Achieving DFT convergence
Some systems are tricky to converge. Here are some collected tips and tricks you can try and which may help. Take these as a source of inspiration for what you can try. Your mileage may vary.
Even if modelling an insulator, add a temperature to your
Model. Values up to1e-2atomic units may be sometimes needed. Note, that this can change the physics of your system, so if in doubt perform a second SCF with a lower temperature afterwards, starting from the final density of the first.Increase the history size of the Anderson acceleration by passing a custom
solvertoself_consistent_field, e.g.solver = scf_anderson_solver(; m=15)(::DFTK.var"#anderson#779"{DFTK.var"#anderson#778#780"{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_ρdiffparameter of theAdaptiveDiagtolalgorithm. For example:diagtolalg = AdaptiveDiagtol(; ratio_ρdiff=0.05)AdaptiveDiagtol(0.05, nothing, 0.005, 0.03)Increase the number of bands, which are fully converged in each SCF step by tweaking the
AdaptiveBandsalgorithm. For example:nbandsalg = AdaptiveBands(model; temperature_factor_converge=1.1)AdaptiveBands(4, 7, 1.0e-6, 0.01)Try the adaptive damping algorithm by using
DFTK.scf_potential_mixing_adaptiveinstead ofself_consistent_field:DFTK.scf_potential_mixing_adaptive(basis; tol=1e-10)(ham = Hamiltonian(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), HamiltonianBlock[DFTK.DftHamiltonianBlock(PlaneWaveBasis(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), [-12.247569668721518 -11.100308396743626 … -8.289845772413681 -11.100308396743689; -11.100308396743626 -9.130057825949237 … -9.130057795897946 -11.10030835676065; … ; -8.289845772413681 -9.130057795897946 … -4.149589921643736 -6.287956198200067; -11.100308396743685 -11.100308356760651 … -6.287956198200068 -9.111848223578592;;; -11.100308396743628 -9.130057825949235 … -9.130057795897947 -11.100308356760653; -9.130057825949239 -6.903159481983454 … -9.13005782729892 -10.05388382655353; … ; -9.130057795897946 -9.13005782729892 … -5.294353669215141 -7.547399206522763; -11.10030835676065 -10.05388382655353 … -7.547399206522764 -10.053883826553635;;; -8.28984577241398 -6.30762193151789 … -8.289845781012934 -9.111848193527262; -6.307621931517891 -4.516655665816806 … -7.547399237612595 -7.547399206522996; … ; -8.289845781012932 -7.547399237612594 … -5.768969083582121 -7.547399237612666; -9.11184819352726 -7.547399206522995 … -7.547399237612667 -9.111848224928499;;; … ;;; -5.301031718250664 -6.307621955790097 … -2.5497035732763838 -3.849582179388363; -6.307621955790098 -6.903159495210282 … -3.3290606985468227 -4.878419358631469; … ; -2.549703573276383 -3.329060698546823 … -1.2567984709027624 -1.814194746041339; -3.849582179388362 -4.87841935863147 … -1.8141947460413386 -2.7147673353229536;;; -8.289845772413683 -9.130057795897946 … -4.149589921643737 -6.2879561982000665; -9.130057795897947 -9.130057827298916 … -5.29435366921514 -7.547399206522762; … ; -4.149589921643737 -5.294353669215141 … -1.9094492399155332 -2.8946123678525257; -6.287956198200067 -7.547399206522763 … -2.8946123678525257 -4.485542759372431;;; -11.100308396743687 -11.100308356760651 … -6.287956198200068 -9.11184822357859; -11.10030835676065 -10.05388382655353 … -7.547399206522765 -10.053883826553635; … ; -6.2879561982000665 -7.547399206522765 … -2.8946123678525257 -4.485542759372432; -9.111848223578592 -10.053883826553635 … -4.485542759372433 -6.871104500135945])], 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), [-12.247569668721518 -11.100308396743626 … -8.289845772413681 -11.100308396743689; -11.100308396743626 -9.130057825949237 … -9.130057795897946 -11.10030835676065; … ; -8.289845772413681 -9.130057795897946 … -4.149589921643736 -6.287956198200067; -11.100308396743685 -11.100308356760651 … -6.287956198200068 -9.111848223578592;;; -11.100308396743628 -9.130057825949235 … -9.130057795897947 -11.100308356760653; -9.130057825949239 -6.903159481983454 … -9.13005782729892 -10.05388382655353; … ; -9.130057795897946 -9.13005782729892 … -5.294353669215141 -7.547399206522763; -11.10030835676065 -10.05388382655353 … -7.547399206522764 -10.053883826553635;;; -8.28984577241398 -6.30762193151789 … -8.289845781012934 -9.111848193527262; -6.307621931517891 -4.516655665816806 … -7.547399237612595 -7.547399206522996; … ; -8.289845781012932 -7.547399237612594 … -5.768969083582121 -7.547399237612666; -9.11184819352726 -7.547399206522995 … -7.547399237612667 -9.111848224928499;;; … ;;; -5.301031718250664 -6.307621955790097 … -2.5497035732763838 -3.849582179388363; -6.307621955790098 -6.903159495210282 … -3.3290606985468227 -4.878419358631469; … ; -2.549703573276383 -3.329060698546823 … -1.2567984709027624 -1.814194746041339; -3.849582179388362 -4.87841935863147 … -1.8141947460413386 -2.7147673353229536;;; -8.289845772413683 -9.130057795897946 … -4.149589921643737 -6.2879561982000665; -9.130057795897947 -9.130057827298916 … -5.29435366921514 -7.547399206522762; … ; -4.149589921643737 -5.294353669215141 … -1.9094492399155332 -2.8946123678525257; -6.287956198200067 -7.547399206522763 … -2.8946123678525257 -4.485542759372431;;; -11.100308396743687 -11.100308356760651 … -6.287956198200068 -9.11184822357859; -11.10030835676065 -10.05388382655353 … -7.547399206522765 -10.053883826553635; … ; -6.2879561982000665 -7.547399206522765 … -2.8946123678525257 -4.485542759372432; -9.111848223578592 -10.053883826553635 … -4.485542759372433 -6.871104500135945]), 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 = [0.010421334737612538 + 0.05220939019874496im 0.0749843247358428 + 0.047225789213093075im … 0.1098248300245879 + 0.022843501795455533im 0.04035692679640114 + 0.012130012109166855im; 0.0493365192277571 + 0.044361728416621386im 0.10176442773553389 - 0.0174175361574408im … 0.052693387513195626 - 0.03587840692475914im 0.01925854775345518 - 0.0003852073941358284im; … ; -0.022329491391080925 + 0.0031133362285707643im -0.02937938083205555 + 0.04483293541475552im … 0.015443556289786307 + 0.0240877219197183im 0.004535638846396375 + 0.021216417205346443im; -0.014058072232023808 + 0.035701284159947416im 0.011757063685080449 + 0.061086863602004354im … 0.044988652060819416 + 0.07770431970737132im 0.0363742711123601 + 0.04512562633046592im;;; 0.04427287078617735 + 0.029113427222221207im 0.009661364975570567 - 0.09111663300589556im … -0.019525454976346043 - 0.0890574642016067im -0.1123761902498728 + 0.06642967907192618im; 0.057108145505503125 + 0.029436595069815864im -0.03676968135598347 - 0.04336629318340177im … -0.07724787282914272 + 0.013431405446418885im 0.001098496615009846 + 0.12204177299384861im; … ; -0.034694008782938296 + 0.01676447967471116im 0.05211785696135207 + 0.032484784926914395im … 0.028520776479953443 - 0.00144538940922221im -0.012022717954277068 - 0.048758483869526914im; 0.013951152268887566 + 0.035589576870013365im 0.08541536876477242 - 0.07804026235971051im … 0.06592864492455286 - 0.027227950256478547im -0.048697287846445725 - 0.028189336119708155im;;; -0.005678565272521141 - 0.09065828373529838im -0.10429150689324587 - 0.02102340917766442im … -0.07806526792901679 + 0.004994907595682244im 0.014432562505127262 + 0.06437011667628115im; -0.11232479334168721 - 0.05955527570497274im -0.021741477885127942 + 0.06852844292440628im … 0.016586160329970775 + 0.05307238960441932im 0.05737008976575446 - 0.011528112754313386im; … ; 0.031683985089662726 + 0.006483196128578103im 0.05647208629476465 - 0.0747923796275417im … 0.014314088179391983 - 0.06805983549577777im -0.04458500579958189 - 0.03666067161469329im; 0.0659175455724228 - 0.0772558038840914im -0.046231363313487824 - 0.13647807283928282im … -0.039470484955024546 - 0.08107904030429294im -0.0319926660155132 + 0.01368766317254902im;;; … ;;; -0.0005181557507842119 + 0.0724373030034767im 0.05251391497750271 + 0.056614794833150926im … 0.10960620840820803 + 0.06632813238423205im 0.057489588500582514 - 0.002863486826042337im; 0.048479284930519104 + 0.07450844526382536im 0.0543288404228812 - 0.004856478547877836im … 0.07373769620167314 - 0.033899316446338944im -0.017597250921065313 + 0.01532128551260694im; … ; 0.035904591093507514 + 0.062117426752916795im 0.008301777311158108 + 0.037274665529346024im … 0.02852530714710327 + 0.062478910051240635im 0.033244021599397884 + 0.11973563951836974im; 0.007257660476134797 + 0.04271045011986281im 0.009431688528635615 + 0.059451839462927286im … 0.038083047424802424 + 0.07799098433281645im 0.07177251799727592 + 0.0677973105591447im;;; 0.07898238381824108 + 0.0640395011108787im 0.04526299484453908 + 0.0024315772993449315im … 0.16895932499444655 - 0.003968091677022222im 0.04404004624181368 + 0.03435732499442703im; 0.08826550342067216 - 0.012260476402678393im -0.02032679157297587 - 0.0029572169163836343im … 0.034460300987605746 - 0.032746559761617416im 0.04854336698810015 + 0.055474850399163764im; … ; 0.000407016999781136 + 0.07909398438232053im 0.015413122180253438 + 0.058386394643675926im … 0.03691062350962126 + 0.13652455093398552im 0.05649253325202471 + 0.11347187455561063im; 0.01437851469710582 + 0.11351814772494026im 0.04764202103774149 + 0.05942760871492291im … 0.14527421994284612 + 0.12510914803385256im 0.06933916483601363 + 0.06651884711262691im;;; 0.057446942743137774 + 0.01387950592411669im -0.03183613281498123 + 0.06641428749780734im … 0.1099489276075946 - 0.008479664980298722im 0.06577980298047556 + 0.017751447551184872im; 0.009533486035342615 - 0.01706320784043769im 0.0363492428103172 + 0.0926794788980631im … 0.060854813608998165 + 0.00411608564199025im 0.11090390361387306 + 0.014545767842075973im; … ; -0.007019810457177341 + 0.07962584502141269im 0.000387827037126396 + 