Achieving DFT convergence
Some systems are tricky to converge. Here are some collected tips and tricks you can try and which may help. Take these as a source of inspiration for what you can try. Your mileage may vary.
Even if modelling an insulator, add a temperature to your
Model. Values up to1e-2atomic units may be sometimes needed. Note, that this can change the physics of your system, so if in doubt perform a second SCF with a lower temperature afterwards, starting from the final density of the first.Increase the history size of the Anderson acceleration by passing a custom
solvertoself_consistent_field, e.g.solver = scf_anderson_solver(; m=15)(::DFTK.var"#anderson#822"{DFTK.var"#anderson#821#823"{Base.Pairs{Symbol, Int64, Nothing, @NamedTuple{m::Int64}}}}) (generic function with 1 method)All keyword arguments are passed through to
DFTK.AndersonAcceleration.Try increasing convergence for for the bands in each SCF step by increasing the
ratio_ρdiffparameter of theAdaptiveDiagtolalgorithm. For example:diagtolalg = AdaptiveDiagtol(; ratio_ρdiff=0.05)AdaptiveDiagtol(0.05, nothing, 0.005, 0.03)Increase the number of bands, which are fully converged in each SCF step by tweaking the
AdaptiveBandsalgorithm. For example:nbandsalg = AdaptiveBands(model; temperature_factor_converge=1.1)AdaptiveBands(4, 7, 1.0e-6, 0.01)Try the adaptive damping algorithm by using
DFTK.scf_potential_mixing_adaptiveinstead ofself_consistent_field:DFTK.scf_potential_mixing_adaptive(basis; tol=1e-10)(ham = Hamiltonian(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), HamiltonianBlock[DFTK.DftHamiltonianBlock(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749), DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749), [0.0, 0.5624107360872233, 2.249642944348893, 5.061696624785009, 8.998571777395572, 14.06026840218058, 14.06026840218058, 8.998571777395572, 5.061696624785009, 2.249642944348893 … 0.7498809814496308, 2.062172698986485, 4.499285888697785, 8.061220550583531, 12.747976684643724, 11.060744476382055, 6.748928833046679, 3.561934661885747, 1.499761962899262, 0.5624107360872233]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749), ComplexF64[0.11162114718647566 + 0.0im 0.17292273765511482 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.10094779392345996 + 0.0im 0.14590894423989453 + 0.0im … -0.05030254922547522 - 0.0im 0.0503025492254752 + 0.0im; … ; 0.08537828309138949 + 0.0im 0.10863402648960857 + 0.0im … -0.0 + 0.08075097926136235im 0.0 + 0.0im; 0.10094779392345996 + 0.0im 0.14590894423989453 + 0.0im … 0.05030254922547522 + 0.0im 0.0503025492254752 + 0.0im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749), [-12.247569668722283 -11.100308396742939 … -8.289845772413004 -11.100308396743; -11.100308396742937 -9.130057825948303 … -9.13005779589701 -11.100308356759962; … ; -8.289845772413004 -9.13005779589701 … -4.149589921643663 -6.287956198199807; -11.100308396742998 -11.100308356759964 … -6.287956198199808 -9.111848223578166;;; -11.10030839674294 -9.1300578259483 … -9.130057795897011 -11.100308356759964; -9.130057825948303 -6.903159481982448 … -9.130057827297984 -10.053883826552829; … ; -9.13005779589701 -9.130057827297984 … -5.294353669214802 -7.5473992065221625; -11.100308356759962 -10.053883826552829 … -7.547399206522163 -10.053883826552934;;; -8.289845772413303 -6.307621931517062 … -8.289845781012257 -9.111848193526836; -6.307621931517064 -4.516655665815938 … -7.5473992376119945 -7.547399206522395; … ; -8.289845781012255 -7.547399237611994 … -5.768969083581643 -7.5473992376120655; -9.111848193526836 -7.547399206522394 … -7.547399237612066 -9.111848224928073;;; … ;;; -5.3010317182501385 -6.307621955789271 … -2.5497035732763105 -3.849582179388152; -6.307621955789271 -6.903159495209277 … -3.3290606985465754 -4.878419358630989; … ; -2.54970357327631 -3.3290606985465754 … -1.2567984709027493 -1.814194746041345; -3.8495821793881526 -4.878419358630991 … -1.814194746041345 -2.714767335322931;;; -8.289845772413006 -9.13005779589701 … -4.149589921643665 -6.287956198199806; -9.130057795897011 -9.130057827297982 … -5.294353669214801 -7.547399206522162; … ; -4.149589921643665 -5.294353669214802 … -1.9094492399156084 -2.89461236785261; -6.287956198199807 -7.547399206522162 … -2.89461236785261 -4.485542759372458;;; -11.100308396743 -11.100308356759964 … -6.287956198199808 -9.111848223578164; -11.100308356759962 -10.053883826552829 … -7.547399206522164 -10.053883826552934; … ; -6.287956198199806 -7.547399206522164 … -2.8946123678526097 -4.485542759372456; -9.111848223578166 -10.053883826552934 … -4.485542759372458 -6.871104500135868])], 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), [-12.247569668722283 -11.100308396742939 … -8.289845772413004 -11.100308396743; -11.100308396742937 -9.130057825948303 … -9.13005779589701 -11.100308356759962; … ; -8.289845772413004 -9.13005779589701 … -4.149589921643663 -6.287956198199807; -11.100308396742998 -11.100308356759964 … -6.287956198199808 -9.111848223578166;;; -11.10030839674294 -9.1300578259483 … -9.130057795897011 -11.100308356759964; -9.130057825948303 -6.903159481982448 … -9.130057827297984 -10.053883826552829; … ; -9.13005779589701 -9.130057827297984 … -5.294353669214802 -7.5473992065221625; -11.100308356759962 -10.053883826552829 … -7.547399206522163 -10.053883826552934;;; -8.289845772413303 -6.307621931517062 … -8.289845781012257 -9.111848193526836; -6.307621931517064 -4.516655665815938 … -7.5473992376119945 -7.547399206522395; … ; -8.289845781012255 -7.547399237611994 … -5.768969083581643 -7.5473992376120655; -9.111848193526836 -7.547399206522394 … -7.547399237612066 -9.111848224928073;;; … ;;; -5.3010317182501385 -6.307621955789271 … -2.5497035732763105 -3.849582179388152; -6.307621955789271 -6.903159495209277 … -3.3290606985465754 -4.878419358630989; … ; -2.54970357327631 -3.3290606985465754 … -1.2567984709027493 -1.814194746041345; -3.8495821793881526 -4.878419358630991 … -1.814194746041345 -2.714767335322931;;; -8.289845772413006 -9.13005779589701 … -4.149589921643665 -6.287956198199806; -9.130057795897011 -9.130057827297982 … -5.294353669214801 -7.547399206522162; … ; -4.149589921643665 -5.294353669214802 … -1.9094492399156084 -2.89461236785261; -6.287956198199807 -7.547399206522162 … -2.89461236785261 -4.485542759372458;;; -11.100308396743 -11.100308356759964 … -6.287956198199808 -9.111848223578164; -11.100308356759962 -10.053883826552829 … -7.547399206522164 -10.053883826552934; … ; -6.287956198199806 -7.547399206522164 … -2.8946123678526097 -4.485542759372456; -9.111848223578166 -10.053883826552934 … -4.485542759372458 -6.871104500135868]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749), ComplexF64[0.11162114718647566 + 0.0im 0.17292273765511482 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.10094779392345996 + 0.0im 0.14590894423989453 + 0.0im … -0.05030254922547522 - 0.0im 0.0503025492254752 + 0.0im; … ; 0.08537828309138949 + 0.0im 0.10863402648960857 + 0.0im … -0.0 + 0.08075097926136235im 0.0 + 0.0im; 0.10094779392345996 + 0.0im 0.14590894423989453 + 0.0im … 0.05030254922547522 + 0.0im 0.0503025492254752 + 0.0im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, @NamedTuple{ψ_reals::Array{ComplexF64, 3}}[(ψ_reals = [-0.07468659453747624 + 0.015264474421902714im -0.019414512208085058 + 0.04167921907580607im … 0.021708492076634053 - 0.0036211268588260633im -0.044649985670889084 - 0.04932598798767728im; -0.005756176762505057 + 0.048315806140001125im 0.04780838433602964 + 0.03020695792380057im … -0.05808005880701449 - 0.04295428797972254im -0.07809174935835955 + 0.017676376697561662im; … ; -0.012267174796830935 - 0.009716835821504736im -0.03635985144900063 - 0.0167881654718173im … -0.08488953548695036 - 0.028240464454385304im -0.04587792264346983 + 0.05067444461656215im; -0.059183750291606205 - 0.035211262260511814im -0.0521619244763714 + 0.014759779759772475im … -0.03531049056156907 + 0.05892665471403081im 0.02027246981636905 - 0.006967156702470677im;;; -0.005112979725906814 - 0.0035924582671364794im -0.047510650696934525 - 0.04765820553269449im … 0.02054264210065048 - 0.05421124130544994im -0.05912068566964075 - 0.025021862157704487im; 0.02642129542410248 - 0.014923335925411521im -0.08117596829866269 - 0.024254765392070617im … -0.06696970100702718 + 0.005098080454407183im -0.01240475119251732 + 0.04045561129809858im; … ; -0.0073376669967497015 - 0.027263198671911695im -0.01089019825418594 - 0.03067736777329114im … -0.02932990076217424 - 0.019569607786586517im 0.003530649950646267 - 0.015704156990177305im; -0.027264356896183443 - 0.029525776815094898im -0.023249823629697918 - 0.05756183417896668im … 0.04559953934121378 + 0.01231584887492032im 0.017045309800286554 - 0.06012856300331485im;;; -0.006369933717468287 - 0.061738786338320285im -0.05574701513427621 - 0.024487982551734268im … 0.029943769672857466 - 0.08956505562390057im -0.0032766456635980393 - 0.05031421644707im; -0.03457032862173601 - 0.05447903028865845im -0.06825694830949153 + 0.03778771393241588im … -0.011523332790666531 + 0.011428622459966432im 0.03226468980485212 - 0.008648667576303854im; … ; 0.03945357191078647 - 0.08848603202608579im -0.018823679903354616 - 0.07815190900986341im … 0.02873019251828158 + 0.016721980639432196im 0.07995321060320004 - 0.0360740349269436im; -0.006730705046260896 - 0.11278072006550596im -0.06432028742071788 - 0.0636558675664317im … 0.11342930192567834 - 0.042708780908644724im 0.05614640768723832 - 0.12012322696472294im;;; … ;;; 0.00802419321301251 - 0.019949215764326893im 0.0857026278058646 + 0.07116790379526414im … 0.006225705010815539 - 0.01459498537146181im 0.05556978960885371 - 0.061924468097750214im; 0.03894478059121685 + 0.0319068944287782im 0.1260424490407743 + 0.0005750143168738869im … -0.03407661700871602 + 0.0007373845515821261im -0.003987632386441342 - 0.03864616421300787im; … ; 0.0873583580995294 - 0.001046577341783525im 0.0037024418768665237 + 0.0017953760366820233im … -0.04956728440760909 + 0.16206095056319725im 0.07099774093195849 + 0.08708641826589966im; 0.061260195493017124 - 0.06297366450325867im 0.012202607379009297 + 0.04498418302715276im … 0.0606885322014669 + 0.06786019873087398im 0.10627841028701898 - 0.008359781200309273im;;; 0.07576288553701535 + 0.07433553103900212im 0.17641532090330986 - 0.01271882414279523im … -0.08755629069866452 + 0.015922940617585292im -0.02331711790602923 + 0.04524762833288322im; 0.1254021412638914 - 0.015854203489270767im 0.10264929491777663 - 0.10631082636089272im … -0.026308732858681384 + 0.007928928955662065im 0.004948544914000394 - 0.004849075379957632im; … ; -0.055348757821552685 + 0.02367612871848971im 0.005597471468215267 + 0.08760046283539846im … 0.04657981642804638 + 0.043470749546971346im -0.03954893729972981 - 0.038811240827002554im; -0.021935598714693208 + 0.07260699913105714im 0.09416640899678602 + 0.08433811907213358im … -0.04319220829794605 - 0.049164991930531164im -0.07182111596262165 - 0.004774211814860374im;;; 0.054786534093582376 - 0.040672389054100984im 0.015917141654862216 - 0.052194350938285526im … -0.0311364278448307 + 0.061609344163279976im 0.0361494452638602 + 0.015942055567380674im; 0.020183413422849752 - 0.04985513529529212im -0.005311695810131745 - 0.014368889436896787im … -0.017833950625652656 - 0.030429884752671242im -0.0180409037028693 - 0.03613168627676606im; … ; -0.028070402596879207 + 0.11870678813804157im 0.04544591251092166 + 0.036661105991430326im … -0.06140275852978085 - 0.061110178535139434im -0.14947911405248038 + 0.04629456847721384im; 0.04276506190900751 + 0.037950523579263054im 0.054978570130502336 - 0.0225567921574365im … -0.12754033911000087 + 0.015485410558384255im -0.034477423142400834 + 0.11687232548748214im],)]), DFTK.DftHamiltonianBlock(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757), DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757), [0.062490081787469245, 0.9998413085995079, 3.062014007585993, 6.249008178746925, 10.5608238220823, 12.248056030343973, 7.561299896283778, 3.9993652343980317, 1.5622520446867312, 0.24996032714987704 … 2.7495635986486464, 5.561617279084762, 9.498492431695325, 14.560189056480331, 14.560189056480338, 9.498492431695325, 5.561617279084762, 2.7495635986486464, 1.0623313903869773, 0.49992065429975385]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757), ComplexF64[0.11038155824020969 + 0.0im 0.1697292679710574 + 0.0im … -0.009426647060181403 - 0.016327431653253982im 0.009426647060181401 + 0.01632743165325398im; 0.09335704685777356 + 0.0im 0.12740009431942179 + 0.0im … -0.052421044862493965 + 0.030265304362562334im 0.05242104486249396 - 0.030265304362562327im; … ; 0.09232028665365559 + 0.0im 0.12492048143428733 + 0.0im … 0.03728123116232768 + 0.06457298654187171im 0.0074562462324655335 + 0.01291459730837434im; 0.10208144135055229 + 0.0im 0.14872488279907023 + 0.0im … 0.029470953026436673 - 0.01701506266308801im 0.05894190605287333 - 0.03403012532617602im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757), [-12.247569668722283 -11.100308396742939 … -8.289845772413004 -11.100308396743; -11.100308396742937 -9.130057825948303 … -9.13005779589701 -11.100308356759962; … ; -8.289845772413004 -9.13005779589701 … -4.149589921643663 -6.287956198199807; -11.100308396742998 -11.100308356759964 … -6.287956198199808 -9.111848223578166;;; -11.10030839674294 -9.1300578259483 … -9.130057795897011 -11.100308356759964; -9.130057825948303 -6.903159481982448 … -9.130057827297984 -10.053883826552829; … ; -9.13005779589701 -9.130057827297984 … -5.294353669214802 -7.5473992065221625; -11.100308356759962 -10.053883826552829 … -7.547399206522163 -10.053883826552934;;; -8.289845772413303 -6.307621931517062 … -8.289845781012257 -9.111848193526836; -6.307621931517064 -4.516655665815938 … -7.5473992376119945 -7.547399206522395; … ; -8.289845781012255 -7.547399237611994 … -5.768969083581643 -7.5473992376120655; -9.111848193526836 -7.547399206522394 … -7.547399237612066 -9.111848224928073;;; … ;;; -5.3010317182501385 -6.307621955789271 … -2.5497035732763105 -3.849582179388152; -6.307621955789271 -6.903159495209277 … -3.3290606985465754 -4.878419358630989; … ; -2.54970357327631 -3.3290606985465754 … -1.2567984709027493 -1.814194746041345; -3.8495821793881526 -4.878419358630991 … -1.814194746041345 -2.714767335322931;;; -8.289845772413006 -9.13005779589701 … -4.149589921643665 -6.287956198199806; -9.130057795897011 -9.130057827297982 … -5.294353669214801 -7.547399206522162; … ; -4.149589921643665 -5.294353669214802 … -1.9094492399156084 -2.89461236785261; -6.287956198199807 -7.547399206522162 … -2.89461236785261 -4.485542759372458;;; -11.100308396743 -11.100308356759964 … -6.287956198199808 -9.111848223578164; -11.100308356759962 -10.053883826552829 … -7.547399206522164 -10.053883826552934; … ; -6.287956198199806 -7.547399206522164 … -2.8946123678526097 -4.485542759372456; -9.111848223578166 -10.053883826552934 … -4.485542759372458 -6.871104500135868])], 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), [-12.247569668722283 -11.100308396742939 … -8.289845772413004 -11.100308396743; -11.100308396742937 -9.130057825948303 … -9.13005779589701 -11.100308356759962; … ; -8.289845772413004 -9.13005779589701 … -4.149589921643663 -6.287956198199807; -11.100308396742998 -11.100308356759964 … -6.287956198199808 -9.111848223578166;;; -11.10030839674294 -9.1300578259483 … -9.130057795897011 -11.100308356759964; -9.130057825948303 -6.903159481982448 … -9.130057827297984 -10.053883826552829; … ; -9.13005779589701 -9.130057827297984 … -5.294353669214802 -7.5473992065221625; -11.100308356759962 -10.053883826552829 … -7.547399206522163 -10.053883826552934;;; -8.289845772413303 -6.307621931517062 … -8.289845781012257 -9.111848193526836; -6.307621931517064 -4.516655665815938 … -7.5473992376119945 -7.547399206522395; … ; -8.289845781012255 -7.547399237611994 … -5.768969083581643 -7.5473992376120655; -9.111848193526836 -7.547399206522394 … -7.547399237612066 -9.111848224928073;;; … ;;; -5.3010317182501385 -6.307621955789271 … -2.5497035732763105 -3.849582179388152; -6.307621955789271 -6.903159495209277 … -3.3290606985465754 -4.878419358630989; … ; -2.54970357327631 -3.3290606985465754 … -1.2567984709027493 -1.814194746041345; -3.8495821793881526 -4.878419358630991 … -1.814194746041345 -2.714767335322931;;; -8.289845772413006 -9.13005779589701 … -4.149589921643665 -6.287956198199806; -9.130057795897011 -9.130057827297982 … -5.294353669214801 -7.547399206522162; … ; -4.149589921643665 -5.294353669214802 … -1.9094492399156084 -2.89461236785261; -6.287956198199807 -7.547399206522162 … -2.89461236785261 -4.485542759372458;;; -11.100308396743 -11.100308356759964 … -6.287956198199808 -9.111848223578164; -11.100308356759962 -10.053883826552829 … -7.547399206522164 -10.053883826552934; … ; -6.287956198199806 -7.547399206522164 … -2.8946123678526097 -4.485542759372456; -9.111848223578166 -10.053883826552934 … -4.485542759372458 -6.871104500135868]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757), ComplexF64[0.11038155824020969 + 0.0im 0.1697292679710574 + 0.0im … -0.009426647060181403 - 0.016327431653253982im 0.009426647060181401 + 0.01632743165325398im; 0.09335704685777356 + 0.0im 0.12740009431942179 + 0.0im … -0.052421044862493965 + 0.030265304362562334im 0.05242104486249396 - 0.030265304362562327im; … ; 0.09232028665365559 + 0.0im 0.12492048143428733 + 0.0im … 0.03728123116232768 + 0.06457298654187171im 0.0074562462324655335 + 0.01291459730837434im; 0.10208144135055229 + 0.0im 0.14872488279907023 + 0.0im … 0.029470953026436673 - 0.01701506266308801im 0.05894190605287333 - 0.03403012532617602im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, @NamedTuple{ψ_reals::Array{ComplexF64, 3}}[(ψ_reals = [-0.07468659453747624 + 0.015264474421902714im -0.019414512208085058 + 0.04167921907580607im … 0.021708492076634053 - 0.0036211268588260633im -0.044649985670889084 - 0.04932598798767728im; -0.005756176762505057 + 0.048315806140001125im 0.04780838433602964 + 0.03020695792380057im … -0.05808005880701449 - 0.04295428797972254im -0.07809174935835955 + 0.017676376697561662im; … ; -0.012267174796830935 - 0.009716835821504736im -0.03635985144900063 - 0.0167881654718173im … -0.08488953548695036 - 0.028240464454385304im -0.04587792264346983 + 0.05067444461656215im; -0.059183750291606205 - 0.035211262260511814im -0.0521619244763714 + 0.014759779759772475im … -0.03531049056156907 + 0.05892665471403081im 0.02027246981636905 - 0.006967156702470677im;;; -0.005112979725906814 - 0.0035924582671364794im -0.047510650696934525 - 0.04765820553269449im … 0.02054264210065048 - 0.05421124130544994im -0.05912068566964075 - 0.025021862157704487im; 0.02642129542410248 - 0.014923335925411521im -0.08117596829866269 - 0.024254765392070617im … -0.06696970100702718 + 0.005098080454407183im -0.01240475119251732 + 0.04045561129809858im; … ; -0.0073376669967497015 - 0.027263198671911695im -0.01089019825418594 - 0.03067736777329114im … -0.02932990076217424 - 0.019569607786586517im 0.003530649950646267 - 0.015704156990177305im; -0.027264356896183443 - 0.029525776815094898im -0.023249823629697918 - 0.05756183417896668im … 0.04559953934121378 + 0.01231584887492032im 0.017045309800286554 - 0.06012856300331485im;;; -0.006369933717468287 - 0.061738786338320285im -0.05574701513427621 - 0.024487982551734268im … 0.029943769672857466 - 0.08956505562390057im -0.0032766456635980393 - 0.05031421644707im; -0.03457032862173601 - 0.05447903028865845im -0.06825694830949153 + 0.03778771393241588im … -0.011523332790666531 + 0.011428622459966432im 0.03226468980485212 - 0.008648667576303854im; … ; 0.03945357191078647 - 0.08848603202608579im -0.018823679903354616 - 0.07815190900986341im … 0.02873019251828158 + 0.016721980639432196im 0.07995321060320004 - 0.0360740349269436im; -0.006730705046260896 - 0.11278072006550596im -0.06432028742071788 - 0.0636558675664317im … 0.11342930192567834 - 0.042708780908644724im 0.05614640768723832 - 0.12012322696472294im;;; … ;;; 0.00802419321301251 - 0.019949215764326893im 0.0857026278058646 + 0.07116790379526414im … 0.006225705010815539 - 0.01459498537146181im 0.05556978960885371 - 0.061924468097750214im; 0.03894478059121685 + 0.0319068944287782im 0.1260424490407743 + 0.0005750143168738869im … -0.03407661700871602 + 0.0007373845515821261im -0.003987632386441342 - 0.03864616421300787im; … ; 0.0873583580995294 - 0.001046577341783525im 0.0037024418768665237 + 0.0017953760366820233im … -0.04956728440760909 + 0.16206095056319725im 0.07099774093195849 + 0.08708641826589966im; 0.061260195493017124 - 0.06297366450325867im 0.012202607379009297 + 0.04498418302715276im … 0.0606885322014669 + 0.06786019873087398im 0.10627841028701898 - 0.008359781200309273im;;; 0.07576288553701535 + 0.07433553103900212im 