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), [-12.247569697883598 -11.100308387033863 … -8.289845769066892 -11.100308387033895; -11.100308387033863 -9.130057818482106 … -9.130057802436282 -11.100308365268866; … ; -8.289845769066892 -9.13005780243628 … -4.149589911945753 -6.287956204739974; -11.100308387033891 -11.100308365268866 … -6.287956204739975 -9.111848216112095;;; -11.100308387033865 -9.130057818482106 … -9.130057802436282 -11.100308365268868; -9.130057818482104 -6.903159504367459 … -9.130057819839246 -10.05388381698806; … ; -9.130057802436282 -9.13005781983924 … -5.294353665850209 -7.547399215037609; -11.100308365268866 -10.05388381698806 … -7.547399215037609 -10.053883816988112;;; -8.289845769067037 -6.307621938057333 … -8.289845773669951 -9.111848200066248; -6.3076219380573315 -4.516655658355755 … -7.547399231892251 -7.547399215037723; … ; -8.289845773669951 -7.547399231892248 … -5.768969098395971 -7.547399231892284; -9.111848200066248 -7.547399215037722 … -7.5473992318922845 -9.111848217469346;;; … ;;; -5.301031708535999 -6.307621951399178 … -2.5497035798117094 -3.849582182332958; -6.307621951399178 -6.903159511447309 … -3.329060694162985 -4.878419351559505; … ; -2.549703579811709 -3.329060694162985 … -1.2567984675346056 -1.8141947489914974; -3.8495821823329575 -4.878419351559505 … -1.8141947489914987 -2.714767336891456;;; -8.289845769066892 -9.130057802436282 … -4.149589911945753 -6.287956204739974; -9.130057802436278 -9.130057819839243 … -5.29435366585021 -7.547399215037609; … ; -4.149589911945753 -5.29435366585021 … -1.9094492500180027 -2.8946123644894843; -6.287956204739974 -7.5473992150376095 … -2.8946123644894852 -4.48554275191253;;; -11.100308387033893 -11.100308365268868 … -6.287956204739974 -9.111848216112097; -11.100308365268866 -10.05388381698806 … -7.54739921503761 -10.05388381698811; … ; -6.287956204739974 -7.547399215037608 … -2.894612364489485 -4.48554275191253; -9.111848216112097 -10.05388381698811 … -4.48554275191253 -6.871104522520838])], 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), [-12.247569697883598 -11.100308387033863 … -8.289845769066892 -11.100308387033895; -11.100308387033863 -9.130057818482106 … -9.130057802436282 -11.100308365268866; … ; -8.289845769066892 -9.13005780243628 … -4.149589911945753 -6.287956204739974; -11.100308387033891 -11.100308365268866 … -6.287956204739975 -9.111848216112095;;; -11.100308387033865 -9.130057818482106 … -9.130057802436282 -11.100308365268868; -9.130057818482104 -6.903159504367459 … -9.130057819839246 -10.05388381698806; … ; -9.130057802436282 -9.13005781983924 … -5.294353665850209 -7.547399215037609; -11.100308365268866 -10.05388381698806 … -7.547399215037609 -10.053883816988112;;; -8.289845769067037 -6.307621938057333 … -8.289845773669951 -9.111848200066248; -6.3076219380573315 -4.516655658355755 … -7.547399231892251 -7.547399215037723; … ; -8.289845773669951 -7.547399231892248 … -5.768969098395971 -7.547399231892284; -9.111848200066248 -7.547399215037722 … -7.5473992318922845 -9.111848217469346;;; … ;;; -5.301031708535999 -6.307621951399178 … -2.5497035798117094 -3.849582182332958; -6.307621951399178 -6.903159511447309 … -3.329060694162985 -4.878419351559505; … ; -2.549703579811709 -3.329060694162985 … -1.2567984675346056 -1.8141947489914974; -3.8495821823329575 -4.878419351559505 … -1.8141947489914987 -2.714767336891456;;; -8.289845769066892 -9.130057802436282 … -4.149589911945753 -6.287956204739974; -9.130057802436278 -9.130057819839243 … -5.29435366585021 -7.547399215037609; … ; -4.149589911945753 -5.29435366585021 … -1.9094492500180027 -2.8946123644894843; -6.287956204739974 -7.5473992150376095 … -2.8946123644894852 -4.48554275191253;;; -11.100308387033893 -11.100308365268868 … -6.287956204739974 -9.111848216112097; -11.100308365268866 -10.05388381698806 … -7.54739921503761 -10.05388381698811; … ; -6.287956204739974 -7.547399215037608 … -2.894612364489485 -4.48554275191253; -9.111848216112097 -10.05388381698811 … -4.48554275191253 -6.871104522520838]), 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 = [-0.00044698714259960946 + 0.00022979759477600135im -0.0012353490630125155 + 0.00446913756005051im … 0.0005879448767781873 + 0.0010621373519428593im 0.0014877133926453263 + 0.0003919561583061353im; -0.00016693277601156952 + 0.0005457460914002235im 0.001127120683569319 + 0.0019579940613140387im … -0.000666514861814905 - 0.00020100853174797196im 0.00039713030508432617 - 0.00027210621686496765im; … ; 0.0016607914634651625 + 0.002929164982874769im 0.0016041787522498455 + 0.00043233514396855545im … 0.0007849424280669845 - 0.00044858704660372594im 6.217961947879778e-5 - 0.0002117080932871108im; 0.0039051803737938946 + 0.0010762632289326914im -0.00018107874296931312 + 9.030076690363692e-5im … -0.0008055532048825465 + 0.002843266078806862im 0.0018503490927477984 + 0.003257466280799915im;;; -0.01329425755922875 + 0.04236065423512009im 0.045777851830946355 + 0.08767440775891515im … -0.0453728972800057 - 0.01427971494468138im -0.03910276134382146 + 0.02036318123906844im; -0.012199662495055441 - 0.023562802055836732im 0.04906897399098678 + 0.015416170362686462im … -0.01833616801858101 + 0.009625045529093379im 0.009315684401887486 - 0.02942245179399822im; … ; 0.05533404568089892 + 0.017321637469712867im 0.0002363941746666466 - 0.00022853000908144155im … -0.016657235819240734 + 0.05276933264991718im 0.033833216782297885 + 0.06488710423046717im; -0.029266664252513487 + 0.015104956191085497im -0.02171001283563892 + 0.0689552850983142im … 0.0034538548092464226 + 0.006522798751093066im -0.00718150649614101 - 0.0023784077935232392im;;; 0.015584610291266931 + 0.02974643360103192im 0.06685487068232138 + 0.020960311945349634im … -0.028615647564810616 + 0.01496951301429689im -0.003731910546074607 + 0.011999653867204526im; -0.08139436577185477 - 0.025756097179138175im -0.015547037889635492 + 0.008075788724945675im … -0.0004219595376236669 + 0.001655463065649726im -0.03990497070388183 - 0.07679857237061419im; … ; -0.021829669133042098 + 0.01119548133588466im -0.02732775391404259 + 0.08644338889071869im … 0.03356000255314298 + 0.06443043523953826im 0.03976411167980017 + 0.012429933953578358im; -0.03082179196348087 + 0.09762668078177417im 0.06489749418425975 + 0.12453070199509217im … -0.003945702104063614 - 0.001282228094711204im -0.04093534165677433 + 0.021192353445777516im;;; … ;;; 0.016845269633699398 - 0.05324157096099898im -0.03154378165530074 - 0.06070503081517029im … 0.03577628840428408 + 0.011203057933779455im 0.016177888692728803 - 0.008501572958073769im; -0.03807389846114594 - 0.07324758959062153im -0.08146071744514743 - 0.02574966332437968im … 0.006005362773465878 - 0.0032776403301858076im 0.01482587311459924 - 0.0472230625314131im; … ; -0.09291499932210262 - 0.029399047263095696im -0.06057756722818124 + 0.031502319415312834im … 0.00777476064525693 - 0.02437007153998237im -0.0448478931125179 - 0.08652677013758717im; -0.03538842452632517 + 0.018419303332401243im -0.0050339800348442945 + 0.0161202996019871im … 0.019948682977357482 + 0.03824673327587862im -0.042005342501793635 - 0.013335109003522971im;;; -0.02367917553868619 - 0.045635185692449426im -0.07829641707618909 - 0.02473590421059401im … 0.031009025775261705 - 0.016193888134571448im -0.006858835796990051 + 0.021618571427817628im; -0.003697978419969078 - 0.0012593136605189431im -0.010861064935513058 + 0.005602079798679041im … -0.0017142077004739281 + 0.00517683793187761im 0.02087479913813154 + 0.04014171435335411im; … ; -0.011716864907702577 + 0.006098693348845851im -2.3660732175884158e-5 + 0.00032328791546416824im … -0.013081283814229495 - 0.02537298430494111im -0.06050174421372865 - 0.019238294910957042im; 0.013018016258494785 - 0.04084029482775347im -0.019955113409520796 - 0.0385722083555394im … 0.0822796484330604 + 0.025937720832768265im 0.014608635338025366 - 0.007602984047629789im;;; -0.046606807240972783 - 0.014791689554533968im -0.03678562004610277 + 0.019211421003494142im … -0.010270820667853994 + 0.03262224368322653im 0.013299208398937317 + 0.025477967083778696im; 0.005490269810902011 - 0.002997749228226704im 0.0003386315612417916 - 0.0009170802683199034im … 0.02660040875220196 + 0.05112005167628707im 0.06329104102736556 + 0.019876318682358233im; … ; 0.020764314968090114 - 0.06553480194405718im -0.020037529685024154 - 0.03872320090020689im … 0.012221667438824937 + 0.0037591657632448892im 0.033782094967014016 - 0.01766540277137707im; -0.04158746643028074 - 0.08031517085222449im -0.05813763425396308 - 0.01840861722183304im … 0.0363824553786037 - 0.018877756905548927im 0.011988695216778231 - 0.03769840470889354im],)]), 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), [-12.247569697883598 -11.100308387033863 … -8.289845769066892 -11.100308387033895; -11.100308387033863 -9.130057818482106 … -9.130057802436282 -11.100308365268866; … ; -8.289845769066892 -9.13005780243628 … -4.149589911945753 -6.287956204739974; -11.100308387033891 -11.100308365268866 … -6.287956204739975 -9.111848216112095;;; -11.100308387033865 -9.130057818482106 … -9.130057802436282 -11.100308365268868; -9.130057818482104 -6.903159504367459 … -9.130057819839246 -10.05388381698806; … ; -9.130057802436282 -9.13005781983924 … -5.294353665850209 -7.547399215037609; -11.100308365268866 -10.05388381698806 … -7.547399215037609 -10.053883816988112;;; -8.289845769067037 -6.307621938057333 … -8.289845773669951 -9.111848200066248; -6.3076219380573315 -4.516655658355755 … -7.547399231892251 -7.547399215037723; … ; -8.289845773669951 -7.547399231892248 … -5.768969098395971 -7.547399231892284; -9.111848200066248 -7.547399215037722 … -7.5473992318922845 -9.111848217469346;;; … ;;; -5.301031708535999 -6.307621951399178 … -2.5497035798117094 -3.849582182332958; -6.307621951399178 -6.903159511447309 … -3.329060694162985 -4.878419351559505; … ; -2.549703579811709 -3.329060694162985 … -1.2567984675346056 -1.8141947489914974; -3.8495821823329575 -4.878419351559505 … -1.8141947489914987 -2.714767336891456;;; -8.289845769066892 -9.130057802436282 … -4.149589911945753 -6.287956204739974; -9.130057802436278 -9.130057819839243 … -5.29435366585021 -7.547399215037609; … ; -4.149589911945753 -5.29435366585021 … -1.9094492500180027 -2.8946123644894843; -6.287956204739974 -7.5473992150376095 … -2.8946123644894852 -4.48554275191253;;; -11.100308387033893 -11.100308365268868 … -6.287956204739974 -9.111848216112097; -11.100308365268866 -10.05388381698806 … -7.54739921503761 -10.05388381698811; … ; -6.287956204739974 -7.547399215037608 … -2.894612364489485 -4.48554275191253; -9.111848216112097 -10.05388381698811 … -4.48554275191253 -6.871104522520838])], 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), [-12.247569697883598 -11.100308387033863 … -8.289845769066892 -11.100308387033895; -11.100308387033863 -9.130057818482106 … -9.130057802436282 -11.100308365268866; … ; -8.289845769066892 -9.13005780243628 … -4.149589911945753 -6.287956204739974; -11.100308387033891 -11.100308365268866 … -6.287956204739975 -9.111848216112095;;; -11.100308387033865 -9.130057818482106 … -9.130057802436282 -11.100308365268868; -9.130057818482104 -6.903159504367459 … -9.130057819839246 -10.05388381698806; … ; -9.130057802436282 -9.13005781983924 … -5.294353665850209 -7.547399215037609; -11.100308365268866 -10.05388381698806 … -7.547399215037609 -10.053883816988112;;; -8.289845769067037 -6.307621938057333 … -8.289845773669951 -9.111848200066248; -6.3076219380573315 -4.516655658355755 … -7.547399231892251 -7.547399215037723; … ; -8.289845773669951 -7.547399231892248 … -5.768969098395971 -7.547399231892284; -9.111848200066248 -7.547399215037722 … -7.5473992318922845 -9.111848217469346;;; … ;;; -5.301031708535999 -6.307621951399178 … -2.5497035798117094 -3.849582182332958; -6.307621951399178 -6.903159511447309 … -3.329060694162985 -4.878419351559505; … ; -2.549703579811709 -3.329060694162985 … -1.2567984675346056 -1.8141947489914974; -3.8495821823329575 -4.878419351559505 … -1.8141947489914987 -2.714767336891456;;; -8.289845769066892 -9.130057802436282 … -4.149589911945753 -6.287956204739974; -9.130057802436278 -9.130057819839243 … -5.29435366585021 -7.547399215037609; … ; -4.149589911945753 -5.29435366585021 … -1.9094492500180027 -2.8946123644894843; -6.287956204739974 -7.5473992150376095 … -2.8946123644894852 -4.48554275191253;;; -11.100308387033893 -11.100308365268868 … -6.287956204739974 -9.111848216112097; -11.100308365268866 -10.05388381698806 … -7.54739921503761 -10.05388381698811; … ; -6.287956204739974 -7.547399215037608 … -2.894612364489485 -4.48554275191253; -9.111848216112097 -10.05388381698811 … -4.48554275191253 -6.871104522520838]), 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 = [-0.00044698714259960946 + 0.00022979759477600135im -0.0012353490630125155 + 0.00446913756005051im … 0.0005879448767781873 + 0.0010621373519428593im 0.0014877133926453263 + 0.0003919561583061353im; -0.00016693277601156952 + 0.0005457460914002235im 0.001127120683569319 + 0.0019579940613140387im … -0.000666514861814905 - 0.00020100853174797196im 0.00039713030508432617 - 0.00027210621686496765im; … ; 0.0016607914634651625 + 0.002929164982874769im 0.0016041787522498455 + 0.00043233514396855545im … 0.0007849424280669845 - 0.00044858704660372594im 6.217961947879778e-5 - 0.0002117080932871108im; 0.0039051803737938946 + 0.0010762632289326914im -0.00018107874296931312 + 9.030076690363692e-5im … -0.0008055532048825465 + 0.002843266078806862im 0.0018503490927477984 + 0.003257466280799915im;;; -0.01329425755922875 + 0.04236065423512009im 0.045777851830946355 + 0.08767440775891515im … -0.0453728972800057 - 0.01427971494468138im -0.03910276134382146 + 0.02036318123906844im; -0.012199662495055441 - 0.023562802055836732im 0.04906897399098678 + 0.015416170362686462im … -0.01833616801858101 + 0.009625045529093379im 0.009315684401887486 - 0.02942245179399822im; … ; 0.05533404568089892 + 0.017321637469712867im 0.0002363941746666466 - 0.00022853000908144155im … -0.016657235819240734 + 0.05276933264991718im 0.033833216782297885 + 0.06488710423046717im; -0.029266664252513487 + 0.015104956191085497im -0.02171001283563892 + 0.0689552850983142im … 0.0034538548092464226 + 0.006522798751093066im -0.00718150649614101 - 0.0023784077935232392im;;; 0.015584610291266931 + 0.02974643360103192im 0.06685487068232138 + 0.020960311945349634im … -0.028615647564810616 + 0.01496951301429689im -0.003731910546074607 + 0.011999653867204526im; -0.08139436577185477 - 0.025756097179138175im -0.015547037889635492 + 0.008075788724945675im … -0.0004219595376236669 + 0.001655463065649726im -0.03990497070388183 - 0.07679857237061419im; … ; -0.021829669133042098 + 0.01119548133588466im -0.02732775391404259 + 0.08644338889071869im … 0.03356000255314298 + 0.06443043523953826im 0.03976411167980017 + 0.012429933953578358im; -0.03082179196348087 + 0.09762668078177417im 0.06489749418425975 + 0.12453070199509217im … -0.003945702104063614 - 0.001282228094711204im -0.04093534165677433 + 0.021192353445777516im;;; … ;;; 0.016845269633699398 - 0.05324157096099898im -0.03154378165530074 - 0.06070503081517029im … 0.03577628840428408 + 0.011203057933779455im 0.016177888692728803 - 0.008501572958073769im; -0.03807389846114594 - 0.07324758959062153im -0.08146071744514743 - 0.02574966332437968im … 0.006005362773465878 - 0.0032776403301858076im 0.01482587311459924 - 0.0472230625314131im; … ; -0.09291499932210262 - 0.029399047263095696im -0.06057756722818124 + 0.031502319415312834im … 0.00777476064525693 - 0.02437007153998237im -0.0448478931125179 - 0.08652677013758717im; -0.03538842452632517 + 0.018419303332401243im -0.0050339800348442945 + 0.0161202996019871im … 0.019948682977357482 + 0.03824673327587862im -0.042005342501793635 - 0.013335109003522971im;;; -0.02367917553868619 - 0.045635185692449426im -0.07829641707618909 - 0.02473590421059401im … 0.031009025775261705 - 0.016193888134571448im -0.006858835796990051 + 0.021618571427817628im; -0.003697978419969078 - 0.0012593136605189431im -0.010861064935513058 + 0.005602079798679041im … -0.0017142077004739281 + 0.00517683793187761im 0.02087479913813154 + 0.04014171435335411im; … ; -0.011716864907702577 + 0.006098693348845851im -2.3660732175884158e-5 + 0.00032328791546416824im … -0.013081283814229495 - 0.02537298430494111im -0.06050174421372865 - 0.019238294910957042im; 0.013018016258494785 - 0.04084029482775347im -0.019955113409520796 - 0.0385722083555394im … 0.0822796484330604 + 0.025937720832768265im 0.014608635338025366 - 0.007602984047629789im;;; -0.046606807240972783 - 0.014791689554533968im -0.03678562004610277 + 0.019211421003494142im … -0.010270820667853994 + 0.03262224368322653im 0.013299208398937317 + 0.025477967083778696im; 0.005490269810902011 - 0.002997749228226704im 0.0003386315612417916 - 0.0009170802683199034im … 0.02660040875220196 + 0.05112005167628707im 0.06329104102736556 + 0.019876318682358233im; … ; 0.020764314968090114 - 0.06553480194405718im -0.020037529685024154 - 0.03872320090020689im … 0.012221667438824937 + 0.0037591657632448892im 0.033782094967014016 - 0.01766540277137707im; -0.04158746643028074 - 0.08031517085222449im -0.05813763425396308 - 0.01840861722183304im … 0.0363824553786037 - 0.018877756905548927im 0.011988695216778231 - 0.03769840470889354im],)]), 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), [-12.247569697883598 -11.100308387033863 … -8.289845769066892 -11.100308387033895; -11.100308387033863 -9.130057818482106 … -9.130057802436282 -11.100308365268866; … ; -8.289845769066892 -9.13005780243628 … -4.149589911945753 -6.287956204739974; -11.100308387033891 -11.100308365268866 … -6.287956204739975 -9.111848216112095;;; -11.100308387033865 -9.130057818482106 … -9.130057802436282 -11.100308365268868; -9.130057818482104 -6.903159504367459 … -9.130057819839246 -10.05388381698806; … ; -9.130057802436282 -9.13005781983924 … -5.294353665850209 -7.547399215037609; -11.100308365268866 -10.05388381698806 … -7.547399215037609 -10.053883816988112;;; -8.289845769067037 -6.307621938057333 … -8.289845773669951 -9.111848200066248; -6.3076219380573315 -4.516655658355755 … -7.547399231892251 -7.547399215037723; … ; -8.289845773669951 -7.547399231892248 … -5.768969098395971 -7.547399231892284; -9.111848200066248 -7.547399215037722 … -7.5473992318922845 -9.111848217469346;;; … ;;; -5.301031708535999 -6.307621951399178 … -2.5497035798117094 -3.849582182332958; -6.307621951399178 -6.903159511447309 … -3.329060694162985 -4.878419351559505; … ; -2.549703579811709 -3.329060694162985 … -1.2567984675346056 -1.8141947489914974; -3.8495821823329575 -4.878419351559505 … -1.8141947489914987 -2.714767336891456;;; -8.289845769066892 -9.130057802436282 … -4.149589911945753 -6.287956204739974; -9.130057802436278 -9.130057819839243 … -5.29435366585021 -7.547399215037609; … ; -4.149589911945753 -5.29435366585021 … -1.9094492500180027 -2.8946123644894843; -6.287956204739974 -7.5473992150376095 … -2.8946123644894852 -4.48554275191253;;; -11.100308387033893 -11.100308365268868 … -6.287956204739974 -9.111848216112097; -11.100308365268866 -10.05388381698806 … -7.54739921503761 -10.05388381698811; … ; -6.287956204739974 -7.547399215037608 … -2.894612364489485 -4.48554275191253; -9.111848216112097 -10.05388381698811 … -4.48554275191253 -6.871104522520838])], 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), [-12.247569697883598 -11.100308387033863 … -8.289845769066892 -11.100308387033895; -11.100308387033863 -9.130057818482106 … -9.130057802436282 -11.100308365268866; … ; -8.289845769066892 -9.13005780243628 … -4.149589911945753 -6.287956204739974; -11.100308387033891 -11.100308365268866 … -6.287956204739975 -9.111848216112095;;; -11.100308387033865 -9.130057818482106 … -9.130057802436282 -11.100308365268868; -9.130057818482104 -6.903159504367459 … -9.130057819839246 -10.05388381698806; … ; -9.130057802436282 -9.13005781983924 … -5.294353665850209 -7.547399215037609; -11.100308365268866 -10.05388381698806 … -7.547399215037609 -10.053883816988112;;; -8.289845769067037 -6.307621938057333 … -8.289845773669951 -9.111848200066248; -6.3076219380573315 -4.516655658355755 … -7.547399231892251 -7.547399215037723; … ; -8.289845773669951 -7.547399231892248 … -5.768969098395971 -7.547399231892284; -9.111848200066248 -7.547399215037722 … -7.5473992318922845 -9.111848217469346;;; … ;;; -5.301031708535999 -6.307621951399178 … -2.5497035798117094 -3.849582182332958; -6.307621951399178 -6.903159511447309 … -3.329060694162985 -4.878419351559505; … ; -2.549703579811709 -3.329060694162985 … -1.2567984675346056 -1.8141947489914974; -3.8495821823329575 -4.878419351559505 … -1.8141947489914987 -2.714767336891456;;; -8.289845769066892 -9.130057802436282 … -4.149589911945753 -6.287956204739974; -9.130057802436278 -9.130057819839243 … -5.29435366585021 -7.547399215037609; … ; -4.149589911945753 -5.29435366585021 … -1.9094492500180027 -2.8946123644894843; -6.287956204739974 -7.5473992150376095 … -2.8946123644894852 -4.48554275191253;;; -11.100308387033893 -11.100308365268868 … -6.287956204739974 -9.111848216112097; -11.100308365268866 -10.05388381698806 … -7.54739921503761 -10.05388381698811; … ; -6.287956204739974 -7.547399215037608 … -2.894612364489485 -4.48554275191253; -9.111848216112097 -10.05388381698811 … -4.48554275191253 -6.871104522520838]), 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 = [-0.00044698714259960946 + 0.00022979759477600135im -0.0012353490630125155 + 0.00446913756005051im … 0.0005879448767781873 + 0.0010621373519428593im 0.0014877133926453263 + 0.0003919561583061353im; -0.00016693277601156952 + 0.0005457460914002235im 0.001127120683569319 + 0.0019579940613140387im … -0.000666514861814905 - 0.00020100853174797196im 0.00039713030508432617 - 0.00027210621686496765im; … ; 0.0016607914634651625 + 0.002929164982874769im 0.0016041787522498455 + 0.00043233514396855545im … 0.0007849424280669845 - 0.00044858704660372594im 6.217961947879778e-5 - 0.0002117080932871108im; 0.0039051803737938946 + 0.0010762632289326914im -0.00018107874296931312 + 9.030076690363692e-5im … -0.0008055532048825465 + 0.002843266078806862im 0.0018503490927477984 + 0.003257466280799915im;;; -0.01329425755922875 + 0.04236065423512009im 0.045777851830946355 + 0.08767440775891515im … -0.0453728972800057 - 0.01427971494468138im -0.03910276134382146 + 0.02036318123906844im; -0.012199662495055441 - 0.023562802055836732im 0.04906897399098678 + 0.015416170362686462im … -0.01833616801858101 + 0.009625045529093379im 0.009315684401887486 - 0.02942245179399822im; … ; 0.05533404568089892 + 0.017321637469712867im 0.0002363941746666466 - 0.00022853000908144155im … -0.016657235819240734 + 0.05276933264991718im 0.033833216782297885 + 0.06488710423046717im; -0.029266664252513487 + 0.015104956191085497im -0.02171001283563892 + 0.0689552850983142im … 0.0034538548092464226 + 0.006522798751093066im -0.00718150649614101 - 0.0023784077935232392im;;; 0.015584610291266931 + 0.02974643360103192im 0.06685487068232138 + 0.020960311945349634im … -0.028615647564810616 + 0.01496951301429689im -0.003731910546074607 + 0.011999653867204526im; -0.08139436577185477 - 0.025756097179138175im -0.015547037889635492 + 0.008075788724945675im … -0.0004219595376236669 + 0.001655463065649726im -0.03990497070388183 - 0.07679857237061419im; … ; -0.021829669133042098 + 0.01119548133588466im -0.02732775391404259 + 0.08644338889071869im … 0.03356000255314298 + 0.06443043523953826im 0.03976411167980017 + 0.012429933953578358im; -0.03082179196348087 + 0.09762668078177417im 0.06489749418425975 + 0.12453070199509217im … -0.003945702104063614 - 0.001282228094711204im -0.04093534165677433 + 0.021192353445777516im;;; … ;;; 0.016845269633699398 - 0.05324157096099898im -0.03154378165530074 - 0.06070503081517029im … 0.03577628840428408 + 0.011203057933779455im 0.016177888692728803 - 0.008501572958073769im; -0.03807389846114594 - 0.07324758959062153im -0.08146071744514743 - 0.02574966332437968im … 0.006005362773465878 - 0.0032776403301858076im 0.01482587311459924 - 0.0472230625314131im; … ; -0.09291499932210262 - 0.029399047263095696im -0.06057756722818124 + 0.031502319415312834im … 0.00777476064525693 - 0.02437007153998237im -0.0448478931125179 - 0.08652677013758717im; -0.03538842452632517 + 0.018419303332401243im -0.0050339800348442945 + 0.0161202996019871im … 0.019948682977357482 + 0.03824673327587862im -0.042005342501793635 - 0.013335109003522971im;;; -0.02367917553868619 - 0.045635185692449426im -0.07829641707618909 - 0.02473590421059401im … 0.031009025775261705 - 0.016193888134571448im -0.006858835796990051 + 0.021618571427817628im; -0.003697978419969078 - 0.0012593136605189431im -0.010861064935513058 + 0.005602079798679041im … -0.0017142077004739281 + 0.00517683793187761im 0.02087479913813154 + 0.04014171435335411im; … ; -0.011716864907702577 + 0.006098693348845851im -2.3660732175884158e-5 + 0.00032328791546416824im … -0.013081283814229495 - 0.02537298430494111im -0.06050174421372865 - 0.019238294910957042im; 0.013018016258494785 - 0.04084029482775347im -0.019955113409520796 - 0.0385722083555394im … 0.0822796484330604 + 0.025937720832768265im 0.014608635338025366 - 0.007602984047629789im;;; -0.046606807240972783 - 0.014791689554533968im -0.03678562004610277 + 0.019211421003494142im … -0.010270820667853994 + 0.03262224368322653im 0.013299208398937317 + 0.025477967083778696im; 0.005490269810902011 - 0.002997749228226704im 0.0003386315612417916 - 0.0009170802683199034im … 0.02660040875220196 + 0.05112005167628707im 0.06329104102736556 + 0.019876318682358233im; … ; 0.020764314968090114 - 0.06553480194405718im -0.020037529685024154 - 0.03872320090020689im … 0.012221667438824937 + 0.0037591657632448892im 0.033782094967014016 - 0.01766540277137707im; -0.04158746643028074 - 0.08031517085222449im -0.05813763425396308 - 0.01840861722183304im … 0.0363824553786037 - 0.018877756905548927im 0.011988695216778231 - 0.03769840470889354im],)]), 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), [-12.247569697883598 -11.100308387033863 … -8.289845769066892 -11.100308387033895; -11.100308387033863 -9.130057818482106 … -9.130057802436282 -11.100308365268866; … ; -8.289845769066892 -9.13005780243628 … -4.149589911945753 -6.287956204739974; -11.100308387033891 -11.100308365268866 … -6.287956204739975 -9.111848216112095;;; -11.100308387033865 -9.130057818482106 … -9.130057802436282 -11.100308365268868; -9.130057818482104 -6.903159504367459 … -9.130057819839246 -10.05388381698806; … ; -9.130057802436282 -9.13005781983924 … -5.294353665850209 -7.547399215037609; -11.100308365268866 -10.05388381698806 … -7.547399215037609 -10.053883816988112;;; -8.289845769067037 -6.307621938057333 … -8.289845773669951 -9.111848200066248; -6.3076219380573315 -4.516655658355755 … -7.547399231892251 -7.547399215037723; … ; -8.289845773669951 -7.547399231892248 … -5.768969098395971 -7.547399231892284; -9.111848200066248 -7.547399215037722 … -7.5473992318922845 -9.111848217469346;;; … ;;; -5.301031708535999 -6.307621951399178 … -2.5497035798117094 -3.849582182332958; -6.307621951399178 -6.903159511447309 … -3.329060694162985 -4.878419351559505; … ; -2.549703579811709 -3.329060694162985 … -1.2567984675346056 -1.8141947489914974; -3.8495821823329575 -4.878419351559505 … -1.8141947489914987 -2.714767336891456;;; -8.289845769066892 -9.130057802436282 … -4.149589911945753 -6.287956204739974; -9.130057802436278 -9.130057819839243 … -5.29435366585021 -7.547399215037609; … ; -4.149589911945753 -5.29435366585021 … -1.9094492500180027 -2.8946123644894843; -6.287956204739974 -7.5473992150376095 … -2.8946123644894852 -4.48554275191253;;; -11.100308387033893 -11.100308365268868 … -6.287956204739974 -9.111848216112097; -11.100308365268866 -10.05388381698806 … -7.54739921503761 -10.05388381698811; … ; -6.287956204739974 -7.547399215037608 … -2.894612364489485 -4.48554275191253; -9.111848216112097 -10.05388381698811 … -4.48554275191253 -6.871104522520838])], 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), [-12.247569697883598 -11.100308387033863 … -8.289845769066892 -11.100308387033895; -11.100308387033863 -9.130057818482106 … -9.130057802436282 -11.100308365268866; … ; -8.289845769066892 -9.13005780243628 … -4.149589911945753 -6.287956204739974; -11.100308387033891 -11.100308365268866 … -6.287956204739975 -9.111848216112095;;; -11.100308387033865 -9.130057818482106 … -9.130057802436282 -11.100308365268868; -9.130057818482104 -6.903159504367459 … -9.130057819839246 -10.05388381698806; … ; -9.130057802436282 -9.13005781983924 … -5.294353665850209 -7.547399215037609; -11.100308365268866 -10.05388381698806 … -7.547399215037609 -10.053883816988112;;; -8.289845769067037 -6.307621938057333 … -8.289845773669951 -9.111848200066248; -6.3076219380573315 -4.516655658355755 … -7.547399231892251 -7.547399215037723; … ; -8.289845773669951 -7.547399231892248 … -5.768969098395971 -7.547399231892284; -9.111848200066248 -7.547399215037722 … -7.5473992318922845 -9.111848217469346;;; … ;;; -5.301031708535999 -6.307621951399178 … -2.5497035798117094 -3.849582182332958; -6.307621951399178 -6.903159511447309 … -3.329060694162985 -4.878419351559505; … ; -2.549703579811709 -3.329060694162985 … -1.2567984675346056 -1.8141947489914974; -3.8495821823329575 -4.878419351559505 … -1.8141947489914987 -2.714767336891456;;; -8.289845769066892 -9.130057802436282 … -4.149589911945753 -6.287956204739974; -9.130057802436278 -9.130057819839243 … -5.29435366585021 -7.547399215037609; … ; -4.149589911945753 -5.29435366585021 … -1.9094492500180027 -2.8946123644894843; -6.287956204739974 -7.5473992150376095 … -2.8946123644894852 -4.48554275191253;;; -11.100308387033893 -11.100308365268868 … -6.287956204739974 -9.111848216112097; -11.100308365268866 -10.05388381698806 … -7.54739921503761 -10.05388381698811; … ; -6.287956204739974 -7.547399215037608 … -2.894612364489485 -4.48554275191253; -9.111848216112097 -10.05388381698811 … -4.48554275191253 -6.871104522520838]), 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 = [-0.00044698714259960946 + 0.00022979759477600135im -0.0012353490630125155 + 0.00446913756005051im … 0.0005879448767781873 + 0.0010621373519428593im 0.0014877133926453263 + 0.0003919561583061353im; -0.00016693277601156952 + 0.0005457460914002235im 0.001127120683569319 + 0.0019579940613140387im … -0.000666514861814905 - 0.00020100853174797196im 0.00039713030508432617 - 0.00027210621686496765im; … ; 0.0016607914634651625 + 0.002929164982874769im 0.0016041787522498455 + 0.00043233514396855545im … 0.0007849424280669845 - 0.00044858704660372594im 6.217961947879778e-5 - 0.0002117080932871108im; 0.0039051803737938946 + 0.0010762632289326914im -0.00018107874296931312 + 9.030076690363692e-5im … -0.0008055532048825465 + 0.002843266078806862im 0.0018503490927477984 + 0.003257466280799915im;;; -0.01329425755922875 + 0.04236065423512009im 0.045777851830946355 + 0.08767440775891515im … -0.0453728972800057 - 0.01427971494468138im -0.03910276134382146 + 0.02036318123906844im; -0.012199662495055441 - 0.023562802055836732im 0.04906897399098678 + 0.015416170362686462im … -0.01833616801858101 + 0.009625045529093379im 0.009315684401887486 - 0.02942245179399822im; … ; 0.05533404568089892 + 0.017321637469712867im 0.0002363941746666466 - 0.00022853000908144155im … -0.016657235819240734 + 0.05276933264991718im 0.033833216782297885 + 0.06488710423046717im; -0.029266664252513487 + 0.015104956191085497im -0.02171001283563892 + 0.0689552850983142im … 0.0034538548092464226 + 0.006522798751093066im -0.00718150649614101 - 0.0023784077935232392im;;; 0.015584610291266931 + 0.02974643360103192im 0.06685487068232138 + 0.020960311945349634im … -0.028615647564810616 + 0.01496951301429689im -0.003731910546074607 + 0.011999653867204526im; -0.08139436577185477 - 0.025756097179138175im -0.015547037889635492 + 0.008075788724945675im … -0.0004219595376236669 + 0.001655463065649726im -0.03990497070388183 - 0.07679857237061419im; … ; -0.021829669133042098 + 0.01119548133588466im -0.02732775391404259 + 0.08644338889071869im … 0.03356000255314298 + 0.06443043523953826im 0.03976411167980017 + 0.012429933953578358im; -0.03082179196348087 + 0.09762668078177417im 0.06489749418425975 + 0.12453070199509217im … -0.003945702104063614 - 0.001282228094711204im -0.04093534165677433 + 0.021192353445777516im;;; … ;;; 0.016845269633699398 - 0.05324157096099898im -0.03154378165530074 - 0.06070503081517029im … 0.03577628840428408 + 0.011203057933779455im 0.016177888692728803 - 0.008501572958073769im; -0.03807389846114594 - 0.07324758959062153im -0.08146071744514743 - 0.02574966332437968im … 0.006005362773465878 - 0.0032776403301858076im 0.01482587311459924 - 0.0472230625314131im; … ; -0.09291499932210262 - 0.029399047263095696im -0.06057756722818124 + 0.031502319415312834im … 0.00777476064525693 - 0.02437007153998237im -0.0448478931125179 - 0.08652677013758717im; -0.03538842452632517 + 0.018419303332401243im -0.0050339800348442945 + 0.0161202996019871im … 0.019948682977357482 + 0.03824673327587862im -0.042005342501793635 - 0.013335109003522971im;;; -0.02367917553868619 - 0.045635185692449426im -0.07829641707618909 - 0.02473590421059401im … 0.031009025775261705 - 0.016193888134571448im -0.006858835796990051 + 0.021618571427817628im; -0.003697978419969078 - 0.0012593136605189431im -0.010861064935513058 + 0.005602079798679041im … -0.0017142077004739281 + 0.00517683793187761im 0.02087479913813154 + 0.04014171435335411im; … ; -0.011716864907702577 + 0.006098693348845851im -2.3660732175884158e-5 + 0.00032328791546416824im … -0.013081283814229495 - 0.02537298430494111im -0.06050174421372865 - 0.019238294910957042im; 0.013018016258494785 - 0.04084029482775347im -0.019955113409520796 - 0.0385722083555394im … 0.0822796484330604 + 0.025937720832768265im 0.014608635338025366 - 0.007602984047629789im;;; -0.046606807240972783 - 0.014791689554533968im -0.03678562004610277 + 0.019211421003494142im … -0.010270820667853994 + 0.03262224368322653im 0.013299208398937317 + 0.025477967083778696im; 0.005490269810902011 - 0.002997749228226704im 0.0003386315612417916 - 0.0009170802683199034im … 0.02660040875220196 + 0.05112005167628707im 0.06329104102736556 + 0.019876318682358233im; … ; 0.020764314968090114 - 0.06553480194405718im -0.020037529685024154 - 0.03872320090020689im … 0.012221667438824937 + 0.0037591657632448892im 0.033782094967014016 - 0.01766540277137707im; -0.04158746643028074 - 0.08031517085222449im -0.05813763425396308 - 0.01840861722183304im … 0.0363824553786037 - 0.018877756905548927im 0.011988695216778231 - 0.03769840470889354im],)])]), basis = PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), energies = Energies(total = -7.910594396488483), converged = true, ρ = [7.589784542608668e-5 0.0011262712728143413 … 0.0066970375499862175 0.0011262712728143532; 0.0011262712728143177 0.005274334457280126 … 0.005274334457280161 0.0011262712728143363; … ; 0.006697037549986208 0.005274334457280161 … 0.02324475419087423 0.012258986825121988; 0.0011262712728143363 0.0011262712728143346 … 0.012258986825121984 0.003770008629849288;;; 0.0011262712728143402 0.00527433445728015 … 0.0052743344572801784 0.0011262712728143498; 0.005274334457280123 0.01462006530449211 … 0.005274334457280158 0.0025880808748085394; … ; 0.005274334457280168 0.005274334457280155 … 0.018107686645960772 0.008922003044629465; 0.0011262712728143424 0.002588080874808539 … 0.00892200304462946 0.0025880808748085515;;; 0.006697037549986182 0.01641210910137098 … 0.006697037549986213 0.0037700086298492847; 0.016412109101370958 0.03127783931552029 … 0.00892200304462943 0.00892200304462941; … ; 0.006697037549986203 0.00892200304462943 … 0.01647675635926414 0.008922003044629458; 0.003770008629849283 0.008922003044629409 … 0.008922003044629456 0.0037700086298492817;;; … ;;; 0.01985383985317718 0.01641210910137099 … 0.03715667363542594 0.02719080068635261; 0.01641210910137097 0.01462006530449212 … 0.03230127212617935 0.022322100931474444; … ; 0.03715667363542593 0.03230127212617935 … 0.04629698070122337 0.04263658273120814; 0.02719080068635261 0.022322100931474444 … 0.042636582731208135 0.03477222914177271;;; 0.00669703754998619 0.00527433445728015 … 0.023244754190874222 0.012258986825121965; 0.00527433445728013 0.005274334457280132 … 0.01810768664596074 0.008922003044629421; … ; 0.02324475419087421 0.018107686645960745 … 0.04037111033536313 0.03149160381119683; 0.012258986825121963 0.008922003044629423 … 0.031491603811196825 0.02004716343259265;;; 0.0011262712728143424 0.0011262712728143485 … 0.01225898682512198 0.00377000862984929; 0.0011262712728143211 0.0025880808748085272 … 0.00892200304462944 0.0025880808748085424; … ; 0.012258986825121972 0.008922003044629439 … 0.03149160381119683 0.02004716343259267; 0.003770008629849284 0.002588080874808543 … 0.020047163432592666 0.008952603496692527;;;;], eigenvalues = [[-0.17836835653842456, 0.262491944993088, 0.26249194499308826, 0.2624919449930883, 0.354692148168582, 0.35469214816858263, 0.3546921481737684], [-0.12755037617811235, 0.06475320594779023, 0.2254516651756088, 0.225451665175609, 0.32197764961222963, 0.3892227690854425, 0.38922276908544295], [-0.10818729216398738, 0.07755003473598995, 0.1727832801157697, 0.17278328011576993, 0.2843518536196353, 0.3305476484326021, 0.5267232426408398], [-0.057773253742964124, 0.012724782206877039, 0.09766073750153259, 0.18417825333088497, 0.315228417959706, 0.4720312194174769, 0.4979135186415573]], 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 = 0.2734218993063618, n_iter = 10, ψ = Matrix{ComplexF64}[[-0.7369821568161874 + 0.5987996223815996im 3.0520389155497363e-14 - 1.742453167741061e-13im … -1.206861208563068e-12 - 1.468393304529021e-12im -5.588828751210626e-8 - 6.985444624388943e-8im; 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