0.038449984987995595im … 0.10117323555542981 + 0.10329227225533413im 0.03166358918348327 + 0.05910905048357043im; 0.03148036761638374 + 0.06150456673104586im 0.0021947062602758055 + 0.040213752674314776im … 0.14812724131158 + 0.039941262646907186im 0.03761836050942413 + 0.0678227711828512im],)]), 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), [-12.247569668721518 -11.100308396743626 … -8.289845772413681 -11.100308396743689; -11.100308396743626 -9.130057825949237 … -9.130057795897946 -11.10030835676065; … ; -8.289845772413681 -9.130057795897946 … -4.149589921643736 -6.287956198200067; -11.100308396743685 -11.100308356760651 … -6.287956198200068 -9.111848223578592;;; -11.100308396743628 -9.130057825949235 … -9.130057795897947 -11.100308356760653; -9.130057825949239 -6.903159481983454 … -9.13005782729892 -10.05388382655353; … ; -9.130057795897946 -9.13005782729892 … -5.294353669215141 -7.547399206522763; -11.10030835676065 -10.05388382655353 … -7.547399206522764 -10.053883826553635;;; -8.28984577241398 -6.30762193151789 … -8.289845781012934 -9.111848193527262; -6.307621931517891 -4.516655665816806 … -7.547399237612595 -7.547399206522996; … ; -8.289845781012932 -7.547399237612594 … -5.768969083582121 -7.547399237612666; -9.11184819352726 -7.547399206522995 … -7.547399237612667 -9.111848224928499;;; … ;;; -5.301031718250664 -6.307621955790097 … -2.5497035732763838 -3.849582179388363; -6.307621955790098 -6.903159495210282 … -3.3290606985468227 -4.878419358631469; … ; -2.549703573276383 -3.329060698546823 … -1.2567984709027624 -1.814194746041339; -3.849582179388362 -4.87841935863147 … -1.8141947460413386 -2.7147673353229536;;; -8.289845772413683 -9.130057795897946 … -4.149589921643737 -6.2879561982000665; -9.130057795897947 -9.130057827298916 … -5.29435366921514 -7.547399206522762; … ; -4.149589921643737 -5.294353669215141 … -1.9094492399155332 -2.8946123678525257; -6.287956198200067 -7.547399206522763 … -2.8946123678525257 -4.485542759372431;;; -11.100308396743687 -11.100308356760651 … -6.287956198200068 -9.11184822357859; -11.10030835676065 -10.05388382655353 … -7.547399206522765 -10.053883826553635; … ; -6.2879561982000665 -7.547399206522765 … -2.8946123678525257 -4.485542759372432; -9.111848223578592 -10.053883826553635 … -4.485542759372433 -6.871104500135945])], 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), [-12.247569668721518 -11.100308396743626 … -8.289845772413681 -11.100308396743689; -11.100308396743626 -9.130057825949237 … -9.130057795897946 -11.10030835676065; … ; -8.289845772413681 -9.130057795897946 … -4.149589921643736 -6.287956198200067; -11.100308396743685 -11.100308356760651 … -6.287956198200068 -9.111848223578592;;; -11.100308396743628 -9.130057825949235 … -9.130057795897947 -11.100308356760653; -9.130057825949239 -6.903159481983454 … -9.13005782729892 -10.05388382655353; … ; -9.130057795897946 -9.13005782729892 … -5.294353669215141 -7.547399206522763; -11.10030835676065 -10.05388382655353 … -7.547399206522764 -10.053883826553635;;; -8.28984577241398 -6.30762193151789 … -8.289845781012934 -9.111848193527262; -6.307621931517891 -4.516655665816806 … -7.547399237612595 -7.547399206522996; … ; -8.289845781012932 -7.547399237612594 … -5.768969083582121 -7.547399237612666; -9.11184819352726 -7.547399206522995 … -7.547399237612667 -9.111848224928499;;; … ;;; -5.301031718250664 -6.307621955790097 … -2.5497035732763838 -3.849582179388363; -6.307621955790098 -6.903159495210282 … -3.3290606985468227 -4.878419358631469; … ; -2.549703573276383 -3.329060698546823 … -1.2567984709027624 -1.814194746041339; -3.849582179388362 -4.87841935863147 … -1.8141947460413386 -2.7147673353229536;;; -8.289845772413683 -9.130057795897946 … -4.149589921643737 -6.2879561982000665; -9.130057795897947 -9.130057827298916 … -5.29435366921514 -7.547399206522762; … ; -4.149589921643737 -5.294353669215141 … -1.9094492399155332 -2.8946123678525257; -6.287956198200067 -7.547399206522763 … -2.8946123678525257 -4.485542759372431;;; -11.100308396743687 -11.100308356760651 … -6.287956198200068 -9.11184822357859; -11.10030835676065 -10.05388382655353 … -7.547399206522765 -10.053883826553635; … ; -6.2879561982000665 -7.547399206522765 … -2.8946123678525257 -4.485542759372432; -9.111848223578592 -10.053883826553635 … -4.485542759372433 -6.871104500135945]), 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 = [0.010421334737612538 + 0.05220939019874496im 0.0749843247358428 + 0.047225789213093075im … 0.1098248300245879 + 0.022843501795455533im 0.04035692679640114 + 0.012130012109166855im; 0.0493365192277571 + 0.044361728416621386im 0.10176442773553389 - 0.0174175361574408im … 0.052693387513195626 - 0.03587840692475914im 0.01925854775345518 - 0.0003852073941358284im; … ; -0.022329491391080925 + 0.0031133362285707643im -0.02937938083205555 + 0.04483293541475552im … 