Achieving DFT convergence
Some systems are tricky to converge. Here are some collected tips and tricks you can try and which may help. Take these as a source of inspiration for what you can try. Your mileage may vary.
Even if modelling an insulator, add a temperature to your
Model. Values up to1e-2atomic units may be sometimes needed. Note, that this can change the physics of your system, so if in doubt perform a second SCF with a lower temperature afterwards, starting from the final density of the first.If you are modelling a magnetic systems near a phase transition it can be worth switching to the
LdosXcDiagonalMixingmixing algorithm in yourself_consistent_fieldcall. This is done by passing this mixer via themixingkeyword argument, e.g.mixing = LdosXcDiagonalMixing()LdosXcDiagonalMixing(reltol=1.0e-6)Even if modelling an insulator, add a temperature to your
Model. Values up to1e-2atomic units may be sometimes needed. Note, that this can change the physics of your system, so if in doubt perform a second SCF with a lower temperature afterwards, starting from the final density of the first.Increase the history size of the Anderson acceleration by passing a custom
solvertoself_consistent_field, e.g.solver = scf_anderson_solver(; m=15)ScfAndersonDensitySolver(; m_start=1, m=15, maxcond=1.0e6, errorfactor=100000.0)All keyword arguments are passed through to
DFTK.AndersonAcceleration.Try increasing convergence for for the bands in each SCF step by increasing the
ratio_ρdiffparameter of theAdaptiveDiagtolalgorithm. For example:diagtolalg = AdaptiveDiagtol(; ratio_ρdiff=0.05)AdaptiveDiagtol(0.05, nothing, 0.005, 0.03)Increase the number of bands, which are fully converged in each SCF step by tweaking the
AdaptiveBandsalgorithm. For example:nbandsalg = AdaptiveBands(model; temperature_factor_converge=1.1)AdaptiveBands(4, 7, 1.0e-6, 0.01)Try the adaptive damping algorithm by using
DFTK.scf_potential_mixing_adaptiveinstead ofself_consistent_field:DFTK.scf_potential_mixing_adaptive(basis; tol=1e-10)(ham = Hamiltonian(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), HamiltonianBlock[DFTK.DftHamiltonianBlock{PlaneWaveBasis{Float64, Float64, DFTK.CPU, FFTGrid{Float64, Float64, Array{StaticArraysCore.SVector{3, Int64}, 3}, Array{StaticArraysCore.SVector{3, Float64}, 3}}, Vector{StaticArraysCore.SVector{3, Int64}}}, Kpoint{Float64, Vector{StaticArraysCore.SVector{3, Int64}}, Vector{Int64}}, DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}, Nothing, Vector{@NamedTuple{ψ_reals::Array{ComplexF64, 3}}}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749), DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749), [0.0, 0.5624107360872233, 2.249642944348893, 5.061696624785009, 8.998571777395572, 14.06026840218058, 14.06026840218058, 8.998571777395572, 5.061696624785009, 2.249642944348893 … 0.7498809814496308, 2.062172698986485, 4.499285888697785, 8.061220550583531, 12.747976684643724, 11.060744476382055, 6.748928833046679, 3.561934661885747, 1.499761962899262, 0.5624107360872233]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749), ComplexF64[0.11162114718647566 + 0.0im 0.17292273765511482 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.10094779392345996 + 0.0im 0.1459089442398946 + 0.0im … -0.05030254922547521 - 0.0im 0.0503025492254752 + 0.0im; … ; 0.08537828309138949 + 0.0im 0.1086340264896086 + 0.0im … -0.0 + 0.08075097926136236im 0.0 + 0.0im; 0.10094779392345996 + 0.0im 0.1459089442398946 + 0.0im … 0.05030254922547521 + 0.0im 0.0503025492254752 + 0.0im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749), [-12.24756969788468 -11.100308387033907 … -8.289845769066876 -11.100308387033937; -11.100308387033909 -9.130057818482129 … -9.130057802436303 -11.100308365268912; … ; -8.289845769066876 -9.130057802436301 … -4.149589911945763 -6.287956204739942; -11.100308387033936 -11.10030836526891 … -6.287956204739943 -9.111848216112012;;; -11.100308387033909 -9.130057818482127 … -9.130057802436303 -11.10030836526891; -9.130057818482127 -6.903159504367539 … -9.130057819839267 -10.053883816988028; … ; -9.130057802436303 -9.130057819839262 … -5.294353665850209 -7.547399215037586; -11.10030836526891 -10.053883816988026 … -7.547399215037586 -10.05388381698808;;; -8.28984576906702 -6.307621938057392 … -8.289845773669935 -9.111848200066165; -6.30762193805739 -4.516655658355877 … -7.5473992318922285 -7.547399215037702; … ; -8.289845773669935 -7.547399231892227 … -5.76896909839597 -7.547399231892261; -9.111848200066165 -7.5473992150377 … -7.547399231892262 -9.111848217469262;;; … ;;; -5.301031708536038 -6.307621951399237 … -2.549703579811763 -3.8495821823329934; -6.307621951399237 -6.90315951144739 … -3.3290606941630303 -4.878419351559542; … ; -2.5497035798117627 -3.3290606941630303 … -1.256798467534696 -1.8141947489915682; -3.8495821823329925 -4.878419351559542 … -1.81419474899157 -2.7147673368915055;;; -8.289845769066874 -9.130057802436303 … -4.149589911945763 -6.287956204739942; -9.130057802436301 -9.130057819839266 … -5.294353665850209 -7.547399215037587; … ; -4.149589911945763 -5.294353665850209 … -1.9094492500180706 -2.894612364489521; -6.287956204739942 -7.547399215037587 … -2.894612364489522 -4.485542751912525;;; -11.100308387033937 -11.10030836526891 … -6.287956204739942 -9.111848216112014; -11.10030836526891 -10.053883816988028 … -7.547399215037588 -10.053883816988078; … ; -6.287956204739942 -7.5473992150375855 … -2.8946123644895216 -4.485542751912525; -9.111848216112014 -10.053883816988076 … -4.485542751912525 -6.871104522520765])], 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), [-12.24756969788468 -11.100308387033907 … -8.289845769066876 -11.100308387033937; -11.100308387033909 -9.130057818482129 … -9.130057802436303 -11.100308365268912; … ; -8.289845769066876 -9.130057802436301 … -4.149589911945763 -6.287956204739942; -11.100308387033936 -11.10030836526891 … -6.287956204739943 -9.111848216112012;;; -11.100308387033909 -9.130057818482127 … -9.130057802436303 -11.10030836526891; -9.130057818482127 -6.903159504367539 … -9.130057819839267 -10.053883816988028; … ; -9.130057802436303 -9.130057819839262 … -5.294353665850209 -7.547399215037586; -11.10030836526891 -10.053883816988026 … -7.547399215037586 -10.05388381698808;;; -8.28984576906702 -6.307621938057392 … -8.289845773669935 -9.111848200066165; -6.30762193805739 -4.516655658355877 … -7.5473992318922285 -7.547399215037702; … ; -8.289845773669935 -7.547399231892227 … -5.76896909839597 -7.547399231892261; -9.111848200066165 -7.5473992150377 … -7.547399231892262 -9.111848217469262;;; … ;;; -5.301031708536038 -6.307621951399237 … -2.549703579811763 -3.8495821823329934; -6.307621951399237 -6.90315951144739 … -3.3290606941630303 -4.878419351559542; … ; -2.5497035798117627 -3.3290606941630303 … -1.256798467534696 -1.8141947489915682; -3.8495821823329925 -4.878419351559542 … -1.81419474899157 -2.7147673368915055;;; -8.289845769066874 -9.130057802436303 … -4.149589911945763 -6.287956204739942; -9.130057802436301 -9.130057819839266 … -5.294353665850209 -7.547399215037587; … ; -4.149589911945763 -5.294353665850209 … -1.9094492500180706 -2.894612364489521; -6.287956204739942 -7.547399215037587 … -2.894612364489522 -4.485542751912525;;; -11.100308387033937 -11.10030836526891 … -6.287956204739942 -9.111848216112014; -11.10030836526891 -10.053883816988028 … -7.547399215037588 -10.053883816988078; … ; -6.287956204739942 -7.5473992150375855 … -2.8946123644895216 -4.485542751912525; -9.111848216112014 -10.053883816988076 … -4.485542751912525 -6.871104522520765]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749), ComplexF64[0.11162114718647566 + 0.0im 0.17292273765511482 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.10094779392345996 + 0.0im 0.1459089442398946 + 0.0im … -0.05030254922547521 - 0.0im 0.0503025492254752 + 0.0im; … ; 0.08537828309138949 + 0.0im 0.1086340264896086 + 0.0im … -0.0 + 0.08075097926136236im 0.0 + 0.0im; 0.10094779392345996 + 0.0im 0.1459089442398946 + 0.0im … 0.05030254922547521 + 0.0im 0.0503025492254752 + 0.0im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, @NamedTuple{ψ_reals::Array{ComplexF64, 3}}[(ψ_reals = [0.00047266210922330314 - 0.00017109041368464951im -0.00288349829401734 + 0.006276577393140557im … 0.0008751772312437268 + 0.002251411357681361im 0.0039082135778781505 + 0.0017777998019015157im; -0.00011908943396532587 + 0.00027221086682001393im 0.0012675176880109424 + 0.003541056097253024im … -0.00011358058839417177 - 3.2803502885815974e-5im 0.00205763991527809 - 0.0007187684060758199im; … ; 0.002083844725155861 + 0.005320889535479095im 0.00301788619741574 + 0.0012845847021796108im … 0.0015608691055731473 - 0.000503820137994881im -6.674986618283212e-5 + 0.00019009165100519157im; 0.007550835662591418 + 0.003302014082703354im 0.0011558053820814446 - 0.0005264840095308009im … -0.001872463817383852 + 0.004376837634295329im 0.002725698873500034 + 0.0071229288358504415im;;; -0.038141212890287754 - 0.002954916197724429im -0.07741083307079784 + 0.061681106246984294im … 0.004335270932285227 - 0.02571276196496712im -0.009497252060410827 - 0.012608673358912133im; -0.000889244002104916 + 0.0039207481750680815im -0.008319383892930084 + 0.060841028708168876im … -0.009118438020196327 - 0.009111611632785241im 0.02751262873254825 + 0.00686948437169721im; … ; -0.005268558431749372 + 0.060363762241826185im 0.006928766109538371 + 0.0039539400371452395im … -0.04742021459577918 - 0.008186709349991418im -0.05834755067848092 + 0.04375363027437581im; -0.004421552871034032 - 0.01512295557020987im -0.06128279548615635 - 0.00960141253207442im … -0.008384311494267504 + 0.009654530034456816im 0.00290090864325461 + 0.01438975777900823im;;; -0.03694780455848816 + 0.031341129599940086im -0.01087095933747665 + 0.09059190357842714im … -0.005723496687651279 - 0.003531039483118281im 0.00689603997869336 + 0.004625032660049261im; 0.010438568840990627 - 0.03896306209515862im -0.001553550928553422 - 0.002809670532838717im … -0.0013411622801639857 + 0.0028021175302929946im 0.05052682440032684 - 0.03174134604746333im; … ; -0.003184461404334815 - 0.013949018260913517im -0.075333782391168 - 0.016355394595090555im … -0.06352594815894778 + 0.044234252529461796im -0.006004472694453389 + 0.05117319159123433im; -0.08443280390140537 - 0.01597401443787003im -0.10644319077511255 + 0.07783082268266932im … -0.002419295864036407 + 0.018008096167701097im -0.0070407906943740555 - 0.015630975862319908im;;; … ;;; 0.08248459360255563 + 0.01724822651045027im 0.06356664069146967 - 0.04182263791975068im … 0.0020122997833160183 + 0.008117687448399458im 0.022356732235995318 + 0.028188891660962972im; 0.09249712571110905 - 0.061398913519830914im 0.018757414143864098 - 0.0894481642655758im … 0.0089340558072914 + 0.003833971090902836im 0.08264391581106004 + 0.012638705263423347im; … ; 0.02117975724386044 - 0.09550176132031207im -0.03510499553668369 - 0.05204613494500661im … 0.021967868105589962 + 0.007435795682080294im 0.0925951831490883 - 0.05552851272911193im; -0.019658230961819623 - 0.02782343146348707im -0.01299470014799686 - 0.0013307052007956038im … 0.0026097000473739515 + 0.0013585423705704085im 0.015111863840760548 - 0.06175097175531362im;;; 0.06472143020712774 - 0.04047978164954923im 0.016705932632225612 - 0.08001589826549907im … 0.016953350689409584 + 0.021440211088669302im 0.009551593820927367 + 0.0017308092648227068im; 0.006010931477579042 - 0.011641706711751973im 0.004509120738728386 + 0.002543585754806027im … 0.01563809732096307 - 0.0007039992296011999im -0.0010108725602421959 + 6.572884321723316e-6im; … ; -0.013471621163927944 - 0.021182968776952294im -0.007331073774689396 + 0.0004331579695976383im … 0.04076784702025592 - 0.02119444690027578im 0.023110616082692804 - 0.085183360289961im; 0.04590415826638757 + 0.013984640813432574im 0.03776261295608633 - 0.020880249097708622im … -0.005219590528605085 + 0.0414149482313193im 0.002085747548055427 + 0.0026056562728941617im;;; 0.014672514987057916 - 0.05789551428589378im -0.02154045612061788 - 0.028409366249796356im … -0.0286973682373579 - 0.003995417312776988im 0.0028240349262528336 + 0.0013896218570250514im; 0.01465692128725959 + 0.0136297490137234im 0.01953611878588788 + 0.005042265079979125im … -0.030387962175531646 + 0.02011035750082789im -0.005944911442064091 + 0.048819303475134225im; … ; 0.0593106894362132 + 0.01377896363265288im 0.03306128005488447 - 0.018190226804609237im … 0.007504264353698036 - 0.009688436016805697im 0.013541468910360687 + 0.011565920890866103im; 0.08309755243692912 - 0.04675614629114008im 0.015397739254856463 - 0.06340232045707421im … 0.007938842672086329 + 0.01332456706949184im 0.03447256794175252 + 0.011120927121694239im],)]), DFTK.DftHamiltonianBlock{PlaneWaveBasis{Float64, Float64, DFTK.CPU, FFTGrid{Float64, Float64, Array{StaticArraysCore.SVector{3, Int64}, 3}, Array{StaticArraysCore.SVector{3, Float64}, 3}}, Vector{StaticArraysCore.SVector{3, Int64}}}, Kpoint{Float64, Vector{StaticArraysCore.SVector{3, Int64}}, Vector{Int64}}, DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}, Nothing, Vector{@NamedTuple{ψ_reals::Array{ComplexF64, 3}}}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757), DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757), [0.062490081787469245, 0.9998413085995079, 3.062014007585993, 6.249008178746925, 10.5608238220823, 12.248056030343973, 7.561299896283778, 3.9993652343980317, 1.5622520446867312, 0.24996032714987704 … 2.7495635986486464, 5.561617279084762, 9.498492431695325, 14.560189056480331, 14.560189056480338, 9.498492431695325, 5.561617279084762, 2.7495635986486464, 1.0623313903869773, 0.49992065429975385]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757), ComplexF64[0.11038155824020969 + 0.0im 0.16972926797105742 + 0.0im … -0.009426647060181401 - 0.01632743165325398im 0.0094266470601814 + 0.016327431653253975im; 0.09335704685777356 + 0.0im 0.12740009431942179 + 0.0im … -0.05242104486249396 + 0.030265304362562327im 0.052421044862493944 - 0.03026530436256232im; … ; 0.09232028665365559 + 0.0im 0.12492048143428733 + 0.0im … 0.03728123116232767 + 0.0645729865418717im 0.0074562462324655335 + 0.01291459730837434im; 0.10208144135055229 + 0.0im 0.14872488279907023 + 0.0im … 0.029470953026436666 - 0.01701506266308801im 0.058941906052873326 - 0.03403012532617601im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757), [-12.24756969788468 -11.100308387033907 … -8.289845769066876 -11.100308387033937; -11.100308387033909 -9.130057818482129 … -9.130057802436303 -11.100308365268912; … ; -8.289845769066876 -9.130057802436301 … -4.149589911945763 -6.287956204739942; -11.100308387033936 -11.10030836526891 … -6.287956204739943 -9.111848216112012;;; -11.100308387033909 -9.130057818482127 … -9.130057802436303 -11.10030836526891; -9.130057818482127 -6.903159504367539 … -9.130057819839267 -10.053883816988028; … ; -9.130057802436303 -9.130057819839262 … -5.294353665850209 -7.547399215037586; -11.10030836526891 -10.053883816988026 … -7.547399215037586 -10.05388381698808;;; -8.28984576906702 -6.307621938057392 … -8.289845773669935 -9.111848200066165; -6.30762193805739 -4.516655658355877 … -7.5473992318922285 -7.547399215037702; … ; -8.289845773669935 -7.547399231892227 … -5.76896909839597 -7.547399231892261; -9.111848200066165 -7.5473992150377 … -7.547399231892262 -9.111848217469262;;; … ;;; -5.301031708536038 -6.307621951399237 … -2.549703579811763 -3.8495821823329934; -6.307621951399237 -6.90315951144739 … -3.3290606941630303 -4.878419351559542; … ; -2.5497035798117627 -3.3290606941630303 … -1.256798467534696 -1.8141947489915682; -3.8495821823329925 -4.878419351559542 … -1.81419474899157 -2.7147673368915055;;; -8.289845769066874 -9.130057802436303 … -4.149589911945763 -6.287956204739942; -9.130057802436301 -9.130057819839266 … -5.294353665850209 -7.547399215037587; … ; -4.149589911945763 -5.294353665850209 … -1.9094492500180706 -2.894612364489521; -6.287956204739942 -7.547399215037587 … -2.894612364489522 -4.485542751912525;;; -11.100308387033937 -11.10030836526891 … -6.287956204739942 -9.111848216112014; -11.10030836526891 -10.053883816988028 … -7.547399215037588 -10.053883816988078; … ; -6.287956204739942 -7.5473992150375855 … -2.8946123644895216 -4.485542751912525; -9.111848216112014 -10.053883816988076 … -4.485542751912525 -6.871104522520765])], 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), [-12.24756969788468 -11.100308387033907 … -8.289845769066876 -11.100308387033937; -11.100308387033909 -9.130057818482129 … -9.130057802436303 -11.100308365268912; … ; -8.289845769066876 -9.130057802436301 … -4.149589911945763 -6.287956204739942; -11.100308387033936 -11.10030836526891 … -6.287956204739943 -9.111848216112012;;; -11.100308387033909 -9.130057818482127 … -9.130057802436303 -11.10030836526891; -9.130057818482127 -6.903159504367539 … -9.130057819839267 -10.053883816988028; … ; -9.130057802436303 -9.130057819839262 … -5.294353665850209 -7.547399215037586; -11.10030836526891 -10.053883816988026 … -7.547399215037586 -10.05388381698808;;; -8.28984576906702 -6.307621938057392 … -8.289845773669935 -9.111848200066165; -6.30762193805739 -4.516655658355877 … -7.5473992318922285 -7.547399215037702; … ; -8.289845773669935 -7.547399231892227 … -5.76896909839597 -7.547399231892261; -9.111848200066165 -7.5473992150377 … -7.547399231892262 -9.111848217469262;;; … ;;; -5.301031708536038 -6.307621951399237 … -2.549703579811763 -3.8495821823329934; -6.307621951399237 -6.90315951144739 … -3.3290606941630303 -4.878419351559542; … ; -2.5497035798117627 -3.3290606941630303 … -1.256798467534696 -1.8141947489915682; -3.8495821823329925 -4.878419351559542 … -1.81419474899157 -2.7147673368915055;;; -8.289845769066874 -9.130057802436303 … -4.149589911945763 -6.287956204739942; -9.130057802436301 -9.130057819839266 … -5.294353665850209 -7.547399215037587; … ; -4.149589911945763 -5.294353665850209 … -1.9094492500180706 -2.894612364489521; -6.287956204739942 -7.547399215037587 … -2.894612364489522 -4.485542751912525;;; -11.100308387033937 -11.10030836526891 … -6.287956204739942 -9.111848216112014; -11.10030836526891 -10.053883816988028 … -7.547399215037588 -10.053883816988078; … ; -6.287956204739942 -7.5473992150375855 … -2.8946123644895216 -4.485542751912525; -9.111848216112014 -10.053883816988076 … -4.485542751912525 -6.871104522520765]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757), ComplexF64[0.11038155824020969 + 0.0im 0.16972926797105742 + 0.0im … -0.009426647060181401 - 0.01632743165325398im 0.0094266470601814 + 0.016327431653253975im; 0.09335704685777356 + 0.0im 0.12740009431942179 + 0.0im … -0.05242104486249396 + 0.030265304362562327im 0.052421044862493944 - 0.03026530436256232im; … ; 0.09232028665365559 + 0.0im 0.12492048143428733 + 0.0im … 0.03728123116232767 + 0.0645729865418717im 0.0074562462324655335 + 0.01291459730837434im; 0.10208144135055229 + 0.0im 0.14872488279907023 + 0.0im … 0.029470953026436666 - 0.01701506266308801im 0.058941906052873326 - 0.03403012532617601im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, @NamedTuple{ψ_reals::Array{ComplexF64, 3}}[(ψ_reals = [0.00047266210922330314 - 0.00017109041368464951im -0.00288349829401734 + 0.006276577393140557im … 0.0008751772312437268 + 0.002251411357681361im 0.0039082135778781505 + 0.0017777998019015157im; -0.00011908943396532587 + 0.00027221086682001393im 0.0012675176880109424 + 0.003541056097253024im … -0.00011358058839417177 - 3.2803502885815974e-5im 0.00205763991527809 - 0.0007187684060758199im; … ; 0.002083844725155861 + 0.005320889535479095im 0.00301788619741574 + 0.0012845847021796108im … 0.0015608691055731473 - 0.000503820137994881im -6.674986618283212e-5 + 0.00019009165100519157im; 0.007550835662591418 + 0.003302014082703354im 0.0011558053820814446 - 0.0005264840095308009im … -0.001872463817383852 + 0.004376837634295329im 0.002725698873500034 + 0.0071229288358504415im;;; -0.038141212890287754 - 0.002954916197724429im -0.07741083307079784 + 0.061681106246984294im … 0.004335270932285227 - 0.02571276196496712im -0.009497252060410827 - 0.012608673358912133im; -0.000889244002104916 + 0.0039207481750680815im -0.008319383892930084 + 0.060841028708168876im … -0.009118438020196327 - 0.009111611632785241im 0.02751262873254825 + 0.00686948437169721im; … ; -0.005268558431749372 + 0.060363762241826185im 0.006928766109538371 + 0.0039539400371452395im … -0.04742021459577918 - 0.008186709349991418im -0.05834755067848092 + 0.04375363027437581im; -0.004421552871034032 - 0.01512295557020987im -0.06128279548615635 - 0.00960141253207442im … -0.008384311494267504 + 0.009654530034456816im 0.00290090864325461 + 0.01438975777900823im;;; -0.03694780455848816 + 0.031341129599940086im -0.01087095933747665 + 0.09059190357842714im … -0.005723496687651279 - 0.003531039483118281im 0.00689603997869336 + 0.004625032660049261im; 0.010438568840990627 - 0.03896306209515862im -0.001553550928553422 - 0.002809670532838717im … -0.0013411622801639857 + 0.0028021175302929946im 0.05052682440032684 - 0.03174134604746333im; … ; -0.003184461404334815 - 0.013949018260913517im -0.075333782391168 - 0.016355394595090555im … -0.06352594815894778 + 0.044234252529461796im -0.006004472694453389 + 0.05117319159123433im; -0.08443280390140537 - 0.01597401443787003im -0.10644319077511255 + 0.07783082268266932im … -0.002419295864036407 + 0.018008096167701097im -0.0070407906943740555 - 0.015630975862319908im;;; … ;;; 0.08248459360255563 + 0.01724822651045027im 0.06356664069146967 - 0.04182263791975068im … 0.0020122997833160183 + 0.008117687448399458im 0.022356732235995318 + 0.028188891660962972im; 0.09249712571110905 - 0.061398913519830914im 0.018757414143864098 - 0.0894481642655758im … 0.0089340558072914 + 0.003833971090902836im 0.08264391581106004 + 0.012638705263423347im; … ; 0.02117975724386044 - 0.09550176132031207im -0.03510499553668369 - 0.05204613494500661im … 0.021967868105589962 + 0.007435795682080294im 0.0925951831490883 - 0.05552851272911193im; -0.019658230961819623 - 0.02782343146348707im -0.01299470014799686 - 0.0013307052007956038im … 0.0026097000473739515 + 0.0013585423705704085im 0.015111863840760548 - 0.06175097175531362im;;; 0.06472143020712774 - 0.04047978164954923im 0.016705932632225612 - 0.08001589826549907im … 0.016953350689409584 + 0.021440211088669302im 0.009551593820927367 + 0.0017308092648227068im; 0.006010931477579042 - 0.011641706711751973im 0.004509120738728386 + 0.002543585754806027im … 0.01563809732096307 - 0.0007039992296011999im -0.0010108725602421959 + 6.572884321723316e-6im; … ; -0.013471621163927944 - 0.021182968776952294im -0.007331073774689396 + 0.0004331579695976383im … 0.04076784702025592 - 0.02119444690027578im 0.023110616082692804 - 0.085183360289961im; 0.04590415826638757 + 0.013984640813432574im 0.03776261295608633 - 0.020880249097708622im … -0.005219590528605085 + 0.0414149482313193im 0.002085747548055427 + 0.0026056562728941617im;;; 0.014672514987057916 - 0.05789551428589378im -0.02154045612061788 - 0.028409366249796356im … -0.0286973682373579 - 0.003995417312776988im 0.0028240349262528336 + 0.0013896218570250514im; 0.01465692128725959 + 0.0136297490137234im 0.01953611878588788 + 0.005042265079979125im … -0.030387962175531646 + 0.02011035750082789im -0.005944911442064091 + 0.048819303475134225im; … ; 0.0593106894362132 + 0.01377896363265288im 0.03306128005488447 - 0.018190226804609237im … 0.007504264353698036 - 0.009688436016805697im 0.013541468910360687 + 0.011565920890866103im; 0.08309755243692912 - 0.04675614629114008im 0.015397739254856463 - 0.06340232045707421im … 0.007938842672086329 + 0.01332456706949184im 0.03447256794175252 + 0.011120927121694239im],)]), DFTK.DftHamiltonianBlock{PlaneWaveBasis{Float64, Float64, DFTK.CPU, FFTGrid{Float64, Float64, Array{StaticArraysCore.SVector{3, Int64}, 