First-principles-simulation-ideas-illustrations-an

INSTITUTEOFPHYSICSPUBLISHINGJOURNALOFPHYSICS:CONDENSEDMATTERJ.Phys.:Condens.Matter14(2002)2717–2744PII:S0953-8984(02)32831-5First-principlessimulation:ideas,illustrationsandtheCASTEPcodeMDSegall1,2,PhilipJDLindan3,7,MJProbert4,CJPickard1,PJHasnip5,SJClark6andMCPayne11TCM,CavendishLaboratory,UniversityofCambridge,UK2Camitro(UK)Ltd,Cambridge,UK3CentreforMaterialsResearch,UniversityofKentatCanterbury,CanterburyCT27NR,UK4PhysicsDepartment,UniversityofYork,UK5DepartmentofMaterials,UniversityofCambridge,UK6DepartmentofPhysics,UniversityofDurham,UKReceived17January2002Published8March2002Onlineatstacks.iop.org/JPhysCM/14/2717AbstractFirst-principlessimulation,meaningdensity-functionaltheorycalculationswithplanewavesandpseudopotentials,hasbecomeaprizedtechniqueincondensed-mattertheory.HereIlookatthebasicsofthesuject,giveabriefreviewofthetheory,examiningthestrengthsandweaknessesofitsimplementation,andillustratingsomeofthewayssimulatorsapproachproblemsthroughasmallcasestudy.IalsodiscusswhyandhowmodernsoftwaredesignmethodshavebeenusedinwritingacompletelynewmodularversionoftheCASTEPcode.1.OverviewThesimulatorbuildsamodelofarealsystemandexploresitsbehaviour.Themodelisamathematicaloneandtheexplorationisdoneonacomputer,andinmanywayssimulationstudiessharethesamementalityasexperimentalones.However,inasimulationthereisabsolutecontrolandaccesstodetail,theabilitytocomputealmostanyobservable,andgivenenoughcomputermuscle,exactanswersforthemodel.Thesestrengthshavebeenexploitedforthelastfiftyyearsandhaveledtomanyadvancesinthetheoryofcondensedmatter.However,itisonlyinthelastfifteenyearsorsothatwehavebeenabletocomputethepropertiesofcondensedmatterfromfirstprinciples.Thefirst-principlesapproachisvastlyambitiousbecauseitsgoalistomodelrealsystemsusingnoapproximationswhatsoever.Thatonecanevenhopetodothisisdowntotheaccuracyofquantummechanicsindescribingthechemicalbond.Dirac’sapocryphalquipthatafterthediscoveryofquantummechanics‘therestischemistry’sumsitup:ifonecansolvetheSchr¨odingerequationforsomething—anatom,a7Authorwhowasinvitedtosubmitthisarticle(thefullauthorlististheCASTEPDevelopmentGroup.)0953-8984/02/112717+28$30.00©2002IOPPublishingLtdPrintedintheUK27172718PJDLindanetalmolecule,assembliesofatomsinsolidsorliquids—onecanpredicteveryphysicalproperty.PerhapsDiracdidn’trealisequitehowdifficultdoing‘therest’is,andithastakengreateffortandingenuitytotakeustothepointofcalculatingsomeofthepropertiesofmaterialswithreasonableaccuracyfromsmallmodelsystems!However,tofocuslimitationsistomissthepoint:theimpactofsimulationsonourthinkingaboutcondensedmatterproblemsisimmense.HereIshallconcentrateonjustafewelementsofwhatisaverylargesubject.FirstIshalldiscussthefirst-principlesrationaleandwhatmakesthetasksodifficult.Ishallfocusononeofthemostsuccessfulapproaches,theapplicationofdensity-functionaltheoryusingplanewavesandpseudopotentials,andconsiderwhythismethodturnedouttobesoimportant.Ishallalsospendsometimediscussingthesimulationapproachingeneral,andthetypesofinformationthatcomeoutofacalculation.ToillustratetheapplicationofthesemethodsIshallpresenthighlightsofanextensivestudyoftheadsorptionofwateronanoxidesurface,aproblemthathasturnedouttobesurprisinglydifficult.InreviewingthemethodologyIshallinthemainlookatpracticalitiesratherthanthefulldetailsoftheformalism.ThisisbecauseIhopetocoverafewtopicsthatseldomappearintheliterature,andbecausetheformaltheoryanditsimplementationarealreadytreatedinmanyexcellentreviews[1–9].ThroughoutIhaveslantedthingstowardsthe‘user’andthenon-specialist.Finally,IshalldescribebrieflythelatestdevelopmentsaroundtheCASTEPcomputercode.Traditionalscientificprogramminghasmanyshortcomingswhichareseriousforlargeandcomplexcodessuchasthoserequiredformodernfirst-principlescalculations.Withthisinmind,CASTEPhasbeenredesignedandrewrittencompletely.Theprimaryaimofthisistomakenewdevelopmentsasrapidandreliableaspossible.Thisisachievedthroughamodulardesignwhichembodiestheideasofdataabstractionandencapsulation.Considerthatourcodesaremorethanjustthe‘equipment’weusetoprobecondensedmatter,theyarealsothelanguageandnotationweusetoimplementnewtheoreticalapproaches.InnewCASTEPwestrivetomakethislanguageflexible,powerfulandidealforthetask.2.Theory2.1.Thefirst-principlesrationaleQuantummechanicsprovidesareliablewaytocalculatewhatelectronsandatomicnucleidoinanysituation.Thebehaviourofelectronsinparticulargovernsmostofthepropertiesofmaterials8.Thisistrueforasingleatomorforassembliesofatomsincondensedmatter,becausequantummechanicsdescribesandexplainschemicalbonds.Thereforewecanunderstandthepropertiesofanymaterialfromfirst-principles,thatis,basedonfundamentalphysicallawsandwithoutusingfreeparameters,bysolvingtheSchr¨odingerequationfortheelectronsinthatmaterial9.This,however,isatallorder.Werapidlyrunintodifficultybecauseelectronsinteractstronglywitheachother.Thealarmingconsequenceisthatexactpencil-and-papersolutionsexistonlyforasingleelectroninsimplepotentials:solvingtheSchr¨odingerequationforthehydrogenatomisaclassicundergraduatetask,butsolvingitforheliumrequiresacomputationa