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 to 1e-2 atomic 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 solver to self_consistent_field, e.g.

    solver = scf_anderson_solver(; m=15)
    (::DFTK.var"#anderson#787"{DFTK.var"#anderson#786#788"{Base.Pairs{Symbol, Int64, Tuple{Symbol}, @NamedTuple{m::Int64}}}}) (generic function with 1 method)

    All keyword arguments are passed through to DFTK.AndersonAcceleration.

  • Try increasing convergence for for the bands in each SCF step by increasing the ratio_ρdiff parameter of the AdaptiveDiagtol algorithm. 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 AdaptiveBands algorithm. 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_adaptive instead of self_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(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 0.14590894423989453 + 0.0im … -0.05030254922547522 - 0.0im 0.0503025492254752 + 0.0im; … ; 0.08537828309138949 + 0.0im 0.10863402648960857 + 0.0im … -0.0 + 0.08075097926136235im 0.0 + 0.0im; 0.10094779392345996 + 0.0im 0.14590894423989453 + 0.0im … 0.05030254922547522 + 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), [-12.247569668724093 -11.100308396741907 … -8.289845772411969 -11.100308396741967; -11.100308396741907 -9.130057825947471 … -9.13005779589618 -11.10030835675893; … ; -8.289845772411969 -9.13005779589618 … -4.149589921642639 -6.28795619819863; -11.100308396741966 -11.100308356758932 … -6.287956198198631 -9.111848223576725;;; -11.100308396741909 -9.13005782594747 … -9.130057795896182 -11.100308356758932; -9.130057825947471 -6.903159481981954 … -9.130057827297154 -10.053883826551658; … ; -9.13005779589618 -9.130057827297154 … -5.294353669213858 -7.547399206521151; -11.10030835675893 -10.053883826551658 … -7.547399206521151 -10.053883826551763;;; -8.289845772412267 -6.3076219315164614 … -8.289845781011222 -9.111848193525395; -6.307621931516463 -4.516655665815588 … -7.547399237610982 -7.547399206521383; … ; -8.28984578101122 -7.547399237610981 … -5.768969083580764 -7.547399237611053; -9.111848193525393 -7.547399206521382 … -7.547399237611055 -9.111848224926632;;; … ;;; -5.301031718249374 -6.307621955788669 … -2.549703573275508 -3.849582179387295; -6.30762195578867 -6.903159495208783 … -3.3290606985458147 -4.878419358630238; … ; -2.549703573275507 -3.329060698545815 … -1.2567984709020936 -1.8141947460405818; -3.8495821793872933 -4.878419358630239 … -1.8141947460405818 -2.7147673353220663;;; -8.28984577241197 -9.130057795896178 … -4.14958992164264 -6.287956198198629; -9.13005779589618 -9.13005782729715 … -5.294353669213856 -7.547399206521149; … ; -4.149589921642639 -5.294353669213857 … -1.909449239914779 -2.8946123678516322; -6.28795619819863 -7.54739920652115 … -2.894612367851632 -4.485542759371293;;; -11.100308396741967 -11.100308356758932 … -6.287956198198631 -9.111848223576724; -11.10030835675893 -10.053883826551656 … -7.547399206521152 -10.053883826551763; … ; -6.287956198198629 -7.547399206521152 … -2.894612367851632 -4.485542759371292; -9.111848223576725 -10.053883826551763 … -4.4855427593712935 -6.8711045001343996])], 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), [-12.247569668724093 -11.100308396741907 … -8.289845772411969 -11.100308396741967; -11.100308396741907 -9.130057825947471 … -9.13005779589618 -11.10030835675893; … ; -8.289845772411969 -9.13005779589618 … -4.149589921642639 -6.28795619819863; -11.100308396741966 -11.100308356758932 … -6.287956198198631 -9.111848223576725;;; -11.100308396741909 -9.13005782594747 … -9.130057795896182 -11.100308356758932; -9.130057825947471 -6.903159481981954 … -9.130057827297154 -10.053883826551658; … ; -9.13005779589618 -9.130057827297154 … -5.294353669213858 -7.547399206521151; -11.10030835675893 -10.053883826551658 … -7.547399206521151 -10.053883826551763;;; -8.289845772412267 -6.3076219315164614 … -8.289845781011222 -9.111848193525395; -6.307621931516463 -4.516655665815588 … -7.547399237610982 -7.547399206521383; … ; -8.28984578101122 -7.547399237610981 … -5.768969083580764 -7.547399237611053; -9.111848193525393 -7.547399206521382 … -7.547399237611055 -9.111848224926632;;; … ;;; -5.301031718249374 -6.307621955788669 … -2.549703573275508 -3.849582179387295; -6.30762195578867 -6.903159495208783 … -3.3290606985458147 -4.878419358630238; … ; -2.549703573275507 -3.329060698545815 … -1.2567984709020936 -1.8141947460405818; -3.8495821793872933 -4.878419358630239 … -1.8141947460405818 -2.7147673353220663;;; -8.28984577241197 -9.130057795896178 … -4.14958992164264 -6.287956198198629; -9.13005779589618 -9.13005782729715 … -5.294353669213856 -7.547399206521149; … ; -4.149589921642639 -5.294353669213857 … -1.909449239914779 -2.8946123678516322; -6.28795619819863 -7.54739920652115 … -2.894612367851632 -4.485542759371293;;; -11.100308396741967 -11.100308356758932 … -6.287956198198631 -9.111848223576724; -11.10030835675893 -10.053883826551656 … -7.547399206521152 -10.053883826551763; … ; -6.287956198198629 -7.547399206521152 … -2.894612367851632 -4.485542759371292; -9.111848223576725 -10.053883826551763 … -4.4855427593712935 -6.8711045001343996]), 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 0.14590894423989453 + 0.0im … -0.05030254922547522 - 0.0im 0.0503025492254752 + 0.0im; … ; 0.08537828309138949 + 0.0im 0.10863402648960857 + 0.0im … -0.0 + 0.08075097926136235im 0.0 + 0.0im; 0.10094779392345996 + 0.0im 0.14590894423989453 + 0.0im … 0.05030254922547522 + 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 = [0.00888547993173295 - 0.00928361170696257im 0.016329769449478462 - 0.03291654964296425im … 0.0053541788714349895 - 0.028641409089287858im -0.009074995440063821 - 0.0005906544713919029im; 0.002464774417843529 - 0.0008707831456203656im -0.0026679304293415673 - 0.0038527305929199926im … -0.01305602133364156 - 0.0181145379401253im 0.0112108973071692 + 0.004049327983964417im; … ; 0.01127436989167333 - 0.025660120488875858im 0.001240903791174895 - 0.030077157692309286im … 0.02148081442295675 + 0.006196981446295912im 0.006477757465997445 - 0.014389748026780301im; -0.01427901657202451 - 0.033573684172023735im 0.0022315668446012864 - 0.01474805710890415im … 0.022843946565287505 - 0.023231531698153483im -0.010471407620549496 - 0.032969657758598316im;;; 0.04904041159576843 + 0.06594385504135508im 0.1342528287516711 - 3.107725327412131e-5im … -0.04551712912441702 + 0.010541296444102254im -0.014047282429392911 + 0.0743917940504712im; 0.056678155810453365 + 0.013794733463134128im 0.06528049233965563 - 0.044838190899482065im … -0.008406062350736567 + 0.038166347664998934im 0.02674196196465126 + 0.012835282685549957im; … ; 0.010156253773139673 - 0.020845752537701833im -0.008893384205940122 + 0.009329758276498883im … 0.023650326910471413 + 0.03206069096075599im 0.031502519376489006 + 0.005835444419122666im; -0.020438852533519965 + 0.0406528020790711im 0.04753756986261625 + 0.05192487754209257im … 0.009000702793547883 - 0.004527533827868625im -0.02488673563634476 + 0.0052749104480701095im;;; 0.0956274815457401 + 0.0244742023642644im 0.04599732796639359 - 0.06113389707558452im … -0.029884145825674266 + 0.06091776580298624im 0.03997400470232902 + 0.08781868098664597im; -0.03299215523127824 - 0.00645970528365611im -0.025744743850329727 + 0.012872736838123185im … 0.026108474479102115 + 0.010921883081756163im 0.00883616442641403 - 0.014063649800700576im; … ; -0.017844608809114985 + 0.04305173488551976im 0.027515652828620805 + 0.050593756400171434im … 0.0025332084428291712 + 0.008072311479430622im -0.015897179282845224 + 0.012835764093460848im; 0.041965851910917576 + 0.09553255019561795im 0.09668761341510777 + 0.00819078097893106im … -0.04051484734069446 + 0.016429767815345594im -0.03340173420149871 + 0.0775239112343612im;;; … ;;; -0.017982476417993852 + 0.010552567102737952im -0.030524423625161713 - 0.018759546292218113im … 0.001507328153848608 - 0.02276853803032704im -0.03215983596893164 + 0.008496609203660594im; 0.003199481232413197 + 0.010979413123653643im -0.02358538994940717 + 0.004811452120938899im … -0.02011747422775661 + 0.0006167953794195616im 0.006449271854839116 + 0.04722566580275376im; … ; -0.06636994635682134 + 0.014078175091297284im -0.008039959082577361 + 0.011245865810467413im … -0.08252992861161672 - 0.07619424349799472im -0.11502144440393477 - 0.025242725083444224im; -0.028420132714603998 + 0.01285950005640249im -0.0051182966841932685 - 0.02580529022048618im … -0.05897886176982764 - 0.005060345692164601im -0.07024766301070164 + 0.02152925262441298im;;; -0.09646435356925356 - 0.020992770921725048im -0.07345167829376412 + 0.02214730579031736im … -0.007379524430805889 - 0.0276195791348059im -0.01945809740532034 + 0.0025465564673048946im; -0.03256080245891865 + 0.0221507733663324im -0.01338686243354317 + 0.0381860864606877im … 0.02468612647179917 + 0.0381063704840063im 0.03585294627327915 + 0.020162558139470852im; … ; -0.0015639988295461614 - 0.013973865693337532im -0.0004988798728321892 - 0.0560340893530211im … -0.11139815676354961 - 0.024924430804875945im -0.0673569770224704 + 0.023679577710585112im; -0.05002912834056736 - 0.07950631264676315im -0.0813056738104971 - 0.05476220105948784im … -0.003158499708542657 - 0.015534398436944992im -0.008409371224780967 - 0.022232837585940572im;;; -0.06726849600155041 + 0.028079505683162732im -0.0002589341443315907 + 0.027704689476579634im … 0.02118828572408327 - 0.017878812089354948im -0.04941359340233691 - 0.027366445459826187im; -0.00494381249964241 + 0.032529742998526im 0.002398044496031565 - 0.008076950134004272im … 0.060658721663531104 - 0.010799987812204355im 0.02669967684149219 - 0.02464997653699073im; … ; -0.02327133881778893 - 0.07275418259032482im -0.035095170767192964 - 0.05101727735858361im … 0.0026891277254903045 + 0.005219398166771234im 0.019998340597587986 - 0.05165104834394915im; -0.12243875317047331 - 0.06598354624120639im -0.06526367785108313 + 0.002076301077302962im … 0.03718695031333938 - 0.0573426270591223im -0.03830611567078547 - 0.10160177386992467im],)]), DFTK.DftHamiltonianBlock(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, 14.560189056480333, 14.560189056480338, 9.498492431695329, 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 0.1697292679710574 + 0.0im … -0.009426647060181403 - 0.016327431653253982im 0.009426647060181401 + 0.01632743165325398im; 0.09335704685777356 + 0.0im 0.12740009431942179 + 0.0im … -0.052421044862493965 + 0.030265304362562334im 0.05242104486249396 - 0.030265304362562327im; … ; 0.09232028665365559 + 0.0im 0.12492048143428733 + 0.0im … 0.03728123116232768 + 0.06457298654187171im 0.007456246232465533 + 0.012914597308374338im; 0.10208144135055229 + 0.0im 0.14872488279907023 + 0.0im … 0.029470953026436673 - 0.01701506266308801im 0.05894190605287333 - 0.03403012532617602im], [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), [-12.247569668724093 -11.100308396741907 … -8.289845772411969 -11.100308396741967; -11.100308396741907 -9.130057825947471 … -9.13005779589618 -11.10030835675893; … ; -8.289845772411969 -9.13005779589618 … -4.149589921642639 -6.28795619819863; -11.100308396741966 -11.100308356758932 … -6.287956198198631 -9.111848223576725;;; -11.100308396741909 -9.13005782594747 … -9.130057795896182 -11.100308356758932; -9.130057825947471 -6.903159481981954 … -9.130057827297154 -10.053883826551658; … ; -9.13005779589618 -9.130057827297154 … -5.294353669213858 -7.547399206521151; -11.10030835675893 -10.053883826551658 … -7.547399206521151 -10.053883826551763;;; -8.289845772412267 -6.3076219315164614 … -8.289845781011222 -9.111848193525395; -6.307621931516463 -4.516655665815588 … -7.547399237610982 -7.547399206521383; … ; -8.28984578101122 -7.547399237610981 … -5.768969083580764 -7.547399237611053; -9.111848193525393 -7.547399206521382 … -7.547399237611055 -9.111848224926632;;; … ;;; -5.301031718249374 -6.307621955788669 … -2.549703573275508 -3.849582179387295; -6.30762195578867 -6.903159495208783 … -3.3290606985458147 -4.878419358630238; … ; -2.549703573275507 -3.329060698545815 … -1.2567984709020936 -1.8141947460405818; -3.8495821793872933 -4.878419358630239 … -1.8141947460405818 -2.7147673353220663;;; -8.28984577241197 -9.130057795896178 … -4.14958992164264 -6.287956198198629; -9.13005779589618 -9.13005782729715 … -5.294353669213856 -7.547399206521149; … ; -4.149589921642639 -5.294353669213857 … -1.909449239914779 -2.8946123678516322; -6.28795619819863 -7.54739920652115 … -2.894612367851632 -4.485542759371293;;; -11.100308396741967 -11.100308356758932 … -6.287956198198631 -9.111848223576724; -11.10030835675893 -10.053883826551656 … -7.547399206521152 -10.053883826551763; … ; -6.287956198198629 -7.547399206521152 … -2.894612367851632 -4.485542759371292; -9.111848223576725 -10.053883826551763 … -4.4855427593712935 -6.8711045001343996])], 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, 14.560189056480333, 14.560189056480338, 9.498492431695329, 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), [-12.247569668724093 -11.100308396741907 … -8.289845772411969 -11.100308396741967; -11.100308396741907 -9.130057825947471 … -9.13005779589618 -11.10030835675893; … ; -8.289845772411969 -9.13005779589618 … -4.149589921642639 -6.28795619819863; -11.100308396741966 -11.100308356758932 … -6.287956198198631 -9.111848223576725;;; -11.100308396741909 -9.13005782594747 … -9.130057795896182 -11.100308356758932; -9.130057825947471 -6.903159481981954 … -9.130057827297154 -10.053883826551658; … ; -9.13005779589618 -9.130057827297154 … -5.294353669213858 -7.547399206521151; -11.10030835675893 -10.053883826551658 … -7.547399206521151 -10.053883826551763;;; -8.289845772412267 -6.3076219315164614 … -8.289845781011222 -9.111848193525395; -6.307621931516463 -4.516655665815588 … -7.547399237610982 -7.547399206521383; … ; -8.28984578101122 -7.547399237610981 … -5.768969083580764 -7.547399237611053; -9.111848193525393 -7.547399206521382 … -7.547399237611055 -9.111848224926632;;; … ;;; -5.301031718249374 -6.307621955788669 … -2.549703573275508 -3.849582179387295; -6.30762195578867 -6.903159495208783 … -3.3290606985458147 -4.878419358630238; … ; -2.549703573275507 -3.329060698545815 … -1.2567984709020936 -1.8141947460405818; -3.8495821793872933 -4.878419358630239 … -1.8141947460405818 -2.7147673353220663;;; -8.28984577241197 -9.130057795896178 … -4.14958992164264 -6.287956198198629; -9.13005779589618 -9.13005782729715 … -5.294353669213856 -7.547399206521149; … ; -4.149589921642639 -5.294353669213857 … -1.909449239914779 -2.8946123678516322; -6.28795619819863 -7.54739920652115 … -2.894612367851632 -4.485542759371293;;; -11.100308396741967 -11.100308356758932 … -6.287956198198631 -9.111848223576724; -11.10030835675893 -10.053883826551656 … -7.547399206521152 -10.053883826551763; … ; -6.287956198198629 -7.547399206521152 … -2.894612367851632 -4.485542759371292; -9.111848223576725 -10.053883826551763 … -4.4855427593712935 -6.8711045001343996]), 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 0.1697292679710574 + 0.0im … -0.009426647060181403 - 0.016327431653253982im 0.009426647060181401 + 0.01632743165325398im; 0.09335704685777356 + 0.0im 0.12740009431942179 + 0.0im … -0.052421044862493965 + 0.030265304362562334im 0.05242104486249396 - 0.030265304362562327im; … ; 0.09232028665365559 + 0.0im 0.12492048143428733 + 0.0im … 0.03728123116232768 + 0.06457298654187171im 0.007456246232465533 + 0.012914597308374338im; 0.10208144135055229 + 0.0im 0.14872488279907023 + 0.0im … 0.029470953026436673 - 0.01701506266308801im 0.05894190605287333 - 0.03403012532617602im], [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 = [0.00888547993173295 - 0.00928361170696257im 0.016329769449478462 - 0.03291654964296425im … 0.0053541788714349895 - 0.028641409089287858im -0.009074995440063821 - 0.0005906544713919029im; 0.002464774417843529 - 0.0008707831456203656im -0.0026679304293415673 - 0.0038527305929199926im … -0.01305602133364156 - 0.0181145379401253im 0.0112108973071692 + 0.004049327983964417im; … ; 0.01127436989167333 - 0.025660120488875858im 0.001240903791174895 - 0.030077157692309286im … 0.02148081442295675 + 0.006196981446295912im 0.006477757465997445 - 0.014389748026780301im; -0.01427901657202451 - 0.033573684172023735im 0.0022315668446012864 - 0.01474805710890415im … 