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#994"{DFTK.var"#anderson#993#995"{Int64, Base.Pairs{Symbol, Int64, Nothing, @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 0.1459089442398946 + 0.0im … -0.05030254922547522 - 0.0im 0.0503025492254752 + 0.0im; … ; 0.08537828309138949 + 0.0im 0.1086340264896086 + 0.0im … -0.0 + 0.08075097926136235im 0.0 + 0.0im; 0.10094779392345996 + 0.0im 0.1459089442398946 + 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), [-12.247569668699787 -11.100308396737555 … -8.289845772407995 -11.100308396737615; -11.100308396737553 -9.130057825943455 … -9.130057795892162 -11.100308356754578; … ; -8.289845772407995 -9.130057795892162 … -4.149589921636905 -6.287956198193854; -11.100308396737613 -11.100308356754578 … -6.2879561981938545 -9.111848223573578;;; -11.100308396737557 -9.130057825943453 … -9.130057795892164 -11.10030835675458; -9.130057825943455 -6.903159481976938 … -9.130057827293136 -10.053883826548267; … ; -9.130057795892162 -9.130057827293136 … -5.2943536692085775 -7.5473992065168956; -11.100308356754576 -10.053883826548267 … -7.547399206516896 -10.053883826548372;;; -8.289845772408293 -6.307621931511362 … -8.289845781007248 -9.111848193522247; -6.307621931511364 -4.5166556658097985 … -7.547399237606728 -7.547399206517128; … ; -8.289845781007246 -7.547399237606727 … -5.768969083575679 -7.547399237606799; -9.111848193522247 -7.547399206517128 … -7.5473992376067995 -9.111848224923484;;; … ;;; -5.30103171824402 -6.307621955783571 … -2.549703573269716 -3.8495821793815224; -6.307621955783571 -6.9031594952037665 … -3.3290606985399807 -4.878419358624751; … ; -2.5497035732697158 -3.3290606985399815 … -1.2567984708974698 -1.8141947460351884; -3.849582179381523 -4.878419358624753 … -1.8141947460351884 -2.7147673353162176;;; -8.289845772407997 -9.130057795892162 … -4.149589921636907 -6.287956198193853; -9.130057795892164 -9.130057827293134 … -5.294353669208577 -7.547399206516895; … ; -4.149589921636907 -5.2943536692085775 … -1.9094492399092444 -2.8946123678456845; -6.287956198193854 -7.547399206516895 … -2.894612367845684 -4.485542759365641;;; -11.100308396737615 -11.10030835675458 … -6.2879561981938545 -9.111848223573578; -11.100308356754576 -10.053883826548267 … -7.547399206516897 -10.053883826548372; … ; -6.287956198193853 -7.547399206516897 … -2.8946123678456845 -4.48554275936564; -9.111848223573578 -10.053883826548372 … -4.485542759365641 -6.871104500130072])], 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), [-12.247569668699787 -11.100308396737555 … -8.289845772407995 -11.100308396737615; -11.100308396737553 -9.130057825943455 … -9.130057795892162 -11.100308356754578; … ; -8.289845772407995 -9.130057795892162 … -4.149589921636905 -6.287956198193854; -11.100308396737613 -11.100308356754578 … -6.2879561981938545 -9.111848223573578;;; -11.100308396737557 -9.130057825943453 … -9.130057795892164 -11.10030835675458; -9.130057825943455 -6.903159481976938 … -9.130057827293136 -10.053883826548267; … ; -9.130057795892162 -9.130057827293136 … -5.2943536692085775 -7.5473992065168956; -11.100308356754576 -10.053883826548267 … -7.547399206516896 -10.053883826548372;;; -8.289845772408293 -6.307621931511362 … -8.289845781007248 -9.111848193522247; -6.307621931511364 -4.5166556658097985 … -7.547399237606728 -7.547399206517128; … ; -8.289845781007246 -7.547399237606727 … -5.768969083575679 -7.547399237606799; -9.111848193522247 -7.547399206517128 … -7.5473992376067995 -9.111848224923484;;; … ;;; -5.30103171824402 -6.307621955783571 … -2.549703573269716 -3.8495821793815224; -6.307621955783571 -6.9031594952037665 … -3.3290606985399807 -4.878419358624751; … ; -2.5497035732697158 -3.3290606985399815 … -1.2567984708974698 -1.8141947460351884; -3.849582179381523 -4.878419358624753 … -1.8141947460351884 -2.7147673353162176;;; -8.289845772407997 -9.130057795892162 … -4.149589921636907 -6.287956198193853; -9.130057795892164 -9.130057827293134 … -5.294353669208577 -7.547399206516895; … ; -4.149589921636907 -5.2943536692085775 … -1.9094492399092444 -2.8946123678456845; -6.287956198193854 -7.547399206516895 … -2.894612367845684 -4.485542759365641;;; -11.100308396737615 -11.10030835675458 … -6.2879561981938545 -9.111848223573578; -11.100308356754576 -10.053883826548267 … -7.547399206516897 -10.053883826548372; … ; -6.287956198193853 -7.547399206516897 … -2.8946123678456845 -4.48554275936564; -9.111848223573578 -10.053883826548372 … -4.485542759365641 -6.871104500130072]), 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 … -0.05030254922547522 - 0.0im 0.0503025492254752 + 0.0im; … ; 0.08537828309138949 + 0.0im 0.1086340264896086 + 0.0im … -0.0 + 0.08075097926136235im 0.0 + 0.0im; 0.10094779392345996 + 0.0im 0.1459089442398946 + 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 = [-0.008094194612718998 + 