3}, Array{StaticArraysCore.SVector{3, Float64}, 3}}, Vector{StaticArraysCore.SVector{3, Int64}}}, Kpoint{Float64, Vector{StaticArraysCore.SVector{3, Int64}}, Vector{Int64}}, DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}, Nothing, Vector{@NamedTuple{ψ_reals::Array{ComplexF64, 3}}}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749), DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749), [0.083320109049959, 0.8956911722870592, 2.8328837076986058, 5.894897715284598, 10.081733195045036, 12.893786875481155, 8.082050577846019, 4.395135752385337, 1.8330423990990978, 0.3957705179873052 … 0.8332010904995898, 2.3954531351863206, 5.082526652047498, 8.894421641083122, 13.83113810229319, 9.89426294968263, 5.832407633497128, 2.895373789486075, 1.083161417649467, 0.3957705179873052]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749), ComplexF64[0.10997142862853636 + 0.0im 0.16867583607081263 + 0.0im … -0.032495727623724026 - 0.018761417091069828im -5.710372280586092e-19 - 3.2968849733693577e-19im; 0.09511091805015323 + 0.0im 0.13162182200636918 + 0.0im … -0.038767079080422394 + 0.0671465506283321im 0.023260247448253425 - 0.040287930376999244im; … ; 0.09197726483082143 + 0.0im 0.12410271910068073 + 0.0im … 0.051406644402565774 + 0.029679639983956736im 6.990521527121635e-18 + 4.0359794854595524e-18im; 0.10399921515860865 + 0.0im 0.15351809108742231 + 0.0im … 0.008717893888213726 - 0.015099835149380354im 0.02615368166464116 - 0.04529950544814103im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749), [-12.24756969788468 -11.100308387033907 … -8.289845769066876 -11.100308387033937; -11.100308387033909 -9.130057818482129 … -9.130057802436303 -11.100308365268912; … ; -8.289845769066876 -9.130057802436301 … -4.149589911945763 -6.287956204739942; -11.100308387033936 -11.10030836526891 … -6.287956204739943 -9.111848216112012;;; -11.100308387033909 -9.130057818482127 … -9.130057802436303 -11.10030836526891; -9.130057818482127 -6.903159504367539 … -9.130057819839267 -10.053883816988028; … ; -9.130057802436303 -9.130057819839262 … -5.294353665850209 -7.547399215037586; -11.10030836526891 -10.053883816988026 … -7.547399215037586 -10.05388381698808;;; -8.28984576906702 -6.307621938057392 … -8.289845773669935 -9.111848200066165; -6.30762193805739 -4.516655658355877 … -7.5473992318922285 -7.547399215037702; … ; -8.289845773669935 -7.547399231892227 … -5.76896909839597 -7.547399231892261; -9.111848200066165 -7.5473992150377 … -7.547399231892262 -9.111848217469262;;; … ;;; -5.301031708536038 -6.307621951399237 … -2.549703579811763 -3.8495821823329934; -6.307621951399237 -6.90315951144739 … -3.3290606941630303 -4.878419351559542; … ; -2.5497035798117627 -3.3290606941630303 … -1.256798467534696 -1.8141947489915682; -3.8495821823329925 -4.878419351559542 … -1.81419474899157 -2.7147673368915055;;; -8.289845769066874 -9.130057802436303 … -4.149589911945763 -6.287956204739942; -9.130057802436301 -9.130057819839266 … -5.294353665850209 -7.547399215037587; … ; -4.149589911945763 -5.294353665850209 … -1.9094492500180706 -2.894612364489521; -6.287956204739942 -7.547399215037587 … -2.894612364489522 -4.485542751912525;;; -11.100308387033937 -11.10030836526891 … -6.287956204739942 -9.111848216112014; -11.10030836526891 -10.053883816988028 … -7.547399215037588 -10.053883816988078; … ; -6.287956204739942 -7.5473992150375855 … -2.8946123644895216 -4.485542751912525; -9.111848216112014 -10.053883816988076 … -4.485542751912525 -6.871104522520765])], 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), [-12.24756969788468 -11.100308387033907 … -8.289845769066876 -11.100308387033937; -11.100308387033909 -9.130057818482129 … -9.130057802436303 -11.100308365268912; … ; -8.289845769066876 -9.130057802436301 … -4.149589911945763 -6.287956204739942; -11.100308387033936 -11.10030836526891 … -6.287956204739943 -9.111848216112012;;; -11.100308387033909 -9.130057818482127 … -9.130057802436303 -11.10030836526891; -9.130057818482127 -6.903159504367539 … -9.130057819839267 -10.053883816988028; … ; -9.130057802436303 -9.130057819839262 … -5.294353665850209 -7.547399215037586; -11.10030836526891 -10.053883816988026 … -7.547399215037586 -10.05388381698808;;; -8.28984576906702 -6.307621938057392 … -8.289845773669935 -9.111848200066165; -6.30762193805739 -4.516655658355877 … -7.5473992318922285 -7.547399215037702; … ; -8.289845773669935 -7.547399231892227 … -5.76896909839597 -7.547399231892261; -9.111848200066165 -7.5473992150377 … -7.547399231892262 -9.111848217469262;;; … ;;; -5.301031708536038 -6.307621951399237 … -2.549703579811763 -3.8495821823329934; -6.307621951399237 -6.90315951144739 … -3.3290606941630303 -4.878419351559542; … ; -2.5497035798117627 -3.3290606941630303 … -1.256798467534696 -1.8141947489915682; -3.8495821823329925 -4.878419351559542 … -1.81419474899157 -2.7147673368915055;;; -8.289845769066874 -9.130057802436303 … -4.149589911945763 -6.287956204739942; -9.130057802436301 -9.130057819839266 … -5.294353665850209 -7.547399215037587; … ; -4.149589911945763 -5.294353665850209 … -1.9094492500180706 -2.894612364489521; -6.287956204739942 -7.547399215037587 … -2.894612364489522 -4.485542751912525;;; -11.100308387033937 -11.10030836526891 … -6.287956204739942 -9.111848216112014; -11.10030836526891 -10.053883816988028 … -7.547399215037588 -10.053883816988078; … ; -6.287956204739942 -7.5473992150375855 … -2.8946123644895216 -4.485542751912525; -9.111848216112014 -10.053883816988076 … -4.485542751912525 -6.871104522520765]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749), ComplexF64[0.10997142862853636 + 0.0im 0.16867583607081263 + 0.0im … -0.032495727623724026 - 0.018761417091069828im -5.710372280586092e-19 - 3.2968849733693577e-19im; 0.09511091805015323 + 0.0im 0.13162182200636918 + 0.0im … -0.038767079080422394 + 0.0671465506283321im 0.023260247448253425 - 0.040287930376999244im; … ; 