVPD-Splitvalencepolarizationwithdiffusefunctions def2-TZVP-Valencetriple-zetapolarization def2-TZVPD-Valencetriple-zetapolarizationwithdiffusefunctions def2-TZVPP-Valencetriple-zetawithtwosetsofpolarizationfunctions def2-TZVPPD-Valencetriple-zetawithtwosetsofpolarizationfunctionsandasetofdiffusefunctions def2-QZVP-Valencequadruple-zetapolarization def2-QZVPD-Valencequadruple-zetapolarizationwithdiffusefunctions def2-QZVPP-Valencequadruple-zetawithtwosetsofpolarizationfunctions def2-QZVPPD-Valencequadruple-zetawithtwosetsofpolarizationfunctionsandasetofdiffusefunctions Completeness-optimizedbasissets[edit] Gaussian-typeorbitalbasissetsaretypicallyoptimizedtoreproducethelowestpossibleenergyforthesystemsusedtotrainthebasisset.However,theconvergenceoftheenergydoesnotimplyconvergenceofotherproperties,suchasnuclearmagneticshieldings,thedipolemoment,ortheelectronmomentumdensity,whichprobedifferentaspectsoftheelectronicwavefunction. ManninenandVaarahaveproposedcompleteness-optimizedbasissets,[9]wheretheexponentsareobtainedbymaximizationoftheone-electroncompletenessprofile[10]insteadofminimizationoftheenergy.Completeness-optimizedbasissetsareawaytoeasilyapproachthecompletebasissetlimitofanypropertyatanyleveloftheory,andtheprocedureissimpletoautomatize.[11] Completeness-optimizedbasissetsaretailoredtoaspecificproperty.Thisway,theflexibilityofthebasissetcanbefocusedonthecomputationaldemandsofthechosenproperty,typicallyyieldingmuchfasterconvergencetothecompletebasissetlimitthanisachievablewithenergy-optimizedbasissets. Even-temperedbasissets[edit] s-typeGaussianfunctionsusingsixdifferentexponentvaluesobtainedfromaneven-temperedschemestartingwithα=0.1andβ=sqrt(10).PlotgeneratedwithGnuplot. In1974BardoandRuedenberg[12]proposedasimpleschemetogeneratetheexponentsofabasissetthatspanstheHilbertspaceevenly[13]byfollowingageometricprogressionoftheform: α i , l = α l β l i − 1 , α l , β l > 0 , β l ≠ 1 i = 1 , 2 , … N l {\displaystyle\alpha_{i,l}=\alpha_{l}\beta_{l}^{i-1},\quad\alpha_{l},\beta_{l}>0,\quad\beta_{l}\neq1\quadi=1,2,\dotsN_{l}} foreachangularmomentum l {\displaystylel} ,where N l {\displaystyleN_{l}} isthenumberofprimitivesfunctions.Here,onlythetwoparameters α l {\displaystyle\alpha_{l}} and β l {\displaystyle\beta_{l}} mustbeoptimized,significantlyreducingthedimensionofthesearchspaceorevenavoidingtheexponentoptimizationproblem.Inordertoproperlydescribeelectronicdelocalizedstates,apreviouslyoptimizedstandardbasissetcanbecomplementedwithadditionaldelocalizedGaussianfunctionswithsmallexponentvalues,generatedbytheeven-temperedscheme.[13]Thisapproachhasalsobeenemployedtogeneratebasissetsforothertypesofquantumparticlesratherthanelectrons,likequantumnuclei,[14]negativemuons[15]orpositrons.[16] Plane-wavebasissets[edit] Inadditiontolocalizedbasissets,plane-wavebasissetscanalsobeusedinquantum-chemicalsimulations.Typically,thechoiceoftheplanewavebasissetisbasedonacutoffenergy.Theplanewavesinthesimulationcellthatfitbelowtheenergycriterionarethenincludedinthecalculation.Thesebasissetsarepopularincalculationsinvolvingthree-dimensionalperiodicboundaryconditions. Themainadvantageofaplane-wavebasisisthatitisguaranteedtoconvergeinasmooth,monotonicmannertothetargetwavefunction.Incontrast,whenlocalizedbasissetsareused,monotonicconvergencetothebasissetlimitmaybedifficultduetoproblemswithover-completeness:inalargebasisset,functionsondifferentatomsstarttolookalike,andmanyeigenvaluesoftheoverlapmatrixapproachzero. Inaddition,certainintegralsandoperationsaremucheasiertoprogramandcarryoutwithplane-wavebasisfunctionsthanwiththeirlocalizedcounterparts.Forexample,thekineticenergyoperatorisdiagonalinthereciprocalspace.Integralsoverreal-spaceoperatorscanbeefficientlycarriedoutusingfastFouriertransforms.ThepropertiesoftheFourierTransformallowavectorrepresentingthegradientofthetotalenergywithrespecttotheplane-wavecoefficientstobecalculatedwithacomputationaleffortthatscalesasNPW*ln(NPW)whereNPWisthenumberofplane-waves.WhenthispropertyiscombinedwithseparablepseudopotentialsoftheKleinman-Bylandertypeandpre-conditionedconjugategradientsolutiontechniques,thedynamicsimulationofperiodicproblemscontaininghundredsofatomsbecomespossible. Inpractice,plane-wavebasissetsareoftenusedincombinationwithan'effectivecorepotential'orpseudopotential,sothattheplanewavesareonlyusedtodescribethevalencechargedensity.Thisisbecausecoreelectronstendtobeconcentratedveryclosetotheatomicnuclei,resultinginlargewavefunctionanddensitygradientsnearthenucleiwhicharenoteasilydescribedbyaplane-wavebasissetunlessaveryhighenergycutoff,andthereforesmallwavelength,isused.Thiscombinedmethodofaplane-wavebasissetwithacorepseudopotentialisoftenabbreviatedasaPSPWcalculation. Furthermore,asallfunctionsinthebasisaremutuallyorthogonalandarenotassociatedwithanyparticularatom,plane-wavebasissetsdonotexhibitbasis-setsuperpositionerror.However,theplane-wavebasissetisdependentonthesizeofthesimulationcell,complicatingcellsizeoptimization. Duetotheassumptionofperiodicboundaryconditions,plane-wavebasissetsarelesswellsuitedtogas-phasecalculationsthanlocalizedbasissets.Largeregionsofvacuumneedtobeaddedonallsidesofthegas-phasemoleculeinordertoavoidinteractionswiththemoleculeanditsperiodiccopies.However,theplanewavesuseasimilaraccuracytodescribethevacuumregionastheregionwherethemoleculeis,meaningthatobtainingthetrulynoninteractinglimitmaybecomputationallycostly. Real-spacebasissets[edit] Real-spaceapproachesofferpowerfulmethodstosolveelectronicstructureproblemsthankstotheircontrollableaccuracy.Real-spacebasissetscanbethoughttoarisefromthetheoryofinterpolation,asthecentralideaistorepresentthe(unknown)orbitalsintermsofsomesetofinterpolationfunctions. Variousmethodshavebeenproposedforconstructingthesolutioninrealspace,includingfiniteelements,basissplines,Lagrangesinc-functions,andwavelets.[1]Finitedifferencealgorithmsarealsooftenincludedinthiscategory,eventhoughpreciselyspeaking,theydonotformaproperbasissetandarenotvariationalunlikee.g.finiteelementmethods.[1] Acommonfeatureofallreal-spacemethodsisthattheaccuracyofthenumericalbasissetisimprovable,sothatthecompletebasissetlimitcanbereachedinasystematicalmanner. Moreover,inthecaseofwaveletsandfiniteelements,itiseasytousedifferentlevelsofaccuracyindifferentpartsofthesystem,sothatmorepointsareusedclosetothenucleiwherethewavefunctionundergoesrapidchangesandwheremostofthetotalenergieslie,whereasacoarserrepresentationissufficientfarawayfromnuclei;thisfeatureisextremelyimportantasitcanbeusedtomakeall-electroncalculationstractable. Forexample,infiniteelementmethods(FEMs),thewavefunctionisrepresentedasalinearcombinationofasetofpiecewisepolynomials.Lagrangeinterpolatingpolynomials(LIPs)areacommonly-usedbasisforFEMcalculations.ThelocalinterpolationerrorinLIPbasisoforder