0.003611463601662479im -0.006615968945047317 + 0.020394186335226876im … 0.03182102868513555 + 0.008397827417943125im 0.011974153750871463 - 0.027616007153768687im; -0.001532075823984644 + 0.009960423600344317im 0.032112736097950914 + 0.005769739482323974im … 0.033192814079434044 - 0.017759346310288544im -0.012682103394393015 - 0.008863285804189928im; … ; -0.004901320849150263 + 0.00542774428909369im -0.0004940323812476235 - 0.004216527726140671im … -0.011044708606218964 - 0.008222353394787857im -0.0025806404719160222 + 0.0013689784746009062im; -0.008029580823668808 + 0.00499832543550193im -0.011738034799603173 + 0.004259484520241709im … -0.007690906814579457 + 0.005671095649362548im 0.0047256559378572975 - 0.005950078492659459im;;; -9.139774643247833e-5 + 0.013400042001149241im -0.0056157487543693 - 0.035473868629812895im … -0.054281827293656715 - 0.05472959591567667im -0.06510924269539477 + 0.00849319903745651im; -0.014324852041470616 - 0.14364411284236928im -0.10161297150952861 - 0.0738033458794177im … 0.008738107552412194 - 0.004393100908182533im 0.03777356172775819 - 0.043295371434141486im; … ; -0.05314298476657904 - 0.03110727128472164im -0.08865327112161556 + 0.02029921829509234im … -0.0036155008153571228 + 0.011480550667076378im -0.0016920621635929944 - 0.019152746563185993im; -0.07760374755745393 + 0.02680367087425479im -0.038521829212508456 + 0.07261093002078722im … -0.0027598613483072916 - 0.050960056341562664im -0.07997128940282627 - 0.06341511374012036im;;; -0.014836312669572298 - 0.12297051984525079im -0.1403711000157868 - 0.08856126742975108im … -0.023452579404903685 + 0.006150559537507092im 0.013130004619482515 - 0.015367710543982317im; -0.1644887898461275 - 0.11712073708548887im -0.13746757595517733 + 0.03840981233060843im … 0.04275797746182499 - 0.04261695065252599im -0.01561855809075921 - 0.1528161558063589im; … ; -0.10919815851500206 + 0.02750161623741184im -0.04934009346838598 + 0.09008256222902286im … 0.003768558704206091 - 0.014590801246566594im -0.049646441354183224 - 0.034121353938145596im; -0.0280366808432553 + 0.05994666242398624im 0.01244618820921593 + 0.005536430858929659im … -0.04333258509428503 - 0.03466507800776912im -0.08110122079570542 + 0.014137341932752782im;;; … ;;; 0.008374351641613861 + 0.004985097423258936im 0.024841908976848404 + 0.03579999099345226im … 0.13827577651899292 + 0.04441421017678168im 0.06763056738181315 - 0.024282720126314546im; 0.04551035051298064 + 0.10413445930099502im 0.07800605125764795 + 0.039725158783057976im … -0.05732809949004441 + 0.0071719608263475995im -0.04504951834397703 + 0.10637323277059826im; … ; 0.11922747051979231 + 0.05020237565383995im 0.10693658621962912 - 0.035417055325178796im … 0.0015374718843062796 - 0.001088620526387505im 0.030883314025197485 + 0.06037895293258927im; 0.16744060616970136 - 0.05419881852702749im 0.0518279365928707 - 0.07857396950177664im … 0.07789877045705323 + 0.18110258458764086im 0.20132693982399372 + 0.0919618195854367im;;; 0.06617370454643859 + 0.1442313357997825im 0.14301045418025293 + 0.058191975482527455im … -0.004815105494012584 - 0.009335255031046756im -0.044406582844396976 + 0.10975410370272512im; 0.13140136613578698 + 0.041309974604432094im 0.0587284468307961 - 0.02379870916238038im … -0.08038337154761979 + 0.16828726856479345im 0.08457813043860349 + 0.17763105084591033im; … ; 0.1442019297928838 - 0.051898868246207215im 0.04954884342782243 - 0.08848511488125507im … 0.04435148596535872 + 0.11502685442862381im 0.1388316293937182 + 0.06400687967380252im; 0.03403650748336632 - 0.05167360414112724im 0.015518411640299153 + 0.00034157781336656163im … 0.17976999792077383 + 0.06862012698418456im 0.115586178015882 - 0.04096006432935607im;;; 0.11909587172301946 + 0.0410366861086136im 0.07265977287278563 - 0.03675249005969899im … -0.034165239370792036 + 0.08160804949058564im 0.06679747774431181 + 0.13264689323907866im; -0.01897035404248943 - 0.014898617815044604im -0.01589021796433579 + 0.04186423730837721im … 0.06464143828224501 + 0.11821306805194368im 0.07465507891363662 + 0.001749518208437325im; … ; 0.023102643919243483 - 0.04793352545492843im 0.0015791341862964048 - 0.013666860060534108im … 0.07602041865186747 + 0.020879238197940936im 0.05795118263580012 - 0.019784220571642853im; 0.019184635434564636 + 0.05386557007023975im 0.07249857194215878 + 0.027789184636890917im … 0.03617780165581058 - 0.028012779780713336im -0.005568867914379133 + 0.012124536045650568im],)]), 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, 14.560189056480331, 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 0.007456246232465533 + 0.012914597308374338im; 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), [-12.247569668699787 -11.100308396737555 … -8.289845772407995 -11.100308396737615; -11.100308396737553 -9.130057825943455 … -9.130057795892162 -11.100308356754578; … ; -8.289845772407995 -9.130057795892162 … -4.149589921636905 -6.287956198193854; -11.100308396737613 -11.100308356754578 … -6.2879561981938545 -9.111848223573578;;; -11.100308396737557 -9.130057825943453 … -9.130057795892164 -11.10030835675458; -9.130057825943455 -6.903159481976938 … -9.130057827293136 -10.053883826548267; … ; -9.130057795892162 -9.130057827293136 … -5.2943536692085775 -7.5473992065168956; -11.100308356754576 -10.053883826548267 … -7.547399206516896 -10.053883826548372;;; -8.289845772408293 -6.307621931511362 … -8.289845781007248 -9.111848193522247; -6.307621931511364 -4.5166556658097985 … -7.547399237606728 -7.547399206517128; … ; -8.289845781007246 -7.547399237606727 … -5.768969083575679 -7.547399237606799; -9.111848193522247 -7.547399206517128 … -7.5473992376067995 -9.111848224923484;;; … ;;; -5.30103171824402 -6.307621955783571 … -2.549703573269716 -3.8495821793815224; -6.307621955783571 -6.9031594952037665 … -3.3290606985399807 -4.878419358624751; … ; -2.5497035732697158 -3.3290606985399815 … -1.2567984708974698 -1.8141947460351884; -3.849582179381523 -4.878419358624753 … -1.8141947460351884 -2.7147673353162176;;; -8.289845772407997 -9.130057795892162 … -4.149589921636907 -6.287956198193853; -9.130057795892164 -9.130057827293134 … -5.294353669208577 -7.547399206516895; … ; -4.149589921636907 -5.2943536692085775 … -1.9094492399092444 -2.8946123678456845; -6.287956198193854 -7.547399206516895 … -2.894612367845684 -4.485542759365641;;; -11.100308396737615 -11.10030835675458 … -6.2879561981938545 -9.111848223573578; -11.100308356754576 -10.053883826548267 … -7.547399206516897 -10.053883826548372; … ; -6.287956198193853 -7.547399206516897 … -2.8946123678456845 -4.48554275936564; -9.111848223573578 -10.053883826548372 … -4.485542759365641 -6.871104500130072])], 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), [-12.247569668699787 -11.100308396737555 … -8.289845772407995 -11.100308396737615; -11.100308396737553 -9.130057825943455 … -9.130057795892162 -11.100308356754578; … ; -8.289845772407995 -9.130057795892162 … -4.149589921636905 -6.287956198193854; -11.100308396737613 -11.100308356754578 … -6.2879561981938545 -9.111848223573578;;; -11.100308396737557 -9.130057825943453 … -9.130057795892164 -11.10030835675458; -9.130057825943455 -6.903159481976938 … -9.130057827293136 -10.053883826548267; … ; -9.130057795892162 -9.130057827293136 … -5.2943536692085775 -7.5473992065168956; -11.100308356754576 -10.053883826548267 … -7.547399206516896 -10.053883826548372;;; -8.289845772408293 -6.307621931511362 … -8.289845781007248 -9.111848193522247; -6.307621931511364 -4.5166556658097985 … -7.547399237606728 -7.547399206517128; … ; -8.289845781007246 -7.547399237606727 … -5.768969083575679 -7.547399237606799; -9.111848193522247 -7.547399206517128 … -7.5473992376067995 -9.111848224923484;;; … ;;; -5.30103171824402 -6.307621955783571 … -2.549703573269716 -3.8495821793815224; -6.307621955783571 -6.9031594952037665 … -3.3290606985399807 -4.878419358624751; … ; -2.5497035732697158 -3.3290606985399815 … -1.2567984708974698 -1.8141947460351884; -3.849582179381523 -4.878419358624753 … -1.8141947460351884 -2.7147673353162176;;; -8.289845772407997 -9.130057795892162 … -4.149589921636907 -6.287956198193853; -9.130057795892164 -9.130057827293134 … -5.294353669208577 -7.547399206516895; … ; -4.149589921636907 -5.2943536692085775 … -1.9094492399092444 -2.8946123678456845; -6.287956198193854 -7.547399206516895 … -2.894612367845684 -4.485542759365641;;; -11.100308396737615 -11.10030835675458 … -6.2879561981938545 -9.111848223573578; -11.100308356754576 -10.053883826548267 … -7.547399206516897 -10.053883826548372; … ; -6.287956198193853 -7.547399206516897 … -2.8946123678456845 -4.48554275936564; -9.111848223573578 -10.053883826548372 … -4.485542759365641 -6.871104500130072]), 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 0.007456246232465533 + 0.012914597308374338im; 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 = [-0.008094194612718998 + 0.003611463601662479im -0.006615968945047317 + 0.020394186335226876im … 0.03182102868513555 + 0.008397827417943125im 0.011974153750871463 - 0.027616007153768687im; -0.001532075823984644 + 0.009960423600344317im 0.032112736097950914 + 0.005769739482323974im … 0.033192814079434044 - 0.017759346310288544im -0.012682103394393015 - 0.008863285804189928im; … ; -0.004901320849150263 + 0.00542774428909369im -0.0004940323812476235 - 0.004216527726140671im … -0.011044708606218964 - 0.008222353394787857im -0.0025806404719160222 + 0.0013689784746009062im; -0.008029580823668808 + 0.00499832543550193im -0.011738034799603173 + 0.004259484520241709im … -0.007690906814579457 + 0.005671095649362548im 0.0047256559378572975 - 0.005950078492659459im;;; -9.139774643247833e-5 + 0.013400042001149241im -0.0056157487543693 - 0.035473868629812895im … -0.054281827293656715 - 0.05472959591567667im -0.06510924269539477 + 0.00849319903745651im; -0.014324852041470616 - 0.14364411284236928im -0.10161297150952861 - 0.0738033458794177im … 0.008738107552412194 - 0.004393100908182533im 0.03777356172775819 - 0.043295371434141486im; … ; -0.05314298476657904 - 0.03110727128472164im -0.08865327112161556 + 0.02029921829509234im … -0.0036155008153571228 + 0.011480550667076378im -0.0016920621635929944 - 0.019152746563185993im; -0.07760374755745393 + 0.02680367087425479im -0.038521829212508456 + 0.07261093002078722im … -0.0027598613483072916 - 0.050960056341562664im -0.07997128940282627 - 0.06341511374012036im;;; -0.014836312669572298 - 0.12297051984525079im -0.1403711000157868 - 0.08856126742975108im … -0.023452579404903685 + 0.006150559537507092im 0.013130004619482515 - 0.015367710543982317im; -0.1644887898461275 - 0.11712073708548887im -0.13746757595517733 + 0.03840981233060843im … 0.04275797746182499 - 0.04261695065252599im -0.01561855809075921 - 0.1528161558063589im; … ; -0.10919815851500206 + 0.02750161623741184im -0.04934009346838598 + 0.09008256222902286im … 0.003768558704206091 - 0.014590801246566594im -0.049646441354183224 - 0.034121353938145596im; -0.0280366808432553 + 0.05994666242398624im 0.01244618820921593 + 0.005536430858929659im … -0.04333258509428503 - 0.03466507800776912im -0.08110122079570542 + 0.014137341932752782im;;; … ;;; 0.008374351641613861 + 0.004985097423258936im 0.024841908976848404 + 0.03579999099345226im … 0.13827577651899292 + 0.04441421017678168im 0.06763056738181315 - 0.024282720126314546im; 0.04551035051298064 + 0.10413445930099502im 0.07800605125764795 + 0.039725158783057976im … -0.05732809949004441 + 0.0071719608263475995im -0.04504951834397703 + 0.10637323277059826im; … ; 0.11922747051979231 + 0.05020237565383995im 0.10693658621962912 - 0.035417055325178796im … 0.0015374718843062796 - 0.001088620526387505im 0.030883314025197485 + 0.06037895293258927im; 0.16744060616970136 - 0.05419881852702749im 0.0518279365928707 - 0.07857396950177664im … 0.07789877045705323 + 0.18110258458764086im 0.20132693982399372 + 0.0919618195854367im;;; 0.06617370454643859 + 0.1442313357997825im 0.14301045418025293 + 0.058191975482527455im … -0.004815105494012584 - 0.009335255031046756im -0.044406582844396976 + 0.10975410370272512im; 0.13140136613578698 + 0.041309974604432094im 0.0587284468307961 - 0.02379870916238038im … -0.08038337154761979 + 0.16828726856479345im 0.08457813043860349 + 0.17763105084591033im; … ; 0.1442019297928838 - 0.051898868246207215im 0.04954884342782243 - 0.08848511488125507im … 0.04435148596535872 + 0.11502685442862381im 0.1388316293937182 + 0.06400687967380252im; 0.03403650748336632 - 0.05167360414112724im 0.015518411640299153 + 0.00034157781336656163im … 0.17976999792077383 + 0.06862012698418456im 0.115586178015882 - 0.04096006432935607im;;; 0.11909587172301946 + 0.0410366861086136im 0.07265977287278563 - 0.03675249005969899im … -0.034165239370792036 + 0.08160804949058564im 0.06679747774431181 + 0.13264689323907866im; -0.01897035404248943 - 0.014898617815044604im -0.01589021796433579 + 0.04186423730837721im … 0.06464143828224501 + 0.11821306805194368im 0.07465507891363662 + 0.001749518208437325im; … ; 0.023102643919243483 - 0.04793352545492843im 0.0015791341862964048 - 0.013666860060534108im … 0.07602041865186747 + 0.020879238197940936im 0.05795118263580012 - 0.019784220571642853im; 0.019184635434564636 + 0.05386557007023975im 0.07249857194215878 + 0.027789184636890917im … 0.03617780165581058 - 0.028012779780713336im -0.005568867914379133 + 0.012124536045650568im],)]), 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, 0.8956911722870592, 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 … -0.03876707908042239 + 0.06714655062833208im 0.02326024744825342 - 0.04028793037699923im; … ; 0.09197726483082143 + 0.0im 0.12410271910068073 + 0.0im … 0.051406644402565774 + 0.029679639983956733im 6.990521527121634e-18 + 4.035979485459552e-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), [-12.247569668699787 -11.100308396737555 … -8.289845772407995 -11.100308396737615; -11.100308396737553 -9.130057825943455 … -9.130057795892162 -11.100308356754578; … ; -8.289845772407995 -9.130057795892162 … -4.149589921636905 -6.287956198193854; -11.100308396737613 -11.100308356754578 … -6.2879561981938545 -9.111848223573578;;; -11.100308396737557 -9.130057825943453 … -9.130057795892164 -11.10030835675458; -9.130057825943455 -6.903159481976938 … -9.130057827293136 -10.053883826548267; … ; -9.130057795892162 -9.130057827293136 … -5.2943536692085775 -7.5473992065168956; -11.100308356754576 -10.053883826548267 … -7.547399206516896 -10.053883826548372;;; -8.289845772408293 -6.307621931511362 … -8.289845781007248 -9.111848193522247; -6.307621931511364 -4.5166556658097985 … -7.547399237606728 -7.547399206517128; … ; -8.289845781007246 -7.547399237606727 … -5.768969083575679 -7.547399237606799; -9.111848193522247 -7.547399206517128 … -7.5473992376067995 -9.111848224923484;;; … ;;; -5.30103171824402 -6.307621955783571 … -2.549703573269716 -3.8495821793815224; -6.307621955783571 -6.9031594952037665 … -3.3290606985399807 -4.878419358624751; … ; -2.5497035732697158 -3.3290606985399815 … -1.2567984708974698 -1.8141947460351884; -3.849582179381523 -4.878419358624753 … -1.8141947460351884 -2.7147673353162176;;; -8.289845772407997 -9.130057795892162 … -4.149589921636907 -6.287956198193853; -9.130057795892164 -9.130057827293134 … -5.294353669208577 -7.547399206516895; … ; -4.149589921636907 -5.2943536692085775 … -1.9094492399092444 -2.8946123678456845; -6.287956198193854 -7.547399206516895 … -2.894612367845684 -4.485542759365641;;; -11.100308396737615 -11.10030835675458 … -6.2879561981938545 -9.111848223573578; -11.100308356754576 -10.053883826548267 … -7.547399206516897 -10.053883826548372; … ; -6.287956198193853 -7.547399206516897 … -2.8946123678456845 -4.48554275936564; -9.111848223573578 -10.053883826548372 … -4.485542759365641 -6.871104500130072])], 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), [-12.247569668699787 -11.100308396737555 … -8.289845772407995 -11.100308396737615; -11.100308396737553 -9.130057825943455 … -9.130057795892162 -11.100308356754578; … ; -8.289845772407995 -9.130057795892162 … -4.149589921636905 -6.287956198193854; -11.100308396737613 -11.100308356754578 … -6.2879561981938545 -9.111848223573578;;; -11.100308396737557 -9.130057825943453 … -9.130057795892164 -11.10030835675458; -9.130057825943455 -6.903159481976938 … -9.130057827293136 -10.053883826548267; … ; -9.130057795892162 -9.130057827293136 … -5.2943536692085775 -7.5473992065168956; -11.100308356754576 -10.053883826548267 … -7.547399206516896 -10.053883826548372;;; -8.289845772408293 -6.307621931511362 … -8.289845781007248 -9.111848193522247; -6.307621931511364 -4.5166556658097985 … -7.547399237606728 -7.547399206517128; … ; -8.289845781007246 -7.547399237606727 … -5.768969083575679 -7.547399237606799; -9.111848193522247 -7.547399206517128 … -7.5473992376067995 -9.111848224923484;;; … ;;; -5.30103171824402 -6.307621955783571 … -2.549703573269716 -3.8495821793815224; -6.307621955783571 -6.9031594952037665 … -3.3290606985399807 -4.878419358624751; … ; -2.5497035732697158 -3.3290606985399815 … -1.2567984708974698 -1.8141947460351884; -3.849582179381523 -4.878419358624753 … -1.8141947460351884 -2.7147673353162176;;; -8.289845772407997 -9.130057795892162 … -4.149589921636907 -6.287956198193853; -9.130057795892164 -9.130057827293134 … -5.294353669208577 -7.547399206516895; … ; -4.149589921636907 -5.2943536692085775 … -1.9094492399092444 -2.8946123678456845; -6.287956198193854 -7.547399206516895 … -2.894612367845684 -4.485542759365641;;; -11.100308396737615 -11.10030835675458 … -6.2879561981938545 -9.111848223573578; -11.100308356754576 -10.053883826548267 … -7.547399206516897 -10.053883826548372; … ; -6.287956198193853 -7.547399206516897 … -2.8946123678456845 -4.48554275936564; -9.111848223573578 -10.053883826548372 … -4.485542759365641 -6.871104500130072]), 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 … -0.03876707908042239 + 0.06714655062833208im 0.02326024744825342 - 0.04028793037699923im; … ; 0.09197726483082143 + 0.0im 0.12410271910068073 + 0.0im … 0.051406644402565774 + 0.029679639983956733im 6.990521527121634e-18 + 4.035979485459552e-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 = [-0.008094194612718998 + 0.003611463601662479im -0.006615968945047317 + 0.020394186335226876im … 0.03182102868513555 + 0.008397827417943125im 0.011974153750871463 - 0.027616007153768687im; -0.001532075823984644 + 0.009960423600344317im 0.032112736097950914 + 0.005769739482323974im … 0.033192814079434044 - 0.017759346310288544im -0.012682103394393015 - 0.008863285804189928im; … ; -0.004901320849150263 + 0.00542774428909369im -0.0004940323812476235 - 0.004216527726140671im … -0.011044708606218964 - 0.008222353394787857im -0.0025806404719160222 + 0.0013689784746009062im; -0.008029580823668808 + 0.00499832543550193im -0.011738034799603173 + 0.004259484520241709im … -0.007690906814579457 + 0.005671095649362548im 0.0047256559378572975 - 0.005950078492659459im;;; -9.139774643247833e-5 + 0.013400042001149241im -0.0056157487543693 - 0.035473868629812895im … -0.054281827293656715 - 0.05472959591567667im -0.06510924269539477 + 0.00849319903745651im; -0.014324852041470616 - 0.14364411284236928im -0.10161297150952861 - 0.0738033458794177im … 0.008738107552412194 - 0.004393100908182533im 0.03777356172775819 - 0.043295371434141486im; … ; -0.05314298476657904 - 0.03110727128472164im -0.08865327112161556 + 0.02029921829509234im … -0.0036155008153571228 + 0.011480550667076378im -0.0016920621635929944 - 0.019152746563185993im; -0.07760374755745393 + 0.02680367087425479im -0.038521829212508456 + 0.07261093002078722im … -0.0027598613483072916 - 0.050960056341562664im -0.07997128940282627 - 0.06341511374012036im;;; -0.014836312669572298 - 0.12297051984525079im -0.1403711000157868 - 0.08856126742975108im … -0.023452579404903685 + 0.006150559537507092im 0.013130004619482515 - 0.015367710543982317im; -0.1644887898461275 - 0.11712073708548887im -0.13746757595517733 + 0.03840981233060843im … 0.04275797746182499 - 0.04261695065252599im -0.01561855809075921 - 0.1528161558063589im; … ; -0.10919815851500206 + 0.02750161623741184im -0.04934009346838598 + 0.09008256222902286im … 0.003768558704206091 - 0.014590801246566594im -0.049646441354183224 - 0.034121353938145596im; -0.0280366808432553 + 0.05994666242398624im 0.01244618820921593 + 0.005536430858929659im … -0.04333258509428503 - 0.03466507800776912im -0.08110122079570542 + 0.014137341932752782im;;; … ;;; 0.008374351641613861 + 0.004985097423258936im 0.024841908976848404 + 0.03579999099345226im … 0.13827577651899292 + 0.04441421017678168im 0.06763056738181315 - 0.024282720126314546im; 0.04551035051298064 + 0.10413445930099502im 0.07800605125764795 + 0.039725158783057976im … -0.05732809949004441 + 0.0071719608263475995im -0.04504951834397703 + 0.10637323277059826im; … ; 0.11922747051979231 + 0.05020237565383995im 0.10693658621962912 - 0.035417055325178796im … 0.0015374718843062796 - 0.001088620526387505im 0.030883314025197485 + 0.06037895293258927im; 0.16744060616970136 - 0.05419881852702749im 0.0518279365928707 - 0.07857396950177664im … 0.07789877045705323 + 0.18110258458764086im 0.20132693982399372 + 0.0919618195854367im;;; 0.06617370454643859 + 0.1442313357997825im 0.14301045418025293 + 0.058191975482527455im … -0.004815105494012584 - 0.009335255031046756im -0.044406582844396976 + 0.10975410370272512im; 0.13140136613578698 + 0.041309974604432094im 0.0587284468307961 - 0.02379870916238038im … -0.08038337154761979 + 0.16828726856479345im 0.08457813043860349 + 0.17763105084591033im; … ; 0.1442019297928838 - 0.051898868246207215im 0.04954884342782243 - 0.08848511488125507im … 0.04435148596535872 + 0.11502685442862381im 0.1388316293937182 + 0.06400687967380252im; 0.03403650748336632 - 0.05167360414112724im 0.015518411640299153 + 0.00034157781336656163im … 0.17976999792077383 + 0.06862012698418456im 0.115586178015882 - 0.04096006432935607im;;; 0.11909587172301946 + 0.0410366861086136im 0.07265977287278563 - 0.03675249005969899im … -0.034165239370792036 + 0.08160804949058564im 0.06679747774431181 + 0.13264689323907866im; -0.01897035404248943 - 0.014898617815044604im -0.01589021796433579 + 0.04186423730837721im … 0.06464143828224501 + 0.11821306805194368im 0.07465507891363662 + 0.001749518208437325im; … ; 0.023102643919243483 - 0.04793352545492843im 0.0015791341862964048 - 0.013666860060534108im … 0.07602041865186747 + 0.020879238197940936im 0.05795118263580012 - 0.019784220571642853im; 0.019184635434564636 + 0.05386557007023975im 0.07249857194215878 + 0.027789184636890917im … 0.03617780165581058 - 0.028012779780713336im -0.005568867914379133 + 0.012124536045650568im],)]), 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, 7.165529378296473, 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 + 1.0213144005610526e-18im 0.0 - 0.03679672923035902im; 0.10714287388793554 + 0.0im 0.16145393303017874 + 0.0im … -0.054392079538503724 - 0.0im 0.018130693179501244 + 0.0im; … ; 0.07579045242767471 + 0.0im 0.08711041809792075 + 0.0im … -0.0 + 0.06906475263474503im 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), [-12.247569668699787 -11.100308396737555 … -8.289845772407995 -11.100308396737615; -11.100308396737553 -9.130057825943455 … -9.130057795892162 -11.100308356754578; … ; -8.289845772407995 -9.130057795892162 … -4.149589921636905 -6.287956198193854; -11.100308396737613 -11.100308356754578 … -6.2879561981938545 -9.111848223573578;;; -11.100308396737557 -9.130057825943453 … -9.130057795892164 -11.10030835675458; -9.130057825943455 -6.903159481976938 … -9.130057827293136 -10.053883826548267; … ; -9.130057795892162 -9.130057827293136 … -5.2943536692085775 -7.5473992065168956; -11.100308356754576 -10.053883826548267 … -7.547399206516896 -10.053883826548372;;; -8.289845772408293 -6.307621931511362 … -8.289845781007248 -9.111848193522247; -6.307621931511364 -4.5166556658097985 … -7.547399237606728 -7.547399206517128; … ; -8.289845781007246 -7.547399237606727 … -5.768969083575679 -7.547399237606799; -9.111848193522247 -7.547399206517128 … -7.5473992376067995 -9.111848224923484;;; … ;;; -5.30103171824402 -6.307621955783571 … -2.549703573269716 -3.8495821793815224; -6.307621955783571 -6.9031594952037665 … -3.3290606985399807 -4.878419358624751; … ; -2.5497035732697158 -3.3290606985399815 … -1.2567984708974698 -1.8141947460351884; -3.849582179381523 -4.878419358624753 … -1.8141947460351884 -2.7147673353162176;;; -8.289845772407997 -9.130057795892162 … -4.149589921636907 -6.287956198193853; -9.130057795892164 -9.130057827293134 … -5.294353669208577 -7.547399206516895; … ; -4.149589921636907 -5.2943536692085775 … -1.9094492399092444 -2.8946123678456845; -6.287956198193854 -7.547399206516895 … -2.894612367845684 -4.485542759365641;;; -11.100308396737615 -11.10030835675458 … -6.2879561981938545 -9.111848223573578; -11.100308356754576 -10.053883826548267 … -7.547399206516897 -10.053883826548372; … ; -6.287956198193853 -7.547399206516897 … -2.8946123678456845 -4.48554275936564; -9.111848223573578 -10.053883826548372 … -4.485542759365641 -6.871104500130072])], 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), [-12.247569668699787 -11.100308396737555 … -8.289845772407995 -11.100308396737615; -11.100308396737553 -9.130057825943455 … -9.130057795892162 -11.100308356754578; … ; -8.289845772407995 -9.130057795892162 … -4.149589921636905 -6.287956198193854; -11.100308396737613 -11.100308356754578 … -6.2879561981938545 -9.111848223573578;;; -11.100308396737557 -9.130057825943453 … -9.130057795892164 -11.10030835675458; -9.130057825943455 -6.903159481976938 … -9.130057827293136 -10.053883826548267; … ; -9.130057795892162 -9.130057827293136 … -5.2943536692085775 -7.5473992065168956; -11.100308356754576 -10.053883826548267 … -7.547399206516896 -10.053883826548372;;; -8.289845772408293 -6.307621931511362 … -8.289845781007248 -9.111848193522247; -6.307621931511364 -4.5166556658097985 … -7.547399237606728 -7.547399206517128; … ; -8.289845781007246 -7.547399237606727 … -5.768969083575679 -7.547399237606799; -9.111848193522247 -7.547399206517128 … -7.5473992376067995 -9.111848224923484;;; … ;;; -5.30103171824402 -6.307621955783571 … -2.549703573269716 -3.8495821793815224; -6.307621955783571 -6.9031594952037665 … -3.3290606985399807 -4.878419358624751; … ; -2.5497035732697158 -3.3290606985399815 … -1.2567984708974698 -1.8141947460351884; -3.849582179381523 -4.878419358624753 … -1.8141947460351884 -2.7147673353162176;;; -8.289845772407997 -9.130057795892162 … -4.149589921636907 -6.287956198193853; -9.130057795892164 -9.130057827293134 … -5.294353669208577 -7.547399206516895; … ; -4.149589921636907 -5.2943536692085775 … -1.9094492399092444 -2.8946123678456845; -6.287956198193854 -7.547399206516895 … -2.894612367845684 -4.485542759365641;;; -11.100308396737615 -11.10030835675458 … -6.2879561981938545 -9.111848223573578; -11.100308356754576 -10.053883826548267 … -7.547399206516897 -10.053883826548372; … ; -6.287956198193853 -7.547399206516897 … -2.8946123678456845 -4.48554275936564; -9.111848223573578 -10.053883826548372 … -4.485542759365641 -6.871104500130072]), 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 0.018130693179501244 + 0.0im; … ; 0.07579045242767471 + 0.0im 0.08711041809792075 + 0.0im … -0.0 + 0.06906475263474503im 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 = [-0.008094194612718998 + 0.003611463601662479im -0.006615968945047317 + 0.020394186335226876im … 0.03182102868513555 + 0.008397827417943125im 0.011974153750871463 - 0.027616007153768687im; -0.001532075823984644 + 0.009960423600344317im 0.032112736097950914 + 0.005769739482323974im … 0.033192814079434044 - 0.017759346310288544im -0.012682103394393015 - 0.008863285804189928im; … ; -0.004901320849150263 + 0.00542774428909369im -0.0004940323812476235 - 0.004216527726140671im … -0.011044708606218964 - 0.008222353394787857im -0.0025806404719160222 + 0.0013689784746009062im; -0.008029580823668808 + 0.00499832543550193im -0.011738034799603173 + 0.004259484520241709im … -0.007690906814579457 + 0.005671095649362548im 0.0047256559378572975 - 0.005950078492659459im;;; -9.139774643247833e-5 + 0.013400042001149241im -0.0056157487543693 - 0.035473868629812895im … -0.054281827293656715 - 0.05472959591567667im -0.06510924269539477 + 0.00849319903745651im; -0.014324852041470616 - 0.14364411284236928im -0.10161297150952861 - 0.0738033458794177im … 0.008738107552412194 - 0.004393100908182533im 0.03777356172775819 - 0.043295371434141486im; … ; -0.05314298476657904 - 0.03110727128472164im -0.08865327112161556 + 0.02029921829509234im … -0.0036155008153571228 + 0.011480550667076378im -0.0016920621635929944 - 0.019152746563185993im; -0.07760374755745393 + 0.02680367087425479im -0.038521829212508456 + 0.07261093002078722im … -0.0027598613483072916 - 0.050960056341562664im -0.07997128940282627 - 0.06341511374012036im;;; 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… ; 0.11922747051979231 + 0.05020237565383995im 0.10693658621962912 - 0.035417055325178796im … 0.0015374718843062796 - 0.001088620526387505im 0.030883314025197485 + 0.06037895293258927im; 0.16744060616970136 - 