0.015443556289786307 + 0.0240877219197183im 0.004535638846396375 + 0.021216417205346443im; -0.014058072232023808 + 0.035701284159947416im 0.011757063685080449 + 0.061086863602004354im … 0.044988652060819416 + 0.07770431970737132im 0.0363742711123601 + 0.04512562633046592im;;; 0.04427287078617735 + 0.029113427222221207im 0.009661364975570567 - 0.09111663300589556im … -0.019525454976346043 - 0.0890574642016067im -0.1123761902498728 + 0.06642967907192618im; 0.057108145505503125 + 0.029436595069815864im -0.03676968135598347 - 0.04336629318340177im … -0.07724787282914272 + 0.013431405446418885im 0.001098496615009846 + 0.12204177299384861im; … ; -0.034694008782938296 + 0.01676447967471116im 0.05211785696135207 + 0.032484784926914395im … 0.028520776479953443 - 0.00144538940922221im -0.012022717954277068 - 0.048758483869526914im; 0.013951152268887566 + 0.035589576870013365im 0.08541536876477242 - 0.07804026235971051im … 0.06592864492455286 - 0.027227950256478547im -0.048697287846445725 - 0.028189336119708155im;;; -0.005678565272521141 - 0.09065828373529838im -0.10429150689324587 - 0.02102340917766442im … -0.07806526792901679 + 0.004994907595682244im 0.014432562505127262 + 0.06437011667628115im; -0.11232479334168721 - 0.05955527570497274im -0.021741477885127942 + 0.06852844292440628im … 0.016586160329970775 + 0.05307238960441932im 0.05737008976575446 - 0.011528112754313386im; … ; 0.031683985089662726 + 0.006483196128578103im 0.05647208629476465 - 0.0747923796275417im … 0.014314088179391983 - 0.06805983549577777im -0.04458500579958189 - 0.03666067161469329im; 0.0659175455724228 - 0.0772558038840914im -0.046231363313487824 - 0.13647807283928282im … -0.039470484955024546 - 0.08107904030429294im -0.0319926660155132 + 0.01368766317254902im;;; … ;;; -0.0005181557507842119 + 0.0724373030034767im 0.05251391497750271 + 0.056614794833150926im … 0.10960620840820803 + 0.06632813238423205im 0.057489588500582514 - 0.002863486826042337im; 0.048479284930519104 + 0.07450844526382536im 0.0543288404228812 - 0.004856478547877836im … 0.07373769620167314 - 0.033899316446338944im -0.017597250921065313 + 0.01532128551260694im; … ; 0.035904591093507514 + 0.062117426752916795im 0.008301777311158108 + 0.037274665529346024im … 0.02852530714710327 + 0.062478910051240635im 0.033244021599397884 + 0.11973563951836974im; 0.007257660476134797 + 0.04271045011986281im 0.009431688528635615 + 0.059451839462927286im … 0.038083047424802424 + 0.07799098433281645im 0.07177251799727592 + 0.0677973105591447im;;; 0.07898238381824108 + 0.0640395011108787im 0.04526299484453908 + 0.0024315772993449315im … 0.16895932499444655 - 0.003968091677022222im 0.04404004624181368 + 0.03435732499442703im; 0.08826550342067216 - 0.012260476402678393im -0.02032679157297587 - 0.0029572169163836343im … 0.034460300987605746 - 0.032746559761617416im 0.04854336698810015 + 0.055474850399163764im; … ; 0.000407016999781136 + 0.07909398438232053im 0.015413122180253438 + 0.058386394643675926im … 0.03691062350962126 + 0.13652455093398552im 0.05649253325202471 + 0.11347187455561063im; 0.01437851469710582 + 0.11351814772494026im 0.04764202103774149 + 0.05942760871492291im … 0.14527421994284612 + 0.12510914803385256im 0.06933916483601363 + 0.06651884711262691im;;; 0.057446942743137774 + 0.01387950592411669im -0.03183613281498123 + 0.06641428749780734im … 0.1099489276075946 - 0.008479664980298722im 0.06577980298047556 + 0.017751447551184872im; 0.009533486035342615 - 0.01706320784043769im 0.0363492428103172 + 0.0926794788980631im … 0.060854813608998165 + 0.00411608564199025im 0.11090390361387306 + 0.014545767842075973im; … ; -0.007019810457177341 + 0.07962584502141269im 0.000387827037126396 + 0.038449984987995595im … 0.10117323555542981 + 0.10329227225533413im 0.03166358918348327 + 0.05910905048357043im; 0.03148036761638374 + 0.06150456673104586im 0.0021947062602758055 + 0.040213752674314776im … 0.14812724131158 + 0.039941262646907186im 0.03761836050942413 + 0.0678227711828512im],)]), 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), [-12.247569668721518 -11.100308396743626 … -8.289845772413681 -11.100308396743689; -11.100308396743626 -9.130057825949237 … -9.130057795897946 -11.10030835676065; … ; -8.289845772413681 -9.130057795897946 … -4.149589921643736 -6.287956198200067; -11.100308396743685 -11.100308356760651 … -6.287956198200068 -9.111848223578592;;; -11.100308396743628 -9.130057825949235 … -9.130057795897947 -11.100308356760653; -9.130057825949239 -6.903159481983454 … -9.13005782729892 -10.05388382655353; … ; -9.130057795897946 -9.13005782729892 … -5.294353669215141 -7.547399206522763; -11.10030835676065 -10.05388382655353 … -7.547399206522764 -10.053883826553635;;; -8.28984577241398 -6.30762193151789 … -8.289845781012934 -9.111848193527262; -6.307621931517891 -4.516655665816806 … -7.547399237612595 -7.547399206522996; … ; -8.289845781012932 -7.547399237612594 … -5.768969083582121 -7.547399237612666; -9.11184819352726 -7.547399206522995 … -7.547399237612667 -9.111848224928499;;; … ;;; -5.301031718250664 -6.307621955790097 … -2.5497035732763838 -3.849582179388363; -6.307621955790098 -6.903159495210282 … -3.3290606985468227 -4.878419358631469; … ; -2.549703573276383 -3.329060698546823 … -1.2567984709027624 -1.814194746041339; -3.849582179388362 -4.87841935863147 … -1.8141947460413386 -2.7147673353229536;;; -8.289845772413683 -9.130057795897946 … -4.149589921643737 -6.2879561982000665; -9.130057795897947 -9.130057827298916 … -5.29435366921514 -7.547399206522762; … ; -4.149589921643737 -5.294353669215141 … -1.9094492399155332 -2.8946123678525257; -6.287956198200067 -7.547399206522763 … -2.8946123678525257 -4.485542759372431;;; -11.100308396743687 -11.100308356760651 … -6.287956198200068 -9.11184822357859; -11.10030835676065 -10.05388382655353 … -7.547399206522765 -10.053883826553635; … ; -6.2879561982000665 -7.547399206522765 … -2.8946123678525257 -4.485542759372432; -9.111848223578592 -10.053883826553635 … -4.485542759372433 -6.871104500135945])], 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), [-12.247569668721518 -11.100308396743626 … -8.289845772413681 -11.100308396743689; -11.100308396743626 -9.130057825949237 … -9.130057795897946 -11.10030835676065; … ; -8.289845772413681 -9.130057795897946 … -4.149589921643736 -6.287956198200067; -11.100308396743685 -11.100308356760651 … -6.287956198200068 -9.111848223578592;;; -11.100308396743628 -9.130057825949235 … -9.130057795897947 -11.100308356760653; -9.130057825949239 -6.903159481983454 … -9.13005782729892 -10.05388382655353; … ; -9.130057795897946 -9.13005782729892 … -5.294353669215141 -7.547399206522763; -11.10030835676065 -10.05388382655353 … -7.547399206522764 -10.053883826553635;;; -8.28984577241398 -6.30762193151789 … -8.289845781012934 -9.111848193527262; -6.307621931517891 -4.516655665816806 … -7.547399237612595 -7.547399206522996; … ; -8.289845781012932 -7.547399237612594 … -5.768969083582121 -7.547399237612666; -9.11184819352726 -7.547399206522995 … -7.547399237612667 -9.111848224928499;;; … ;;; -5.301031718250664 -6.307621955790097 … -2.5497035732763838 -3.849582179388363; -6.307621955790098 -6.903159495210282 … -3.3290606985468227 -4.878419358631469; … ; -2.549703573276383 -3.329060698546823 … -1.2567984709027624 -1.814194746041339; -3.849582179388362 -4.87841935863147 … -1.8141947460413386 -2.7147673353229536;;; -8.289845772413683 -9.130057795897946 … -4.149589921643737 -6.2879561982000665; -9.130057795897947 -9.130057827298916 … -5.29435366921514 -7.547399206522762; … ; -4.149589921643737 -5.294353669215141 … -1.9094492399155332 -2.8946123678525257; -6.287956198200067 -7.547399206522763 … -2.8946123678525257 -4.485542759372431;;; -11.100308396743687 -11.100308356760651 … -6.287956198200068 -9.11184822357859; -11.10030835676065 -10.05388382655353 … -7.547399206522765 -10.053883826553635; … ; -6.2879561982000665 -7.547399206522765 … -2.8946123678525257 -4.485542759372432; -9.111848223578592 -10.053883826553635 … -4.485542759372433 -6.871104500135945]), 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 = [0.010421334737612538 + 0.05220939019874496im 0.0749843247358428 + 0.047225789213093075im … 0.1098248300245879 + 0.022843501795455533im 0.04035692679640114 + 0.012130012109166855im; 0.0493365192277571 + 0.044361728416621386im 0.10176442773553389 - 0.0174175361574408im … 0.052693387513195626 - 0.03587840692475914im 0.01925854775345518 - 0.0003852073941358284im; … ; -0.022329491391080925 + 0.0031133362285707643im -0.02937938083205555 + 0.04483293541475552im … 0.015443556289786307 + 0.0240877219197183im 0.004535638846396375 + 0.021216417205346443im; -0.014058072232023808 + 0.035701284159947416im 0.011757063685080449 + 0.061086863602004354im … 0.044988652060819416 + 0.07770431970737132im 0.0363742711123601 + 0.04512562633046592im;;; 0.04427287078617735 + 0.029113427222221207im 0.009661364975570567 - 0.09111663300589556im … -0.019525454976346043 - 0.0890574642016067im -0.1123761902498728 + 0.06642967907192618im; 0.057108145505503125 + 0.029436595069815864im -0.03676968135598347 - 0.04336629318340177im … -0.07724787282914272 + 0.013431405446418885im 0.001098496615009846 + 0.12204177299384861im; … ; -0.034694008782938296 + 0.01676447967471116im 0.05211785696135207 + 0.032484784926914395im … 0.028520776479953443 - 0.00144538940922221im -0.012022717954277068 - 0.048758483869526914im; 0.013951152268887566 + 0.035589576870013365im 0.08541536876477242 - 0.07804026235971051im … 0.06592864492455286 - 0.027227950256478547im -0.048697287846445725 - 0.028189336119708155im;;; -0.005678565272521141 - 0.09065828373529838im -0.10429150689324587 - 0.02102340917766442im … -0.07806526792901679 + 