Achieving DFT convergence
Some systems are tricky to converge. Here are some collected tips and tricks you can try and which may help. Take these as a source of inspiration for what you can try. Your mileage may vary.
Even if modelling an insulator, add a temperature to your
Model. Values up to1e-2atomic units may be sometimes needed. Note, that this can change the physics of your system, so if in doubt perform a second SCF with a lower temperature afterwards, starting from the final density of the first.If you are modelling a magnetic systems near a phase transition it can be worth switching to the
LdosXcDiagonalMixingmixing algorithm in yourself_consistent_fieldcall. This is done by passing this mixer via themixingkeyword argument, e.g.mixing = LdosXcDiagonalMixing()LdosXcDiagonalMixing(reltol=1.0e-6)Even if modelling an insulator, add a temperature to your
Model. Values up to1e-2atomic units may be sometimes needed. Note, that this can change the physics of your system, so if in doubt perform a second SCF with a lower temperature afterwards, starting from the final density of the first.Increase the history size of the Anderson acceleration by passing a custom
solvertoself_consistent_field, e.g.solver = scf_anderson_solver(; m=15)ScfAndersonDensitySolver(; m_start=1, m=15, maxcond=1.0e6, errorfactor=100000.0)All keyword arguments are passed through to
DFTK.AndersonAcceleration.Try increasing convergence for for the bands in each SCF step by increasing the
ratio_ρdiffparameter of theAdaptiveDiagtolalgorithm. For example:diagtolalg = AdaptiveDiagtol(; ratio_ρdiff=0.05)AdaptiveDiagtol(0.05, nothing, 0.005, 0.03)Increase the number of bands, which are fully converged in each SCF step by tweaking the
AdaptiveBandsalgorithm. For example:nbandsalg = AdaptiveBands(model; temperature_factor_converge=1.1)AdaptiveBands(4, 7, 1.0e-6, 0.01)Try the adaptive damping algorithm by using
DFTK.scf_potential_mixing_adaptiveinstead ofself_consistent_field:DFTK.scf_potential_mixing_adaptive(basis; tol=1e-10)(ham = Hamiltonian(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), HamiltonianBlock[DFTK.DftHamiltonianBlock{PlaneWaveBasis{Float64, Float64, DFTK.CPU, FFTGrid{Float64, Float64, Array{StaticArraysCore.SVector{3, Int64}, 3}, Array{StaticArraysCore.SVector{3, Float64}, 3}}, Vector{StaticArraysCore.SVector{3, Int64}}}, Kpoint{Float64, Vector{StaticArraysCore.SVector{3, Int64}}, Vector{Int64}}, DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}, Nothing, Vector{@NamedTuple{ψ_reals::Array{ComplexF64, 3}}}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749), DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749), [0.0, 0.5624107360872233, 2.249642944348893, 5.061696624785009, 8.998571777395572, 14.06026840218058, 14.06026840218058, 8.998571777395572, 5.061696624785009, 2.249642944348893 … 0.7498809814496308, 2.062172698986485, 4.499285888697785, 8.061220550583531, 12.747976684643724, 11.060744476382055, 6.748928833046679, 3.561934661885747, 1.499761962899262, 0.5624107360872233]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749), ComplexF64[0.11162114718647566 + 0.0im 0.17292273765511482 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.10094779392345996 + 0.0im 0.1459089442398946 + 0.0im … -0.05030254922547521 - 0.0im 0.0503025492254752 + 0.0im; … ; 0.08537828309138949 + 0.0im 0.1086340264896086 + 0.0im … -0.0 + 0.08075097926136236im 0.0 + 0.0im; 0.10094779392345996 + 0.0im 0.1459089442398946 + 0.0im … 0.05030254922547521 + 0.0im 0.0503025492254752 + 0.0im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749), [-12.2475696978844 -11.100308387033913 … -8.289845769066893 -11.100308387033943; -11.10030838703391 -9.130057818482163 … -9.130057802436339 -11.100308365268916; … ; -8.289845769066893 -9.130057802436337 … -4.14958991194573 -6.2879562047399284; -11.10030838703394 -11.100308365268914 … -6.287956204739929 -9.111848216112016;;; -11.100308387033914 -9.130057818482161 … -9.130057802436339 -11.100308365268914; -9.130057818482161 -6.903159504367577 … -9.130057819839301 -10.053883816988046; … ; -9.130057802436339 -9.130057819839298 … -5.294353665850196 -7.547399215037599; -11.100308365268914 -10.053883816988046 … -7.547399215037599 -10.053883816988098;;; -8.289845769067037 -6.307621938057417 … -8.289845773669953 -9.111848200066168; -6.307621938057414 -4.516655658355899 … -7.547399231892241 -7.547399215037713; … ; -8.289845773669953 -7.547399231892238 … -5.768969098395969 -7.547399231892274; -9.111848200066168 -7.5473992150377125 … -7.547399231892275 -9.111848217469266;;; … ;;; -5.301031708536039 -6.307621951399262 … -2.5497035798117262 -3.8495821823329694; -6.307621951399262 -6.903159511447426 … -3.3290606941630063 -4.878419351559539; … ; -2.549703579811726 -3.3290606941630063 … -1.2567984675346517 -1.8141947489915244; -3.849582182332969 -4.878419351559539 … -1.8141947489915258 -2.714767336891466;;; -8.289845769066892 -9.130057802436337 … -4.14958991194573 -6.2879562047399284; -9.130057802436335 -9.1300578198393 … -5.294353665850197 -7.547399215037599; … ; -4.14958991194573 -5.294353665850197 … -1.9094492500180213 -2.8946123644894746; -6.2879562047399284 -7.5473992150376 … -2.8946123644894755 -4.485542751912487;;; -11.100308387033943 -11.100308365268916 … -6.2879562047399284 -9.111848216112017; -11.100308365268914 -10.053883816988048 … -7.547399215037601 -10.053883816988096; … ; -6.2879562047399284 -7.547399215037598 … -2.894612364489475 -4.485542751912487; -9.111848216112017 -10.053883816988096 … -4.485542751912487 -6.87110452252074])], DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749), [0.0, 0.5624107360872233, 2.249642944348893, 5.061696624785009, 8.998571777395572, 14.06026840218058, 14.06026840218058, 8.998571777395572, 5.061696624785009, 2.249642944348893 … 0.7498809814496308, 2.062172698986485, 4.499285888697785, 8.061220550583531, 12.747976684643724, 11.060744476382055, 6.748928833046679, 3.561934661885747, 1.499761962899262, 0.5624107360872233]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749), [-12.2475696978844 -11.100308387033913 … -8.289845769066893 -11.100308387033943; -11.10030838703391 -9.130057818482163 … -9.130057802436339 -11.100308365268916; … ; -8.289845769066893 -9.130057802436337 … -4.14958991194573 -6.2879562047399284; -11.10030838703394 -11.100308365268914 … -6.287956204739929 -9.111848216112016;;; -11.100308387033914 -9.130057818482161 … -9.130057802436339 -11.100308365268914; -9.130057818482161 -6.903159504367577 … -9.130057819839301 -10.053883816988046; … ; -9.130057802436339 -9.130057819839298 … -5.294353665850196 -7.547399215037599; -11.100308365268914 -10.053883816988046 … -7.547399215037599 -10.053883816988098;;; -8.289845769067037 -6.307621938057417 … -8.289845773669953 -9.111848200066168; -6.307621938057414 -4.516655658355899 … -7.547399231892241 -7.547399215037713; … ; -8.289845773669953 -7.547399231892238 … -5.768969098395969 -7.547399231892274; -9.111848200066168 -7.5473992150377125 … -7.547399231892275 -9.111848217469266;;; … ;;; -5.301031708536039 -6.307621951399262 … -2.5497035798117262 -3.8495821823329694; -6.307621951399262 -6.903159511447426 … -3.3290606941630063 -4.878419351559539; … ; -2.549703579811726 -3.3290606941630063 … -1.2567984675346517 -1.8141947489915244; -3.849582182332969 -4.878419351559539 … -1.8141947489915258 -2.714767336891466;;; -8.289845769066892 -9.130057802436337 … -4.14958991194573 -6.2879562047399284; -9.130057802436335 -9.1300578198393 … -5.294353665850197 -7.547399215037599; … ; -4.14958991194573 -5.294353665850197 … -1.9094492500180213 -2.8946123644894746; -6.2879562047399284 -7.5473992150376 … -2.8946123644894755 -4.485542751912487;;; -11.100308387033943 -11.100308365268916 … -6.2879562047399284 -9.111848216112017; -11.100308365268914 -10.053883816988048 … -7.547399215037601 -10.053883816988096; … ; -6.2879562047399284 -7.547399215037598 … -2.894612364489475 -4.485542751912487; -9.111848216112017 -10.053883816988096 … -4.485542751912487 -6.87110452252074]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749), ComplexF64[0.11162114718647566 + 0.0im 0.17292273765511482 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.10094779392345996 + 0.0im 0.1459089442398946 + 0.0im … -0.05030254922547521 - 0.0im 0.0503025492254752 + 0.0im; … ; 0.08537828309138949 + 0.0im 0.1086340264896086 + 0.0im … -0.0 + 0.08075097926136236im 0.0 + 0.0im; 0.10094779392345996 + 0.0im 0.1459089442398946 + 0.0im … 0.05030254922547521 + 0.0im 0.0503025492254752 + 0.0im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, @NamedTuple{ψ_reals::Array{ComplexF64, 3}}[(ψ_reals = [-1.7788048193691577e-6 + 0.0008976655748475599im -0.0035485627180988927 - 0.004438614492265291im … -0.00144505433124814 - 0.00013726129198712335im -0.0027012573412004944 + 0.002366566187481845im; 0.00038699692000509665 + 0.0004533665080298005im -0.0028716154101844633 - 0.00017427504784827959im … 0.0005037860776012071 - 0.00025045561823621294im -7.037613464528454e-5 + 0.0026589143195040036im; … ; -0.004981990696411377 - 0.0006206963576591217im -0.002645993433684053 + 0.0020030273365509725im … -0.0001294033247711381 + 0.001738211710460575im 0.00029242540279260647 + 0.0005451977128713136im; -0.0060545192815659905 + 0.004651670142355966im -0.00032019824935716886 + 0.001686383384289115im … -0.002575972059648394 - 0.0033675449774419938im -0.006422203056065211 - 0.0007071066622620658im;;; -0.0038226163397192467 - 0.04247581132210683im -0.07717422690855255 - 0.06541393396293858im … 0.028713837018167248 - 0.002350500325848201im 0.012722013639403666 - 0.01468281851470838im; -0.0007340879881196135 + 0.0009912881714227752im -0.056516213270514704 + 0.004494298748578804im … 0.008640297123026972 - 0.011946964908447325im 0.0006946537762353086 + 0.027829325820015585im; … ; -0.06484836940592374 + 0.006659785130398499im -0.004156274678323753 + 0.008041837829271564im … -0.002383115305502895 - 0.048352347535757845im -0.05735842093567942 - 0.049825773095518104im; 0.013553844451098467 - 0.010381081812075539im -0.003751061628773592 - 0.06636039756892843im … -0.011047969299694855 - 0.0081138487745765im -0.013763643094201842 + 0.0036581947553949966im;;; -0.038037843235910127 - 0.031219041007441543im -0.08805480213903537 + 0.007576613983880556im … 0.0036446193439703435 - 0.00680852768225375im -0.0013652794271663323 + 0.004941857155660707im; 0.04754976628227655 - 0.0006429553886491803im 0.007713636110634636 - 0.007646361287274245im … -0.0017090685963981342 + 0.0008504579716408604im 0.04612770752188608 + 0.04314446888003458im; … ; 0.008205814894687875 - 0.003944003765504795im -0.0024032810489415255 - 0.07910695765920259im … -0.058476873415902686 - 0.05260889328243454im -0.05676288693922369 + 0.0050268500145765095im; -0.003802433274523936 - 0.08872234692386402im -0.10391886934327811 - 0.09149132146489876im … -0.018722143000648575 + 0.0012694530364994803im 0.012125903674445285 - 0.010401219805098767im;;; … ;;; 0.003320951666864233 + 0.08477755954910168im 0.055337529010860975 + 0.05123239519681432im … -0.022987141011324375 + 0.0033493699110132245im -0.029938551126563323 + 0.03583294791818136im; 0.07618514820016624 + 0.07023834073920063im 0.0848718677758278 - 0.0029508395454156972im … -0.008873118801253445 + 0.015161239299042891im 0.005996296823253838 + 0.08296578256596752im; … ; 0.09583364792458124 - 0.002699138564671244im 0.04227214752995155 - 0.046011936982386294im … -0.00039412709114974333 + 0.02270664491082569im 0.07424036829115585 + 0.07216972526436341im; 0.01883261351296065 - 0.021035674739191865im -0.001040479027121094 - 0.009766221713831538im … -0.007432378162925409 - 0.005177610928899089im 0.0506754011245881 - 0.0004144556047203235im;;; 0.050466407734821375 + 0.04770238149110915im 0.07521925084065016 - 0.002881420914128449im … -0.021538772549005675 + 0.02608948369350987im 0.0011445431667381069 + 0.009840556355884832im; -0.0026231701312300695 + 0.0024312755378171425im -0.007257622103696709 + 0.009979423015657221im … 0.0031397170938199616 + 0.01463067623478001im -0.00919704227391287 - 0.00887545771677178im; … ; 0.012807543265872644 - 0.013084698863108596im -0.0009259456107790175 - 0.0030603076610066574im … 0.029340263050459725 + 0.030456028459311252im 0.07829650692511322 + 0.00021089243966302155im; -0.0002125554352034385 + 0.049451635783458577im 0.029334298899170705 + 0.029475294984534866im … -0.0506246052745762 + 0.0037624762498490853im -0.0075519070777689615 + 0.009055264651538249im;;; 0.05174597227986482 - 0.0003135606242265117im 0.021595404602497714 - 0.025362992029764206im … -0.0018471104772870006 - 0.029728787464671225im -0.0031291925293420618 - 0.0011923391480727803im; -0.01650624327378552 + 0.022921770318646863im 0.0003340056907440332 + 0.019948596072093778im … -0.030343063854793333 - 0.02795666952148573im -0.05885448939464806 + 0.005183346646091063im; … ; 0.0020556990091730315 + 0.06439056536607482im 0.027419768699795656 + 0.0274181648899878im … 0.00601034383813513 + 0.0028085722153329516im -0.014906288179199513 + 0.0207522695156939im; 0.06406852469037932 + 0.06382003848774653im 0.06059781964322325 - 0.0012085288775092878im … -0.01203168674844944 + 0.012417296143491668im -0.00028103626538319125 + 0.037127530754935065im],)]), DFTK.DftHamiltonianBlock{PlaneWaveBasis{Float64, Float64, DFTK.CPU, FFTGrid{Float64, Float64, Array{StaticArraysCore.SVector{3, Int64}, 3}, Array{StaticArraysCore.SVector{3, Float64}, 3}}, Vector{StaticArraysCore.SVector{3, Int64}}}, Kpoint{Float64, Vector{StaticArraysCore.SVector{3, Int64}}, Vector{Int64}}, DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}, Nothing, Vector{@NamedTuple{ψ_reals::Array{ComplexF64, 3}}}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757), DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757), [0.062490081787469245, 0.9998413085995079, 3.062014007585993, 6.249008178746925, 10.5608238220823, 12.248056030343973, 7.561299896283778, 3.9993652343980317, 1.5622520446867312, 0.24996032714987704 … 2.7495635986486464, 5.561617279084762, 9.498492431695325, 14.560189056480331, 14.560189056480338, 9.498492431695325, 5.561617279084762, 2.7495635986486464, 1.0623313903869773, 0.49992065429975385]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757), ComplexF64[0.11038155824020969 + 0.0im 0.16972926797105742 + 0.0im … -0.009426647060181401 - 0.01632743165325398im 0.0094266470601814 + 0.016327431653253975im; 0.09335704685777356 + 0.0im 0.12740009431942179 + 0.0im … -0.05242104486249396 + 0.030265304362562327im 0.052421044862493944 - 0.03026530436256232im; … ; 0.09232028665365559 + 0.0im 0.12492048143428733 + 0.0im … 0.03728123116232767 + 0.0645729865418717im 0.0074562462324655335 + 0.01291459730837434im; 0.10208144135055229 + 0.0im 0.14872488279907023 + 0.0im … 0.029470953026436666 - 0.01701506266308801im 0.058941906052873326 - 0.03403012532617601im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757), [-12.2475696978844 -11.100308387033913 … -8.289845769066893 -11.100308387033943; -11.10030838703391 -9.130057818482163 … -9.130057802436339 -11.100308365268916; … ; -8.289845769066893 -9.130057802436337 … -4.14958991194573 -6.2879562047399284; -11.10030838703394 -11.100308365268914 … -6.287956204739929 -9.111848216112016;;; -11.100308387033914 -9.130057818482161 … -9.130057802436339 -11.100308365268914; -9.130057818482161 -6.903159504367577 … -9.130057819839301 -10.053883816988046; … ; -9.130057802436339 -9.130057819839298 … -5.294353665850196 -7.547399215037599; -11.100308365268914 -10.053883816988046 … -7.547399215037599 -10.053883816988098;;; -8.289845769067037 -6.307621938057417 … -8.289845773669953 -9.111848200066168; -6.307621938057414 -4.516655658355899 … -7.547399231892241 -7.547399215037713; … ; -8.289845773669953 -7.547399231892238 … -5.768969098395969 -7.547399231892274; -9.111848200066168 -7.5473992150377125 … -7.547399231892275 -9.111848217469266;;; … ;;; -5.301031708536039 -6.307621951399262 … -2.5497035798117262 -3.8495821823329694; -6.307621951399262 -6.903159511447426 … -3.3290606941630063 -4.878419351559539; … ; -2.549703579811726 -3.3290606941630063 … -1.2567984675346517 -1.8141947489915244; -3.849582182332969 -4.878419351559539 … -1.8141947489915258 -2.714767336891466;;; -8.289845769066892 -9.130057802436337 … -4.14958991194573 -6.2879562047399284; -9.130057802436335 -9.1300578198393 … -5.294353665850197 -7.547399215037599; … ; -4.14958991194573 -5.294353665850197 … -1.9094492500180213 -2.8946123644894746; -6.2879562047399284 -7.5473992150376 … -2.8946123644894755 -4.485542751912487;;; -11.100308387033943 -11.100308365268916 … -6.2879562047399284 -9.111848216112017; -11.100308365268914 -10.053883816988048 … -7.547399215037601 -10.053883816988096; … ; -6.2879562047399284 -7.547399215037598 … -2.894612364489475 -4.485542751912487; -9.111848216112017 -10.053883816988096 … -4.485542751912487 -6.87110452252074])], DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757), [0.062490081787469245, 0.9998413085995079, 3.062014007585993, 6.249008178746925, 10.5608238220823, 12.248056030343973, 7.561299896283778, 3.9993652343980317, 1.5622520446867312, 0.24996032714987704 … 2.7495635986486464, 5.561617279084762, 9.498492431695325, 14.560189056480331, 14.560189056480338, 9.498492431695325, 5.561617279084762, 2.7495635986486464, 1.0623313903869773, 0.49992065429975385]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757), [-12.2475696978844 -11.100308387033913 … -8.289845769066893 -11.100308387033943; -11.10030838703391 -9.130057818482163 … -9.130057802436339 -11.100308365268916; … ; -8.289845769066893 -9.130057802436337 … -4.14958991194573 -6.2879562047399284; -11.10030838703394 -11.100308365268914 … -6.287956204739929 -9.111848216112016;;; -11.100308387033914 -9.130057818482161 … -9.130057802436339 -11.100308365268914; -9.130057818482161 -6.903159504367577 … -9.130057819839301 -10.053883816988046; … ; -9.130057802436339 -9.130057819839298 … -5.294353665850196 -7.547399215037599; -11.100308365268914 -10.053883816988046 … -7.547399215037599 -10.053883816988098;;; -8.289845769067037 -6.307621938057417 … -8.289845773669953 -9.111848200066168; -6.307621938057414 -4.516655658355899 … -7.547399231892241 -7.547399215037713; … ; -8.289845773669953 -7.547399231892238 … -5.768969098395969 -7.547399231892274; -9.111848200066168 -7.5473992150377125 … -7.547399231892275 -9.111848217469266;;; … ;;; -5.301031708536039 -6.307621951399262 … -2.5497035798117262 -3.8495821823329694; -6.307621951399262 -6.903159511447426 … -3.3290606941630063 -4.878419351559539; … ; -2.549703579811726 -3.3290606941630063 … -1.2567984675346517 -1.8141947489915244; -3.849582182332969 -4.878419351559539 … -1.8141947489915258 -2.714767336891466;;; -8.289845769066892 -9.130057802436337 … -4.14958991194573 -6.2879562047399284; -9.130057802436335 -9.1300578198393 … -5.294353665850197 -7.547399215037599; … ; -4.14958991194573 -5.294353665850197 … -1.9094492500180213 -2.8946123644894746; -6.2879562047399284 -7.5473992150376 … -2.8946123644894755 -4.485542751912487;;; -11.100308387033943 -11.100308365268916 … -6.2879562047399284 -9.111848216112017; -11.100308365268914 -10.053883816988048 … -7.547399215037601 -10.053883816988096; … ; -6.2879562047399284 -7.547399215037598 … -2.894612364489475 -4.485542751912487; -9.111848216112017 -10.053883816988096 … -4.485542751912487 -6.87110452252074]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757), ComplexF64[0.11038155824020969 + 0.0im 0.16972926797105742 + 0.0im … -0.009426647060181401 - 0.01632743165325398im 0.0094266470601814 + 0.016327431653253975im; 0.09335704685777356 + 0.0im 0.12740009431942179 + 0.0im … -0.05242104486249396 + 0.030265304362562327im 0.052421044862493944 - 0.03026530436256232im; … ; 0.09232028665365559 + 0.0im 0.12492048143428733 + 0.0im … 0.03728123116232767 + 0.0645729865418717im 0.0074562462324655335 + 0.01291459730837434im; 0.10208144135055229 + 0.0im 0.14872488279907023 + 0.0im … 0.029470953026436666 - 0.01701506266308801im 0.058941906052873326 - 0.03403012532617601im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, @NamedTuple{ψ_reals::Array{ComplexF64, 3}}[(ψ_reals = [-1.7788048193691577e-6 + 0.0008976655748475599im -0.0035485627180988927 - 0.004438614492265291im … -0.00144505433124814 - 0.00013726129198712335im -0.0027012573412004944 + 0.002366566187481845im; 0.00038699692000509665 + 0.0004533665080298005im -0.0028716154101844633 - 0.00017427504784827959im … 0.0005037860776012071 - 0.00025045561823621294im -7.037613464528454e-5 + 0.0026589143195040036im; … ; -0.004981990696411377 - 0.0006206963576591217im -0.002645993433684053 + 0.0020030273365509725im … -0.0001294033247711381 + 0.001738211710460575im 0.00029242540279260647 + 0.0005451977128713136im; -0.0060545192815659905 + 0.004651670142355966im -0.00032019824935716886 + 0.001686383384289115im … -0.002575972059648394 - 0.0033675449774419938im -0.006422203056065211 - 0.0007071066622620658im;;; -0.0038226163397192467 - 0.04247581132210683im -0.07717422690855255 - 0.06541393396293858im … 0.028713837018167248 - 0.002350500325848201im 0.012722013639403666 - 0.01468281851470838im; -0.0007340879881196135 + 0.0009912881714227752im -0.056516213270514704 + 0.004494298748578804im … 0.008640297123026972 - 0.011946964908447325im 0.0006946537762353086 + 0.027829325820015585im; … ; -0.06484836940592374 + 0.006659785130398499im -0.004156274678323753 + 0.008041837829271564im … -0.002383115305502895 - 0.048352347535757845im -0.05735842093567942 - 0.049825773095518104im; 0.013553844451098467 - 0.010381081812075539im -0.003751061628773592 - 0.06636039756892843im … -0.011047969299694855 - 0.0081138487745765im -0.013763643094201842 + 0.0036581947553949966im;;; -0.038037843235910127 - 0.031219041007441543im -0.08805480213903537 + 0.007576613983880556im … 0.0036446193439703435 - 0.00680852768225375im -0.0013652794271663323 + 0.004941857155660707im; 0.04754976628227655 - 0.0006429553886491803im 0.007713636110634636 - 0.007646361287274245im … -0.0017090685963981342 + 0.0008504579716408604im 0.04612770752188608 + 0.04314446888003458im; … ; 0.008205814894687875 - 0.003944003765504795im -0.0024032810489415255 - 0.07910695765920259im … -0.058476873415902686 - 0.05260889328243454im -0.05676288693922369 + 0.0050268500145765095im; -0.003802433274523936 - 0.08872234692386402im -0.10391886934327811 - 0.09149132146489876im … -0.018722143000648575 + 0.0012694530364994803im 0.012125903674445285 - 0.010401219805098767im;;; … ;;; 0.003320951666864233 + 0.08477755954910168im 0.055337529010860975 + 0.05123239519681432im … -0.022987141011324375 + 0.0033493699110132245im -0.029938551126563323 + 0.03583294791818136im; 0.07618514820016624 + 0.07023834073920063im 0.0848718677758278 - 0.0029508395454156972im … -0.008873118801253445 + 0.015161239299042891im 0.005996296823253838 + 0.08296578256596752im; … ; 0.09583364792458124 - 0.002699138564671244im 0.04227214752995155 - 0.046011936982386294im … -0.00039412709114974333 + 0.02270664491082569im 0.07424036829115585 + 0.07216972526436341im; 0.01883261351296065 - 0.021035674739191865im -0.001040479027121094 - 0.009766221713831538im … -0.007432378162925409 - 0.005177610928899089im 0.0506754011245881 - 0.0004144556047203235im;;; 0.050466407734821375 + 0.04770238149110915im 0.07521925084065016 - 0.002881420914128449im … -0.021538772549005675 + 0.02608948369350987im 0.0011445431667381069 + 0.009840556355884832im; -0.0026231701312300695 + 0.0024312755378171425im -0.007257622103696709 + 0.009979423015657221im … 0.0031397170938199616 + 0.01463067623478001im -0.00919704227391287 - 0.00887545771677178im; … ; 0.012807543265872644 - 0.013084698863108596im -0.0009259456107790175 - 0.0030603076610066574im … 0.029340263050459725 + 0.030456028459311252im 0.07829650692511322 + 0.00021089243966302155im; -0.0002125554352034385 + 0.049451635783458577im 0.029334298899170705 + 0.029475294984534866im … -0.0506246052745762 + 0.0037624762498490853im -0.0075519070777689615 + 0.009055264651538249im;;; 0.05174597227986482 - 0.0003135606242265117im 0.021595404602497714 - 0.025362992029764206im … -0.0018471104772870006 - 0.029728787464671225im -0.0031291925293420618 - 0.0011923391480727803im; -0.01650624327378552 + 0.022921770318646863im 0.0003340056907440332 + 0.019948596072093778im … -0.030343063854793333 - 0.02795666952148573im -0.05885448939464806 + 0.005183346646091063im; … ; 0.0020556990091730315 + 0.06439056536607482im 0.027419768699795656 + 0.0274181648899878im … 0.00601034383813513 + 0.0028085722153329516im -0.014906288179199513 + 0.0207522695156939im; 0.06406852469037932 + 0.06382003848774653im 0.06059781964322325 - 0.0012085288775092878im … -0.01203168674844944 + 0.012417296143491668im -0.00028103626538319125 + 0.037127530754935065im],)]), DFTK.DftHamiltonianBlock{PlaneWaveBasis{Float64, Float64, DFTK.CPU, FFTGrid{Float64, Float64, Array{StaticArraysCore.SVector{3, Int64}, 