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.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), [-12.247569697868094 -11.100308387037481 … -8.289845769070482 -11.100308387037513; -11.100308387037481 -9.13005781848603 … -9.130057802440204 -11.100308365272484; … ; -8.289845769070482 -9.130057802440202 … -4.149589911946472 -6.287956204742144; -11.100308387037511 -11.100308365272486 … -6.2879562047421445 -9.111848216116286;;; -11.100308387037483 -9.130057818486028 … -9.130057802440204 -11.100308365272486; -9.130057818486028 -6.903159504370278 … -9.130057819843168 -10.053883816992455; … ; -9.130057802440204 -9.130057819843163 … -5.294353665851816 -7.547399215040784; -11.100308365272486 -10.053883816992455 … -7.547399215040784 -10.053883816992508;;; -8.289845769070627 -6.307621938059807 … -8.289845773673541 -9.111848200070439; -6.307621938059805 -4.516655658357428 … -7.547399231895425 -7.5473992150408975; … ; -8.289845773673541 -7.547399231895422 … -5.768969098397977 -7.547399231895459; -9.111848200070439 -7.547399215040897 … -7.54739923189546 -9.111848217473536;;; … ;;; -5.301031708537768 -6.307621951401652 … -2.5497035798118617 -3.849582182333718; -6.307621951401652 -6.903159511450127 … -3.3290606941635192 -4.87841935156101; … ; -2.5497035798118612 -3.3290606941635192 … -1.256798467534796 -1.8141947489915387; -3.8495821823337177 -4.87841935156101 … -1.8141947489915402 -2.714767336891615;;; -8.289845769070482 -9.130057802440204 … -4.149589911946471 -6.287956204742144; -9.130057802440202 -9.130057819843167 … -5.294353665851816 -7.547399215040783; … ; -4.149589911946471 -5.294353665851816 … -1.9094492500179376 -2.894612364489525; -6.287956204742144 -7.547399215040784 … -2.894612364489526 -4.485542751913324;;; -11.100308387037511 -11.100308365272484 … -6.287956204742144 -9.111848216116288; -11.100308365272484 -10.053883816992457 … -7.547399215040785 -10.053883816992505; … ; -6.287956204742144 -7.547399215040782 … -2.8946123644895256 -4.485542751913324; -9.111848216116288 -10.053883816992506 … -4.485542751913324 -6.871104522523317])], 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), [-12.247569697868094 -11.100308387037481 … -8.289845769070482 -11.100308387037513; -11.100308387037481 -9.13005781848603 … -9.130057802440204 -11.100308365272484; … ; -8.289845769070482 -9.130057802440202 … -4.149589911946472 -6.287956204742144; -11.100308387037511 -11.100308365272486 … -6.2879562047421445 -9.111848216116286;;; -11.100308387037483 -9.130057818486028 … -9.130057802440204 -11.100308365272486; -9.130057818486028 -6.903159504370278 … -9.130057819843168 -10.053883816992455; … ; -9.130057802440204 -9.130057819843163 … -5.294353665851816 -7.547399215040784; -11.100308365272486 -10.053883816992455 … -7.547399215040784 -10.053883816992508;;; -8.289845769070627 -6.307621938059807 … -8.289845773673541 -9.111848200070439; -6.307621938059805 -4.516655658357428 … -7.547399231895425 -7.5473992150408975; … ; -8.289845773673541 -7.547399231895422 … -5.768969098397977 -7.547399231895459; -9.111848200070439 -7.547399215040897 … -7.54739923189546 -9.111848217473536;;; … ;;; -5.301031708537768 -6.307621951401652 … -2.5497035798118617 -3.849582182333718; -6.307621951401652 -6.903159511450127 … -3.3290606941635192 -4.87841935156101; … ; -2.5497035798118612 -3.3290606941635192 … -1.256798467534796 -1.8141947489915387; -3.8495821823337177 -4.87841935156101 … -1.8141947489915402 -2.714767336891615;;; -8.289845769070482 -9.130057802440204 … -4.149589911946471 -6.287956204742144; -9.130057802440202 -9.130057819843167 … -5.294353665851816 -7.547399215040783; … ; -4.149589911946471 -5.294353665851816 … -1.9094492500179376 -2.894612364489525; -6.287956204742144 -7.547399215040784 … -2.894612364489526 -4.485542751913324;;; -11.100308387037511 -11.100308365272484 … -6.287956204742144 -9.111848216116288; -11.100308365272484 -10.053883816992457 … -7.547399215040785 -10.053883816992505; … ; -6.287956204742144 -7.547399215040782 … -2.8946123644895256 -4.485542751913324; -9.111848216116288 -10.053883816992506 … -4.485542751913324 -6.871104522523317]), 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 = [-0.0015288831477095225 - 0.04744971182333164im -0.032980965973811234 - 0.027582468563407216im … 0.031680934136940626 - 0.0013889502089711038im 0.027643171572372102 - 0.022513234124314035im; -0.022608097594180455 - 0.018454980718917338im 0.008970757834272904 - 0.006909077934226024im … 0.017182426951885744 - 0.024112931531235112im -0.006711777273313637 - 0.032670571178416624im; … ; -0.008415785830978455 + 0.0013102182117994297im 0.010092473671850073 - 0.018576709739500895im … 0.010361996637758553 - 0.017989604215722245im -0.009350435840198235 - 0.010516766033359645im; 