0.022843946565287505 - 0.023231531698153483im -0.010471407620549496 - 0.032969657758598316im;;; 0.04904041159576843 + 0.06594385504135508im 0.1342528287516711 - 3.107725327412131e-5im … -0.04551712912441702 + 0.010541296444102254im -0.014047282429392911 + 0.0743917940504712im; 0.056678155810453365 + 0.013794733463134128im 0.06528049233965563 - 0.044838190899482065im … -0.008406062350736567 + 0.038166347664998934im 0.02674196196465126 + 0.012835282685549957im; … ; 0.010156253773139673 - 0.020845752537701833im -0.008893384205940122 + 0.009329758276498883im … 0.023650326910471413 + 0.03206069096075599im 0.031502519376489006 + 0.005835444419122666im; -0.020438852533519965 + 0.0406528020790711im 0.04753756986261625 + 0.05192487754209257im … 0.009000702793547883 - 0.004527533827868625im -0.02488673563634476 + 0.0052749104480701095im;;; 0.0956274815457401 + 0.0244742023642644im 0.04599732796639359 - 0.06113389707558452im … -0.029884145825674266 + 0.06091776580298624im 0.03997400470232902 + 0.08781868098664597im; -0.03299215523127824 - 0.00645970528365611im -0.025744743850329727 + 0.012872736838123185im … 0.026108474479102115 + 0.010921883081756163im 0.00883616442641403 - 0.014063649800700576im; … ; -0.017844608809114985 + 0.04305173488551976im 0.027515652828620805 + 0.050593756400171434im … 0.0025332084428291712 + 0.008072311479430622im -0.015897179282845224 + 0.012835764093460848im; 0.041965851910917576 + 0.09553255019561795im 0.09668761341510777 + 0.00819078097893106im … -0.04051484734069446 + 0.016429767815345594im -0.03340173420149871 + 0.0775239112343612im;;; … ;;; -0.017982476417993852 + 0.010552567102737952im -0.030524423625161713 - 0.018759546292218113im … 0.001507328153848608 - 0.02276853803032704im -0.03215983596893164 + 0.008496609203660594im; 0.003199481232413197 + 0.010979413123653643im -0.02358538994940717 + 0.004811452120938899im … -0.02011747422775661 + 0.0006167953794195616im 0.006449271854839116 + 0.04722566580275376im; … ; -0.06636994635682134 + 0.014078175091297284im -0.008039959082577361 + 0.011245865810467413im … -0.08252992861161672 - 0.07619424349799472im -0.11502144440393477 - 0.025242725083444224im; -0.028420132714603998 + 0.01285950005640249im -0.0051182966841932685 - 0.02580529022048618im … -0.05897886176982764 - 0.005060345692164601im -0.07024766301070164 + 0.02152925262441298im;;; -0.09646435356925356 - 0.020992770921725048im -0.07345167829376412 + 0.02214730579031736im … -0.007379524430805889 - 0.0276195791348059im -0.01945809740532034 + 0.0025465564673048946im; -0.03256080245891865 + 0.0221507733663324im -0.01338686243354317 + 0.0381860864606877im … 0.02468612647179917 + 0.0381063704840063im 0.03585294627327915 + 0.020162558139470852im; … ; -0.0015639988295461614 - 0.013973865693337532im -0.0004988798728321892 - 0.0560340893530211im … -0.11139815676354961 - 0.024924430804875945im -0.0673569770224704 + 0.023679577710585112im; -0.05002912834056736 - 0.07950631264676315im -0.0813056738104971 - 0.05476220105948784im … -0.003158499708542657 - 0.015534398436944992im -0.008409371224780967 - 0.022232837585940572im;;; -0.06726849600155041 + 0.028079505683162732im -0.0002589341443315907 + 0.027704689476579634im … 0.02118828572408327 - 0.017878812089354948im -0.04941359340233691 - 0.027366445459826187im; -0.00494381249964241 + 0.032529742998526im 0.002398044496031565 - 0.008076950134004272im … 0.060658721663531104 - 0.010799987812204355im 0.02669967684149219 - 0.02464997653699073im; … ; -0.02327133881778893 - 0.07275418259032482im -0.035095170767192964 - 0.05101727735858361im … 0.0026891277254903045 + 0.005219398166771234im 0.019998340597587986 - 0.05165104834394915im; -0.12243875317047331 - 0.06598354624120639im -0.06526367785108313 + 0.002076301077302962im … 0.03718695031333938 - 0.0573426270591223im -0.03830611567078547 - 0.10160177386992467im],)]), DFTK.DftHamiltonianBlock(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, 0.8956911722870593, 2.8328837076986058, 5.8948977152846, 10.08173319504504, 12.893786875481156, 8.082050577846022, 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 0.1686758360708126 + 0.0im … -0.032495727623724026 - 0.018761417091069828im 5.710372280586092e-19 + 3.2968849733693577e-19im; 0.09511091805015323 + 0.0im 0.13162182200636915 + 0.0im … -0.03876707908042238 + 0.06714655062833207im 0.02326024744825342 - 0.04028793037699923im; … ; 0.09197726483082143 + 0.0im 0.12410271910068073 + 0.0im … 0.051406644402565774 + 0.029679639983956733im 0.0 - 0.0im; 0.10399921515860865 + 0.0im 0.15351809108742234 + 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), [-12.247569668724093 -11.100308396741907 … -8.289845772411969 -11.100308396741967; -11.100308396741907 -9.130057825947471 … -9.13005779589618 -11.10030835675893; … ; -8.289845772411969 -9.13005779589618 … -4.149589921642639 -6.28795619819863; -11.100308396741966 -11.100308356758932 … -6.287956198198631 -9.111848223576725;;; -11.100308396741909 -9.13005782594747 … -9.130057795896182 -11.100308356758932; -9.130057825947471 -6.903159481981954 … -9.130057827297154 -10.053883826551658; … ; -9.13005779589618 -9.130057827297154 … -5.294353669213858 -7.547399206521151; -11.10030835675893 -10.053883826551658 … -7.547399206521151 -10.053883826551763;;; -8.289845772412267 -6.3076219315164614 … -8.289845781011222 -9.111848193525395; -6.307621931516463 -4.516655665815588 … -7.547399237610982 -7.547399206521383; … ; -8.28984578101122 -7.547399237610981 … -5.768969083580764 -7.547399237611053; -9.111848193525393 -7.547399206521382 … -7.547399237611055 -9.111848224926632;;; … ;;; -5.301031718249374 -6.307621955788669 … -2.549703573275508 -3.849582179387295; -6.30762195578867 -6.903159495208783 … -3.3290606985458147 -4.878419358630238; … ; -2.549703573275507 -3.329060698545815 … -1.2567984709020936 -1.8141947460405818; -3.8495821793872933 -4.878419358630239 … -1.8141947460405818 -2.7147673353220663;;; -8.28984577241197 -9.130057795896178 … -4.14958992164264 -6.287956198198629; -9.13005779589618 -9.13005782729715 … -5.294353669213856 -7.547399206521149; … ; -4.149589921642639 -5.294353669213857 … -1.909449239914779 -2.8946123678516322; -6.28795619819863 -7.54739920652115 … -2.894612367851632 -4.485542759371293;;; -11.100308396741967 -11.100308356758932 … -6.287956198198631 -9.111848223576724; -11.10030835675893 -10.053883826551656 … -7.547399206521152 -10.053883826551763; … ; -6.287956198198629 -7.547399206521152 … -2.894612367851632 -4.485542759371292; -9.111848223576725 -10.053883826551763 … -4.4855427593712935 -6.8711045001343996])], 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, 0.8956911722870593, 2.8328837076986058, 5.8948977152846, 10.08173319504504, 12.893786875481156, 8.082050577846022, 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), [-12.247569668724093 -11.100308396741907 … -8.289845772411969 -11.100308396741967; -11.100308396741907 -9.130057825947471 … -9.13005779589618 -11.10030835675893; … ; -8.289845772411969 -9.13005779589618 … -4.149589921642639 -6.28795619819863; -11.100308396741966 -11.100308356758932 … -6.287956198198631 -9.111848223576725;;; -11.100308396741909 -9.13005782594747 … -9.130057795896182 -11.100308356758932; -9.130057825947471 -6.903159481981954 … -9.130057827297154 -10.053883826551658; … ; -9.13005779589618 -9.130057827297154 … -5.294353669213858 -7.547399206521151; -11.10030835675893 -10.053883826551658 … -7.547399206521151 -10.053883826551763;;; -8.289845772412267 -6.3076219315164614 … -8.289845781011222 -9.111848193525395; -6.307621931516463 -4.516655665815588 … -7.547399237610982 -7.547399206521383; … ; -8.28984578101122 -7.547399237610981 … -5.768969083580764 -7.547399237611053; -9.111848193525393 -7.547399206521382 … -7.547399237611055 -9.111848224926632;;; … ;;; -5.301031718249374 -6.307621955788669 … -2.549703573275508 -3.849582179387295; -6.30762195578867 -6.903159495208783 … -3.3290606985458147 -4.878419358630238; … ; -2.549703573275507 -3.329060698545815 … -1.2567984709020936 -1.8141947460405818; -3.8495821793872933 -4.878419358630239 … -1.8141947460405818 -2.7147673353220663;;; -8.28984577241197 -9.130057795896178 … -4.14958992164264 -6.287956198198629; -9.13005779589618 -9.13005782729715 … -5.294353669213856 -7.547399206521149; … ; -4.149589921642639 -5.294353669213857 … -1.909449239914779 -2.8946123678516322; -6.28795619819863 -7.54739920652115 … -2.894612367851632 -4.485542759371293;;; -11.100308396741967 -11.100308356758932 … -6.287956198198631 -9.111848223576724; -11.10030835675893 -10.053883826551656 … -7.547399206521152 -10.053883826551763; … ; -6.287956198198629 -7.547399206521152 … -2.894612367851632 -4.485542759371292; -9.111848223576725 -10.053883826551763 … -4.4855427593712935 -6.8711045001343996]), 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 0.1686758360708126 + 0.0im … -0.032495727623724026 - 0.018761417091069828im 5.710372280586092e-19 + 3.2968849733693577e-19im; 0.09511091805015323 + 0.0im 0.13162182200636915 + 0.0im … -0.03876707908042238 + 0.06714655062833207im 0.02326024744825342 - 0.04028793037699923im; … ; 0.09197726483082143 + 0.0im 0.12410271910068073 + 0.0im … 0.051406644402565774 + 0.029679639983956733im 0.0 - 0.0im; 0.10399921515860865 + 0.0im 0.15351809108742234 + 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 = [0.00888547993173295 - 0.00928361170696257im 0.016329769449478462 - 0.03291654964296425im … 0.0053541788714349895 - 0.028641409089287858im -0.009074995440063821 - 0.0005906544713919029im; 0.002464774417843529 - 0.0008707831456203656im -0.0026679304293415673 - 0.0038527305929199926im … -0.01305602133364156 - 0.0181145379401253im 0.0112108973071692 + 0.004049327983964417im; … ; 0.01127436989167333 - 0.025660120488875858im 0.001240903791174895 - 0.030077157692309286im … 0.02148081442295675 + 0.006196981446295912im 0.006477757465997445 - 0.014389748026780301im; -0.01427901657202451 - 0.033573684172023735im 0.0022315668446012864 - 0.01474805710890415im … 0.022843946565287505 - 0.023231531698153483im -0.010471407620549496 - 0.032969657758598316im;;; 0.04904041159576843 + 0.06594385504135508im 0.1342528287516711 - 3.107725327412131e-5im … -0.04551712912441702 + 0.010541296444102254im -0.014047282429392911 + 0.0743917940504712im; 0.056678155810453365 + 0.013794733463134128im 0.06528049233965563 - 0.044838190899482065im … -0.008406062350736567 + 0.038166347664998934im 0.02674196196465126 + 0.012835282685549957im; … ; 0.010156253773139673 - 0.020845752537701833im -0.008893384205940122 + 0.009329758276498883im … 0.023650326910471413 + 0.03206069096075599im 0.031502519376489006 + 0.005835444419122666im; -0.020438852533519965 + 0.0406528020790711im 0.04753756986261625 + 0.05192487754209257im … 0.009000702793547883 - 0.004527533827868625im -0.02488673563634476 + 0.0052749104480701095im;;; 0.0956274815457401 + 0.0244742023642644im 0.04599732796639359 - 