n {\displaystylen} isoftheform h n + 1 max f ( n + 1 ) ( ξ ) {\displaystyleh^{n+1}\maxf^{(n+1)}(\xi)} .Thecompletebasissetcantherebybereachedeitherbygoingtosmallerandsmallerelements(i.e.dividingspaceinsmallerandsmallersubdivisions; h {\displaystyleh} -adaptiveFEM),byswitchingtotheuseofhigherandhigherorderpolynomials( p {\displaystylep} -adaptiveFEM),orbyacombinationofbothstrategies( h p {\displaystylehp} -adaptiveFEM).Theuseofhigh-orderLIPshasbeenshowntobehighlybeneficialforaccuracy.[17] Seealso[edit] Basissetsuperpositionerror Angularmomentum Atomicorbitals Molecularorbitals Listofquantumchemistryandsolidstatephysicssoftware References[edit] ^abcLehtola,Susi(2019)."Areviewonnon-relativisticfullynumericalelectronicstructurecalculationsonatomsanddiatomicmolecules".Int.J.QuantumChem.119:e25968.arXiv:1902.01431.doi:10.1002/qua.25968. ^Jensen,Frank(2013)."Atomicorbitalbasissets".WIREsComput.Mol.Sci.3(3):273–295.doi:10.1002/wcms.1123. ^ErrolG.Lewars(2003-01-01).ComputationalChemistry:IntroductiontotheTheoryandApplicationsofMolecularandQuantumMechanics(1st ed.).Springer.ISBN 978-1402072857. ^Davidson,Ernest;Feller,David(1986)."Basissetselectionformolecularcalculations".Chem.Rev.86(4):681–696.doi:10.1021/cr00074a002. ^Ditchfield,R;Hehre,W.J;Pople,J.A.(1971)."Self-ConsistentMolecular-OrbitalMethods.IX.AnExtendedGaussian-TypeBasisforMolecular-OrbitalStudiesofOrganicMolecules".J.Chem.Phys.54(2):724–728.Bibcode:1971JChPh..54..724D.doi:10.1063/1.1674902. ^Moran,Damian;Simmonett,AndrewC.;Leach,FranklinE.III;Allen,WesleyD.;Schleyer,Paulv.R.;Schaefer,HenryF.(2006)."Populartheoreticalmethodspredictbenzeneandarenestobenonplanar".J.Am.Chem.Soc.128(29):9342–9343.doi:10.1021/ja0630285.PMID 16848464. ^Dunning,ThomasH.(1989)."Gaussianbasissetsforuseincorrelatedmolecularcalculations.I.Theatomsboronthroughneonandhydrogen".J.Chem.Phys.90(2):1007–1023.Bibcode:1989JChPh..90.1007D.doi:10.1063/1.456153. ^Jensen,Frank(2001)."Polarizationconsistentbasissets:Principles".J.Chem.Phys.115(20):9113–9125.Bibcode:2001JChPh.115.9113J.doi:10.1063/1.1413524. ^Manninen,Pekka;Vaara,Juha(2006)."SystematicGaussianbasis-setlimitusingcompleteness-optimizedprimitivesets.Acaseformagneticproperties".J.Comput.Chem.27(4):434–445.doi:10.1002/jcc.20358.PMID 16419020. ^Chong,DelanoP.(1995)."Completenessprofilesofone-electronbasissets".Can.J.Chem.73(1):79–83.doi:10.1139/v95-011. ^Lehtola,Susi(2015)."Automaticalgorithmsforcompleteness-optimizationofGaussianbasissets".J.Comput.Chem.36(5):335–347.doi:10.1002/jcc.23802.PMID 25487276. ^Bardo,RichardD.;Ruedenberg,Klaus(February1974)."Even‐temperedatomicorbitals.VI.OptimalorbitalexponentsandoptimalcontractionsofGaussianprimitivesforhydrogen,carbon,andoxygeninmolecules".TheJournalofChemicalPhysics.60(3):918–931.Bibcode:1974JChPh..60..918B.doi:10.1063/1.1681168.ISSN 0021-9606. ^abCherkes,Ira;Klaiman,Shachar;Moiseyev,Nimrod(2009-11-05)."SpanningtheHilbertspacewithaneventemperedGaussianbasisset".InternationalJournalofQuantumChemistry.109(13):2996–3002.Bibcode:2009IJQC..109.2996C.doi:10.1002/qua.22090. ^Nakai,Hiromi(2002)."SimultaneousdeterminationofnuclearandelectronicwavefunctionswithoutBorn-Oppenheimerapproximation:AbinitioNO+MO/HFtheory".InternationalJournalofQuantumChemistry.86(6):511–517.doi:10.1002/qua.1106.ISSN 