0.02400824338412074 - 0.022595748816401782im -0.008242280869696233 - 0.059431539375280326im … 0.007374279635232291 + 0.000479389055603852im 0.01696508968204597 + 0.0004571120990736128im;;; 0.06024021224404828 - 0.006459214635094067im 0.06137917514812722 - 0.053023940042687755im … 0.021660568456136526 - 0.031051107794643363im 0.026881262329420844 + 0.004118647215521951im; 0.05851198870078535 - 0.03876159691296473im 0.029105849903726666 - 0.09305811894789705im … -0.0006370897643465446 + 0.005352759542079095im 0.02698699034728439 + 0.005348401309082523im; … ; 0.01418596363496663 - 0.029696797756018516im 0.0002175694487019167 - 0.030075554815404446im … 0.03591309122667484 - 0.0005442968178973118im 0.03980595193290894 - 0.023618943664143417im; 0.04123440920030201 + 0.010485222503339067im 0.021198951337821192 - 0.018308004703870496im … 0.042363764995933084 - 0.014408791831928242im 0.023809574364968354 - 0.019654534071357265im;;; 0.07461322326641553 - 0.05915215967240073im 0.019229733490050364 - 0.059349806022516015im … 0.02589874189241243 + 0.014872293965562408im 0.07447179977729754 - 0.0011011580906428245im; 0.018283443525700334 - 0.08234343619659708im -0.003151872832652551 - 0.03153378362738087im … 0.037688169263103394 + 0.008636090737230078im 0.043775036873904556 - 0.029920583463211234im; … ; 0.017209037175492818 - 0.0043678301168671545im 0.023488032054161393 - 0.012809000395775021im … -0.001734975137871922 + 0.010380381158401168im 0.017913873338365756 - 0.00258970563930331im; 0.08962444837466332 - 0.003689071210896438im 0.05364250071616106 - 0.052066640405892914im … 0.016957805751492312 + 0.022932295291181782im 0.045193331931320246 + 0.022439751511441862im;;; … ;;; 0.06820750934835766 - 0.003805397232276529im 0.03986404762156025 - 0.025216197717291163im … 0.0213650026979913 + 0.04556582315924866im 0.049066983587293264 + 0.021282144302958442im; 0.03014664378610726 + 0.0010012048755596934im 0.024608713985072125 + 0.04930942377973945im … 0.033897715005391904 + 0.011978418576896285im 0.04008485405242679 + 0.0014630110982670518im; … ; 0.004084192355254885 + 0.03094933722241336im 0.05413712755669703 + 0.05040859950848396im … -0.06713092541683413 - 0.02435945838845349im -0.033970818475145784 + 0.02177227354246524im; 0.04156351650767531 + 0.016712537289479624im 0.08322195401561532 - 0.003184765789241109im … -0.009141359882494714 + 0.018870310264990985im 0.016981988731477292 + 0.027770945493835165im;;; -0.006742437206232327 + 0.004394825292745555im 0.020283727427670827 + 0.026840649641765614im … 0.035461059551009304 - 0.0039635101946817065im -0.016800342977833095 - 0.022505949790327405im; 0.02242691395374271 + 0.05395117393241243im 0.06877257683369387 + 0.030601739359747172im … -0.014050062624888976 - 0.009023170537837275im -0.008796243650493203 + 0.018856651139444736im; … ; -0.004945506863565234 - 0.0419657703703645im 0.016867868185854184 - 0.011701716552521845im … -0.05629390165129111 + 0.05546621868794383im 0.016887309715009853 + 0.007888993429484278im; -0.03657516008161699 - 0.02976467500243037im 0.005293800913221052 - 0.006945871340959555im … 0.028504919620232508 + 0.038575611868469806im -0.0026205794360026693 - 0.05482880652229325im;;; 0.021896321269908495 + 0.016264659932680336im 0.015975805436470446 - 0.04044087453016163im … -0.030685006420014507 - 0.007829105753249962im -0.024517395512812814 + 0.030984723856931795im; 0.04332095560042304 - 0.00012586461627587392im 0.0059199570770653 - 0.02716188312634442im … -0.00357276461962093 + 0.018183541257766063im 0.019484781838528413 + 0.03834035292769411im; … ; -0.07781561373194823 - 0.030245049340764545im -0.01742699679963694 + 0.008092618351334912im … 0.027910130796763393 - 0.002968165471310685im -0.03010207057779402 - 0.07988435733734833im; -0.054620803068926596 + 0.0426048176107196im 0.02470550614107098 - 0.01728185542855022im … -0.0095321850654837 - 0.05623724423980549im -0.07672319058392318 - 0.027682035835022597im],)]), 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), [-12.247569697868094 -11.100308387037481 … -8.289845769070482 -11.100308387037513; -11.100308387037481 -9.13005781848603 … -9.130057802440204 -11.100308365272484; … ; -8.289845769070482 -9.130057802440202 … -4.149589911946472 -6.287956204742144; -11.100308387037511 -11.100308365272486 … -6.2879562047421445 -9.111848216116286;;; -11.100308387037483 -9.130057818486028 … -9.130057802440204 -11.100308365272486; -9.130057818486028 -6.903159504370278 … -9.130057819843168 -10.053883816992455; … ; -9.130057802440204 -9.130057819843163 … -5.294353665851816 -7.547399215040784; -11.100308365272486 -10.053883816992455 … -7.547399215040784 -10.053883816992508;;; -8.289845769070627 -6.307621938059807 … -8.289845773673541 -9.111848200070439; -6.307621938059805 -4.516655658357428 … -7.547399231895425 -7.5473992150408975; … ; -8.289845773673541 -7.547399231895422 … -5.768969098397977 -7.547399231895459; -9.111848200070439 -7.547399215040897 … -7.54739923189546 -9.111848217473536;;; … ;;; -5.301031708537768 -6.307621951401652 … -2.5497035798118617 -3.849582182333718; -6.307621951401652 -6.903159511450127 … -3.3290606941635192 -4.87841935156101; … ; -2.5497035798118612 -3.3290606941635192 … -1.256798467534796 -1.8141947489915387; -3.8495821823337177 -4.87841935156101 … -1.8141947489915402 -2.714767336891615;;; -8.289845769070482 -9.130057802440204 … -4.149589911946471 -6.287956204742144; -9.130057802440202 -9.130057819843167 … -5.294353665851816 -7.547399215040783; … ; -4.149589911946471 -5.294353665851816 … -1.9094492500179376 -2.894612364489525; -6.287956204742144 -7.547399215040784 … -2.894612364489526 -4.485542751913324;;; -11.100308387037511 -11.100308365272484 … -6.287956204742144 -9.111848216116288; -11.100308365272484 -10.053883816992457 … -7.547399215040785 -10.053883816992505; … ; -6.287956204742144 -7.547399215040782 … -2.8946123644895256 -4.485542751913324; -9.111848216116288 -10.053883816992506 … -4.485542751913324 -6.871104522523317])], 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), [-12.247569697868094 -11.100308387037481 … -8.289845769070482 -11.100308387037513; -11.100308387037481 -9.13005781848603 … -9.130057802440204 -11.100308365272484; … ; -8.289845769070482 -9.130057802440202 … -4.149589911946472 -6.287956204742144; -11.100308387037511 -11.100308365272486 … -6.2879562047421445 -9.111848216116286;;; -11.100308387037483 -9.130057818486028 … -9.130057802440204 -11.100308365272486; -9.130057818486028 -6.903159504370278 … -9.130057819843168 -10.053883816992455; … ; -9.130057802440204 -9.130057819843163 … -5.294353665851816 -7.547399215040784; -11.100308365272486 -10.053883816992455 … -7.547399215040784 -10.053883816992508;;; -8.289845769070627 -6.307621938059807 … -8.289845773673541 -9.111848200070439; -6.307621938059805 -4.516655658357428 … -7.547399231895425 -7.5473992150408975; … ; -8.289845773673541 -7.547399231895422 … -5.768969098397977 -7.547399231895459; -9.111848200070439 -7.547399215040897 … -7.54739923189546 -9.111848217473536;;; … ;;; -5.301031708537768 -6.307621951401652 … -2.5497035798118617 -3.849582182333718; -6.307621951401652 -6.903159511450127 … -3.3290606941635192 -4.87841935156101; … ; -2.5497035798118612 -3.3290606941635192 … -1.256798467534796 -1.8141947489915387; -3.8495821823337177 -4.87841935156101 … -1.8141947489915402 -2.714767336891615;;; -8.289845769070482 -9.130057802440204 … -4.149589911946471 -6.287956204742144; -9.130057802440202 -9.130057819843167 … -5.294353665851816 -7.547399215040783; … ; -4.149589911946471 -5.294353665851816 … -1.9094492500179376 -2.894612364489525; -6.287956204742144 -7.547399215040784 … -2.894612364489526 -4.485542751913324;;; -11.100308387037511 -11.100308365272484 … -6.287956204742144 -9.111848216116288; -11.100308365272484 -10.053883816992457 … -7.547399215040785 -10.053883816992505; … ; -6.287956204742144 -7.547399215040782 … -2.8946123644895256 -4.485542751913324; -9.111848216116288 -10.053883816992506 … -4.485542751913324 -6.871104522523317]), 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 = [-0.0015288831477095225 - 0.04744971182333164im -0.032980965973811234 - 0.027582468563407216im … 0.031680934136940626 - 0.0013889502089711038im 0.027643171572372102 - 0.022513234124314035im; -0.022608097594180455 - 0.018454980718917338im 0.008970757834272904 - 0.006909077934226024im … 0.017182426951885744 - 0.024112931531235112im -0.006711777273313637 - 0.032670571178416624im; … ; -0.008415785830978455 + 0.0013102182117994297im 0.010092473671850073 - 0.018576709739500895im … 0.010361996637758553 - 0.017989604215722245im -0.009350435840198235 - 0.010516766033359645im; 0.02400824338412074 - 0.022595748816401782im -0.008242280869696233 - 0.059431539375280326im … 0.007374279635232291 + 0.000479389055603852im 0.01696508968204597 + 0.0004571120990736128im;;; 0.06024021224404828 - 0.006459214635094067im 0.06137917514812722 - 0.053023940042687755im … 0.021660568456136526 - 0.031051107794643363im 0.026881262329420844 + 0.004118647215521951im; 0.05851198870078535 - 0.03876159691296473im 0.029105849903726666 - 0.09305811894789705im … -0.0006370897643465446 + 0.005352759542079095im 0.02698699034728439 + 0.005348401309082523im; … ; 0.01418596363496663 - 0.029696797756018516im 0.0002175694487019167 - 0.030075554815404446im … 0.03591309122667484 - 0.0005442968178973118im 0.03980595193290894 - 0.023618943664143417im; 0.04123440920030201 + 0.010485222503339067im 0.021198951337821192 - 0.018308004703870496im … 0.042363764995933084 - 0.014408791831928242im 0.023809574364968354 - 0.019654534071357265im;;; 0.07461322326641553 - 0.05915215967240073im 0.019229733490050364 - 0.059349806022516015im … 0.02589874189241243 + 0.014872293965562408im 0.07447179977729754 - 0.0011011580906428245im; 0.018283443525700334 - 0.08234343619659708im -0.003151872832652551 - 0.03153378362738087im … 0.037688169263103394 + 0.008636090737230078im 0.043775036873904556 - 0.029920583463211234im; … ; 0.017209037175492818 - 0.0043678301168671545im 0.023488032054161393 - 0.012809000395775021im … -0.001734975137871922 + 0.010380381158401168im 0.017913873338365756 - 0.00258970563930331im; 0.08962444837466332 - 0.003689071210896438im 0.05364250071616106 - 0.052066640405892914im … 0.016957805751492312 + 0.022932295291181782im 0.045193331931320246 + 0.022439751511441862im;;; … ;;; 0.06820750934835766 - 0.003805397232276529im 0.03986404762156025 - 0.025216197717291163im … 0.0213650026979913 + 0.04556582315924866im 0.049066983587293264 + 0.021282144302958442im; 0.03014664378610726 + 0.0010012048755596934im 0.024608713985072125 + 0.04930942377973945im … 0.033897715005391904 + 0.011978418576896285im 0.04008485405242679 + 0.0014630110982670518im; … ; 0.004084192355254885 + 0.03094933722241336im 0.05413712755669703 + 0.05040859950848396im … -0.06713092541683413 - 0.02435945838845349im -0.033970818475145784 + 0.02177227354246524im; 0.04156351650767531 + 0.016712537289479624im 0.08322195401561532 - 0.003184765789241109im … -0.009141359882494714 + 0.018870310264990985im 0.016981988731477292 + 0.027770945493835165im;;; -0.006742437206232327 + 0.004394825292745555im 0.020283727427670827 + 0.026840649641765614im … 0.035461059551009304 - 0.0039635101946817065im -0.016800342977833095 - 0.022505949790327405im; 0.02242691395374271 + 0.05395117393241243im 0.06877257683369387 + 0.030601739359747172im … -0.014050062624888976 - 0.009023170537837275im -0.008796243650493203 + 0.018856651139444736im; … ; -0.004945506863565234 - 0.0419657703703645im 0.016867868185854184 - 0.011701716552521845im … -0.05629390165129111 + 0.05546621868794383im 0.016887309715009853 + 0.007888993429484278im; -0.03657516008161699 - 0.02976467500243037im 0.005293800913221052 - 0.006945871340959555im … 0.028504919620232508 + 0.038575611868469806im -0.0026205794360026693 - 0.05482880652229325im;;; 0.021896321269908495 + 0.016264659932680336im 0.015975805436470446 - 0.04044087453016163im … -0.030685006420014507 - 0.007829105753249962im -0.024517395512812814 + 0.030984723856931795im; 0.04332095560042304 - 0.00012586461627587392im 0.0059199570770653 - 0.02716188312634442im … -0.00357276461962093 + 0.018183541257766063im 0.019484781838528413 + 0.03834035292769411im; … ; -0.07781561373194823 - 0.030245049340764545im -0.01742699679963694 + 0.008092618351334912im … 0.027910130796763393 - 0.002968165471310685im -0.03010207057779402 - 0.07988435733734833im; -0.054620803068926596 + 0.0426048176107196im 0.02470550614107098 - 0.01728185542855022im … -0.0095321850654837 - 0.05623724423980549im -0.07672319058392318 - 0.027682035835022597im],)]), 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), [-12.247569697868094 -11.100308387037481 … -8.289845769070482 -11.100308387037513; -11.100308387037481 -9.13005781848603 … -9.130057802440204 -11.100308365272484; … ; -8.289845769070482 -9.130057802440202 … -4.149589911946472 -6.287956204742144; -11.100308387037511 -11.100308365272486 … -6.2879562047421445 -9.111848216116286;;; -11.100308387037483 -9.130057818486028 … -9.130057802440204 -11.100308365272486; -9.130057818486028 -6.903159504370278 … -9.130057819843168 -10.053883816992455; … ; -9.130057802440204 -9.130057819843163 … -5.294353665851816 -7.547399215040784; -11.100308365272486 -10.053883816992455 … -7.547399215040784 -10.053883816992508;;; -8.289845769070627 -6.307621938059807 … -8.289845773673541 -9.111848200070439; -6.307621938059805 -4.516655658357428 … -7.547399231895425 -7.5473992150408975; … ; -8.289845773673541 -7.547399231895422 … -5.768969098397977 -7.547399231895459; -9.111848200070439 -7.547399215040897 … -7.54739923189546 -9.111848217473536;;; … ;;; -5.301031708537768 -6.307621951401652 … -2.5497035798118617 -3.849582182333718; -6.307621951401652 -6.903159511450127 … -3.3290606941635192 -4.87841935156101; … ; -2.5497035798118612 -3.3290606941635192 … -1.256798467534796 -1.8141947489915387; -3.8495821823337177 -4.87841935156101 … -1.8141947489915402 -2.714767336891615;;; -8.289845769070482 -9.130057802440204 … -4.149589911946471 -6.287956204742144; -9.130057802440202 -9.130057819843167 … -5.294353665851816 -7.547399215040783; … ; -4.149589911946471 -5.294353665851816 … -1.9094492500179376 -2.894612364489525; -6.287956204742144 -7.547399215040784 … -2.894612364489526 -4.485542751913324;;; -11.100308387037511 -11.100308365272484 … -6.287956204742144 -9.111848216116288; -11.100308365272484 -10.053883816992457 … -7.547399215040785 -10.053883816992505; … ; -6.287956204742144 -7.547399215040782 … -2.8946123644895256 -4.485542751913324; -9.111848216116288 -10.053883816992506 … -4.485542751913324 -6.871104522523317])], 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), [-12.247569697868094 -11.100308387037481 … -8.289845769070482 -11.100308387037513; -11.100308387037481 -9.13005781848603 … -9.130057802440204 -11.100308365272484; … ; -8.289845769070482 -9.130057802440202 … -4.149589911946472 -6.287956204742144; -11.100308387037511 -11.100308365272486 … -6.2879562047421445 -9.111848216116286;;; -11.100308387037483 -9.130057818486028 … -9.130057802440204 -11.100308365272486; -9.130057818486028 -6.903159504370278 … -9.130057819843168 -10.053883816992455; … ; -9.130057802440204 -9.130057819843163 … -5.294353665851816 -7.547399215040784; -11.100308365272486 -10.053883816992455 … -7.547399215040784 -10.053883816992508;;; -8.289845769070627 -6.307621938059807 … -8.289845773673541 -9.111848200070439; -6.307621938059805 -4.516655658357428 … -7.547399231895425 -7.5473992150408975; … ; -8.289845773673541 -7.547399231895422 … -5.768969098397977 -7.547399231895459; -9.111848200070439 -7.547399215040897 … -7.54739923189546 -9.111848217473536;;; … ;;; -5.301031708537768 -6.307621951401652 … -2.5497035798118617 -3.849582182333718; -6.307621951401652 -6.903159511450127 … -3.3290606941635192 -4.87841935156101; … ; -2.5497035798118612 -3.3290606941635192 … -1.256798467534796 -1.8141947489915387; -3.8495821823337177 -4.87841935156101 … -1.8141947489915402 -2.714767336891615;;; -8.289845769070482 -9.130057802440204 … -4.149589911946471 -6.287956204742144; -9.130057802440202 -9.130057819843167 … -5.294353665851816 -7.547399215040783; … ; -4.149589911946471 -5.294353665851816 … -1.9094492500179376 -2.894612364489525; -6.287956204742144 -7.547399215040784 … -2.894612364489526 -4.485542751913324;;; -11.100308387037511 -11.100308365272484 … -6.287956204742144 -9.111848216116288; -11.100308365272484 -10.053883816992457 … -7.547399215040785 -10.053883816992505; … ; -6.287956204742144 -7.547399215040782 … -2.8946123644895256 -4.485542751913324; -9.111848216116288 -10.053883816992506 … -4.485542751913324 -6.871104522523317]), 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 = [-0.0015288831477095225 - 0.04744971182333164im -0.032980965973811234 - 0.027582468563407216im … 0.031680934136940626 - 0.0013889502089711038im 0.027643171572372102 - 0.022513234124314035im; -0.022608097594180455 - 0.018454980718917338im 0.008970757834272904 - 0.006909077934226024im … 0.017182426951885744 - 0.024112931531235112im -0.006711777273313637 - 0.032670571178416624im; … ; -0.008415785830978455 + 0.0013102182117994297im 0.010092473671850073 - 0.018576709739500895im … 0.010361996637758553 - 0.017989604215722245im -0.009350435840198235 - 0.010516766033359645im; 0.02400824338412074 - 0.022595748816401782im -0.008242280869696233 - 0.059431539375280326im … 0.007374279635232291 + 0.000479389055603852im 0.01696508968204597 + 0.0004571120990736128im;;; 0.06024021224404828 - 0.006459214635094067im 0.06137917514812722 - 0.053023940042687755im … 0.021660568456136526 - 0.031051107794643363im 0.026881262329420844 + 0.004118647215521951im; 0.05851198870078535 - 0.03876159691296473im 0.029105849903726666 - 0.09305811894789705im … -0.0006370897643465446 + 0.005352759542079095im 0.02698699034728439 + 0.005348401309082523im; … ; 0.01418596363496663 - 0.029696797756018516im 0.0002175694487019167 - 0.030075554815404446im … 0.03591309122667484 - 0.0005442968178973118im 0.03980595193290894 - 0.023618943664143417im; 0.04123440920030201 + 0.010485222503339067im 0.021198951337821192 - 0.018308004703870496im … 0.042363764995933084 - 0.014408791831928242im 0.023809574364968354 - 0.019654534071357265im;;; 0.07461322326641553 - 0.05915215967240073im 0.019229733490050364 - 0.059349806022516015im … 0.02589874189241243 + 0.014872293965562408im 0.07447179977729754 - 0.0011011580906428245im; 0.018283443525700334 - 0.08234343619659708im -0.003151872832652551 - 0.03153378362738087im … 0.037688169263103394 + 0.008636090737230078im 0.043775036873904556 - 0.029920583463211234im; … ; 0.017209037175492818 - 0.0043678301168671545im 0.023488032054161393 - 0.012809000395775021im … -0.001734975137871922 + 0.010380381158401168im 0.017913873338365756 - 0.00258970563930331im; 0.08962444837466332 - 0.003689071210896438im 0.05364250071616106 - 0.052066640405892914im … 0.016957805751492312 + 0.022932295291181782im 