0.05419881852702749im 0.0518279365928707 - 0.07857396950177664im … 0.07789877045705323 + 0.18110258458764086im 0.20132693982399372 + 0.0919618195854367im;;; 0.06617370454643859 + 0.1442313357997825im 0.14301045418025293 + 0.058191975482527455im … -0.004815105494012584 - 0.009335255031046756im -0.044406582844396976 + 0.10975410370272512im; 0.13140136613578698 + 0.041309974604432094im 0.0587284468307961 - 0.02379870916238038im … -0.08038337154761979 + 0.16828726856479345im 0.08457813043860349 + 0.17763105084591033im; … ; 0.1442019297928838 - 0.051898868246207215im 0.04954884342782243 - 0.08848511488125507im … 0.04435148596535872 + 0.11502685442862381im 0.1388316293937182 + 0.06400687967380252im; 0.03403650748336632 - 0.05167360414112724im 0.015518411640299153 + 0.00034157781336656163im … 0.17976999792077383 + 0.06862012698418456im 0.115586178015882 - 0.04096006432935607im;;; 0.11909587172301946 + 0.0410366861086136im 0.07265977287278563 - 0.03675249005969899im … -0.034165239370792036 + 0.08160804949058564im 0.06679747774431181 + 0.13264689323907866im; -0.01897035404248943 - 0.014898617815044604im -0.01589021796433579 + 0.04186423730837721im … 0.06464143828224501 + 0.11821306805194368im 0.07465507891363662 + 0.001749518208437325im; … ; 0.023102643919243483 - 0.04793352545492843im 0.0015791341862964048 - 0.013666860060534108im … 0.07602041865186747 + 0.020879238197940936im 0.05795118263580012 - 0.019784220571642853im; 0.019184635434564636 + 0.05386557007023975im 0.07249857194215878 + 0.027789184636890917im … 0.03617780165581058 - 0.028012779780713336im -0.005568867914379133 + 0.012124536045650568im],)])]), basis = PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), energies = Energies(total = -7.9105943964885075), converged = true, ρ = [7.589784536078864e-5 0.001126271272941499 … 0.006697037550472786 0.0011262712729415176; 0.001126271272941489 0.005274334457722664 … 0.005274334457722692 0.001126271272941499; … ; 0.006697037550472775 0.005274334457722702 … 0.023244754191275658 0.012258986825628784; 0.001126271272941499 0.0011262712729414922 … 0.012258986825628778 0.0037700086301972907;;; 0.0011262712729414972 0.005274334457722688 … 0.005274334457722714 0.0011262712729415108; 0.005274334457722673 0.014620065305312313 … 0.005274334457722686 0.002588080875086246; … ; 0.0052743344577227 0.0052743344577226995 … 0.018107686646565136 0.008922003045183563; 0.0011262712729414922 0.0025880808750862417 … 0.008922003045183556 0.0025880808750862513;;; 0.006697037550472747 0.0164121091021826 … 0.006697037550472782 0.003770008630197283; 0.01641210910218259 0.031277839316771396 … 0.008922003045183521 0.008922003045183516; … ; 0.006697037550472773 0.008922003045183534 … 0.01647675635993514 0.008922003045183563; 0.003770008630197266 0.008922003045183511 … 0.008922003045183554 0.003770008630197287;;; … ;;; 0.019853839853902724 0.016412109102182614 … 0.03715667363572312 0.02719080068687855; 0.0164121091021826 0.014620065305312327 … 0.03230127212675927 0.022322100932211094; … ; 0.037156673635723114 0.032301272126759276 … 0.046296980701040574 0.04263658273122616; 0.027190800686878534 0.022322100932211087 … 0.04263658273122615 0.03477222914201578;;; 0.006697037550472757 0.005274334457722687 … 0.023244754191275644 0.012258986825628761; 0.005274334457722671 0.005274334457722667 … 0.018107686646565094 0.00892200304518353; … ; 0.023244754191275637 0.018107686646565105 … 0.04037111033527387 0.031491603811320545; 0.012258986825628745 0.008922003045183521 … 0.03149160381132054 0.020047163432932242;;; 0.0011262712729415009 0.0011262712729415082 … 0.012258986825628778 0.0037700086301972976; 0.001126271272941493 0.0025880808750862244 … 0.008922003045183535 0.00258808087508625; … ; 0.012258986825628761 0.008922003045183546 … 0.03149160381132055 0.020047163432932256; 0.003770008630197279 0.0025880808750862443 … 0.02004716343293225 0.00895260349710968;;;;], eigenvalues = [[-0.1783683565457035, 0.2624919449823095, 0.2624919449823099, 0.26249194498231015, 0.3546921481629408, 0.35469214816294115, 0.3546921481744554], [-0.1275503761861208, 0.06475320594028146, 0.22545166516595816, 0.2254516651659589, 0.32197764960541164, 0.38922276908034603, 0.3892227690803465], [-0.10818729217207244, 0.07755003472560228, 0.1727832801078147, 0.17278328010781496, 0.2843518536178608, 0.3305476484318035, 0.52672324263317], [-0.0577732537523382, 0.01272478219762739, 0.09766073749723786, 0.18417825332252138, 0.31522841795774864, 0.47203122046739504, 0.49791351774401926]], 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 = 0.2734218993000855, n_iter = 9, ψ = Matrix{ComplexF64}[[0.9365906521824007 + 0.156529989033109im 1.202624372364689e-12 + 2.434223583174077e-12im … -2.489268002710957e-13 + 7.798002632472443e-13im -3.065772503034487e-8 + 2.1113577603594596e-7im; 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