0.09197726483082143 + 0.0im 0.12410271910068073 + 0.0im … 0.051406644402565774 + 0.029679639983956736im 6.990521527121635e-18 + 4.0359794854595524e-18im; 0.10399921515860865 + 0.0im 0.15351809108742231 + 0.0im … 0.008717893888213726 - 0.015099835149380354im 0.02615368166464116 - 0.04529950544814103im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, @NamedTuple{ψ_reals::Array{ComplexF64, 3}}[(ψ_reals = [0.00047266210922330314 - 0.00017109041368464951im -0.00288349829401734 + 0.006276577393140557im … 0.0008751772312437268 + 0.002251411357681361im 0.0039082135778781505 + 0.0017777998019015157im; -0.00011908943396532587 + 0.00027221086682001393im 0.0012675176880109424 + 0.003541056097253024im … -0.00011358058839417177 - 3.2803502885815974e-5im 0.00205763991527809 - 0.0007187684060758199im; … ; 0.002083844725155861 + 0.005320889535479095im 0.00301788619741574 + 0.0012845847021796108im … 0.0015608691055731473 - 0.000503820137994881im -6.674986618283212e-5 + 0.00019009165100519157im; 0.007550835662591418 + 0.003302014082703354im 0.0011558053820814446 - 0.0005264840095308009im … -0.001872463817383852 + 0.004376837634295329im 0.002725698873500034 + 0.0071229288358504415im;;; -0.038141212890287754 - 0.002954916197724429im -0.07741083307079784 + 0.061681106246984294im … 0.004335270932285227 - 0.02571276196496712im -0.009497252060410827 - 0.012608673358912133im; -0.000889244002104916 + 0.0039207481750680815im -0.008319383892930084 + 0.060841028708168876im … -0.009118438020196327 - 0.009111611632785241im 0.02751262873254825 + 0.00686948437169721im; … ; -0.005268558431749372 + 0.060363762241826185im 0.006928766109538371 + 0.0039539400371452395im … -0.04742021459577918 - 0.008186709349991418im -0.05834755067848092 + 0.04375363027437581im; -0.004421552871034032 - 0.01512295557020987im -0.06128279548615635 - 0.00960141253207442im … -0.008384311494267504 + 0.009654530034456816im 0.00290090864325461 + 0.01438975777900823im;;; -0.03694780455848816 + 0.031341129599940086im -0.01087095933747665 + 0.09059190357842714im … -0.005723496687651279 - 0.003531039483118281im 0.00689603997869336 + 0.004625032660049261im; 0.010438568840990627 - 0.03896306209515862im -0.001553550928553422 - 0.002809670532838717im … -0.0013411622801639857 + 0.0028021175302929946im 0.05052682440032684 - 0.03174134604746333im; … ; -0.003184461404334815 - 0.013949018260913517im -0.075333782391168 - 0.016355394595090555im … -0.06352594815894778 + 0.044234252529461796im -0.006004472694453389 + 0.05117319159123433im; -0.08443280390140537 - 0.01597401443787003im -0.10644319077511255 + 0.07783082268266932im … -0.002419295864036407 + 0.018008096167701097im -0.0070407906943740555 - 0.015630975862319908im;;; … ;;; 0.08248459360255563 + 0.01724822651045027im 0.06356664069146967 - 0.04182263791975068im … 0.0020122997833160183 + 0.008117687448399458im 0.022356732235995318 + 0.028188891660962972im; 0.09249712571110905 - 0.061398913519830914im 0.018757414143864098 - 0.0894481642655758im … 0.0089340558072914 + 0.003833971090902836im 0.08264391581106004 + 0.012638705263423347im; … ; 0.02117975724386044 - 0.09550176132031207im -0.03510499553668369 - 0.05204613494500661im … 0.021967868105589962 + 0.007435795682080294im 0.0925951831490883 - 0.05552851272911193im; -0.019658230961819623 - 0.02782343146348707im -0.01299470014799686 - 0.0013307052007956038im … 0.0026097000473739515 + 0.0013585423705704085im 0.015111863840760548 - 0.06175097175531362im;;; 0.06472143020712774 - 0.04047978164954923im 0.016705932632225612 - 0.08001589826549907im … 0.016953350689409584 + 0.021440211088669302im 0.009551593820927367 + 0.0017308092648227068im; 0.006010931477579042 - 0.011641706711751973im 0.004509120738728386 + 0.002543585754806027im … 0.01563809732096307 - 0.0007039992296011999im -0.0010108725602421959 + 6.572884321723316e-6im; … ; -0.013471621163927944 - 0.021182968776952294im -0.007331073774689396 + 0.0004331579695976383im … 0.04076784702025592 - 0.02119444690027578im 0.023110616082692804 - 0.085183360289961im; 0.04590415826638757 + 0.013984640813432574im 0.03776261295608633 - 0.020880249097708622im … -0.005219590528605085 + 0.0414149482313193im 0.002085747548055427 + 0.0026056562728941617im;;; 0.014672514987057916 - 0.05789551428589378im -0.02154045612061788 - 0.028409366249796356im … -0.0286973682373579 - 0.003995417312776988im 0.0028240349262528336 + 0.0013896218570250514im; 0.01465692128725959 + 0.0136297490137234im 0.01953611878588788 + 0.005042265079979125im … -0.030387962175531646 + 0.02011035750082789im -0.005944911442064091 + 0.048819303475134225im; … ; 0.0593106894362132 + 0.01377896363265288im 0.03306128005488447 - 0.018190226804609237im … 0.007504264353698036 - 0.009688436016805697im 0.013541468910360687 + 0.011565920890866103im; 0.08309755243692912 - 0.04675614629114008im 0.015397739254856463 - 0.06340232045707421im … 0.007938842672086329 + 0.01332456706949184im 0.03447256794175252 + 0.011120927121694239im],)]), DFTK.DftHamiltonianBlock{PlaneWaveBasis{Float64, Float64, DFTK.CPU, FFTGrid{Float64, Float64, Array{StaticArraysCore.SVector{3, Int64}, 3}, Array{StaticArraysCore.SVector{3, Float64}, 3}}, Vector{StaticArraysCore.SVector{3, Int64}}}, Kpoint{Float64, Vector{StaticArraysCore.SVector{3, Int64}}, Vector{Int64}}, DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}, Nothing, Vector{@NamedTuple{ψ_reals::Array{ComplexF64, 3}}}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740), DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740), [0.16664021809991797, 0.22913029988738726, 1.4164418538493029, 3.728574879985665, 7.165529378296473, 11.727305348781728, 11.164894612694503, 6.728098805784188, 3.4161244710483185, 1.2289716084868951 … 0.41660054524979495, 1.228971608486895, 3.1661641438984414, 6.2281781514844345, 10.415013631244872, 13.22706731168099, 8.415331014045858, 4.7284161885851725, 2.166322835298934, 0.7290509541871413]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740), ComplexF64[0.1083460922901765 + 0.0im 0.16451669692939747 + 0.0im … -0.0 + 1.0213144005610528e-18im 0.0 - 0.03679672923035902im; 0.10714287388793554 + 0.0im 0.16145393303017874 + 0.0im … -0.054392079538503724 - 0.0im 0.018130693179501247 + 0.0im; … ; 0.07579045242767471 + 0.0im 0.08711041809792075 + 0.0im … -0.0 + 0.06906475263474504im 0.0 - 0.023021584211581677im; 0.09798590385967747 + 0.0im 0.13861415332258223 + 0.0im … 0.04837457477358332 + 0.0im 0.01612485825786111 + 0.0im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740), [-12.24756969788468 -11.100308387033907 … -8.289845769066876 -11.100308387033937; -11.100308387033909 -9.130057818482129 … -9.130057802436303 -11.100308365268912; … ; -8.289845769066876 -9.130057802436301 … -4.149589911945763 -6.287956204739942; -11.100308387033936 -11.10030836526891 … -6.287956204739943 -9.111848216112012;;; -11.100308387033909 -9.130057818482127 … -9.130057802436303 -11.10030836526891; -9.130057818482127 -6.903159504367539 … -9.130057819839267 -10.053883816988028; … ; -9.130057802436303 -9.130057819839262 … -5.294353665850209 -7.547399215037586; -11.10030836526891 -10.053883816988026 … -7.547399215037586 -10.05388381698808;;; -8.28984576906702 -6.307621938057392 … -8.289845773669935 -9.111848200066165; -6.30762193805739 -4.516655658355877 … -7.5473992318922285 -7.547399215037702; … ; -8.289845773669935 -7.547399231892227 … -5.76896909839597 -7.547399231892261; -9.111848200066165 -7.5473992150377 … -7.547399231892262 -9.111848217469262;;; … ;;; -5.301031708536038 -6.307621951399237 … -2.549703579811763 -3.8495821823329934; -6.307621951399237 -6.90315951144739 … -3.3290606941630303 -4.878419351559542; … ; -2.5497035798117627 -3.3290606941630303 … -1.256798467534696 -1.8141947489915682; -3.8495821823329925 -4.878419351559542 … -1.81419474899157 -2.7147673368915055;;; -8.289845769066874 -9.130057802436303 … -4.149589911945763 -6.287956204739942; -9.130057802436301 -9.130057819839266 … -5.294353665850209 -7.547399215037587; … ; -4.149589911945763 -5.294353665850209 … -1.9094492500180706 -2.894612364489521; -6.287956204739942 -7.547399215037587 … -2.894612364489522 -4.485542751912525;;; -11.100308387033937 -11.10030836526891 … -6.287956204739942 -9.111848216112014; -11.10030836526891 -10.053883816988028 … -7.547399215037588 -10.053883816988078; … ; -6.287956204739942 -7.5473992150375855 … -2.8946123644895216 -4.485542751912525; -9.111848216112014 -10.053883816988076 … -4.485542751912525 -6.871104522520765])], 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), [-12.24756969788468 -11.100308387033907 … -8.289845769066876 -11.100308387033937; -11.100308387033909 -9.130057818482129 … -9.130057802436303 -11.100308365268912; … ; -8.289845769066876 -9.130057802436301 … -4.149589911945763 -6.287956204739942; -11.100308387033936 -11.10030836526891 … -6.287956204739943 -9.111848216112012;;; -11.100308387033909 -9.130057818482127 … -9.130057802436303 -11.10030836526891; -9.130057818482127 -6.903159504367539 … -9.130057819839267 -10.053883816988028; … ; -9.130057802436303 -9.130057819839262 … -5.294353665850209 -7.547399215037586; -11.10030836526891 -10.053883816988026 … -7.547399215037586 -10.05388381698808;;; -8.28984576906702 -6.307621938057392 … -8.289845773669935 -9.111848200066165; -6.30762193805739 -4.516655658355877 … -7.5473992318922285 -7.547399215037702; … ; -8.289845773669935 -7.547399231892227 … -5.76896909839597 -7.547399231892261; -9.111848200066165 -7.5473992150377 … -7.547399231892262 -9.111848217469262;;; … ;;; -5.301031708536038 -6.307621951399237 … -2.549703579811763 -3.8495821823329934; -6.307621951399237 -6.90315951144739 … -3.3290606941630303 -4.878419351559542; … ; -2.5497035798117627 -3.3290606941630303 … -1.256798467534696 -1.8141947489915682; -3.8495821823329925 -4.878419351559542 … -1.81419474899157 -2.7147673368915055;;; -8.289845769066874 -9.130057802436303 … -4.149589911945763 -6.287956204739942; -9.130057802436301 -9.130057819839266 … -5.294353665850209 -7.547399215037587; … ; -4.149589911945763 -5.294353665850209 … -1.9094492500180706 -2.894612364489521; -6.287956204739942 -7.547399215037587 … -2.894612364489522 -4.485542751912525;;; -11.100308387033937 -11.10030836526891 … -6.287956204739942 -9.111848216112014; -11.10030836526891 -10.053883816988028 … -7.547399215037588 -10.053883816988078; … ; -6.287956204739942 -7.5473992150375855 … -2.8946123644895216 -4.485542751912525; -9.111848216112014 -10.053883816988076 … -4.485542751912525 -6.871104522520765]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740), ComplexF64[0.1083460922901765 + 0.0im 0.16451669692939747 + 0.0im … -0.0 + 1.0213144005610528e-18im 0.0 - 0.03679672923035902im; 0.10714287388793554 + 0.0im 0.16145393303017874 + 0.0im … -0.054392079538503724 - 0.0im 0.018130693179501247 + 0.0im; … ; 0.07579045242767471 + 0.0im 0.08711041809792075 + 0.0im … -0.0 + 0.06906475263474504im 0.0 - 0.023021584211581677im; 0.09798590385967747 + 0.0im 0.13861415332258223 + 0.0im … 0.04837457477358332 + 0.0im 0.01612485825786111 + 0.0im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, @NamedTuple{ψ_reals::Array{ComplexF64, 3}}[(ψ_reals = [0.00047266210922330314 - 0.00017109041368464951im -0.00288349829401734 + 0.006276577393140557im … 0.0008751772312437268 + 0.002251411357681361im 0.0039082135778781505 + 0.0017777998019015157im; -0.00011908943396532587 + 0.00027221086682001393im 0.0012675176880109424 + 0.003541056097253024im … -0.00011358058839417177 - 3.2803502885815974e-5im 0.00205763991527809 - 0.0007187684060758199im; … ; 0.002083844725155861 + 0.005320889535479095im 0.00301788619741574 + 0.0012845847021796108im … 0.0015608691055731473 - 0.000503820137994881im -6.674986618283212e-5 + 0.00019009165100519157im; 0.007550835662591418 + 0.003302014082703354im 0.0011558053820814446 - 0.0005264840095308009im … -0.001872463817383852 + 0.004376837634295329im 0.002725698873500034 + 