0.045193331931320246 + 0.022439751511441862im;;; … ;;; 0.06820750934835766 - 0.003805397232276529im 0.03986404762156025 - 0.025216197717291163im … 0.0213650026979913 + 0.04556582315924866im 0.049066983587293264 + 0.021282144302958442im; 0.03014664378610726 + 0.0010012048755596934im 0.024608713985072125 + 0.04930942377973945im … 0.033897715005391904 + 0.011978418576896285im 0.04008485405242679 + 0.0014630110982670518im; … ; 0.004084192355254885 + 0.03094933722241336im 0.05413712755669703 + 0.05040859950848396im … -0.06713092541683413 - 0.02435945838845349im -0.033970818475145784 + 0.02177227354246524im; 0.04156351650767531 + 0.016712537289479624im 0.08322195401561532 - 0.003184765789241109im … -0.009141359882494714 + 0.018870310264990985im 0.016981988731477292 + 0.027770945493835165im;;; -0.006742437206232327 + 0.004394825292745555im 0.020283727427670827 + 0.026840649641765614im … 0.035461059551009304 - 0.0039635101946817065im -0.016800342977833095 - 0.022505949790327405im; 0.02242691395374271 + 0.05395117393241243im 0.06877257683369387 + 0.030601739359747172im … -0.014050062624888976 - 0.009023170537837275im -0.008796243650493203 + 0.018856651139444736im; … ; -0.004945506863565234 - 0.0419657703703645im 0.016867868185854184 - 0.011701716552521845im … -0.05629390165129111 + 0.05546621868794383im 0.016887309715009853 + 0.007888993429484278im; -0.03657516008161699 - 0.02976467500243037im 0.005293800913221052 - 0.006945871340959555im … 0.028504919620232508 + 0.038575611868469806im -0.0026205794360026693 - 0.05482880652229325im;;; 0.021896321269908495 + 0.016264659932680336im 0.015975805436470446 - 0.04044087453016163im … -0.030685006420014507 - 0.007829105753249962im -0.024517395512812814 + 0.030984723856931795im; 0.04332095560042304 - 0.00012586461627587392im 0.0059199570770653 - 0.02716188312634442im … -0.00357276461962093 + 0.018183541257766063im 0.019484781838528413 + 0.03834035292769411im; … ; -0.07781561373194823 - 0.030245049340764545im -0.01742699679963694 + 0.008092618351334912im … 0.027910130796763393 - 0.002968165471310685im -0.03010207057779402 - 0.07988435733734833im; -0.054620803068926596 + 0.0426048176107196im 0.02470550614107098 - 0.01728185542855022im … -0.0095321850654837 - 0.05623724423980549im -0.07672319058392318 - 0.027682035835022597im],)]), 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), [-12.247569697868094 -11.100308387037481 … -8.289845769070482 -11.100308387037513; -11.100308387037481 -9.13005781848603 … -9.130057802440204 -11.100308365272484; … ; -8.289845769070482 -9.130057802440202 … -4.149589911946472 -6.287956204742144; -11.100308387037511 -11.100308365272486 … -6.2879562047421445 -9.111848216116286;;; -11.100308387037483 -9.130057818486028 … -9.130057802440204 -11.100308365272486; -9.130057818486028 -6.903159504370278 … -9.130057819843168 -10.053883816992455; … ; -9.130057802440204 -9.130057819843163 … -5.294353665851816 -7.547399215040784; -11.100308365272486 -10.053883816992455 … -7.547399215040784 -10.053883816992508;;; -8.289845769070627 -6.307621938059807 … -8.289845773673541 -9.111848200070439; -6.307621938059805 -4.516655658357428 … -7.547399231895425 -7.5473992150408975; … ; -8.289845773673541 -7.547399231895422 … -5.768969098397977 -7.547399231895459; -9.111848200070439 -7.547399215040897 … -7.54739923189546 -9.111848217473536;;; … ;;; -5.301031708537768 -6.307621951401652 … -2.5497035798118617 -3.849582182333718; -6.307621951401652 -6.903159511450127 … -3.3290606941635192 -4.87841935156101; … ; -2.5497035798118612 -3.3290606941635192 … -1.256798467534796 -1.8141947489915387; -3.8495821823337177 -4.87841935156101 … -1.8141947489915402 -2.714767336891615;;; -8.289845769070482 -9.130057802440204 … -4.149589911946471 -6.287956204742144; -9.130057802440202 -9.130057819843167 … -5.294353665851816 -7.547399215040783; … ; -4.149589911946471 -5.294353665851816 … -1.9094492500179376 -2.894612364489525; -6.287956204742144 -7.547399215040784 … -2.894612364489526 -4.485542751913324;;; -11.100308387037511 -11.100308365272484 … -6.287956204742144 -9.111848216116288; -11.100308365272484 -10.053883816992457 … -7.547399215040785 -10.053883816992505; … ; -6.287956204742144 -7.547399215040782 … -2.8946123644895256 -4.485542751913324; -9.111848216116288 -10.053883816992506 … -4.485542751913324 -6.871104522523317])], 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), [-12.247569697868094 -11.100308387037481 … -8.289845769070482 -11.100308387037513; -11.100308387037481 -9.13005781848603 … -9.130057802440204 -11.100308365272484; … ; -8.289845769070482 -9.130057802440202 … -4.149589911946472 -6.287956204742144; -11.100308387037511 -11.100308365272486 … -6.2879562047421445 -9.111848216116286;;; -11.100308387037483 -9.130057818486028 … -9.130057802440204 -11.100308365272486; -9.130057818486028 -6.903159504370278 … -9.130057819843168 -10.053883816992455; … ; -9.130057802440204 -9.130057819843163 … -5.294353665851816 -7.547399215040784; -11.100308365272486 -10.053883816992455 … -7.547399215040784 -10.053883816992508;;; -8.289845769070627 -6.307621938059807 … -8.289845773673541 -9.111848200070439; -6.307621938059805 -4.516655658357428 … -7.547399231895425 -7.5473992150408975; … ; -8.289845773673541 -7.547399231895422 … -5.768969098397977 -7.547399231895459; -9.111848200070439 -7.547399215040897 … -7.54739923189546 -9.111848217473536;;; … ;;; -5.301031708537768 -6.307621951401652 … -2.5497035798118617 -3.849582182333718; -6.307621951401652 -6.903159511450127 … -3.3290606941635192 -4.87841935156101; … ; -2.5497035798118612 -3.3290606941635192 … -1.256798467534796 -1.8141947489915387; -3.8495821823337177 -4.87841935156101 … -1.8141947489915402 -2.714767336891615;;; -8.289845769070482 -9.130057802440204 … -4.149589911946471 -6.287956204742144; -9.130057802440202 -9.130057819843167 … -5.294353665851816 -7.547399215040783; … ; -4.149589911946471 -5.294353665851816 … -1.9094492500179376 -2.894612364489525; -6.287956204742144 -7.547399215040784 … -2.894612364489526 -4.485542751913324;;; -11.100308387037511 -11.100308365272484 … -6.287956204742144 -9.111848216116288; -11.100308365272484 -10.053883816992457 … -7.547399215040785 -10.053883816992505; … ; -6.287956204742144 -7.547399215040782 … -2.8946123644895256 -4.485542751913324; -9.111848216116288 -10.053883816992506 … -4.485542751913324 -6.871104522523317]), 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 = [-0.0015288831477095225 - 0.04744971182333164im -0.032980965973811234 - 0.027582468563407216im … 0.031680934136940626 - 0.0013889502089711038im 0.027643171572372102 - 0.022513234124314035im; -0.022608097594180455 - 0.018454980718917338im 0.008970757834272904 - 0.006909077934226024im … 0.017182426951885744 - 0.024112931531235112im -0.006711777273313637 - 0.032670571178416624im; … ; -0.008415785830978455 + 0.0013102182117994297im 0.010092473671850073 - 0.018576709739500895im … 0.010361996637758553 - 0.017989604215722245im -0.009350435840198235 - 0.010516766033359645im; 0.02400824338412074 - 0.022595748816401782im -0.008242280869696233 - 0.059431539375280326im … 0.007374279635232291 + 0.000479389055603852im 0.01696508968204597 + 0.0004571120990736128im;;; 0.06024021224404828 - 0.006459214635094067im 0.06137917514812722 - 0.053023940042687755im … 0.021660568456136526 - 0.031051107794643363im 0.026881262329420844 + 0.004118647215521951im; 0.05851198870078535 - 0.03876159691296473im 0.029105849903726666 - 0.09305811894789705im … -0.0006370897643465446 + 0.005352759542079095im 0.02698699034728439 + 0.005348401309082523im; … ; 0.01418596363496663 - 0.029696797756018516im 0.0002175694487019167 - 0.030075554815404446im … 0.03591309122667484 - 0.0005442968178973118im 0.03980595193290894 - 0.023618943664143417im; 0.04123440920030201 + 0.010485222503339067im 0.021198951337821192 - 0.018308004703870496im … 0.042363764995933084 - 0.014408791831928242im 0.023809574364968354 - 0.019654534071357265im;;; 0.07461322326641553 - 0.05915215967240073im 0.019229733490050364 - 0.059349806022516015im … 0.02589874189241243 + 0.014872293965562408im 0.07447179977729754 - 0.0011011580906428245im; 0.018283443525700334 - 0.08234343619659708im -0.003151872832652551 - 0.03153378362738087im … 0.037688169263103394 + 0.008636090737230078im 0.043775036873904556 - 0.029920583463211234im; … ; 0.017209037175492818 - 0.0043678301168671545im 0.023488032054161393 - 0.012809000395775021im … -0.001734975137871922 + 0.010380381158401168im 0.017913873338365756 - 0.00258970563930331im; 0.08962444837466332 - 0.003689071210896438im 0.05364250071616106 - 0.052066640405892914im … 0.016957805751492312 + 0.022932295291181782im 0.045193331931320246 + 0.022439751511441862im;;; … ;;; 0.06820750934835766 - 0.003805397232276529im 0.03986404762156025 - 0.025216197717291163im … 0.0213650026979913 + 0.04556582315924866im 0.049066983587293264 + 0.021282144302958442im; 0.03014664378610726 + 0.0010012048755596934im 0.024608713985072125 + 0.04930942377973945im … 0.033897715005391904 + 0.011978418576896285im 0.04008485405242679 + 0.0014630110982670518im; … ; 0.004084192355254885 + 0.03094933722241336im 0.05413712755669703 + 0.05040859950848396im … -0.06713092541683413 - 0.02435945838845349im -0.033970818475145784 + 0.02177227354246524im; 0.04156351650767531 + 0.016712537289479624im 0.08322195401561532 - 0.003184765789241109im … -0.009141359882494714 + 0.018870310264990985im 0.016981988731477292 + 0.027770945493835165im;;; -0.006742437206232327 + 0.004394825292745555im 0.020283727427670827 + 0.026840649641765614im … 0.035461059551009304 - 0.0039635101946817065im -0.016800342977833095 - 0.022505949790327405im; 0.02242691395374271 + 0.05395117393241243im 0.06877257683369387 + 0.030601739359747172im … -0.014050062624888976 - 0.009023170537837275im -0.008796243650493203 + 0.018856651139444736im; … ; -0.004945506863565234 - 0.0419657703703645im 0.016867868185854184 - 0.011701716552521845im … -0.05629390165129111 + 0.05546621868794383im 0.016887309715009853 + 0.007888993429484278im; -0.03657516008161699 - 0.02976467500243037im 0.005293800913221052 - 0.006945871340959555im … 0.028504919620232508 + 0.038575611868469806im -0.0026205794360026693 - 0.05482880652229325im;;; 0.021896321269908495 + 0.016264659932680336im 0.015975805436470446 - 0.04044087453016163im … -0.030685006420014507 - 0.007829105753249962im -0.024517395512812814 + 0.030984723856931795im; 0.04332095560042304 - 0.00012586461627587392im 0.0059199570770653 - 0.02716188312634442im … -0.00357276461962093 + 0.018183541257766063im 0.019484781838528413 + 0.03834035292769411im; … ; -0.07781561373194823 - 0.030245049340764545im -0.01742699679963694 + 0.008092618351334912im … 0.027910130796763393 - 0.002968165471310685im -0.03010207057779402 - 0.07988435733734833im; -0.054620803068926596 + 0.0426048176107196im 0.02470550614107098 - 0.01728185542855022im … -0.0095321850654837 - 0.05623724423980549im -0.07672319058392318 - 0.027682035835022597im],)])]), basis = PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), energies = Energies(total = -7.910594396488506), converged = true, ρ = [7.589784535773525e-5 0.0011262712729021766 … 0.006697037550282431 0.0011262712729021918; 0.0011262712729021834 0.005274334457561453 … 0.005274334457561488 0.0011262712729021868; … ; 0.006697037550282429 0.005274334457561493 … 0.02324475419085145 0.01225898682534536; 0.0011262712729022035 0.0011262712729021936 … 0.012258986825345354 0.003770008630088348;;; 0.0011262712729021818 0.005274334457561465 … 0.005274334457561502 0.0011262712729021899; 0.005274334457561468 0.014620065304867612 … 0.00527433445756149 0.00258808087500439; … ; 0.005274334457561497 0.005274334457561496 … 0.018107686646134012 0.00892200304493811; 0.0011262712729021985 0.002588080875004394 … 0.008922003044938101 0.002588080875004406;;; 0.006697037550282396 0.016412109101708164 … 0.006697037550282422 0.003770008630088323; 0.01641210910170817 0.03127783931579447 … 0.008922003044938074 0.008922003044938058; … ; 0.006697037550282419 0.008922003044938079 … 0.016476756359506496 0.008922003044938101; 0.0037700086300883327 0.008922003044938065 … 0.008922003044938098 0.0037700086300883383;;; … ;;; 0.019853839853399682 0.01641210910170818 … 0.03715667363518193 0.027190800686337106; 0.016412109101708178 0.01462006530486763 … 0.0323012721260859 0.022322100931649345; … ; 0.03715667363518193 0.032301272126085905 … 0.04629698070097249 0.042636582730895864; 0.02719080068633711 0.022322100931649345 … 0.04263658273089587 0.03477222914154279;;; 0.006697037550282405 0.005274334457561472 … 0.023244754190851414 0.012258986825345332; 0.005274334457561478 0.0052743344575614595 … 0.018107686646133964 0.008922003044938072; … ; 0.023244754190851414 0.018107686646133974 … 0.040371110335021484 0.031491603810946775; 0.012258986825345338 0.008922003044938075 … 0.031491603810946775 0.020047163432590973;;; 0.0011262712729021849 0.0011262712729021816 … 0.01225898682534535 0.00377000863008833; 0.001126271272902185 0.0025880808750043693 … 0.008922003044938086 0.0025880808750043957; … ; 0.012258986825345345 0.008922003044938091 … 0.03149160381094679 0.020047163432590987; 0.0037700086300883383 0.0025880808750043983 … 0.02004716343259098 0.008952603496911248;;;;], eigenvalues = [[-0.17836835653522284, 0.26249194499699635, 0.26249194499699674, 0.2624919449969972, 0.3546921481708319, 0.35469214817083233, 0.354692148186192], [-0.12755037617484513, 0.06475320595094178, 0.22545166517915363, 0.2254516651791539, 0.32197764961490394, 0.3892227690876181, 0.3892227690876186], [-0.10818729216071676, 0.07755003473950053, 0.1727832801189244, 0.17278328011892463, 0.2843518536220073, 0.33054764843476736, 0.5267232426440859], [-0.05777325373956106, 0.01272478221024808, 0.09766073750427803, 0.1841782533341218, 0.31522841796198275, 0.47203122071326153, 0.49791351775344883]], 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 = 0.2734218993095022, n_iter = 9, ψ = Matrix{ComplexF64}[[-0.7030311640467678 + 0.6383187836862052im -4.1781911210948664e-12 + 1.5216188338097484e-12im … 1.5675803016389266e-12 + 1.8731844985621594e-12im -1.4634206646099133e-7 + 9.964387574318368e-8im; 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