宏剑培训 Electronic structure, atomic forces and structural relaxations by WIEN2k 2

《宏剑培训 Electronic structure, atomic forces and structural relaxations by WIEN2k 2》由会员上传分享，免费在线阅读，更多相关内容在行业资料-天天文库。

1、Electronicstructure,atomicforcesandstructuralrelaxationsbyWIEN2kPeterBlahaInstituteofMaterialsChemistryTUVienna,AustriaOutline:¢APW-basedmethods(historyandstate-of-the-art)¢WIEN2k¢programstructure+usage¢forces,structurerelaxation¢Applications¢PhasetransitionsinAurivilliusphases¢StructureofPyrochlore

2、YNbO227APWbasedschemes¢APW(J.C.Slater1937)¢Non-lineareigenvalueproblem¢Computationallyverydemanding¢LAPW(O.K.Anderssen1975)¢Generalizedeigenvalueproblem¢Full-potentialtotal-energies(A.Freemanetal.)¢Localorbitals(D.J.Singh1991)¢treatmentofsemi-corestates(avoidsghostbands)¢APW+lo(E.Sjöstedt,L.Nordstör

3、m,D.J.Singh2000)¢EfficienceofAPW+convenienceofLAPW¢BasisforK.Schwarz,P.Blaha,G.K.H.Madsen,Comp.Phys.Commun.147,71-76(2002)APWAugmentedPlaneWavemethodTheunitcellispartitionedinto:Blochwavefunction:atomicspheresatomicpartialwavesInterstitialregionPlaneWaves(PWs)unitcellRmtAtomicpartialwavesrrrKPW:ei(k

4、+K).rjoin∑au(r′,ε)Y(rˆ′)lmllmlmmatchingcoefficient,radialfunction,sphericalharmonicsSlater‘sAPW(1937)AtomicpartialwavesK∑almul(r′,ε)Ylm(rˆ′)lmEnergydependentRadialbasisfunctionsleadtoHHamiltonianNon-lineareigenvalueproblemSOverlapmatrixComputationallyverydemandingOnehadtonumericallysearchfortheenerg

5、y,forwhichthedet

6、H-ES

7、vanishes.LinearizationofenergydependenceLAPWsuggestedbyO.K.Andersen,Phys.Rev.B12,3060(1975)Φkn=∑[Alm(kn)ul(El,r)+Blm(kn)u&l(El,r)]Ylm(rˆ)lmu&=∂u/∂εlljoinPWsinvalueandslopeAtomicsphereuexpandedatE(„energyparameter“)LAPWllPWÆadditionalconstraintrequiresmoreAPWPWsthanAPWbasisflexi

8、bleenoughforsinglediagonalizationFull-potentialtotal-energy(A.Freemanetal.)¢Thepotential(andchargedensity)canbeofgeneralformSrTiO3(noshapeapproximation)V(r)Y(rˆ)r

9、eO2Core,semi-coreandvalencestatesForexample:Ti¢Valencesstates¢Highinenergy¢Delocalizedwavefunctions¢Semi-corestates¢Mediumenergy¢PrincipalQNonelessthanvalence(e.g.inTi3pand4p)¢notcompletelyconfinedins