0.004994907595682244im 0.014432562505127262 + 0.06437011667628115im; -0.11232479334168721 - 0.05955527570497274im -0.021741477885127942 + 0.06852844292440628im … 0.016586160329970775 + 0.05307238960441932im 0.05737008976575446 - 0.011528112754313386im; … ; 0.031683985089662726 + 0.006483196128578103im 0.05647208629476465 - 0.0747923796275417im … 0.014314088179391983 - 0.06805983549577777im -0.04458500579958189 - 0.03666067161469329im; 0.0659175455724228 - 0.0772558038840914im -0.046231363313487824 - 0.13647807283928282im … -0.039470484955024546 - 0.08107904030429294im -0.0319926660155132 + 0.01368766317254902im;;; … ;;; -0.0005181557507842119 + 0.0724373030034767im 0.05251391497750271 + 0.056614794833150926im … 0.10960620840820803 + 0.06632813238423205im 0.057489588500582514 - 0.002863486826042337im; 0.048479284930519104 + 0.07450844526382536im 0.0543288404228812 - 0.004856478547877836im … 0.07373769620167314 - 0.033899316446338944im -0.017597250921065313 + 0.01532128551260694im; … ; 0.035904591093507514 + 0.062117426752916795im 0.008301777311158108 + 0.037274665529346024im … 0.02852530714710327 + 0.062478910051240635im 0.033244021599397884 + 0.11973563951836974im; 0.007257660476134797 + 0.04271045011986281im 0.009431688528635615 + 0.059451839462927286im … 0.038083047424802424 + 0.07799098433281645im 0.07177251799727592 + 0.0677973105591447im;;; 0.07898238381824108 + 0.0640395011108787im 0.04526299484453908 + 0.0024315772993449315im … 0.16895932499444655 - 0.003968091677022222im 0.04404004624181368 + 0.03435732499442703im; 0.08826550342067216 - 0.012260476402678393im -0.02032679157297587 - 0.0029572169163836343im … 0.034460300987605746 - 0.032746559761617416im 0.04854336698810015 + 0.055474850399163764im; … ; 0.000407016999781136 + 0.07909398438232053im 0.015413122180253438 + 0.058386394643675926im … 0.03691062350962126 + 0.13652455093398552im 0.05649253325202471 + 0.11347187455561063im; 0.01437851469710582 + 0.11351814772494026im 0.04764202103774149 + 0.05942760871492291im … 0.14527421994284612 + 0.12510914803385256im 0.06933916483601363 + 0.06651884711262691im;;; 0.057446942743137774 + 0.01387950592411669im -0.03183613281498123 + 0.06641428749780734im … 0.1099489276075946 - 0.008479664980298722im 0.06577980298047556 + 0.017751447551184872im; 0.009533486035342615 - 0.01706320784043769im 0.0363492428103172 + 0.0926794788980631im … 0.060854813608998165 + 0.00411608564199025im 0.11090390361387306 + 0.014545767842075973im; … ; -0.007019810457177341 + 0.07962584502141269im 0.000387827037126396 + 0.038449984987995595im … 0.10117323555542981 + 0.10329227225533413im 0.03166358918348327 + 0.05910905048357043im; 0.03148036761638374 + 0.06150456673104586im 0.0021947062602758055 + 0.040213752674314776im … 0.14812724131158 + 0.039941262646907186im 0.03761836050942413 + 0.0678227711828512im],)]), 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), [-12.247569668721518 -11.100308396743626 … -8.289845772413681 -11.100308396743689; -11.100308396743626 -9.130057825949237 … -9.130057795897946 -11.10030835676065; … ; -8.289845772413681 -9.130057795897946 … -4.149589921643736 -6.287956198200067; -11.100308396743685 -11.100308356760651 … -6.287956198200068 -9.111848223578592;;; -11.100308396743628 -9.130057825949235 … -9.130057795897947 -11.100308356760653; -9.130057825949239 -6.903159481983454 … -9.13005782729892 -10.05388382655353; … ; -9.130057795897946 -9.13005782729892 … -5.294353669215141 -7.547399206522763; -11.10030835676065 -10.05388382655353 … -7.547399206522764 -10.053883826553635;;; -8.28984577241398 -6.30762193151789 … -8.289845781012934 -9.111848193527262; -6.307621931517891 -4.516655665816806 … -7.547399237612595 -7.547399206522996; … ; -8.289845781012932 -7.547399237612594 … -5.768969083582121 -7.547399237612666; -9.11184819352726 -7.547399206522995 … -7.547399237612667 -9.111848224928499;;; … ;;; -5.301031718250664 -6.307621955790097 … -2.5497035732763838 -3.849582179388363; -6.307621955790098 -6.903159495210282 … -3.3290606985468227 -4.878419358631469; … ; -2.549703573276383 -3.329060698546823 … -1.2567984709027624 -1.814194746041339; -3.849582179388362 -4.87841935863147 … -1.8141947460413386 -2.7147673353229536;;; -8.289845772413683 -9.130057795897946 … -4.149589921643737 -6.2879561982000665; -9.130057795897947 -9.130057827298916 … -5.29435366921514 -7.547399206522762; … ; -4.149589921643737 -5.294353669215141 … -1.9094492399155332 -2.8946123678525257; -6.287956198200067 -7.547399206522763 … -2.8946123678525257 -4.485542759372431;;; -11.100308396743687 -11.100308356760651 … -6.287956198200068 -9.11184822357859; -11.10030835676065 -10.05388382655353 … -7.547399206522765 -10.053883826553635; … ; -6.2879561982000665 -7.547399206522765 … -2.8946123678525257 -4.485542759372432; -9.111848223578592 -10.053883826553635 … -4.485542759372433 -6.871104500135945])], 