0.06113389707558452im … -0.029884145825674266 + 0.06091776580298624im 0.03997400470232902 + 0.08781868098664597im; -0.03299215523127824 - 0.00645970528365611im -0.025744743850329727 + 0.012872736838123185im … 0.026108474479102115 + 0.010921883081756163im 0.00883616442641403 - 0.014063649800700576im; … ; -0.017844608809114985 + 0.04305173488551976im 0.027515652828620805 + 0.050593756400171434im … 0.0025332084428291712 + 0.008072311479430622im -0.015897179282845224 + 0.012835764093460848im; 0.041965851910917576 + 0.09553255019561795im 0.09668761341510777 + 0.00819078097893106im … -0.04051484734069446 + 0.016429767815345594im -0.03340173420149871 + 0.0775239112343612im;;; … ;;; -0.017982476417993852 + 0.010552567102737952im -0.030524423625161713 - 0.018759546292218113im … 0.001507328153848608 - 0.02276853803032704im -0.03215983596893164 + 0.008496609203660594im; 0.003199481232413197 + 0.010979413123653643im -0.02358538994940717 + 0.004811452120938899im … -0.02011747422775661 + 0.0006167953794195616im 0.006449271854839116 + 0.04722566580275376im; … ; -0.06636994635682134 + 0.014078175091297284im -0.008039959082577361 + 0.011245865810467413im … -0.08252992861161672 - 0.07619424349799472im -0.11502144440393477 - 0.025242725083444224im; -0.028420132714603998 + 0.01285950005640249im -0.0051182966841932685 - 0.02580529022048618im … -0.05897886176982764 - 0.005060345692164601im -0.07024766301070164 + 0.02152925262441298im;;; -0.09646435356925356 - 0.020992770921725048im -0.07345167829376412 + 0.02214730579031736im … -0.007379524430805889 - 0.0276195791348059im -0.01945809740532034 + 0.0025465564673048946im; -0.03256080245891865 + 0.0221507733663324im -0.01338686243354317 + 0.0381860864606877im … 0.02468612647179917 + 0.0381063704840063im 0.03585294627327915 + 0.020162558139470852im; … ; -0.0015639988295461614 - 0.013973865693337532im -0.0004988798728321892 - 0.0560340893530211im … -0.11139815676354961 - 0.024924430804875945im -0.0673569770224704 + 0.023679577710585112im; -0.05002912834056736 - 0.07950631264676315im -0.0813056738104971 - 0.05476220105948784im … -0.003158499708542657 - 0.015534398436944992im -0.008409371224780967 - 0.022232837585940572im;;; -0.06726849600155041 + 0.028079505683162732im -0.0002589341443315907 + 0.027704689476579634im … 0.02118828572408327 - 0.017878812089354948im -0.04941359340233691 - 0.027366445459826187im; -0.00494381249964241 + 0.032529742998526im 0.002398044496031565 - 0.008076950134004272im … 0.060658721663531104 - 0.010799987812204355im 0.02669967684149219 - 0.02464997653699073im; … ; -0.02327133881778893 - 0.07275418259032482im -0.035095170767192964 - 0.05101727735858361im … 0.0026891277254903045 + 0.005219398166771234im 0.019998340597587986 - 0.05165104834394915im; -0.12243875317047331 - 0.06598354624120639im -0.06526367785108313 + 0.002076301077302962im … 0.03718695031333938 - 0.0573426270591223im -0.03830611567078547 - 0.10160177386992467im],)]), DFTK.DftHamiltonianBlock(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, 7.1655293782964735, 11.72730534878173, 11.164894612694503, 6.72809880578419, 3.4161244710483185, 1.2289716084868951  …  0.41660054524979495, 1.228971608486895, 3.1661641438984414, 6.228178151484434, 10.415013631244872, 13.227067311680987, 8.415331014045858, 4.7284161885851725, 2.166322835298934, 0.729050954187141]), 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 - 1.0213144005610526e-18im 0.0 - 0.03679672923035902im; 0.10714287388793554 + 0.0im 0.16145393303017874 + 0.0im … -0.054392079538503724 - 0.0im 0.01813069317950125 + 0.0im; … ; 0.07579045242767471 + 0.0im 0.08711041809792076 + 0.0im … -0.0 + 0.06906475263474504im 0.0 - 0.023021584211581677im; 0.09798590385967748 + 0.0im 0.13861415332258226 + 0.0im … 0.048374574773583326 + 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), [-12.247569668724093 -11.100308396741907 … -8.289845772411969 -11.100308396741967; -11.100308396741907 -9.130057825947471 … -9.13005779589618 -11.10030835675893; … ; -8.289845772411969 -9.13005779589618 … -4.149589921642639 -6.28795619819863; -11.100308396741966 -11.100308356758932 … -6.287956198198631 -9.111848223576725;;; -11.100308396741909 -9.13005782594747 … -9.130057795896182 -11.100308356758932; -9.130057825947471 -6.903159481981954 … -9.130057827297154 -10.053883826551658; … ; -9.13005779589618 -9.130057827297154 … -5.294353669213858 -7.547399206521151; -11.10030835675893 -10.053883826551658 … -7.547399206521151 -10.053883826551763;;; -8.289845772412267 -6.3076219315164614 … -8.289845781011222 -9.111848193525395; -6.307621931516463 -4.516655665815588 … -7.547399237610982 -7.547399206521383; … ; -8.28984578101122 -7.547399237610981 … -5.768969083580764 -7.547399237611053; -9.111848193525393 -7.547399206521382 … -7.547399237611055 -9.111848224926632;;; … ;;; -5.301031718249374 -6.307621955788669 … -2.549703573275508 -3.849582179387295; -6.30762195578867 -6.903159495208783 … -3.3290606985458147 -4.878419358630238; … ; -2.549703573275507 -3.329060698545815 … -1.2567984709020936 -1.8141947460405818; -3.8495821793872933 -4.878419358630239 … -1.8141947460405818 -2.7147673353220663;;; -8.28984577241197 -9.130057795896178 … -4.14958992164264 -6.287956198198629; -9.13005779589618 -9.13005782729715 … -5.294353669213856 -7.547399206521149; … ; -4.149589921642639 -5.294353669213857 … -1.909449239914779 -2.8946123678516322; -6.28795619819863 -7.54739920652115 … -2.894612367851632 -4.485542759371293;;; -11.100308396741967 -11.100308356758932 … -6.287956198198631 -9.111848223576724; -11.10030835675893 -10.053883826551656 … -7.547399206521152 -10.053883826551763; … ; -6.287956198198629 -7.547399206521152 … -2.894612367851632 -4.485542759371292; -9.111848223576725 -10.053883826551763 … -4.4855427593712935 -6.8711045001343996])], 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, 7.1655293782964735, 11.72730534878173, 11.164894612694503, 6.72809880578419, 3.4161244710483185, 1.2289716084868951  …  0.41660054524979495, 1.228971608486895, 3.1661641438984414, 6.228178151484434, 10.415013631244872, 13.227067311680987, 8.415331014045858, 4.7284161885851725, 2.166322835298934, 0.729050954187141]), 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), [-12.247569668724093 -11.100308396741907 … -8.289845772411969 -11.100308396741967; -11.100308396741907 -9.130057825947471 … -9.13005779589618 -11.10030835675893; … ; -8.289845772411969 -9.13005779589618 … -4.149589921642639 -6.28795619819863; -11.100308396741966 -11.100308356758932 … -6.287956198198631 -9.111848223576725;;; -11.100308396741909 -9.13005782594747 … -9.130057795896182 -11.100308356758932; -9.130057825947471 -6.903159481981954 … -9.130057827297154 -10.053883826551658; … ; -9.13005779589618 -9.130057827297154 … -5.294353669213858 -7.547399206521151; -11.10030835675893 -10.053883826551658 … -7.547399206521151 -10.053883826551763;;; -8.289845772412267 -6.3076219315164614 … -8.289845781011222 -9.111848193525395; -6.307621931516463 -4.516655665815588 … -7.547399237610982 -7.547399206521383; … ; -8.28984578101122 -7.547399237610981 … -5.768969083580764 -7.547399237611053; -9.111848193525393 -7.547399206521382 … -7.547399237611055 -9.111848224926632;;; … ;;; -5.301031718249374 -6.307621955788669 … -2.549703573275508 -3.849582179387295; -6.30762195578867 -6.903159495208783 … -3.3290606985458147 -4.878419358630238; … ; -2.549703573275507 -3.329060698545815 … -1.2567984709020936 -1.8141947460405818; -3.8495821793872933 -4.878419358630239 … -1.8141947460405818 -2.7147673353220663;;; -8.28984577241197 -9.130057795896178 … -4.14958992164264 -6.287956198198629; -9.13005779589618 -9.13005782729715 … -5.294353669213856 -7.547399206521149; … ; -4.149589921642639 -5.294353669213857 … -1.909449239914779 -2.8946123678516322; -6.28795619819863 -7.54739920652115 … -2.894612367851632 -4.485542759371293;;; -11.100308396741967 -11.100308356758932 … -6.287956198198631 -9.111848223576724; -11.10030835675893 -10.053883826551656 … -7.547399206521152 -10.053883826551763; … ; -6.287956198198629 -7.547399206521152 … -2.894612367851632 -4.485542759371292; -9.111848223576725 -10.053883826551763 … -4.4855427593712935 -6.8711045001343996]), 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 - 1.0213144005610526e-18im 0.0 - 0.03679672923035902im; 0.10714287388793554 + 0.0im 0.16145393303017874 + 0.0im … -0.054392079538503724 - 0.0im 0.01813069317950125 + 0.0im; … ; 0.07579045242767471 + 0.0im 0.08711041809792076 + 0.0im … -0.0 + 0.06906475263474504im 0.0 - 0.023021584211581677im; 0.09798590385967748 + 0.0im 0.13861415332258226 + 0.0im … 0.048374574773583326 + 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 = [0.00888547993173295 - 0.00928361170696257im 0.016329769449478462 - 0.03291654964296425im … 0.0053541788714349895 - 0.028641409089287858im -0.009074995440063821 - 0.0005906544713919029im; 0.002464774417843529 - 0.0008707831456203656im -0.0026679304293415673 - 0.0038527305929199926im … -0.01305602133364156 - 0.0181145379401253im 0.0112108973071692 + 0.004049327983964417im; … ; 0.01127436989167333 - 0.025660120488875858im 0.001240903791174895 - 0.030077157692309286im … 0.02148081442295675 + 0.006196981446295912im 0.006477757465997445 - 0.014389748026780301im; -0.01427901657202451 - 0.033573684172023735im 0.0022315668446012864 - 0.01474805710890415im … 0.022843946565287505 - 0.023231531698153483im -0.010471407620549496 - 0.032969657758598316im;;; 0.04904041159576843 + 0.06594385504135508im 0.1342528287516711 - 3.107725327412131e-5im … -0.04551712912441702 + 0.010541296444102254im -0.014047282429392911 + 0.0743917940504712im; 0.056678155810453365 + 0.013794733463134128im 0.06528049233965563 - 0.044838190899482065im … -0.008406062350736567 + 0.038166347664998934im 0.02674196196465126 + 0.012835282685549957im; … ; 0.010156253773139673 - 0.020845752537701833im -0.008893384205940122 + 0.009329758276498883im … 0.023650326910471413 + 0.03206069096075599im 0.031502519376489006 + 0.005835444419122666im; -0.020438852533519965 + 0.0406528020790711im 0.04753756986261625 + 0.05192487754209257im … 0.009000702793547883 - 0.004527533827868625im -0.02488673563634476 + 0.0052749104480701095im;;; 0.0956274815457401 + 0.0244742023642644im 0.04599732796639359 - 0.06113389707558452im … -0.029884145825674266 + 0.06091776580298624im 0.03997400470232902 + 0.08781868098664597im; -0.03299215523127824 - 0.00645970528365611im -0.025744743850329727 + 0.012872736838123185im … 0.026108474479102115 + 0.010921883081756163im 0.00883616442641403 - 0.014063649800700576im; … ; -0.017844608809114985 + 0.04305173488551976im 0.027515652828620805 + 0.050593756400171434im … 0.0025332084428291712 + 0.008072311479430622im -0.015897179282845224 + 0.012835764093460848im; 0.041965851910917576 + 0.09553255019561795im 0.09668761341510777 + 0.00819078097893106im … -0.04051484734069446 + 0.016429767815345594im -0.03340173420149871 + 0.0775239112343612im;;; … ;;; -0.017982476417993852 + 0.010552567102737952im -0.030524423625161713 - 0.018759546292218113im … 0.001507328153848608 - 0.02276853803032704im -0.03215983596893164 + 0.008496609203660594im; 0.003199481232413197 + 0.010979413123653643im -0.02358538994940717 + 0.004811452120938899im … -0.02011747422775661 + 0.0006167953794195616im 0.006449271854839116 + 0.04722566580275376im; … ; -0.06636994635682134 + 0.014078175091297284im -0.008039959082577361 + 0.011245865810467413im … -0.08252992861161672 - 0.07619424349799472im -0.11502144440393477 - 0.025242725083444224im; -0.028420132714603998 + 0.01285950005640249im -0.0051182966841932685 - 0.02580529022048618im … -0.05897886176982764 - 0.005060345692164601im -0.07024766301070164 + 0.02152925262441298im;;; -0.09646435356925356 - 0.020992770921725048im -0.07345167829376412 + 0.02214730579031736im … -0.007379524430805889 - 0.0276195791348059im -0.01945809740532034 + 0.0025465564673048946im; -0.03256080245891865 + 0.0221507733663324im -0.01338686243354317 + 0.0381860864606877im … 0.02468612647179917 + 0.0381063704840063im 0.03585294627327915 + 0.020162558139470852im; … ; -0.0015639988295461614 - 0.013973865693337532im -0.0004988798728321892 - 0.0560340893530211im … -0.11139815676354961 - 0.024924430804875945im -0.0673569770224704 + 0.023679577710585112im; -0.05002912834056736 - 0.07950631264676315im -0.0813056738104971 - 0.05476220105948784im … -0.003158499708542657 - 0.015534398436944992im -0.008409371224780967 - 0.022232837585940572im;;; -0.06726849600155041 + 0.028079505683162732im -0.0002589341443315907 + 0.027704689476579634im … 0.02118828572408327 - 0.017878812089354948im -0.04941359340233691 - 0.027366445459826187im; -0.00494381249964241 + 0.032529742998526im 0.002398044496031565 - 0.008076950134004272im … 0.060658721663531104 - 0.010799987812204355im 0.02669967684149219 - 0.02464997653699073im; … ; -0.02327133881778893 - 0.07275418259032482im -0.035095170767192964 - 0.05101727735858361im … 0.0026891277254903045 + 0.005219398166771234im 0.019998340597587986 - 0.05165104834394915im; -0.12243875317047331 - 0.06598354624120639im -0.06526367785108313 + 0.002076301077302962im … 0.03718695031333938 - 0.0573426270591223im -0.03830611567078547 - 0.10160177386992467im],)])]), 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 = [7.589784543172564e-5 0.001126271272847383 … 0.006697037550115229 0.0011262712728473982; 0.0011262712728473897 0.0052743344574143385 … 0.005274334457414378 0.0011262712728474017; … ; 0.00669703755011523 0.005274334457414367 … 0.02324475419104717 0.01225898682525526; 0.0011262712728474017 0.0011262712728474 … 0.01225898682525526 0.0037700086299067926;;; 0.001126271272847401 0.005274334457414337 … 0.005274334457414373 0.0011262712728474036; 0.005274334457414347 0.01462006530482689 … 0.005274334457414377 0.0025880808748699243; … ; 0.005274334457414374 0.005274334457414368 … 0.018107686646178806 0.008922003044785718; 0.001126271272847402 0.0025880808748699243 … 0.008922003044785715 0.0025880808748699456;;; 0.006697037550115203 0.01641210910169489 … 0.006697037550115228 0.0037700086299067783; 0.0164121091016949 0.031277839316108745 … 0.008922003044785697 0.008922003044785675; … ; 0.006697037550115228 0.008922003044785696 … 0.016476756359503866 0.008922003044785713; 0.0037700086299067757 0.008922003044785673 … 0.008922003044785713 0.003770008629906784;;; … ;;; 0.01985383985346545 0.016412109101694897 … 0.03715667363565796 0.02719080068660203; 0.016412109101694907 0.014620065304826905 … 0.03230127212648407 0.022322100931781323; … ; 0.03715667363565796 0.03230127212648408 … 0.046296980701371344 0.04263658273138571; 0.027190800686602037 0.022322100931781327 … 0.042636582731385715 0.03477222914197294;;; 0.00669703755011521 0.0052743344574143385 … 0.023244754191047146 0.012258986825255226; 0.005274334457414349 0.00527433445741434 … 0.018107686646178768 0.008922003044785682; … ; 0.023244754191047146 0.018107686646178768 … 0.04037111033550507 0.03149160381133945; 0.01225898682525523 0.008922003044785683 … 0.031491603811339454 0.020047163432713854;;; 0.001126271272847402 0.001126271272847388 … 0.012258986825255244 0.0037700086299067835; 0.0011262712728473982 0.002588080874869911 … 0.008922003044785708 0.002588080874869928; … ; 0.012258986825255244 0.008922003044785699 … 0.03149160381133946 0.020047163432713865; 0.003770008629906785 0.002588080874869928 … 0.020047163432713865 0.0089526034967603;;;;], eigenvalues = [[-0.17836835653944377, 0.2624919449914078, 0.2624919449914081, 0.2624919449914085, 0.35469214816767813, 0.3546921481676789, 0.35469214818495304], [-0.12755037617928475, 0.06475320594672904, 0.22545166517409848, 0.22545166517409887, 0.3219776496112958, 0.3892227690847651, 0.38922276908476516], [-0.1081872921651748, 0.07755003473432913, 0.17278328011460545, 0.17278328011460553, 0.28435185361971627, 0.3305476484329304, 0.5267232426389559], [-0.05777325374442137, 0.012724782205450307, 0.09766073750113388, 0.1841782533296329, 0.3152284179597776, 0.4720312192839739, 0.4979135179530418]], 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 = 0.2734218993055624, n_iter = 10, ψ = Matrix{ComplexF64}[[-0.026262316640002906 - 0.9492175609155202im 6.315163504117626e-14 - 3.003700013865325e-15im … 2.2907589127076443e-13 + 9.868415985525725e-14im -2.4197388863622e-8 - 9.105785344625445e-8im; 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