0020-7608. ^Moncada,Félix;Cruz,Daniel;Reyes,Andrés(June2012)."Muonicalchemy:Transmutingelementswiththeinclusionofnegativemuons".ChemicalPhysicsLetters.539–540:209–213.Bibcode:2012CPL...539..209M.doi:10.1016/j.cplett.2012.04.062. ^Reyes,Andrés;Moncada,Félix;Charry,Jorge(2019-01-15)."Theanyparticlemolecularorbitalapproach:Ashortreviewofthetheoryandapplications".InternationalJournalofQuantumChemistry.119(2):e25705.doi:10.1002/qua.25705.ISSN 0020-7608. ^Lehtola,Susi(2019)."FullynumericalHartree–Fockanddensityfunctionalcalculations.I.Atoms".Int.J.QuantumChem.119:e25945.doi:10.1002/qua.25945.hdl:10138/311128. Allthemanybasissetsdiscussedherealongwithothersarediscussedinthereferencesbelowwhichthemselvesgivereferencestotheoriginaljournalarticles: Levine,IraN.(1991).QuantumChemistry.EnglewoodCliffs,Newjersey:PrenticeHall.pp. 461–466.ISBN 978-0-205-12770-2. Cramer,ChristopherJ.(2002).EssentialsofComputationalChemistry.Chichester:JohnWiley&Sons,Ltd.pp. 154–168.ISBN 978-0-471-48552-0. Jensen,Frank(1999).IntroductiontoComputationalChemistry.JohnWileyandSons.pp. 150–176.ISBN 978-0471980858. Leach,AndrewR.(1996).MolecularModelling:PrinciplesandApplications.Singapore:Longman.pp. 68–77.ISBN 978-0-582-23933-3. Hehre,WarrenJ..(2003).AGuidetoMolecularMechanicsandQuantumChemicalCalculations.Irvine,California:Wavefunction,Inc.pp. 40–47.ISBN 978-1-890661-18-2. https://web.archive.org/web/20070830043639/http://www.chem.swin.edu.au/modules/mod8/basis1.html Moran,Damian;Simmonett,AndrewC.;Leach,FranklinE.;Allen,WesleyD.;Schleyer,Paulv.R.;Schaefer,HenryF.(2006)."PopularTheoreticalMethodsPredictBenzeneandArenesToBeNonplanar".JournaloftheAmericanChemicalSociety.128(29):9342–3.doi:10.1021/ja0630285.PMID 16848464. Choi,Sunghwan;Kwangwoo,Hong;Jaewook,Kim;WooYoun,Kim(2015)."AccuracyofLagrange-sincfunctionsasabasissetforelectronicstructurecalculationsofatomsandmolecules".TheJournalofChemicalPhysics.142(9):094116.Bibcode:2015JChPh.142i4116C.doi:10.1063/1.4913569.PMID 25747070. Externallinks[edit] EMSLBasisSetExchange TURBOMOLEbasissetlibrary CRYSTAL-BasisSetsLibrary DyallBasisSetsLibrary PetersonGroupCorrelationConsistentBasisSets SapporoSegmentedGaussianBasisSetsLibrary[permanentdeadlink] Stuttgart/Cologneenergy-consistent(abinitio)pseudopotentialsLibrary ChemViz-BasisSetsLabActivity Retrievedfrom"https://en.wikipedia.org/w/index.php?title=Basis_set_(chemistry)&oldid=1077048484" Categories:QuantumchemistryComputationalchemistryTheoreticalchemistryHiddencategories:CS1:longvolumevalueAllarticleswithdeadexternallinksArticleswithdeadexternallinksfromOctober2019Articleswithpermanentlydeadexternallinks Navigationmenu Personaltools NotloggedinTalkContributionsCreateaccountLogin Namespaces ArticleTalk English Views ReadEditViewhistory More Search Navigation MainpageContentsCurrenteventsRandomarticleAboutWikipediaContactusDonate Contribute HelpLearntoeditCommunityportalRecentchangesUploadfile Tools WhatlinkshereRelatedchangesUploadfileSpecialpagesPermanentlinkPageinformationCitethispageWikidataitem Print/export DownloadasPDFPrintableversion Languages DeutschFrançais한국어BahasaIndonesia日本語PolskiPortuguêsРусскийTürkçeУкраїнська中文 Editlinks