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), [-12.247569697884419 -11.100308387033586 … -8.289845769066552 -11.100308387033616; -11.100308387033586 -9.13005781848181 … -9.130057802435983 -11.100308365268589; … ; -8.289845769066552 -9.130057802435982 … -4.149589911945458 -6.287956204739622; -11.100308387033614 -11.100308365268589 … -6.287956204739623 -9.111848216111685;;; -11.100308387033587 -9.130057818481808 … -9.130057802435983 -11.100308365268589; -9.130057818481808 -6.903159504367228 … -9.130057819838948 -10.053883816987707; … ; -9.130057802435983 -9.130057819838942 … -5.294353665849902 -7.547399215037271; -11.100308365268589 -10.053883816987707 … -7.547399215037271 -10.053883816987758;;; -8.289845769066698 -6.307621938057083 … -8.289845773669612 -9.111848200065838; -6.307621938057082 -4.516655658355579 … -7.547399231891912 -7.547399215037385; … ; -8.289845773669612 -7.54739923189191 … -5.768969098395666 -7.547399231891946; -9.11184820006584 -7.547399215037384 … -7.547399231891947 -9.111848217468935;;; … ;;; -5.301031708535731 -6.307621951398928 … -2.5497035798114878 -3.8495821823326954; -6.307621951398928 -6.903159511447077 … -3.3290606941627447 -4.878419351559241; … ; -2.5497035798114873 -3.3290606941627447 … -1.256798467534477 -1.8141947489913153; -3.849582182332695 -4.878419351559241 … -1.8141947489913173 -2.7147673368912235;;; -8.289845769066552 -9.130057802435983 … -4.149589911945458 -6.287956204739621; -9.130057802435982 -9.130057819838946 … -5.294353665849902 -7.54739921503727; … ; -4.149589911945458 -5.294353665849902 … -1.9094492500178113 -2.894612364489231; -6.287956204739621 -7.547399215037271 … -2.894612364489232 -4.4855427519122095;;; -11.100308387033616 -11.100308365268589 … -6.287956204739622 -9.111848216111687; -11.100308365268589 -10.053883816987708 … -7.547399215037272 -10.053883816987756; … ; -6.287956204739622 -7.547399215037269 … -2.8946123644892316 -4.4855427519122095; -9.111848216111687 -10.053883816987756 … -4.4855427519122095 -6.871104522520434])], 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), [-12.247569697884419 -11.100308387033586 … -8.289845769066552 -11.100308387033616; -11.100308387033586 -9.13005781848181 … -9.130057802435983 -11.100308365268589; … ; -8.289845769066552 -9.130057802435982 … -4.149589911945458 -6.287956204739622; -11.100308387033614 -11.100308365268589 … -6.287956204739623 -9.111848216111685;;; -11.100308387033587 -9.130057818481808 … -9.130057802435983 -11.100308365268589; -9.130057818481808 -6.903159504367228 … -9.130057819838948 -10.053883816987707; … ; -9.130057802435983 -9.130057819838942 … -5.294353665849902 -7.547399215037271; -11.100308365268589 -10.053883816987707 … -7.547399215037271 -10.053883816987758;;; -8.289845769066698 -6.307621938057083 … -8.289845773669612 -9.111848200065838; -6.307621938057082 -4.516655658355579 … -7.547399231891912 -7.547399215037385; … ; -8.289845773669612 -7.54739923189191 … -5.768969098395666 -7.547399231891946; -9.11184820006584 -7.547399215037384 … -7.547399231891947 -9.111848217468935;;; … ;;; -5.301031708535731 -6.307621951398928 … -2.5497035798114878 -3.8495821823326954; -6.307621951398928 -6.903159511447077 … -3.3290606941627447 -4.878419351559241; … ; -2.5497035798114873 -3.3290606941627447 … -1.256798467534477 -1.8141947489913153; -3.849582182332695 -4.878419351559241 … -1.8141947489913173 -2.7147673368912235;;; -8.289845769066552 -9.130057802435983 … -4.149589911945458 -6.287956204739621; -9.130057802435982 -9.130057819838946 … -5.294353665849902 -7.54739921503727; … ; -4.149589911945458 -5.294353665849902 … -1.9094492500178113 -2.894612364489231; -6.287956204739621 -7.547399215037271 … -2.894612364489232 -4.4855427519122095;;; -11.100308387033616 -11.100308365268589 … -6.287956204739622 -9.111848216111687; -11.100308365268589 -10.053883816987708 … -7.547399215037272 -10.053883816987756; … ; -6.287956204739622 -7.547399215037269 … -2.8946123644892316 -4.4855427519122095; -9.111848216111687 -10.053883816987756 … -4.4855427519122095 -6.871104522520434]), 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 = [0.0011111008046654344 - 0.0003609848301014372im -0.0010470880192735392 + 0.0018738890577838993im … 7.793440493785754e-5 + 9.63711391803253e-5im 0.0019543266163967467 + 0.0009901637454476566im; 0.00067633480650981 - 0.0011460197480392094im 0.00029882228061928933 + 0.000614236588738006im … -0.0005718318630828644 - 0.00041149806967471624im 0.002036803803375606 - 0.0006457528885053349im; … ; 0.0005945457499440192 + 0.002242473868971182im 0.0016225897956232897 + 0.0009811832591925644im … 0.001316168039486847 - 0.00039348984725216677im 0.0005121619438004932 - 0.0007877498330243145im; 0.0040515745103603725 + 0.0023545551691197897im 0.0019167871184487813 - 0.00043748603830696476im … -0.0010299317010713542 + 0.0017367976363040134im 0.0009740315071975472 + 0.003482887788203453im;;; 0.0035304211102000736 + 0.03629979479619541im 0.07464106551336375 + 0.060868805246715715im … -0.016118258182833026 + 0.0010757667192022105im -0.002200807621577921 + 0.0025202425583950422im; 0.013507220734812034 + 0.01094065906291535im 0.05537445876284958 - 0.005778868606278185im … -0.006047496571957141 + 0.006379067320621193im -0.0030698671053859816 - 0.026127919967649304im; … ; 0.06326133108829655 - 0.005327965302632978im 0.007510538406257008 - 0.006721282554515092im … 0.005335809771311353 + 0.04255193873414672im 0.056807422789042154 + 0.045534825450053336im; -0.003290182942341617 + 0.007946087015301823im 0.0073842969235161475 + 0.05859835999102836im … 0.011485690680737116 + 0.009680688584762762im 0.02318263236960778 - 0.0009202445938811497im;;; 0.042362989246126775 + 0.03490246481902899im 0.09172084280291154 - 0.008851845071836313im … 0.00300567965722672 - 0.005721870400202224im -0.0025704317445895165 - 0.015025375616562997im; -0.02444149648382394 + 0.0038043907750448776im -0.003395871067504821 + 0.0051405720195620876im … -0.0007977927991669482 - 0.0011669399002903254im -0.03586734126745522 - 0.02797559097269353im; … ; -0.0010628182645064013 + 0.00504695192442382im 0.009981419515803036 + 0.07258771956958979im … 0.06273462481635125 + 0.049100418636208426im 0.05944367257288431 - 0.005840752189575883im; 0.009962391579486276 + 0.07731696691011333im 0.1014908960849431 + 0.08103966401126132im … 0.02879573130917226 - 0.003526102178134681im -0.00013265740138293514 + 0.002269688070651514im;;; … ;;; -0.01197635594059224 - 0.09767569205590984im -0.06128241515415424 - 0.047939437574638186im … 0.00947634871069059 + 0.00015628742190249706im 0.036492866987928155 - 0.04445305772200311im; -0.09109831814478021 - 0.07127784774673644im -0.08442213474596584 + 0.010797984817910063im … 0.01306819009317476 - 0.01268427136448052im -0.01017852790375735 - 0.09847844397366823im; … ; -0.09027122697133064 + 0.011961385838465101im -0.03594603174968401 + 0.04656113350261856im … -0.0031326915545403997 - 0.020947657083525622im -0.08306792176585194 - 0.06292285772801803im; -0.013171110164753808 + 0.01688481470207278im 0.0009887117944930648 + 0.007561793526455161im … -0.011632158756530793 - 0.008502449899360203im -0.054479025862260166 + 0.007704789597660716im;;; -0.06311656846711247 - 0.04895788107819672im -0.06935877938965401 + 0.008645451373759596im … 0.019270106702243238 - 0.022842223803308415im -0.0026553162812238103 - 0.027232340643639212im; 0.0025622252397323395 + 0.0008176915184831086im 0.014454949773204372 - 0.01682818294398337im … -0.0010344524846069457 - 0.02616399094326409im -0.006919476445718881 - 0.00650179644905865im; … ; -0.012297073669282945 + 0.0171173045639065im 0.0008614018004894277 + 0.005994233265573162im … -0.040981894848265234 - 0.03032560297957791im -0.08491523702009625 + 0.012700569604062389im; -0.007261593679778307 - 0.051291529491994635im -0.03102555958823147 - 0.02337451729509406im … 0.027255023994147785 - 0.0025075374820679236im 0.005145915580225766 - 0.005792590345454402im;;; -0.052184947395726225 + 0.007340337531336836im -0.016832126587676806 + 0.021054970877049984im … 0.0032538617704216746 + 0.02565476498905643im -0.012994936278389935 - 0.009801232693879008im; 0.024335276528172915 - 0.027809989653528808im -0.0033574990712947894 - 0.029588556391179674im … 0.0219723177108724 + 0.016118217722045566im 0.05020584483734247 - 0.005066145053279524im; … ; -0.006975022265331494 - 0.059150288560092176im -0.02862042712097038 - 0.021699942076349347im … -0.017463873240777687 + 0.004040321316782898im 0.010647495019168403 - 0.009855987734906334im; -0.07291463734189754 - 0.05459750573490611im -0.058550999012526736 + 0.008093979280173805im … 0.001849226283715282 - 0.0026481522311379863im -0.0050183166302241 - 0.033796993993657334im],)]), 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), [-12.247569697884419 -11.100308387033586 … -8.289845769066552 -11.100308387033616; -11.100308387033586 -9.13005781848181 … -9.130057802435983 -11.100308365268589; … ; -8.289845769066552 -9.130057802435982 … -4.149589911945458 -6.287956204739622; -11.100308387033614 -11.100308365268589 … -6.287956204739623 -9.111848216111685;;; -11.100308387033587 -9.130057818481808 … -9.130057802435983 -11.100308365268589; -9.130057818481808 -6.903159504367228 … -9.130057819838948 -10.053883816987707; … ; -9.130057802435983 -9.130057819838942 … -5.294353665849902 -7.547399215037271; -11.100308365268589 -10.053883816987707 … -7.547399215037271 -10.053883816987758;;; -8.289845769066698 -6.307621938057083 … -8.289845773669612 -9.111848200065838; -6.307621938057082 -4.516655658355579 … -7.547399231891912 -7.547399215037385; … ; -8.289845773669612 -7.54739923189191 … -5.768969098395666 -7.547399231891946; -9.11184820006584 -7.547399215037384 … -7.547399231891947 -9.111848217468935;;; … ;;; -5.301031708535731 -6.307621951398928 … -2.5497035798114878 -3.8495821823326954; -6.307621951398928 -6.903159511447077 … -3.3290606941627447 -4.878419351559241; … ; -2.5497035798114873 -3.3290606941627447 … -1.256798467534477 -1.8141947489913153; -3.849582182332695 -4.878419351559241 … -1.8141947489913173 -2.7147673368912235;;; -8.289845769066552 -9.130057802435983 … -4.149589911945458 -6.287956204739621; -9.130057802435982 -9.130057819838946 … -5.294353665849902 -7.54739921503727; … ; -4.149589911945458 -5.294353665849902 … -1.9094492500178113 -2.894612364489231; -6.287956204739621 -7.547399215037271 … -2.894612364489232 -4.4855427519122095;;; -11.100308387033616 -11.100308365268589 … -6.287956204739622 -9.111848216111687; -11.100308365268589 -10.053883816987708 … -7.547399215037272 -10.053883816987756; … ; -6.287956204739622 -7.547399215037269 … -2.8946123644892316 -4.4855427519122095; -9.111848216111687 -10.053883816987756 … -4.4855427519122095 -6.871104522520434])], 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), [-12.247569697884419 -11.100308387033586 … -8.289845769066552 -11.100308387033616; -11.100308387033586 -9.13005781848181 … -9.130057802435983 -11.100308365268589; … ; -8.289845769066552 -9.130057802435982 … -4.149589911945458 -6.287956204739622; -11.100308387033614 -11.100308365268589 … -6.287956204739623 -9.111848216111685;;; -11.100308387033587 -9.130057818481808 … -9.130057802435983 -11.100308365268589; -9.130057818481808 -6.903159504367228 … -9.130057819838948 -10.053883816987707; … ; -9.130057802435983 -9.130057819838942 … -5.294353665849902 -7.547399215037271; -11.100308365268589 -10.053883816987707 … -7.547399215037271 -10.053883816987758;;; -8.289845769066698 -6.307621938057083 … -8.289845773669612 -9.111848200065838; -6.307621938057082 -4.516655658355579 … -7.547399231891912 -7.547399215037385; … ; -8.289845773669612 -7.54739923189191 … -5.768969098395666 -7.547399231891946; -9.11184820006584 -7.547399215037384 … -7.547399231891947 -9.111848217468935;;; … ;;; -5.301031708535731 -6.307621951398928 … -2.5497035798114878 -3.8495821823326954; -6.307621951398928 -6.903159511447077 … -3.3290606941627447 -4.878419351559241; … ; -2.5497035798114873 -3.3290606941627447 … -1.256798467534477 -1.8141947489913153; -3.849582182332695 -4.878419351559241 … -1.8141947489913173 -2.7147673368912235;;; -8.289845769066552 -9.130057802435983 … -4.149589911945458 -6.287956204739621; -9.130057802435982 -9.130057819838946 … -5.294353665849902 -7.54739921503727; … ; -4.149589911945458 -5.294353665849902 … -1.9094492500178113 -2.894612364489231; -6.287956204739621 -7.547399215037271 … -2.894612364489232 -4.4855427519122095;;; -11.100308387033616 -11.100308365268589 … -6.287956204739622 -9.111848216111687; -11.100308365268589 -10.053883816987708 … -7.547399215037272 -10.053883816987756; … ; -6.287956204739622 -7.547399215037269 … -2.8946123644892316 -4.4855427519122095; -9.111848216111687 -10.053883816987756 … -4.4855427519122095 -6.871104522520434]), 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 = [0.0011111008046654344 - 0.0003609848301014372im -0.0010470880192735392 + 0.0018738890577838993im … 7.793440493785754e-5 + 9.63711391803253e-5im 0.0019543266163967467 + 0.0009901637454476566im; 0.00067633480650981 - 0.0011460197480392094im 0.00029882228061928933 + 0.000614236588738006im … -0.0005718318630828644 - 0.00041149806967471624im 0.002036803803375606 - 0.0006457528885053349im; … ; 0.0005945457499440192 + 0.002242473868971182im 0.0016225897956232897 + 0.0009811832591925644im … 0.001316168039486847 - 0.00039348984725216677im 0.0005121619438004932 - 0.0007877498330243145im; 0.0040515745103603725 + 0.0023545551691197897im 0.0019167871184487813 - 0.00043748603830696476im … -0.0010299317010713542 + 0.0017367976363040134im 0.0009740315071975472 + 0.003482887788203453im;;; 0.0035304211102000736 + 0.03629979479619541im 0.07464106551336375 + 0.060868805246715715im … -0.016118258182833026 + 0.0010757667192022105im -0.002200807621577921 + 0.0025202425583950422im; 0.013507220734812034 + 0.01094065906291535im 0.05537445876284958 - 0.005778868606278185im … -0.006047496571957141 + 0.006379067320621193im -0.0030698671053859816 - 0.026127919967649304im; … ; 0.06326133108829655 - 0.005327965302632978im 0.007510538406257008 - 0.006721282554515092im … 0.005335809771311353 + 0.04255193873414672im 0.056807422789042154 + 0.045534825450053336im; -0.003290182942341617 + 0.007946087015301823im 0.0073842969235161475 + 0.05859835999102836im … 0.011485690680737116 + 0.009680688584762762im 0.02318263236960778 - 0.0009202445938811497im;;; 0.042362989246126775 + 0.03490246481902899im 0.09172084280291154 - 0.008851845071836313im … 0.00300567965722672 - 0.005721870400202224im -0.0025704317445895165 - 0.015025375616562997im; -0.02444149648382394 + 0.0038043907750448776im -0.003395871067504821 + 0.0051405720195620876im … -0.0007977927991669482 - 0.0011669399002903254im -0.03586734126745522 - 0.02797559097269353im; … ; -0.0010628182645064013 + 0.00504695192442382im 0.009981419515803036 + 0.07258771956958979im … 0.06273462481635125 + 0.049100418636208426im 0.05944367257288431 - 0.005840752189575883im; 0.009962391579486276 + 0.07731696691011333im 0.1014908960849431 + 0.08103966401126132im … 0.02879573130917226 - 0.003526102178134681im -0.00013265740138293514 + 0.002269688070651514im;;; … ;;; -0.01197635594059224 - 0.09767569205590984im -0.06128241515415424 - 0.047939437574638186im … 0.00947634871069059 + 0.00015628742190249706im 0.036492866987928155 - 0.04445305772200311im; -0.09109831814478021 - 0.07127784774673644im -0.08442213474596584 + 0.010797984817910063im … 0.01306819009317476 - 0.01268427136448052im -0.01017852790375735 - 0.09847844397366823im; … ; -0.09027122697133064 + 0.011961385838465101im -0.03594603174968401 + 0.04656113350261856im … -0.0031326915545403997 - 0.020947657083525622im -0.08306792176585194 - 0.06292285772801803im; -0.013171110164753808 + 0.01688481470207278im 0.0009887117944930648 + 0.007561793526455161im … -0.011632158756530793 - 0.008502449899360203im -0.054479025862260166 + 0.007704789597660716im;;; -0.06311656846711247 - 0.04895788107819672im -0.06935877938965401 + 0.008645451373759596im … 0.019270106702243238 - 0.022842223803308415im -0.0026553162812238103 - 0.027232340643639212im; 0.0025622252397323395 + 0.0008176915184831086im 0.014454949773204372 - 0.01682818294398337im … -0.0010344524846069457 - 0.02616399094326409im -0.006919476445718881 - 0.00650179644905865im; … ; -0.012297073669282945 + 0.0171173045639065im 0.0008614018004894277 + 0.005994233265573162im … -0.040981894848265234 - 0.03032560297957791im -0.08491523702009625 + 0.012700569604062389im; -0.007261593679778307 - 0.051291529491994635im -0.03102555958823147 - 0.02337451729509406im … 0.027255023994147785 - 0.0025075374820679236im 0.005145915580225766 - 0.005792590345454402im;;; -0.052184947395726225 + 0.007340337531336836im -0.016832126587676806 + 0.021054970877049984im … 0.0032538617704216746 + 0.02565476498905643im -0.012994936278389935 - 0.009801232693879008im; 0.024335276528172915 - 0.027809989653528808im -0.0033574990712947894 - 0.029588556391179674im … 0.0219723177108724 + 0.016118217722045566im 0.05020584483734247 - 0.005066145053279524im; … ; -0.006975022265331494 - 0.059150288560092176im -0.02862042712097038 - 0.021699942076349347im … -0.017463873240777687 + 0.004040321316782898im 0.010647495019168403 - 0.009855987734906334im; -0.07291463734189754 - 0.05459750573490611im -0.058550999012526736 + 0.008093979280173805im … 0.001849226283715282 - 0.0026481522311379863im -0.0050183166302241 - 0.033796993993657334im],)]), 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), [-12.247569697884419 -11.100308387033586 … -8.289845769066552 -11.100308387033616; -11.100308387033586 -9.13005781848181 … -9.130057802435983 -11.100308365268589; … ; -8.289845769066552 -9.130057802435982 … -4.149589911945458 -6.287956204739622; -11.100308387033614 -11.100308365268589 … -6.287956204739623 -9.111848216111685;;; -11.100308387033587 -9.130057818481808 … -9.130057802435983 -11.100308365268589; -9.130057818481808 -6.903159504367228 … -9.130057819838948 -10.053883816987707; … ; -9.130057802435983 -9.130057819838942 … -5.294353665849902 -7.547399215037271; -11.100308365268589 -10.053883816987707 … -7.547399215037271 -10.053883816987758;;; -8.289845769066698 -6.307621938057083 … -8.289845773669612 -9.111848200065838; -6.307621938057082 -4.516655658355579 … -7.547399231891912 -7.547399215037385; … ; -8.289845773669612 -7.54739923189191 … -5.768969098395666 -7.547399231891946; -9.11184820006584 -7.547399215037384 … -7.547399231891947 -9.111848217468935;;; … ;;; -5.301031708535731 -6.307621951398928 … -2.5497035798114878 -3.8495821823326954; -6.307621951398928 -6.903159511447077 … -3.3290606941627447 -4.878419351559241; … ; -2.5497035798114873 -3.3290606941627447 … -1.256798467534477 -1.8141947489913153; -3.849582182332695 -4.878419351559241 … -1.8141947489913173 -2.7147673368912235;;; -8.289845769066552 -9.130057802435983 … -4.149589911945458 -6.287956204739621; -9.130057802435982 -9.130057819838946 … -5.294353665849902 -7.54739921503727; … ; -4.149589911945458 -5.294353665849902 … -1.9094492500178113 -2.894612364489231; -6.287956204739621 -7.547399215037271 … -2.894612364489232 -4.4855427519122095;;; -11.100308387033616 -11.100308365268589 … -6.287956204739622 -9.111848216111687; -11.100308365268589 -10.053883816987708 … -7.547399215037272 -10.053883816987756; … ; -6.287956204739622 -7.547399215037269 … -2.8946123644892316 -4.4855427519122095; -9.111848216111687 -10.053883816987756 … -4.4855427519122095 -6.871104522520434])], 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), [-12.247569697884419 -11.100308387033586 … -8.289845769066552 -11.100308387033616; -11.100308387033586 -9.13005781848181 … -9.130057802435983 -11.100308365268589; … ; -8.289845769066552 -9.130057802435982 … -4.149589911945458 -6.287956204739622; -11.100308387033614 -11.100308365268589 … -6.287956204739623 -9.111848216111685;;; -11.100308387033587 -9.130057818481808 … -9.130057802435983 -11.100308365268589; -9.130057818481808 -6.903159504367228 … -9.130057819838948 -10.053883816987707; … ; -9.130057802435983 -9.130057819838942 … -5.294353665849902 -7.547399215037271; -11.100308365268589 -10.053883816987707 … -7.547399215037271 -10.053883816987758;;; -8.289845769066698 -6.307621938057083 … -8.289845773669612 -9.111848200065838; -6.307621938057082 -4.516655658355579 … -7.547399231891912 -7.547399215037385; … ; -8.289845773669612 -7.54739923189191 … -5.768969098395666 -7.547399231891946; -9.11184820006584 -7.547399215037384 … -7.547399231891947 -9.111848217468935;;; … ;;; -5.301031708535731 -6.307621951398928 … -2.5497035798114878 -3.8495821823326954; -6.307621951398928 -6.903159511447077 … -3.3290606941627447 -4.878419351559241; … ; -2.5497035798114873 -3.3290606941627447 … -1.256798467534477 -1.8141947489913153; -3.849582182332695 -4.878419351559241 … -1.8141947489913173 -2.7147673368912235;;; -8.289845769066552 -9.130057802435983 … -4.149589911945458 -6.287956204739621; -9.130057802435982 -9.130057819838946 … -5.294353665849902 -7.54739921503727; … ; -4.149589911945458 -5.294353665849902 … -1.9094492500178113 -2.894612364489231; -6.287956204739621 -7.547399215037271 … -2.894612364489232 -4.4855427519122095;;; -11.100308387033616 -11.100308365268589 … -6.287956204739622 -9.111848216111687; -11.100308365268589 -10.053883816987708 … -7.547399215037272 -10.053883816987756; … ; -6.287956204739622 -7.547399215037269 … -2.8946123644892316 -4.4855427519122095; -9.111848216111687 -10.053883816987756 … -4.4855427519122095 -6.871104522520434]), 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 = [0.0011111008046654344 - 0.0003609848301014372im -0.0010470880192735392 + 0.0018738890577838993im … 7.793440493785754e-5 + 9.63711391803253e-5im 0.0019543266163967467 + 0.0009901637454476566im; 0.00067633480650981 - 0.0011460197480392094im 0.00029882228061928933 + 0.000614236588738006im … -0.0005718318630828644 - 0.00041149806967471624im 0.002036803803375606 - 0.0006457528885053349im; … ; 0.0005945457499440192 + 0.002242473868971182im 0.0016225897956232897 + 0.0009811832591925644im … 0.001316168039486847 - 0.00039348984725216677im 0.0005121619438004932 - 0.0007877498330243145im; 0.0040515745103603725 + 0.0023545551691197897im 0.0019167871184487813 - 0.00043748603830696476im … -0.0010299317010713542 + 0.0017367976363040134im 0.0009740315071975472 + 0.003482887788203453im;;; 0.0035304211102000736 + 0.03629979479619541im 0.07464106551336375 + 0.060868805246715715im … -0.016118258182833026 + 0.0010757667192022105im -0.002200807621577921 + 0.0025202425583950422im; 0.013507220734812034 + 0.01094065906291535im 0.05537445876284958 - 0.005778868606278185im … -0.006047496571957141 + 0.006379067320621193im -0.0030698671053859816 - 0.026127919967649304im; … ; 0.06326133108829655 - 0.005327965302632978im 0.007510538406257008 - 0.006721282554515092im … 0.005335809771311353 + 0.04255193873414672im 0.056807422789042154 + 0.045534825450053336im; -0.003290182942341617 + 0.007946087015301823im 0.0073842969235161475 + 0.05859835999102836im … 0.011485690680737116 + 0.009680688584762762im 0.02318263236960778 - 0.0009202445938811497im;;; 0.042362989246126775 + 0.03490246481902899im 0.09172084280291154 - 0.008851845071836313im … 0.00300567965722672 - 0.005721870400202224im -0.0025704317445895165 - 0.015025375616562997im; -0.02444149648382394 + 0.0038043907750448776im -0.003395871067504821 + 0.0051405720195620876im … -0.0007977927991669482 - 0.0011669399002903254im -0.03586734126745522 - 0.02797559097269353im; … ; -0.0010628182645064013 + 0.00504695192442382im 0.009981419515803036 + 0.07258771956958979im … 0.06273462481635125 + 0.049100418636208426im 0.05944367257288431 - 0.005840752189575883im; 0.009962391579486276 + 0.07731696691011333im 0.1014908960849431 + 0.08103966401126132im … 0.02879573130917226 - 0.003526102178134681im -0.00013265740138293514 + 0.002269688070651514im;;; … ;;; -0.01197635594059224 - 0.09767569205590984im -0.06128241515415424 - 0.047939437574638186im … 0.00947634871069059 + 0.00015628742190249706im 0.036492866987928155 - 0.04445305772200311im; -0.09109831814478021 - 0.07127784774673644im -0.08442213474596584 + 0.010797984817910063im … 0.01306819009317476 - 0.01268427136448052im -0.01017852790375735 - 0.09847844397366823im; … ; -0.09027122697133064 + 0.011961385838465101im -0.03594603174968401 + 0.04656113350261856im … -0.0031326915545403997 - 0.020947657083525622im -0.08306792176585194 - 0.06292285772801803im; -0.013171110164753808 + 0.01688481470207278im 0.0009887117944930648 + 0.007561793526455161im … -0.011632158756530793 - 0.008502449899360203im -0.054479025862260166 + 0.007704789597660716im;;; -0.06311656846711247 - 0.04895788107819672im -0.06935877938965401 + 0.008645451373759596im … 0.019270106702243238 - 0.022842223803308415im -0.0026553162812238103 - 0.027232340643639212im; 0.0025622252397323395 + 0.0008176915184831086im 0.014454949773204372 - 0.01682818294398337im … -0.0010344524846069457 - 0.02616399094326409im -0.006919476445718881 - 0.00650179644905865im; … ; -0.012297073669282945 + 0.0171173045639065im 0.0008614018004894277 + 0.005994233265573162im … -0.040981894848265234 - 0.03032560297957791im -0.08491523702009625 + 0.012700569604062389im; -0.007261593679778307 - 0.051291529491994635im -0.03102555958823147 - 0.02337451729509406im … 0.027255023994147785 - 0.0025075374820679236im 0.005145915580225766 - 0.005792590345454402im;;; -0.052184947395726225 + 0.007340337531336836im -0.016832126587676806 + 0.021054970877049984im … 0.0032538617704216746 + 0.02565476498905643im -0.012994936278389935 - 0.009801232693879008im; 0.024335276528172915 - 0.027809989653528808im -0.0033574990712947894 - 0.029588556391179674im … 0.0219723177108724 + 0.016118217722045566im 0.05020584483734247 - 0.005066145053279524im; … ; -0.006975022265331494 - 0.059150288560092176im -0.02862042712097038 - 0.021699942076349347im … -0.017463873240777687 + 0.004040321316782898im 0.010647495019168403 - 0.009855987734906334im; -0.07291463734189754 - 0.05459750573490611im -0.058550999012526736 + 0.008093979280173805im … 0.001849226283715282 - 0.0026481522311379863im -0.0050183166302241 - 0.033796993993657334im],)]), 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), [-12.247569697884419 -11.100308387033586 … -8.289845769066552 -11.100308387033616; -11.100308387033586 -9.13005781848181 … -9.130057802435983 -11.100308365268589; … ; -8.289845769066552 -9.130057802435982 … -4.149589911945458 -6.287956204739622; -11.100308387033614 -11.100308365268589 … -6.287956204739623 -9.111848216111685;;; -11.100308387033587 -9.130057818481808 … -9.130057802435983 -11.100308365268589; -9.130057818481808 -6.903159504367228 … -9.130057819838948 -10.053883816987707; … ; -9.130057802435983 -9.130057819838942 … -5.294353665849902 -7.547399215037271; -11.100308365268589 -10.053883816987707 … -7.547399215037271 -10.053883816987758;;; -8.289845769066698 -6.307621938057083 … -8.289845773669612 -9.111848200065838; -6.307621938057082 -4.516655658355579 … -7.547399231891912 -7.547399215037385; … ; -8.289845773669612 -7.54739923189191 … -5.768969098395666 -7.547399231891946; -9.11184820006584 -7.547399215037384 … -7.547399231891947 -9.111848217468935;;; … ;;; -5.301031708535731 -6.307621951398928 … -2.5497035798114878 -3.8495821823326954; -6.307621951398928 -6.903159511447077 … -3.3290606941627447 -4.878419351559241; … ; -2.5497035798114873 -3.3290606941627447 … -1.256798467534477 -1.8141947489913153; -3.849582182332695 -4.878419351559241 … -1.8141947489913173 -2.7147673368912235;;; -8.289845769066552 -9.130057802435983 … -4.149589911945458 -6.287956204739621; -9.130057802435982 -9.130057819838946 … -5.294353665849902 -7.54739921503727; … ; -4.149589911945458 -5.294353665849902 … -1.9094492500178113 -2.894612364489231; -6.287956204739621 -7.547399215037271 … -2.894612364489232 -4.4855427519122095;;; -11.100308387033616 -11.100308365268589 … -6.287956204739622 -9.111848216111687; -11.100308365268589 -10.053883816987708 … -7.547399215037272 -10.053883816987756; … ; -6.287956204739622 -7.547399215037269 … -2.8946123644892316 -4.4855427519122095; -9.111848216111687 -10.053883816987756 … -4.4855427519122095 -6.871104522520434])], 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), [-12.247569697884419 -11.100308387033586 … -8.289845769066552 -11.100308387033616; -11.100308387033586 -9.13005781848181 … -9.130057802435983 -11.100308365268589; … ; -8.289845769066552 -9.130057802435982 … -4.149589911945458 -6.287956204739622; -11.100308387033614 -11.100308365268589 … -6.287956204739623 -9.111848216111685;;; -11.100308387033587 -9.130057818481808 … -9.130057802435983 -11.100308365268589; -9.130057818481808 -6.903159504367228 … -9.130057819838948 -10.053883816987707; … ; -9.130057802435983 -9.130057819838942 … -5.294353665849902 -7.547399215037271; -11.100308365268589 -10.053883816987707 … -7.547399215037271 -10.053883816987758;;; -8.289845769066698 -6.307621938057083 … -8.289845773669612 -9.111848200065838; -6.307621938057082 -4.516655658355579 … -7.547399231891912 -7.547399215037385; … ; -8.289845773669612 -7.54739923189191 … -5.768969098395666 -7.547399231891946; -9.11184820006584 -7.547399215037384 … -7.547399231891947 -9.111848217468935;;; … ;;; -5.301031708535731 -6.307621951398928 … -2.5497035798114878 -3.8495821823326954; -6.307621951398928 -6.903159511447077 … -3.3290606941627447 -4.878419351559241; … ; -2.5497035798114873 -3.3290606941627447 … -1.256798467534477 -1.8141947489913153; -3.849582182332695 -4.878419351559241 … -1.8141947489913173 -2.7147673368912235;;; -8.289845769066552 -9.130057802435983 … -4.149589911945458 -6.287956204739621; -9.130057802435982 -9.130057819838946 … -5.294353665849902 -7.54739921503727; … ; -4.149589911945458 -5.294353665849902 … -1.9094492500178113 -2.894612364489231; -6.287956204739621 -7.547399215037271 … -2.894612364489232 -4.4855427519122095;;; -11.100308387033616 -11.100308365268589 … -6.287956204739622 -9.111848216111687; -11.100308365268589 -10.053883816987708 … -7.547399215037272 -10.053883816987756; … ; -6.287956204739622 -7.547399215037269 … -2.8946123644892316 -4.4855427519122095; -9.111848216111687 -10.053883816987756 … -4.4855427519122095 -6.871104522520434]), 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 = [0.0011111008046654344 - 0.0003609848301014372im -0.0010470880192735392 + 0.0018738890577838993im … 7.793440493785754e-5 + 9.63711391803253e-5im 0.0019543266163967467 + 0.0009901637454476566im; 0.00067633480650981 - 0.0011460197480392094im 0.00029882228061928933 + 0.000614236588738006im … -0.0005718318630828644 - 0.00041149806967471624im 0.002036803803375606 - 0.0006457528885053349im; … ; 0.0005945457499440192 + 0.002242473868971182im 0.0016225897956232897 + 0.0009811832591925644im … 0.001316168039486847 - 0.00039348984725216677im 0.0005121619438004932 - 0.0007877498330243145im; 0.0040515745103603725 + 0.0023545551691197897im 0.0019167871184487813 - 0.00043748603830696476im … -0.0010299317010713542 + 0.0017367976363040134im 0.0009740315071975472 + 0.003482887788203453im;;; 0.0035304211102000736 + 0.03629979479619541im 0.07464106551336375 + 0.060868805246715715im … -0.016118258182833026 + 0.0010757667192022105im -0.002200807621577921 + 0.0025202425583950422im; 0.013507220734812034 + 0.01094065906291535im 0.05537445876284958 - 0.005778868606278185im … -0.006047496571957141 + 0.006379067320621193im -0.0030698671053859816 - 0.026127919967649304im; … ; 0.06326133108829655 - 0.005327965302632978im 0.007510538406257008 - 0.006721282554515092im … 0.005335809771311353 + 0.04255193873414672im 0.056807422789042154 + 0.045534825450053336im; -0.003290182942341617 + 0.007946087015301823im 0.0073842969235161475 + 0.05859835999102836im … 0.011485690680737116 + 0.009680688584762762im 0.02318263236960778 - 0.0009202445938811497im;;; 0.042362989246126775 + 0.03490246481902899im 0.09172084280291154 - 0.008851845071836313im … 0.00300567965722672 - 0.005721870400202224im -0.0025704317445895165 - 0.015025375616562997im; -0.02444149648382394 + 0.0038043907750448776im -0.003395871067504821 + 0.0051405720195620876im … -0.0007977927991669482 - 0.0011669399002903254im -0.03586734126745522 - 0.02797559097269353im; … ; -0.0010628182645064013 + 0.00504695192442382im 0.009981419515803036 + 0.07258771956958979im … 0.06273462481635125 + 0.049100418636208426im 0.05944367257288431 - 0.005840752189575883im; 0.009962391579486276 + 0.07731696691011333im 0.1014908960849431 + 0.08103966401126132im … 0.02879573130917226 - 0.003526102178134681im -0.00013265740138293514 + 0.002269688070651514im;;; … ;;; -0.01197635594059224 - 0.09767569205590984im -0.06128241515415424 - 0.047939437574638186im … 0.00947634871069059 + 0.00015628742190249706im 0.036492866987928155 - 0.04445305772200311im; -0.09109831814478021 - 0.07127784774673644im -0.08442213474596584 + 0.010797984817910063im … 0.01306819009317476 - 0.01268427136448052im -0.01017852790375735 - 0.09847844397366823im; … ; -0.09027122697133064 + 0.011961385838465101im -0.03594603174968401 + 0.04656113350261856im … -0.0031326915545403997 - 0.020947657083525622im -0.08306792176585194 - 0.06292285772801803im; -0.013171110164753808 + 0.01688481470207278im 0.0009887117944930648 + 0.007561793526455161im … -0.011632158756530793 - 0.008502449899360203im -0.054479025862260166 + 0.007704789597660716im;;; -0.06311656846711247 - 0.04895788107819672im -0.06935877938965401 + 0.008645451373759596im … 0.019270106702243238 - 0.022842223803308415im -0.0026553162812238103 - 0.027232340643639212im; 0.0025622252397323395 + 0.0008176915184831086im 0.014454949773204372 - 0.01682818294398337im … -0.0010344524846069457 - 0.02616399094326409im -0.006919476445718881 - 0.00650179644905865im; … ; -0.012297073669282945 + 0.0171173045639065im 0.0008614018004894277 + 0.005994233265573162im … -0.040981894848265234 - 0.03032560297957791im -0.08491523702009625 + 0.012700569604062389im; -0.007261593679778307 - 0.051291529491994635im -0.03102555958823147 - 0.02337451729509406im … 0.027255023994147785 - 0.0025075374820679236im 0.005145915580225766 - 0.005792590345454402im;;; -0.052184947395726225 + 0.007340337531336836im -0.016832126587676806 + 0.021054970877049984im … 0.0032538617704216746 + 0.02565476498905643im -0.012994936278389935 - 0.009801232693879008im; 0.024335276528172915 - 0.027809989653528808im -0.0033574990712947894 - 0.029588556391179674im … 0.0219723177108724 + 0.016118217722045566im 0.05020584483734247 - 0.005066145053279524im; … ; -0.006975022265331494 - 0.059150288560092176im -0.02862042712097038 - 0.021699942076349347im … -0.017463873240777687 + 0.004040321316782898im 0.010647495019168403 - 0.009855987734906334im; -0.07291463734189754 - 0.05459750573490611im -0.058550999012526736 + 0.008093979280173805im … 0.001849226283715282 - 0.0026481522311379863im -0.0050183166302241 - 0.033796993993657334im],)])]), 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 = [7.589784543012971e-5 0.0011262712728101142 … 0.006697037549965901 0.0011262712728101227; 0.001126271272810116 0.005274334457266426 … 0.005274334457266456 0.0011262712728101294; … ; 0.006697037549965888 0.005274334457266448 … 0.02324475419083496 0.012258986825088448; 0.0011262712728101192 0.0011262712728101227 … 0.012258986825088459 0.003770008629830578;;; 0.0011262712728101181 0.005274334457266428 … 0.005274334457266466 0.001126271272810122; 0.0052743344572664325 0.014620065304478435 … 0.005274334457266455 0.0025880808747971865; … ; 0.0052743344572664585 0.005274334457266449 … 0.018107686645926564 0.008922003044604816; 0.0011262712728101192 0.0025880808747971835 … 0.008922003044604823 0.002588080874797193;;; 0.006697037549965861 0.016412109101352417 … 0.006697037549965891 0.00377000862983055; 0.016412109101352424 0.031277839315521305 … 0.00892200304460479 0.008922003044604783; … ; 0.006697037549965883 0.008922003044604783 … 0.016476756359233024 0.008922003044604812; 0.0037700086298305476 0.008922003044604776 … 0.00892200304460482 0.003770008629830566;;; … ;;; 0.01985383985315085 0.016412109101352438 … 0.03715667363539696 0.02719080068631961; 0.016412109101352445 0.01462006530447845 … 0.03230127212614944 0.022322100931446806; … ; 0.037156673635396945 0.03230127212614942 … 0.046296980701222346 0.04263658273118894; 0.0271908006863196 0.022322100931446796 … 0.042636582731188956 0.03477222914174091;;; 0.006697037549965877 0.005274334457266439 … 0.02324475419083493 0.012258986825088426; 0.005274334457266442 0.005274334457266426 … 0.018107686645926525 0.008922003044604797; … ; 0.023244754190834924 0.018107686645926522 … 0.04037111033534005 0.031491603811159515; 0.01225898682508842 0.00892200304460479 … 0.03149160381115953 0.020047163432551182;;; 0.001126271272810124 0.0011262712728101142 … 0.012258986825088442 0.0037700086298305636; 0.0011262712728101168 0.0025880808747971626 … 0.008922003044604802 0.002588080874797191; … ; 0.012258986825088435 0.008922003044604795 … 0.031491603811159535 0.020047163432551193; 0.0037700086298305593 0.0025880808747971874 … 0.020047163432551203 0.008952603496658714;;;;], eigenvalues = [[-0.17836835653828503, 0.26249194499331546, 0.2624919449933158, 0.26249194499331624, 0.35469214816864625, 0.35469214816864675, 0.35469214816894445], [-0.127550376177972, 0.06475320594793701, 0.22545166517580442, 0.2254516651758047, 0.3219776496122813, 0.38922276908554443, 0.38922276908554465], [-0.1081872921638458, 0.07755003473613922, 0.1727832801159487, 0.17278328011594882, 0.28435185361970894, 0.33054764843268536, 0.5267232426407323], [-0.05777325374281933, 0.012724782207023284, 0.09766073750167825, 0.18417825333106705, 0.3152284179597873, 0.4720312195091266, 0.49791351865919853]], 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 = 0.2734218993065126, n_iter = 10, ψ = Matrix{ComplexF64}[[0.31891365028269125 + 0.8944259448896305im 2.544262355697539e-13 + 2.2845571263726247e-13im … -7.33758667817217e-12 - 5.182941107154617e-12im -7.856056833456431e-8 - 4.873615521303269e-8im; 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0.207314802656641 - 0.33252514449494763im 0.3143952425477569 - 0.5352689493471704im … -0.09902439648584233 + 0.15270338174591613im 8.194099390146057e-7 - 1.3585031077781227e-6im; … ; -0.01290850160195798 + 0.0029939946214212238im -0.00024571176260281707 + 6.387378487597506e-5im … -0.012760649997856999 + 0.002721168761334491im 0.028405839880604678 - 0.03631102644313263im; 0.035495154792244146 - 0.05693289299611489im -0.002690978047427155 + 0.00458148469579183im … -0.07803901321645437 + 0.12034281460010364im -0.057131615938787135 - 0.46781247703229323im]], residual_norms = [[0.0, 0.0, 2.250668853555951e-12, 5.407850234579443e-12, 9.684468296798016e-11, 7.549653890203051e-11, 7.45400681976491e-7], [0.0, 0.0, 4.397609830040813e-12, 4.438469021049958e-12, 2.073539356276193e-10, 1.8371103756552236e-9, 1.805487651062926e-9], [0.0, 0.0, 2.921255255344674e-12, 4.711014812207785e-12, 3.224692421752087e-11, 7.419203009689656e-10, 1.0084479840713627e-6], [4.703953998295821e-12, 2.2364553289860037e-12, 5.803956530820655e-12, 4.503337186218019e-12, 2.3348192564124416e-9, 3.167269294753617e-5, 2.7008852631615396e-5]], n_iter = [4, 3, 3, 2], converged = 1, n_matvec = 106)], stage = :finalize, algorithm = "SCF", history_Δρ = [0.2107184035008771, 0.027653668349994682, 0.002315604585235642, 0.00025736576963159165, 9.354926554141446e-6, 8.855015438138895e-7, 3.6449867472177953e-8, 4.058840444297735e-9, 3.328191056128468e-10, 1.6941947810416034e-11], history_Etot = [-7.905262730602777, -7.910544161887576, -7.910593453015286, -7.910594393454353, -7.910594396445923, -7.910594396488381, -7.910594396488484, -7.9105943964884835, -7.910594396488483, -7.910594396488486], occupation_threshold = 1.0e-6, seed = 0x960665187e97f29b, runtime_ns = 0x00000000925a2380)