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), [-12.247569668721518 -11.100308396743626 … -8.289845772413681 -11.100308396743689; -11.100308396743626 -9.130057825949237 … -9.130057795897946 -11.10030835676065; … ; -8.289845772413681 -9.130057795897946 … -4.149589921643736 -6.287956198200067; -11.100308396743685 -11.100308356760651 … -6.287956198200068 -9.111848223578592;;; -11.100308396743628 -9.130057825949235 … -9.130057795897947 -11.100308356760653; -9.130057825949239 -6.903159481983454 … -9.13005782729892 -10.05388382655353; … ; -9.130057795897946 -9.13005782729892 … -5.294353669215141 -7.547399206522763; -11.10030835676065 -10.05388382655353 … -7.547399206522764 -10.053883826553635;;; -8.28984577241398 -6.30762193151789 … -8.289845781012934 -9.111848193527262; -6.307621931517891 -4.516655665816806 … -7.547399237612595 -7.547399206522996; … ; -8.289845781012932 -7.547399237612594 … -5.768969083582121 -7.547399237612666; -9.11184819352726 -7.547399206522995 … -7.547399237612667 -9.111848224928499;;; … ;;; -5.301031718250664 -6.307621955790097 … -2.5497035732763838 -3.849582179388363; -6.307621955790098 -6.903159495210282 … -3.3290606985468227 -4.878419358631469; … ; -2.549703573276383 -3.329060698546823 … -1.2567984709027624 -1.814194746041339; -3.849582179388362 -4.87841935863147 … -1.8141947460413386 -2.7147673353229536;;; -8.289845772413683 -9.130057795897946 … -4.149589921643737 -6.2879561982000665; -9.130057795897947 -9.130057827298916 … -5.29435366921514 -7.547399206522762; … ; -4.149589921643737 -5.294353669215141 … -1.9094492399155332 -2.8946123678525257; -6.287956198200067 -7.547399206522763 … -2.8946123678525257 -4.485542759372431;;; -11.100308396743687 -11.100308356760651 … -6.287956198200068 -9.11184822357859; -11.10030835676065 -10.05388382655353 … -7.547399206522765 -10.053883826553635; … ; -6.2879561982000665 -7.547399206522765 … -2.8946123678525257 -4.485542759372432; -9.111848223578592 -10.053883826553635 … -4.485542759372433 -6.871104500135945]), 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 = [0.010421334737612538 + 0.05220939019874496im 0.0749843247358428 + 0.047225789213093075im … 0.1098248300245879 + 0.022843501795455533im 0.04035692679640114 + 0.012130012109166855im; 0.0493365192277571 + 0.044361728416621386im 0.10176442773553389 - 0.0174175361574408im … 0.052693387513195626 - 0.03587840692475914im 0.01925854775345518 - 0.0003852073941358284im; … ; -0.022329491391080925 + 0.0031133362285707643im -0.02937938083205555 + 0.04483293541475552im … 0.015443556289786307 + 0.0240877219197183im 0.004535638846396375 + 0.021216417205346443im; -0.014058072232023808 + 0.035701284159947416im 0.011757063685080449 + 0.061086863602004354im … 0.044988652060819416 + 0.07770431970737132im 0.0363742711123601 + 0.04512562633046592im;;; 0.04427287078617735 + 0.029113427222221207im 0.009661364975570567 - 0.09111663300589556im … -0.019525454976346043 - 0.0890574642016067im -0.1123761902498728 + 0.06642967907192618im; 0.057108145505503125 + 0.029436595069815864im -0.03676968135598347 - 0.04336629318340177im … -0.07724787282914272 + 0.013431405446418885im 0.001098496615009846 + 0.12204177299384861im; … ; -0.034694008782938296 + 0.01676447967471116im 0.05211785696135207 + 0.032484784926914395im … 0.028520776479953443 - 0.00144538940922221im -0.012022717954277068 - 0.048758483869526914im; 0.013951152268887566 + 0.035589576870013365im 0.08541536876477242 - 0.07804026235971051im … 0.06592864492455286 - 0.027227950256478547im -0.048697287846445725 - 0.028189336119708155im;;; -0.005678565272521141 - 0.09065828373529838im -0.10429150689324587 - 0.02102340917766442im … -0.07806526792901679 + 0.004994907595682244im 0.014432562505127262 + 0.06437011667628115im; -0.11232479334168721 - 0.05955527570497274im -0.021741477885127942 + 0.06852844292440628im … 0.016586160329970775 + 0.05307238960441932im 0.05737008976575446 - 0.011528112754313386im; … ; 0.031683985089662726 + 0.006483196128578103im 0.05647208629476465 - 0.0747923796275417im … 0.014314088179391983 - 0.06805983549577777im -0.04458500579958189 - 0.03666067161469329im; 0.0659175455724228 - 0.0772558038840914im -0.046231363313487824 - 0.13647807283928282im … -0.039470484955024546 - 0.08107904030429294im -0.0319926660155132 + 0.01368766317254902im;;; … ;;; -0.0005181557507842119 + 0.0724373030034767im 0.05251391497750271 + 0.056614794833150926im … 0.10960620840820803 + 0.06632813238423205im 0.057489588500582514 - 0.002863486826042337im; 0.048479284930519104 + 0.07450844526382536im 0.0543288404228812 - 0.004856478547877836im … 0.07373769620167314 - 0.033899316446338944im -0.017597250921065313 + 0.01532128551260694im; … ; 0.035904591093507514 + 0.062117426752916795im 0.008301777311158108 + 0.037274665529346024im … 0.02852530714710327 + 0.062478910051240635im 0.033244021599397884 + 0.11973563951836974im; 0.007257660476134797 + 0.04271045011986281im 0.009431688528635615 + 0.059451839462927286im … 0.038083047424802424 + 0.07799098433281645im 0.07177251799727592 + 0.0677973105591447im;;; 0.07898238381824108 + 0.0640395011108787im 0.04526299484453908 + 0.0024315772993449315im … 0.16895932499444655 - 0.003968091677022222im 0.04404004624181368 + 0.03435732499442703im; 0.08826550342067216 - 0.012260476402678393im -0.02032679157297587 - 0.0029572169163836343im … 0.034460300987605746 - 0.032746559761617416im 0.04854336698810015 + 0.055474850399163764im; … ; 0.000407016999781136 + 0.07909398438232053im 0.015413122180253438 + 0.058386394643675926im … 0.03691062350962126 + 0.13652455093398552im 0.05649253325202471 + 0.11347187455561063im; 0.01437851469710582 + 0.11351814772494026im 0.04764202103774149 + 0.05942760871492291im … 0.14527421994284612 + 0.12510914803385256im 0.06933916483601363 + 0.06651884711262691im;;; 0.057446942743137774 + 0.01387950592411669im -0.03183613281498123 + 0.06641428749780734im … 0.1099489276075946 - 0.008479664980298722im 0.06577980298047556 + 0.017751447551184872im; 0.009533486035342615 - 0.01706320784043769im 0.0363492428103172 + 0.0926794788980631im … 0.060854813608998165 + 0.00411608564199025im 0.11090390361387306 + 0.014545767842075973im; … ; -0.007019810457177341 + 0.07962584502141269im 0.000387827037126396 + 0.038449984987995595im … 0.10117323555542981 + 0.10329227225533413im 0.03166358918348327 + 0.05910905048357043im; 0.03148036761638374 + 0.06150456673104586im 0.0021947062602758055 + 0.040213752674314776im … 0.14812724131158 + 0.039941262646907186im 0.03761836050942413 + 0.0678227711828512im],)])]), 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 = [7.589784541413493e-5 0.001126271272852223 … 0.006697037550130943 0.001126271272852245; 0.0011262712728522316 0.005274334457431759 … 0.005274334457431802 0.0011262712728522333; … ; 0.006697037550130927 0.005274334457431791 … 0.023244754190954186 0.012258986825240526; 0.0011262712728522383 0.001126271272852228 … 0.012258986825240532 0.0037700086299281;;; 0.0011262712728522333 0.005274334457431764 … 0.005274334457431807 0.001126271272852245; 0.005274334457431773 0.014620065304812758 … 0.005274334457431797 0.002588080874886337; … ; 0.005274334457431794 0.005274334457431787 … 0.01810768664612932 0.008922003044792971; 0.001126271272852238 0.002588080874886328 … 0.008922003044792976 0.0025880808748863513;;; 0.0066970375501309055 0.016412109101668043 … 0.006697037550130932 0.003770008629928091; 0.016412109101668054 0.03127783931599682 … 0.008922003044792955 0.008922003044792935; … ; 0.006697037550130924 0.008922003044792943 … 0.01647675635946845 0.008922003044792967; 0.0037700086299280824 0.008922003044792928 … 0.008922003044792971 0.003770008629928092;;; … ;;; 0.019853839853410306 0.01641210910166806 … 0.03715667363548576 0.027190800686488655; 0.016412109101668064 0.014620065304812756 … 0.03230127212634245 0.022322100931709377; … ; 0.037156673635485755 0.032301272126342435 … 0.04629698070121588 0.04263658273120191; 0.027190800686488648 0.022322100931709374 … 0.042636582731201925 0.034772229141809406;;; 0.006697037550130916 0.0052743344574317725 … 0.02324475419095417 0.012258986825240513; 0.0052743344574317785 0.00527433445743176 … 0.018107686646129287 0.008922003044792941; … ; 0.023244754190954158 0.018107686646129283 … 0.04037111033532496 0.0314916038111891; 0.012258986825240506 0.008922003044792938 … 0.03149160381118911 0.02004716343263883;;; 0.0011262712728522366 0.0011262712728522266 … 0.012258986825240528 0.003770008629928095; 0.0011262712728522333 0.002588080874886319 … 0.008922003044792955 0.0025880808748863387; … ; 0.012258986825240514 0.008922003044792952 … 0.03149160381118912 0.02004716343263884; 0.0037700086299280885 0.0025880808748863313 … 0.020047163432638848 0.008952603496762176;;;;], eigenvalues = [[-0.17836835653885835, 0.26249194499220235, 0.2624919449922026, 0.2624919449922029, 0.35469214816808015, 0.3546921481680809, 0.3546921481683708], [-0.12755037617866766, 0.06475320594732178, 0.22545166517480886, 0.2254516651748091, 0.3219776496118081, 0.3892227690851672, 0.38922276908516734], [-0.1081872921645546, 0.07755003473505563, 0.17278328011521746, 0.17278328011521796, 0.2843518536200206, 0.33054764843319606, 0.5267232426398014], [-0.057773253743743466, 0.012724782206122755, 0.09766073750157678, 0.18417825333026794, 0.3152284179600873, 0.4720312186141863, 0.4979135177526799]], 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 = 0.2734218993061117, n_iter = 10, ψ = Matrix{ComplexF64}[[0.6909865361737172 - 0.6513380796898952im -2.325214388282239e-13 - 8.032924865949124e-14im … -2.96637829438435e-12 + 7.53306800440808e-12im 3.343927363561233e-8 - 5.06942481928669e-8im; 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