0.17641532090330986 - 0.01271882414279523im … -0.08755629069866452 + 0.015922940617585292im -0.02331711790602923 + 0.04524762833288322im; 0.1254021412638914 - 0.015854203489270767im 0.10264929491777663 - 0.10631082636089272im … -0.026308732858681384 + 0.007928928955662065im 0.004948544914000394 - 0.004849075379957632im; … ; -0.055348757821552685 + 0.02367612871848971im 0.005597471468215267 + 0.08760046283539846im … 0.04657981642804638 + 0.043470749546971346im -0.03954893729972981 - 0.038811240827002554im; -0.021935598714693208 + 0.07260699913105714im 0.09416640899678602 + 0.08433811907213358im … -0.04319220829794605 - 0.049164991930531164im -0.07182111596262165 - 0.004774211814860374im;;; 0.054786534093582376 - 0.040672389054100984im 0.015917141654862216 - 0.052194350938285526im … -0.0311364278448307 + 0.061609344163279976im 0.0361494452638602 + 0.015942055567380674im; 0.020183413422849752 - 0.04985513529529212im -0.005311695810131745 - 0.014368889436896787im … -0.017833950625652656 - 0.030429884752671242im -0.0180409037028693 - 0.03613168627676606im; … ; -0.028070402596879207 + 0.11870678813804157im 0.04544591251092166 + 0.036661105991430326im … -0.06140275852978085 - 0.061110178535139434im -0.14947911405248038 + 0.04629456847721384im; 0.04276506190900751 + 0.037950523579263054im 0.054978570130502336 - 0.0225567921574365im … -0.12754033911000087 + 0.015485410558384255im -0.034477423142400834 + 0.11687232548748214im],)]), DFTK.DftHamiltonianBlock(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749), DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749), [0.083320109049959, 0.8956911722870592, 2.8328837076986058, 5.894897715284598, 10.081733195045036, 12.893786875481155, 8.082050577846019, 4.395135752385337, 1.8330423990990978, 0.3957705179873052 … 0.8332010904995898, 2.3954531351863206, 5.082526652047498, 8.894421641083122, 13.83113810229319, 9.89426294968263, 5.832407633497128, 2.895373789486075, 1.083161417649467, 0.3957705179873052]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749), ComplexF64[0.10997142862853636 + 0.0im 0.1686758360708126 + 0.0im … -0.032495727623724026 - 0.018761417091069828im -5.710372280586092e-19 - 3.2968849733693577e-19im; 0.09511091805015323 + 0.0im 0.13162182200636915 + 0.0im … -0.03876707908042239 + 0.06714655062833208im 0.02326024744825342 - 0.04028793037699923im; … ; 0.09197726483082143 + 0.0im 0.12410271910068073 + 0.0im … 0.051406644402565774 + 0.029679639983956733im 6.990521527121634e-18 + 4.035979485459552e-18im; 0.10399921515860865 + 0.0im 0.15351809108742234 + 0.0im … 0.008717893888213726 - 0.015099835149380354im 0.02615368166464116 - 0.04529950544814103im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749), [-12.247569668722283 -11.100308396742939 … -8.289845772413004 -11.100308396743; -11.100308396742937 -9.130057825948303 … -9.13005779589701 -11.100308356759962; … ; -8.289845772413004 -9.13005779589701 … -4.149589921643663 -6.287956198199807; -11.100308396742998 -11.100308356759964 … -6.287956198199808 -9.111848223578166;;; -11.10030839674294 -9.1300578259483 … -9.130057795897011 -11.100308356759964; -9.130057825948303 -6.903159481982448 … -9.130057827297984 -10.053883826552829; … ; -9.13005779589701 -9.130057827297984 … -5.294353669214802 -7.5473992065221625; -11.100308356759962 -10.053883826552829 … -7.547399206522163 -10.053883826552934;;; -8.289845772413303 -6.307621931517062 … -8.289845781012257 -9.111848193526836; -6.307621931517064 -4.516655665815938 … -7.5473992376119945 -7.547399206522395; … ; -8.289845781012255 -7.547399237611994 … -5.768969083581643 -7.5473992376120655; -9.111848193526836 -7.547399206522394 … -7.547399237612066 -9.111848224928073;;; … ;;; -5.3010317182501385 -6.307621955789271 … -2.5497035732763105 -3.849582179388152; -6.307621955789271 -6.903159495209277 … -3.3290606985465754 -4.878419358630989; … ; -2.54970357327631 -3.3290606985465754 … -1.2567984709027493 -1.814194746041345; -3.8495821793881526 -4.878419358630991 … -1.814194746041345 -2.714767335322931;;; -8.289845772413006 -9.13005779589701 … -4.149589921643665 -6.287956198199806; -9.130057795897011 -9.130057827297982 … -5.294353669214801 -7.547399206522162; … ; -4.149589921643665 -5.294353669214802 … -1.9094492399156084 -2.89461236785261; -6.287956198199807 -7.547399206522162 … -2.89461236785261 -4.485542759372458;;; -11.100308396743 -11.100308356759964 … -6.287956198199808 -9.111848223578164; -11.100308356759962 -10.053883826552829 … -7.547399206522164 -10.053883826552934; … ; -6.287956198199806 -7.547399206522164 … -2.8946123678526097 -4.485542759372456; -9.111848223578166 -10.053883826552934 … -4.485542759372458 -6.871104500135868])], 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), [-12.247569668722283 -11.100308396742939 … -8.289845772413004 -11.100308396743; -11.100308396742937 -9.130057825948303 … -9.13005779589701 -11.100308356759962; … ; -8.289845772413004 -9.13005779589701 … -4.149589921643663 -6.287956198199807; -11.100308396742998 -11.100308356759964 … -6.287956198199808 -9.111848223578166;;; -11.10030839674294 -9.1300578259483 … -9.130057795897011 -11.100308356759964; -9.130057825948303 -6.903159481982448 … -9.130057827297984 -10.053883826552829; … ; -9.13005779589701 -9.130057827297984 … -5.294353669214802 -7.5473992065221625; -11.100308356759962 -10.053883826552829 … -7.547399206522163 -10.053883826552934;;; -8.289845772413303 -6.307621931517062 … -8.289845781012257 -9.111848193526836; -6.307621931517064 -4.516655665815938 … -7.5473992376119945 -7.547399206522395; … ; -8.289845781012255 -7.547399237611994 … -5.768969083581643 -7.5473992376120655; -9.111848193526836 -7.547399206522394 … -7.547399237612066 -9.111848224928073;;; … ;;; -5.3010317182501385 -6.307621955789271 … -2.5497035732763105 -3.849582179388152; -6.307621955789271 -6.903159495209277 … -3.3290606985465754 -4.878419358630989; … ; -2.54970357327631 -3.3290606985465754 … -1.2567984709027493 -1.814194746041345; -3.8495821793881526 -4.878419358630991 … -1.814194746041345 -2.714767335322931;;; -8.289845772413006 -9.13005779589701 … -4.149589921643665 -6.287956198199806; -9.130057795897011 -9.130057827297982 … -5.294353669214801 -7.547399206522162; … ; -4.149589921643665 -5.294353669214802 … -1.9094492399156084 -2.89461236785261; -6.287956198199807 -7.547399206522162 … -2.89461236785261 -4.485542759372458;;; -11.100308396743 -11.100308356759964 … -6.287956198199808 -9.111848223578164; -11.100308356759962 -10.053883826552829 … -7.547399206522164 -10.053883826552934; … ; -6.287956198199806 -7.547399206522164 … -2.8946123678526097 -4.485542759372456; -9.111848223578166 -10.053883826552934 … -4.485542759372458 -6.871104500135868]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749), ComplexF64[0.10997142862853636 + 0.0im 0.1686758360708126 + 0.0im … -0.032495727623724026 - 0.018761417091069828im -5.710372280586092e-19 - 3.2968849733693577e-19im; 0.09511091805015323 + 0.0im 0.13162182200636915 + 0.0im … -0.03876707908042239 + 0.06714655062833208im 0.02326024744825342 - 0.04028793037699923im; … ; 0.09197726483082143 + 0.0im 0.12410271910068073 + 0.0im … 0.051406644402565774 + 0.029679639983956733im 6.990521527121634e-18 + 4.035979485459552e-18im; 0.10399921515860865 + 0.0im 0.15351809108742234 + 0.0im … 0.008717893888213726 - 0.015099835149380354im 0.02615368166464116 - 0.04529950544814103im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, @NamedTuple{ψ_reals::Array{ComplexF64, 3}}[(ψ_reals = [-0.07468659453747624 + 0.015264474421902714im -0.019414512208085058 + 0.04167921907580607im … 0.021708492076634053 - 0.0036211268588260633im -0.044649985670889084 - 0.04932598798767728im; -0.005756176762505057 + 0.048315806140001125im 0.04780838433602964 + 0.03020695792380057im … -0.05808005880701449 - 0.04295428797972254im -0.07809174935835955 + 0.017676376697561662im; … ; -0.012267174796830935 - 0.009716835821504736im -0.03635985144900063 - 0.0167881654718173im … -0.08488953548695036 - 0.028240464454385304im -0.04587792264346983 + 0.05067444461656215im; -0.059183750291606205 - 0.035211262260511814im -0.0521619244763714 + 0.014759779759772475im … -0.03531049056156907 + 0.05892665471403081im 0.02027246981636905 - 0.006967156702470677im;;; -0.005112979725906814 - 0.0035924582671364794im -0.047510650696934525 - 0.04765820553269449im … 0.02054264210065048 - 0.05421124130544994im -0.05912068566964075 - 0.025021862157704487im; 0.02642129542410248 - 0.014923335925411521im -0.08117596829866269 - 0.024254765392070617im … -0.06696970100702718 + 0.005098080454407183im -0.01240475119251732 + 0.04045561129809858im; … ; -0.0073376669967497015 - 0.027263198671911695im -0.01089019825418594 - 0.03067736777329114im … -0.02932990076217424 - 0.019569607786586517im 0.003530649950646267 - 0.015704156990177305im; -0.027264356896183443 - 0.029525776815094898im -0.023249823629697918 - 0.05756183417896668im … 0.04559953934121378 + 0.01231584887492032im 0.017045309800286554 - 0.06012856300331485im;;; -0.006369933717468287 - 0.061738786338320285im -0.05574701513427621 - 0.024487982551734268im … 0.029943769672857466 - 0.08956505562390057im -0.0032766456635980393 - 0.05031421644707im; -0.03457032862173601 - 0.05447903028865845im -0.06825694830949153 + 0.03778771393241588im … -0.011523332790666531 + 0.011428622459966432im 0.03226468980485212 - 0.008648667576303854im; … ; 0.03945357191078647 - 0.08848603202608579im -0.018823679903354616 - 0.07815190900986341im … 0.02873019251828158 + 0.016721980639432196im 0.07995321060320004 - 0.0360740349269436im; -0.006730705046260896 - 0.11278072006550596im -0.06432028742071788 - 0.0636558675664317im … 0.11342930192567834 - 0.042708780908644724im 0.05614640768723832 - 0.12012322696472294im;;; … ;;; 0.00802419321301251 - 0.019949215764326893im 0.0857026278058646 + 0.07116790379526414im … 0.006225705010815539 - 0.01459498537146181im 0.05556978960885371 - 0.061924468097750214im; 0.03894478059121685 + 0.0319068944287782im 0.1260424490407743 + 0.0005750143168738869im … -0.03407661700871602 + 0.0007373845515821261im -0.003987632386441342 - 0.03864616421300787im; … ; 0.0873583580995294 - 0.001046577341783525im 0.0037024418768665237 + 0.0017953760366820233im … -0.04956728440760909 + 0.16206095056319725im 0.07099774093195849 + 0.08708641826589966im; 0.061260195493017124 - 0.06297366450325867im 0.012202607379009297 + 0.04498418302715276im … 