3}, Array{StaticArraysCore.SVector{3, Float64}, 3}}, Vector{StaticArraysCore.SVector{3, Int64}}}, Kpoint{Float64, Vector{StaticArraysCore.SVector{3, Int64}}, Vector{Int64}}, DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}, Nothing, Vector{@NamedTuple{ψ_reals::Array{ComplexF64, 3}}}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749), DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749), [0.083320109049959, 0.8956911722870592, 2.8328837076986058, 5.894897715284598, 10.081733195045036, 12.893786875481155, 8.082050577846019, 4.395135752385337, 1.8330423990990978, 0.3957705179873052 … 0.8332010904995898, 2.3954531351863206, 5.082526652047498, 8.894421641083122, 13.83113810229319, 9.89426294968263, 5.832407633497128, 2.895373789486075, 1.083161417649467, 0.3957705179873052]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749), ComplexF64[0.10997142862853636 + 0.0im 0.16867583607081263 + 0.0im … -0.032495727623724026 - 0.018761417091069828im -5.710372280586092e-19 - 3.2968849733693577e-19im; 0.09511091805015323 + 0.0im 0.13162182200636918 + 0.0im … -0.038767079080422394 + 0.0671465506283321im 0.023260247448253425 - 0.040287930376999244im; … ; 0.09197726483082143 + 0.0im 0.12410271910068073 + 0.0im … 0.051406644402565774 + 0.029679639983956736im 6.990521527121635e-18 + 4.0359794854595524e-18im; 0.10399921515860865 + 0.0im 0.15351809108742231 + 0.0im … 0.008717893888213726 - 0.015099835149380354im 0.02615368166464116 - 0.04529950544814103im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749), [-12.2475696978844 -11.100308387033913 … -8.289845769066893 -11.100308387033943; -11.10030838703391 -9.130057818482163 … -9.130057802436339 -11.100308365268916; … ; -8.289845769066893 -9.130057802436337 … -4.14958991194573 -6.2879562047399284; -11.10030838703394 -11.100308365268914 … -6.287956204739929 -9.111848216112016;;; -11.100308387033914 -9.130057818482161 … -9.130057802436339 -11.100308365268914; -9.130057818482161 -6.903159504367577 … -9.130057819839301 -10.053883816988046; … ; -9.130057802436339 -9.130057819839298 … -5.294353665850196 -7.547399215037599; -11.100308365268914 -10.053883816988046 … -7.547399215037599 -10.053883816988098;;; -8.289845769067037 -6.307621938057417 … -8.289845773669953 -9.111848200066168; -6.307621938057414 -4.516655658355899 … -7.547399231892241 -7.547399215037713; … ; -8.289845773669953 -7.547399231892238 … -5.768969098395969 -7.547399231892274; -9.111848200066168 -7.5473992150377125 … -7.547399231892275 -9.111848217469266;;; … ;;; -5.301031708536039 -6.307621951399262 … -2.5497035798117262 -3.8495821823329694; -6.307621951399262 -6.903159511447426 … -3.3290606941630063 -4.878419351559539; … ; -2.549703579811726 -3.3290606941630063 … -1.2567984675346517 -1.8141947489915244; -3.849582182332969 -4.878419351559539 … -1.8141947489915258 -2.714767336891466;;; -8.289845769066892 -9.130057802436337 … -4.14958991194573 -6.2879562047399284; -9.130057802436335 -9.1300578198393 … -5.294353665850197 -7.547399215037599; … ; -4.14958991194573 -5.294353665850197 … -1.9094492500180213 -2.8946123644894746; -6.2879562047399284 -7.5473992150376 … -2.8946123644894755 -4.485542751912487;;; -11.100308387033943 -11.100308365268916 … -6.2879562047399284 -9.111848216112017; -11.100308365268914 -10.053883816988048 … -7.547399215037601 -10.053883816988096; … ; -6.2879562047399284 -7.547399215037598 … -2.894612364489475 -4.485542751912487; -9.111848216112017 -10.053883816988096 … -4.485542751912487 -6.87110452252074])], DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749), [0.083320109049959, 0.8956911722870592, 2.8328837076986058, 5.894897715284598, 10.081733195045036, 12.893786875481155, 8.082050577846019, 4.395135752385337, 1.8330423990990978, 0.3957705179873052 … 0.8332010904995898, 2.3954531351863206, 5.082526652047498, 8.894421641083122, 13.83113810229319, 9.89426294968263, 5.832407633497128, 2.895373789486075, 1.083161417649467, 0.3957705179873052]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749), [-12.2475696978844 -11.100308387033913 … -8.289845769066893 -11.100308387033943; -11.10030838703391 -9.130057818482163 … -9.130057802436339 -11.100308365268916; … ; -8.289845769066893 -9.130057802436337 … -4.14958991194573 -6.2879562047399284; -11.10030838703394 -11.100308365268914 … -6.287956204739929 -9.111848216112016;;; -11.100308387033914 -9.130057818482161 … -9.130057802436339 -11.100308365268914; -9.130057818482161 -6.903159504367577 … -9.130057819839301 -10.053883816988046; … ; -9.130057802436339 -9.130057819839298 … -5.294353665850196 -7.547399215037599; -11.100308365268914 -10.053883816988046 … -7.547399215037599 -10.053883816988098;;; -8.289845769067037 -6.307621938057417 … -8.289845773669953 -9.111848200066168; -6.307621938057414 -4.516655658355899 … -7.547399231892241 -7.547399215037713; … ; -8.289845773669953 -7.547399231892238 … -5.768969098395969 -7.547399231892274; -9.111848200066168 -7.5473992150377125 … -7.547399231892275 -9.111848217469266;;; … ;;; -5.301031708536039 -6.307621951399262 … -2.5497035798117262 -3.8495821823329694; -6.307621951399262 -6.903159511447426 … -3.3290606941630063 -4.878419351559539; … ; -2.549703579811726 -3.3290606941630063 … -1.2567984675346517 -1.8141947489915244; -3.849582182332969 -4.878419351559539 … -1.8141947489915258 -2.714767336891466;;; -8.289845769066892 -9.130057802436337 … -4.14958991194573 -6.2879562047399284; -9.130057802436335 -9.1300578198393 … -5.294353665850197 -7.547399215037599; … ; -4.14958991194573 -5.294353665850197 … -1.9094492500180213 -2.8946123644894746; -6.2879562047399284 -7.5473992150376 … -2.8946123644894755 -4.485542751912487;;; -11.100308387033943 -11.100308365268916 … -6.2879562047399284 -9.111848216112017; -11.100308365268914 -10.053883816988048 … -7.547399215037601 -10.053883816988096; … ; -6.2879562047399284 -7.547399215037598 … -2.894612364489475 -4.485542751912487; -9.111848216112017 -10.053883816988096 … -4.485542751912487 -6.87110452252074]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749), ComplexF64[0.10997142862853636 + 0.0im 0.16867583607081263 + 0.0im … -0.032495727623724026 - 0.018761417091069828im -5.710372280586092e-19 - 3.2968849733693577e-19im; 0.09511091805015323 + 0.0im 0.13162182200636918 + 0.0im … -0.038767079080422394 + 0.0671465506283321im 0.023260247448253425 - 0.040287930376999244im; … ; 0.09197726483082143 + 0.0im 0.12410271910068073 + 0.0im … 0.051406644402565774 + 0.029679639983956736im 6.990521527121635e-18 + 4.0359794854595524e-18im; 0.10399921515860865 + 0.0im 0.15351809108742231 + 0.0im … 0.008717893888213726 - 0.015099835149380354im 0.02615368166464116 - 0.04529950544814103im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, @NamedTuple{ψ_reals::Array{ComplexF64, 3}}[(ψ_reals = [-1.7788048193691577e-6 + 0.0008976655748475599im -0.0035485627180988927 - 0.004438614492265291im … -0.00144505433124814 - 0.00013726129198712335im -0.0027012573412004944 + 0.002366566187481845im; 0.00038699692000509665 + 0.0004533665080298005im -0.0028716154101844633 - 0.00017427504784827959im … 0.0005037860776012071 - 0.00025045561823621294im -7.037613464528454e-5 + 0.0026589143195040036im; … ; -0.004981990696411377 - 0.0006206963576591217im -0.002645993433684053 + 0.0020030273365509725im … -0.0001294033247711381 + 0.001738211710460575im 0.00029242540279260647 + 0.0005451977128713136im; -0.0060545192815659905 + 0.004651670142355966im -0.00032019824935716886 + 0.001686383384289115im … -0.002575972059648394 - 0.0033675449774419938im -0.006422203056065211 - 0.0007071066622620658im;;; -0.0038226163397192467 - 0.04247581132210683im -0.07717422690855255 - 0.06541393396293858im … 0.028713837018167248 - 0.002350500325848201im 0.012722013639403666 - 0.01468281851470838im; -0.0007340879881196135 + 0.0009912881714227752im -0.056516213270514704 + 0.004494298748578804im … 0.008640297123026972 - 0.011946964908447325im 0.0006946537762353086 + 0.027829325820015585im; … ; -0.06484836940592374 + 0.006659785130398499im -0.004156274678323753 + 0.008041837829271564im … -0.002383115305502895 - 0.048352347535757845im -0.05735842093567942 - 0.049825773095518104im; 0.013553844451098467 - 0.010381081812075539im -0.003751061628773592 - 0.06636039756892843im … -0.011047969299694855 - 0.0081138487745765im -0.013763643094201842 + 0.0036581947553949966im;;; -0.038037843235910127 - 0.031219041007441543im -0.08805480213903537 + 0.007576613983880556im … 0.0036446193439703435 - 0.00680852768225375im -0.0013652794271663323 + 0.004941857155660707im; 0.04754976628227655 - 0.0006429553886491803im 0.007713636110634636 - 0.007646361287274245im … -0.0017090685963981342 + 0.0008504579716408604im 0.04612770752188608 + 0.04314446888003458im; … ; 0.008205814894687875 - 0.003944003765504795im -0.0024032810489415255 - 0.07910695765920259im … -0.058476873415902686 - 0.05260889328243454im -0.05676288693922369 + 0.0050268500145765095im; -0.003802433274523936 - 0.08872234692386402im -0.10391886934327811 - 0.09149132146489876im … -0.018722143000648575 + 0.0012694530364994803im 0.012125903674445285 - 0.010401219805098767im;;; … ;;; 0.003320951666864233 + 0.08477755954910168im 0.055337529010860975 + 0.05123239519681432im … -0.022987141011324375 + 0.0033493699110132245im -0.029938551126563323 + 0.03583294791818136im; 0.07618514820016624 + 0.07023834073920063im 0.0848718677758278 - 0.0029508395454156972im … -0.008873118801253445 + 0.015161239299042891im 0.005996296823253838 + 0.08296578256596752im; … ; 0.09583364792458124 - 0.002699138564671244im 0.04227214752995155 - 0.046011936982386294im … -0.00039412709114974333 + 0.02270664491082569im 0.07424036829115585 + 0.07216972526436341im; 0.01883261351296065 - 0.021035674739191865im -0.001040479027121094 - 0.009766221713831538im … -0.007432378162925409 - 0.005177610928899089im 0.0506754011245881 - 0.0004144556047203235im;;; 0.050466407734821375 + 0.04770238149110915im 0.07521925084065016 - 0.002881420914128449im … -0.021538772549005675 + 0.02608948369350987im 0.0011445431667381069 + 0.009840556355884832im; -0.0026231701312300695 + 0.0024312755378171425im -0.007257622103696709 + 0.009979423015657221im … 0.0031397170938199616 + 0.01463067623478001im -0.00919704227391287 - 0.00887545771677178im; … ; 0.012807543265872644 - 0.013084698863108596im -0.0009259456107790175 - 0.0030603076610066574im … 0.029340263050459725 + 0.030456028459311252im 0.07829650692511322 + 0.00021089243966302155im; -0.0002125554352034385 + 0.049451635783458577im 0.029334298899170705 + 0.029475294984534866im … -0.0506246052745762 + 0.0037624762498490853im -0.0075519070777689615 + 0.009055264651538249im;;; 0.05174597227986482 - 0.0003135606242265117im 0.021595404602497714 - 0.025362992029764206im … -0.0018471104772870006 - 0.029728787464671225im -0.0031291925293420618 - 0.0011923391480727803im; -0.01650624327378552 + 0.022921770318646863im 0.0003340056907440332 + 0.019948596072093778im … -0.030343063854793333 - 0.02795666952148573im -0.05885448939464806 + 0.005183346646091063im; … ; 0.0020556990091730315 + 0.06439056536607482im 0.027419768699795656 + 0.0274181648899878im … 0.00601034383813513 + 0.0028085722153329516im -0.014906288179199513 + 0.0207522695156939im; 0.06406852469037932 + 0.06382003848774653im 0.06059781964322325 - 0.0012085288775092878im … -0.01203168674844944 + 0.012417296143491668im -0.00028103626538319125 + 0.037127530754935065im],)]), DFTK.DftHamiltonianBlock{PlaneWaveBasis{Float64, Float64, DFTK.CPU, FFTGrid{Float64, Float64, Array{StaticArraysCore.SVector{3, Int64}, 3}, Array{StaticArraysCore.SVector{3, Float64}, 3}}, Vector{StaticArraysCore.SVector{3, Int64}}}, Kpoint{Float64, Vector{StaticArraysCore.SVector{3, Int64}}, Vector{Int64}}, DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}, Nothing, Vector{@NamedTuple{ψ_reals::Array{ComplexF64, 3}}}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740), DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740), [0.16664021809991797, 0.22913029988738726, 1.4164418538493029, 3.728574879985665, 7.165529378296473, 11.727305348781728, 11.164894612694503, 6.728098805784188, 3.4161244710483185, 1.2289716084868951 … 0.41660054524979495, 1.228971608486895, 3.1661641438984414, 6.2281781514844345, 10.415013631244872, 13.22706731168099, 8.415331014045858, 4.7284161885851725, 2.166322835298934, 0.7290509541871413]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740), ComplexF64[0.1083460922901765 + 0.0im 0.16451669692939747 + 0.0im … -0.0 + 1.0213144005610528e-18im 0.0 - 0.03679672923035902im; 0.10714287388793554 + 0.0im 0.16145393303017874 + 0.0im … -0.054392079538503724 - 0.0im 0.018130693179501247 + 0.0im; … ; 0.07579045242767471 + 0.0im 0.08711041809792075 + 0.0im … -0.0 + 0.06906475263474504im 0.0 - 0.023021584211581677im; 0.09798590385967747 + 0.0im 0.13861415332258223 + 0.0im … 0.04837457477358332 + 0.0im 0.01612485825786111 + 0.0im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740), [-12.2475696978844 -11.100308387033913 … -8.289845769066893 -11.100308387033943; -11.10030838703391 -9.130057818482163 … -9.130057802436339 -11.100308365268916; … ; -8.289845769066893 -9.130057802436337 … -4.14958991194573 -6.2879562047399284; -11.10030838703394 -11.100308365268914 … -6.287956204739929 -9.111848216112016;;; -11.100308387033914 -9.130057818482161 … -9.130057802436339 -11.100308365268914; -9.130057818482161 -6.903159504367577 … -9.130057819839301 -10.053883816988046; … ; -9.130057802436339 -9.130057819839298 … -5.294353665850196 -7.547399215037599; -11.100308365268914 -10.053883816988046 … -7.547399215037599 -10.053883816988098;;; -8.289845769067037 -6.307621938057417 … -8.289845773669953 -9.111848200066168; -6.307621938057414 -4.516655658355899 … -7.547399231892241 -7.547399215037713; … ; -8.289845773669953 -7.547399231892238 … -5.768969098395969 -7.547399231892274; -9.111848200066168 -7.5473992150377125 … -7.547399231892275 -9.111848217469266;;; … ;;; -5.301031708536039 -6.307621951399262 … -2.5497035798117262 -3.8495821823329694; -6.307621951399262 -6.903159511447426 … -3.3290606941630063 -4.878419351559539; … ; -2.549703579811726 -3.3290606941630063 … -1.2567984675346517 -1.8141947489915244; -3.849582182332969 -4.878419351559539 … -1.8141947489915258 -2.714767336891466;;; -8.289845769066892 -9.130057802436337 … -4.14958991194573 -6.2879562047399284; -9.130057802436335 -9.1300578198393 … -5.294353665850197 -7.547399215037599; … ; -4.14958991194573 -5.294353665850197 … -1.9094492500180213 -2.8946123644894746; -6.2879562047399284 -7.5473992150376 … -2.8946123644894755 -4.485542751912487;;; -11.100308387033943 -11.100308365268916 … -6.2879562047399284 -9.111848216112017; -11.100308365268914 -10.053883816988048 … -7.547399215037601 -10.053883816988096; … ; -6.2879562047399284 -7.547399215037598 … -2.894612364489475 -4.485542751912487; -9.111848216112017 -10.053883816988096 … -4.485542751912487 -6.87110452252074])], DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740), [0.16664021809991797, 0.22913029988738726, 1.4164418538493029, 3.728574879985665, 7.165529378296473, 11.727305348781728, 11.164894612694503, 6.728098805784188, 3.4161244710483185, 1.2289716084868951 … 0.41660054524979495, 1.228971608486895, 3.1661641438984414, 6.2281781514844345, 10.415013631244872, 13.22706731168099, 8.415331014045858, 4.7284161885851725, 2.166322835298934, 0.7290509541871413]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740), [-12.2475696978844 -11.100308387033913 … -8.289845769066893 -11.100308387033943; -11.10030838703391 -9.130057818482163 … -9.130057802436339 -11.100308365268916; … ; -8.289845769066893 -9.130057802436337 … -4.14958991194573 -6.2879562047399284; -11.10030838703394 -11.100308365268914 … -6.287956204739929 -9.111848216112016;;; -11.100308387033914 -9.130057818482161 … -9.130057802436339 -11.100308365268914; -9.130057818482161 -6.903159504367577 … -9.130057819839301 -10.053883816988046; … ; -9.130057802436339 -9.130057819839298 … -5.294353665850196 -7.547399215037599; -11.100308365268914 -10.053883816988046 … -7.547399215037599 -10.053883816988098;;; -8.289845769067037 -6.307621938057417 … -8.289845773669953 -9.111848200066168; -6.307621938057414 -4.516655658355899 … -7.547399231892241 -7.547399215037713; … ; -8.289845773669953 -7.547399231892238 … -5.768969098395969 -7.547399231892274; -9.111848200066168 -7.5473992150377125 … -7.547399231892275 -9.111848217469266;;; … ;;; -5.301031708536039 -6.307621951399262 … -2.5497035798117262 -3.8495821823329694; -6.307621951399262 -6.903159511447426 … -3.3290606941630063 -4.878419351559539; … ; -2.549703579811726 -3.3290606941630063 … -1.2567984675346517 -1.8141947489915244; -3.849582182332969 -4.878419351559539 … -1.8141947489915258 -2.714767336891466;;; -8.289845769066892 -9.130057802436337 … -4.14958991194573 -6.2879562047399284; -9.130057802436335 -9.1300578198393 … -5.294353665850197 -7.547399215037599; … ; -4.14958991194573 -5.294353665850197 … -1.9094492500180213 -2.8946123644894746; -6.2879562047399284 -7.5473992150376 … -2.8946123644894755 -4.485542751912487;;; -11.100308387033943 -11.100308365268916 … -6.2879562047399284 -9.111848216112017; -11.100308365268914 -10.053883816988048 … -7.547399215037601 -10.053883816988096; … ; -6.2879562047399284 -7.547399215037598 … -2.894612364489475 -4.485542751912487; -9.111848216112017 -10.053883816988096 … -4.485542751912487 -6.87110452252074]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740), ComplexF64[0.1083460922901765 + 0.0im 0.16451669692939747 + 0.0im … -0.0 + 1.0213144005610528e-18im 0.0 - 0.03679672923035902im; 0.10714287388793554 + 0.0im 0.16145393303017874 + 0.0im … -0.054392079538503724 - 0.0im 0.018130693179501247 + 0.0im; … ; 0.07579045242767471 + 0.0im 0.08711041809792075 + 0.0im … -0.0 + 0.06906475263474504im 0.0 - 0.023021584211581677im; 0.09798590385967747 + 0.0im 0.13861415332258223 + 0.0im … 0.04837457477358332 + 0.0im 0.01612485825786111 + 0.0im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, @NamedTuple{ψ_reals::Array{ComplexF64, 3}}[(ψ_reals = [-1.7788048193691577e-6 + 0.0008976655748475599im -0.0035485627180988927 - 0.004438614492265291im … -0.00144505433124814 - 0.00013726129198712335im -0.0027012573412004944 + 0.002366566187481845im; 0.00038699692000509665 + 0.0004533665080298005im -0.0028716154101844633 - 0.00017427504784827959im … 0.0005037860776012071 - 0.00025045561823621294im -7.037613464528454e-5 + 0.0026589143195040036im; … ; -0.004981990696411377 - 0.0006206963576591217im -0.002645993433684053 + 0.0020030273365509725im … -0.0001294033247711381 + 0.001738211710460575im 0.00029242540279260647 + 0.0005451977128713136im; -0.0060545192815659905 + 0.004651670142355966im -0.00032019824935716886 + 0.001686383384289115im … -0.002575972059648394 - 0.0033675449774419938im -0.006422203056065211 - 0.0007071066622620658im;;; -0.0038226163397192467 - 0.04247581132210683im -0.07717422690855255 - 0.06541393396293858im … 0.028713837018167248 - 0.002350500325848201im 0.012722013639403666 - 0.01468281851470838im; -0.0007340879881196135 + 0.0009912881714227752im -0.056516213270514704 + 0.004494298748578804im … 0.008640297123026972 - 0.011946964908447325im 0.0006946537762353086 + 0.027829325820015585im; … ; -0.06484836940592374 + 0.006659785130398499im -0.004156274678323753 + 0.008041837829271564im … -0.002383115305502895 - 0.048352347535757845im -0.05735842093567942 - 0.049825773095518104im; 0.013553844451098467 - 0.010381081812075539im -0.003751061628773592 - 0.06636039756892843im … -0.011047969299694855 - 0.0081138487745765im -0.013763643094201842 + 0.0036581947553949966im;;; 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… ; 0.09583364792458124 - 0.002699138564671244im 0.04227214752995155 - 0.046011936982386294im … -0.00039412709114974333 + 0.02270664491082569im 0.07424036829115585 + 0.07216972526436341im; 0.01883261351296065 - 0.021035674739191865im -0.001040479027121094 - 0.009766221713831538im … -0.007432378162925409 - 0.005177610928899089im 0.0506754011245881 - 0.0004144556047203235im;;; 0.050466407734821375 + 0.04770238149110915im 0.07521925084065016 - 0.002881420914128449im … -0.021538772549005675 + 0.02608948369350987im 0.0011445431667381069 + 0.009840556355884832im; -0.0026231701312300695 + 0.0024312755378171425im -0.007257622103696709 + 0.009979423015657221im … 0.0031397170938199616 + 0.01463067623478001im -0.00919704227391287 - 0.00887545771677178im; … ; 0.012807543265872644 - 0.013084698863108596im -0.0009259456107790175 - 0.0030603076610066574im … 0.029340263050459725 + 0.030456028459311252im 0.07829650692511322 + 0.00021089243966302155im; -0.0002125554352034385 + 0.049451635783458577im 0.029334298899170705 + 0.029475294984534866im … -0.0506246052745762 + 0.0037624762498490853im -0.0075519070777689615 + 0.009055264651538249im;;; 0.05174597227986482 - 0.0003135606242265117im 0.021595404602497714 - 0.025362992029764206im … -0.0018471104772870006 - 0.029728787464671225im -0.0031291925293420618 - 0.0011923391480727803im; -0.01650624327378552 + 0.022921770318646863im 0.0003340056907440332 + 0.019948596072093778im … -0.030343063854793333 - 0.02795666952148573im -0.05885448939464806 + 0.005183346646091063im; … ; 0.0020556990091730315 + 0.06439056536607482im 0.027419768699795656 + 0.0274181648899878im … 0.00601034383813513 + 0.0028085722153329516im -0.014906288179199513 + 0.0207522695156939im; 0.06406852469037932 + 0.06382003848774653im 0.06059781964322325 - 0.0012085288775092878im … -0.01203168674844944 + 0.012417296143491668im -0.00028103626538319125 + 0.037127530754935065im],)])]), basis = PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), energies = Energies(total = -7.9105943964884835), converged = true, ρ = [7.589784542854559e-5 0.0011262712728093813 … 0.006697037549964719 0.0011262712728093897; 0.001126271272809371 0.005274334457266555 … 0.005274334457266579 0.0011262712728093796; … ; 0.006697037549964714 0.0052743344572665956 … 0.023244754190820966 0.012258986825082741; 0.0011262712728093863 0.0011262712728093845 … 0.012258986825082733 0.0037700086298292487;;; 0.0011262712728093815 0.005274334457266562 … 0.005274334457266603 0.0011262712728093976; 0.005274334457266553 0.014620065304476659 … 0.005274334457266576 0.002588080874796522; … ; 0.005274334457266597 0.005274334457266592 … 0.018107686645916537 0.00892200304460202; 0.0011262712728093952 0.002588080874796526 … 0.008922003044602014 0.002588080874796544;;; 0.006697037549964683 0.016412109101348032 … 0.006697037549964714 0.003770008629829248; 0.01641210910134802 0.031277839315507275 … 0.00892200304460198 0.008922003044601967; … ; 0.006697037549964708 0.008922003044601997 … 0.01647675635922441 0.008922003044602018; 0.0037700086298292444 0.00892200304460197 … 0.008922003044602007 0.0037700086298292452;;; … ;;; 0.019853839853142125 0.016412109101348046 … 0.03715667363537333 0.027190800686303515; 0.016412109101348032 0.014620065304476668 … 0.03230127212612817 0.022322100931435187; … ; 0.03715667363537333 0.03230127212612818 … 0.046296980701199975 0.04263658273116427; 0.027190800686303508 0.02232210093143519 … 0.04263658273116427 0.0347722291417194;;; 0.006697037549964691 0.0052743344572665695 … 0.023244754190820945 0.01225898682508272; 0.005274334457266555 0.005274334457266562 … 0.01810768664591649 0.008922003044601978; … ; 0.02324475419082094 0.018107686645916506 … 0.04037111033531689 0.03149160381114024; 0.012258986825082713 0.008922003044601976 … 0.031491603811140224 0.020047163432539525;;; 0.0011262712728093843 0.001126271272809376 … 0.012258986825082734 0.0037700086298292548; 0.0011262712728093674 0.0025880808747965173 … 0.008922003044601987 0.0025880808747965247; … ; 0.012258986825082729 0.008922003044602004 … 0.031491603811140245 0.02004716343253955; 0.00377000862982925 0.0025880808747965277 … 0.02004716343253954 0.008952603496654289;;;;], eigenvalues = [[-0.17836835653815838, 0.2624919449935, 0.2624919449935005, 0.2624919449935008, 0.3546921481687572, 0.3546921481687579, 0.3546921481743482], [-0.1275503761778277, 0.06475320594806462, 0.2254516651759745, 0.2254516651759748, 0.32197764961241265, 0.3892227690856161, 0.3892227690856167], [-0.10818729216370004, 0.07755003473633745, 0.17278328011607597, 0.17278328011607627, 0.28435185361972737, 0.3305476484326673, 0.5267232426409736], [-0.05777325374264351, 0.0127247822071946, 0.09766073750172845, 0.18417825333120563, 0.3152284179597974, 0.4720312194636732, 0.4979135187010129]], occupation = [[2.0, 2.0, 2.0, 2.0, 0.0, 0.0, 0.0], [2.0, 2.0, 2.0, 2.0, 0.0, 0.0, 0.0], [2.0, 2.0, 2.0, 2.0, 0.0, 0.0, 0.0], [2.0, 2.0, 2.0, 2.0, 0.0, 0.0, 0.0]], εF = 0.2734218993066141, n_iter = 10, ψ = Matrix{ComplexF64}[[0.041611863141190954 - 0.9486686144667617im -2.2108544153411427e-13 + 2.5626453495943577e-13im … -2.1455116805450795e-12 + 2.3036245326045384e-12im -1.801919362633126e-7 + 1.912995696473302e-7im; 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