0.0071229288358504415im;;; -0.038141212890287754 - 0.002954916197724429im -0.07741083307079784 + 0.061681106246984294im … 0.004335270932285227 - 0.02571276196496712im -0.009497252060410827 - 0.012608673358912133im; -0.000889244002104916 + 0.0039207481750680815im -0.008319383892930084 + 0.060841028708168876im … -0.009118438020196327 - 0.009111611632785241im 0.02751262873254825 + 0.00686948437169721im; … ; -0.005268558431749372 + 0.060363762241826185im 0.006928766109538371 + 0.0039539400371452395im … -0.04742021459577918 - 0.008186709349991418im -0.05834755067848092 + 0.04375363027437581im; -0.004421552871034032 - 0.01512295557020987im -0.06128279548615635 - 0.00960141253207442im … -0.008384311494267504 + 0.009654530034456816im 0.00290090864325461 + 0.01438975777900823im;;; 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… ; 0.02117975724386044 - 0.09550176132031207im -0.03510499553668369 - 0.05204613494500661im … 0.021967868105589962 + 0.007435795682080294im 0.0925951831490883 - 0.05552851272911193im; -0.019658230961819623 - 0.02782343146348707im -0.01299470014799686 - 0.0013307052007956038im … 0.0026097000473739515 + 0.0013585423705704085im 0.015111863840760548 - 0.06175097175531362im;;; 0.06472143020712774 - 0.04047978164954923im 0.016705932632225612 - 0.08001589826549907im … 0.016953350689409584 + 0.021440211088669302im 0.009551593820927367 + 0.0017308092648227068im; 0.006010931477579042 - 0.011641706711751973im 0.004509120738728386 + 0.002543585754806027im … 0.01563809732096307 - 0.0007039992296011999im -0.0010108725602421959 + 6.572884321723316e-6im; … ; -0.013471621163927944 - 0.021182968776952294im -0.007331073774689396 + 0.0004331579695976383im … 0.04076784702025592 - 0.02119444690027578im 0.023110616082692804 - 0.085183360289961im; 0.04590415826638757 + 0.013984640813432574im 0.03776261295608633 - 0.020880249097708622im … -0.005219590528605085 + 0.0414149482313193im 0.002085747548055427 + 0.0026056562728941617im;;; 0.014672514987057916 - 0.05789551428589378im -0.02154045612061788 - 0.028409366249796356im … -0.0286973682373579 - 0.003995417312776988im 0.0028240349262528336 + 0.0013896218570250514im; 0.01465692128725959 + 0.0136297490137234im 0.01953611878588788 + 0.005042265079979125im … -0.030387962175531646 + 0.02011035750082789im -0.005944911442064091 + 0.048819303475134225im; … ; 0.0593106894362132 + 0.01377896363265288im 0.03306128005488447 - 0.018190226804609237im … 0.007504264353698036 - 0.009688436016805697im 0.013541468910360687 + 0.011565920890866103im; 0.08309755243692912 - 0.04675614629114008im 0.015397739254856463 - 0.06340232045707421im … 0.007938842672086329 + 0.01332456706949184im 0.03447256794175252 + 0.011120927121694239im],)])]), basis = PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), energies = Energies(total = -7.910594396488486), converged = true, ρ = [7.5897845429542e-5 0.001126271272807875 … 0.006697037549958296 0.0011262712728078866; 0.0011262712728078933 0.00527433445725954 … 0.005274334457259565 0.0011262712728079035; … ; 0.006697037549958296 0.005274334457259573 … 0.02324475419082102 0.01225898682507864; 0.0011262712728078834 0.0011262712728078866 … 0.012258986825078637 0.0037700086298259996;;; 0.0011262712728078786 0.005274334457259533 … 0.0052743344572595725 0.0011262712728078844; 0.005274334457259538 0.014620065304461654 … 0.005274334457259565 0.002588080874793157; … ; 0.005274334457259572 0.005274334457259574 … 0.018107686645910833 0.008922003044595008; 0.0011262712728078836 0.002588080874793141 … 0.008922003044595004 0.0025880808747931476;;; 0.006697037549958252 0.01641210910133458 … 0.006697037549958294 0.0037700086298259826; 0.016412109101334584 0.03127783931548572 … 0.008922003044594978 0.00892200304459497; … ; 0.006697037549958294 0.008922003044594983 … 0.016476756359216565 0.008922003044595004; 0.003770008629825981 0.008922003044594956 … 0.008922003044594997 0.0037700086298259996;;; … ;;; 0.01985383985313264 0.016412109101334598 … 0.037156673635377856 0.02719080068630079; 0.0164121091013346 0.014620065304461659 … 0.03230127212612522 0.02232210093142621; … ; 0.037156673635377856 0.03230127212612523 … 0.04629698070121715 0.042636582731176376; 0.027190800686300788 0.022322100931426194 … 0.042636582731176376 0.03477222914172468;;; 0.006697037549958261 0.0052743344572595335 … 0.023244754190821 0.012258986825078597; 0.005274334457259538 0.00527433445725954 … 0.0181076866459108 0.00892200304459498; … ; 0.023244754190821 0.018107686645910802 … 0.04037111033533084 0.03149160381114774; 0.012258986825078592 0.008922003044594963 … 0.03149160381114773 0.020047163432540812;;; 0.0011262712728078812 0.0011262712728078803 … 0.012258986825078623 0.0037700086298259913; 0.0011262712728078849 0.002588080874793137 … 0.008922003044594985 0.0025880808747931615; … ; 0.012258986825078625 0.008922003044594994 … 0.03149160381114775 0.02004716343254084; 0.003770008629825989 0.0025880808747931437 … 0.020047163432540836 0.008952603496652336;;;;], eigenvalues = [[-0.17836835653818037, 0.26249194499346995, 0.2624919449934702, 0.2624919449934705, 0.3546921481687473, 0.3546921481687477, 0.3546921481747942], [-0.12755037617785067, 0.0647532059480438, 0.22545166517594842, 0.22545166517594853, 0.32197764961239855, 0.389222769085607, 0.3892227690856074], [-0.10818729216372328, 0.07755003473631243, 0.17278328011605482, 0.17278328011605507, 0.2843518536197148, 0.33054764843265905, 0.5267232426409535], [-0.05777325374266785, 0.012724782207170758, 0.09766073750171238, 0.1841782533311835, 0.3152284179597875, 0.47203121951264854, 0.49791351875386886]], 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 = 0.27342189930659266, n_iter = 10, ψ = Matrix{ComplexF64}[[0.21881648952821722 - 0.9240254493998923im -1.2224488504592843e-14 + 9.268573402325212e-14im … 1.5279472374453265e-12 - 4.839264550618962e-12im -2.0939464059723737e-7 + 7.54067578356361e-7im; 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