0.0606885322014669 + 0.06786019873087398im 0.10627841028701898 - 0.008359781200309273im;;; 0.07576288553701535 + 0.07433553103900212im 0.17641532090330986 - 0.01271882414279523im … -0.08755629069866452 + 0.015922940617585292im -0.02331711790602923 + 0.04524762833288322im; 0.1254021412638914 - 0.015854203489270767im 0.10264929491777663 - 0.10631082636089272im … -0.026308732858681384 + 0.007928928955662065im 0.004948544914000394 - 0.004849075379957632im; … ; -0.055348757821552685 + 0.02367612871848971im 0.005597471468215267 + 0.08760046283539846im … 0.04657981642804638 + 0.043470749546971346im -0.03954893729972981 - 0.038811240827002554im; -0.021935598714693208 + 0.07260699913105714im 0.09416640899678602 + 0.08433811907213358im … -0.04319220829794605 - 0.049164991930531164im -0.07182111596262165 - 0.004774211814860374im;;; 0.054786534093582376 - 0.040672389054100984im 0.015917141654862216 - 0.052194350938285526im … -0.0311364278448307 + 0.061609344163279976im 0.0361494452638602 + 0.015942055567380674im; 0.020183413422849752 - 0.04985513529529212im -0.005311695810131745 - 0.014368889436896787im … -0.017833950625652656 - 0.030429884752671242im -0.0180409037028693 - 0.03613168627676606im; … ; -0.028070402596879207 + 0.11870678813804157im 0.04544591251092166 + 0.036661105991430326im … -0.06140275852978085 - 0.061110178535139434im -0.14947911405248038 + 0.04629456847721384im; 0.04276506190900751 + 0.037950523579263054im 0.054978570130502336 - 0.0225567921574365im … -0.12754033911000087 + 0.015485410558384255im -0.034477423142400834 + 0.11687232548748214im],)]), DFTK.DftHamiltonianBlock(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740), DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740), [0.16664021809991797, 0.22913029988738726, 1.4164418538493029, 3.728574879985665, 7.165529378296473, 11.727305348781728, 11.164894612694503, 6.728098805784188, 3.4161244710483185, 1.2289716084868951 … 0.41660054524979495, 1.228971608486895, 3.1661641438984414, 6.2281781514844345, 10.415013631244872, 13.22706731168099, 8.415331014045858, 4.7284161885851725, 2.166322835298934, 0.7290509541871413]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740), ComplexF64[0.1083460922901765 + 0.0im 0.16451669692939747 + 0.0im … -0.0 + 1.0213144005610526e-18im 0.0 - 0.03679672923035902im; 0.10714287388793554 + 0.0im 0.16145393303017874 + 0.0im … -0.054392079538503724 - 0.0im 0.018130693179501244 + 0.0im; … ; 0.07579045242767471 + 0.0im 0.08711041809792076 + 0.0im … -0.0 + 0.06906475263474503im 0.0 - 0.023021584211581677im; 0.09798590385967747 + 0.0im 0.13861415332258223 + 0.0im … 0.048374574773583326 + 0.0im 0.016124858257861113 + 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), [-12.247569668722283 -11.100308396742939 … -8.289845772413004 -11.100308396743; -11.100308396742937 -9.130057825948303 … -9.13005779589701 -11.100308356759962; … ; -8.289845772413004 -9.13005779589701 … -4.149589921643663 -6.287956198199807; -11.100308396742998 -11.100308356759964 … -6.287956198199808 -9.111848223578166;;; -11.10030839674294 -9.1300578259483 … -9.130057795897011 -11.100308356759964; -9.130057825948303 -6.903159481982448 … -9.130057827297984 -10.053883826552829; … ; -9.13005779589701 -9.130057827297984 … -5.294353669214802 -7.5473992065221625; -11.100308356759962 -10.053883826552829 … -7.547399206522163 -10.053883826552934;;; -8.289845772413303 -6.307621931517062 … -8.289845781012257 -9.111848193526836; -6.307621931517064 -4.516655665815938 … -7.5473992376119945 -7.547399206522395; … ; -8.289845781012255 -7.547399237611994 … -5.768969083581643 -7.5473992376120655; -9.111848193526836 -7.547399206522394 … -7.547399237612066 -9.111848224928073;;; … ;;; -5.3010317182501385 -6.307621955789271 … -2.5497035732763105 -3.849582179388152; -6.307621955789271 -6.903159495209277 … -3.3290606985465754 -4.878419358630989; … ; -2.54970357327631 -3.3290606985465754 … -1.2567984709027493 -1.814194746041345; -3.8495821793881526 -4.878419358630991 … -1.814194746041345 -2.714767335322931;;; -8.289845772413006 -9.13005779589701 … -4.149589921643665 -6.287956198199806; -9.130057795897011 -9.130057827297982 … -5.294353669214801 -7.547399206522162; … ; -4.149589921643665 -5.294353669214802 … -1.9094492399156084 -2.89461236785261; -6.287956198199807 -7.547399206522162 … -2.89461236785261 -4.485542759372458;;; -11.100308396743 -11.100308356759964 … -6.287956198199808 -9.111848223578164; -11.100308356759962 -10.053883826552829 … -7.547399206522164 -10.053883826552934; … ; -6.287956198199806 -7.547399206522164 … -2.8946123678526097 -4.485542759372456; -9.111848223578166 -10.053883826552934 … -4.485542759372458 -6.871104500135868])], 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), [-12.247569668722283 -11.100308396742939 … -8.289845772413004 -11.100308396743; -11.100308396742937 -9.130057825948303 … -9.13005779589701 -11.100308356759962; … ; -8.289845772413004 -9.13005779589701 … -4.149589921643663 -6.287956198199807; -11.100308396742998 -11.100308356759964 … -6.287956198199808 -9.111848223578166;;; -11.10030839674294 -9.1300578259483 … -9.130057795897011 -11.100308356759964; -9.130057825948303 -6.903159481982448 … -9.130057827297984 -10.053883826552829; … ; -9.13005779589701 -9.130057827297984 … -5.294353669214802 -7.5473992065221625; -11.100308356759962 -10.053883826552829 … -7.547399206522163 -10.053883826552934;;; -8.289845772413303 -6.307621931517062 … -8.289845781012257 -9.111848193526836; -6.307621931517064 -4.516655665815938 … -7.5473992376119945 -7.547399206522395; … ; -8.289845781012255 -7.547399237611994 … -5.768969083581643 -7.5473992376120655; -9.111848193526836 -7.547399206522394 … -7.547399237612066 -9.111848224928073;;; … ;;; -5.3010317182501385 -6.307621955789271 … -2.5497035732763105 -3.849582179388152; -6.307621955789271 -6.903159495209277 … -3.3290606985465754 -4.878419358630989; … ; -2.54970357327631 -3.3290606985465754 … -1.2567984709027493 -1.814194746041345; -3.8495821793881526 -4.878419358630991 … -1.814194746041345 -2.714767335322931;;; -8.289845772413006 -9.13005779589701 … -4.149589921643665 -6.287956198199806; -9.130057795897011 -9.130057827297982 … -5.294353669214801 -7.547399206522162; … ; -4.149589921643665 -5.294353669214802 … -1.9094492399156084 -2.89461236785261; -6.287956198199807 -7.547399206522162 … -2.89461236785261 -4.485542759372458;;; -11.100308396743 -11.100308356759964 … -6.287956198199808 -9.111848223578164; -11.100308356759962 -10.053883826552829 … -7.547399206522164 -10.053883826552934; … ; -6.287956198199806 -7.547399206522164 … -2.8946123678526097 -4.485542759372456; -9.111848223578166 -10.053883826552934 … -4.485542759372458 -6.871104500135868]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740), ComplexF64[0.1083460922901765 + 0.0im 0.16451669692939747 + 0.0im … -0.0 + 1.0213144005610526e-18im 0.0 - 0.03679672923035902im; 0.10714287388793554 + 0.0im 0.16145393303017874 + 0.0im … -0.054392079538503724 - 0.0im 0.018130693179501244 + 0.0im; … ; 0.07579045242767471 + 0.0im 0.08711041809792076 + 0.0im … -0.0 + 0.06906475263474503im 0.0 - 0.023021584211581677im; 0.09798590385967747 + 0.0im 0.13861415332258223 + 0.0im … 0.048374574773583326 + 0.0im 0.016124858257861113 + 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 = [-0.07468659453747624 + 0.015264474421902714im -0.019414512208085058 + 0.04167921907580607im … 0.021708492076634053 - 0.0036211268588260633im -0.044649985670889084 - 0.04932598798767728im; -0.005756176762505057 + 0.048315806140001125im 0.04780838433602964 + 0.03020695792380057im … -0.05808005880701449 - 0.04295428797972254im -0.07809174935835955 + 0.017676376697561662im; … ; -0.012267174796830935 - 0.009716835821504736im -0.03635985144900063 - 0.0167881654718173im … -0.08488953548695036 - 0.028240464454385304im -0.04587792264346983 + 0.05067444461656215im; -0.059183750291606205 - 0.035211262260511814im -0.0521619244763714 + 0.014759779759772475im … -0.03531049056156907 + 0.05892665471403081im 0.02027246981636905 - 0.006967156702470677im;;; -0.005112979725906814 - 0.0035924582671364794im -0.047510650696934525 - 0.04765820553269449im … 0.02054264210065048 - 0.05421124130544994im -0.05912068566964075 - 0.025021862157704487im; 0.02642129542410248 - 0.014923335925411521im -0.08117596829866269 - 0.024254765392070617im … -0.06696970100702718 + 0.005098080454407183im -0.01240475119251732 + 0.04045561129809858im; … ; -0.0073376669967497015 - 0.027263198671911695im -0.01089019825418594 - 0.03067736777329114im … -0.02932990076217424 - 0.019569607786586517im 0.003530649950646267 - 0.015704156990177305im; -0.027264356896183443 - 0.029525776815094898im -0.023249823629697918 - 0.05756183417896668im … 0.04559953934121378 + 0.01231584887492032im 0.017045309800286554 - 0.06012856300331485im;;; -0.006369933717468287 - 0.061738786338320285im -0.05574701513427621 - 0.024487982551734268im … 0.029943769672857466 - 0.08956505562390057im -0.0032766456635980393 - 0.05031421644707im; -0.03457032862173601 - 0.05447903028865845im -0.06825694830949153 + 0.03778771393241588im … -0.011523332790666531 + 0.011428622459966432im 0.03226468980485212 - 0.008648667576303854im; … ; 0.03945357191078647 - 0.08848603202608579im -0.018823679903354616 - 0.07815190900986341im … 0.02873019251828158 + 0.016721980639432196im 0.07995321060320004 - 0.0360740349269436im; -0.006730705046260896 - 0.11278072006550596im -0.06432028742071788 - 0.0636558675664317im … 0.11342930192567834 - 0.042708780908644724im 0.05614640768723832 - 0.12012322696472294im;;; … ;;; 0.00802419321301251 - 0.019949215764326893im 0.0857026278058646 + 0.07116790379526414im … 0.006225705010815539 - 0.01459498537146181im 0.05556978960885371 - 0.061924468097750214im; 0.03894478059121685 + 0.0319068944287782im 0.1260424490407743 + 0.0005750143168738869im … -0.03407661700871602 + 0.0007373845515821261im -0.003987632386441342 - 0.03864616421300787im; … ; 0.0873583580995294 - 0.001046577341783525im 0.0037024418768665237 + 0.0017953760366820233im … -0.04956728440760909 + 0.16206095056319725im 0.07099774093195849 + 0.08708641826589966im; 0.061260195493017124 - 0.06297366450325867im 0.012202607379009297 + 0.04498418302715276im … 0.0606885322014669 + 0.06786019873087398im 0.10627841028701898 - 0.008359781200309273im;;; 0.07576288553701535 + 0.07433553103900212im 0.17641532090330986 - 0.01271882414279523im … -0.08755629069866452 + 0.015922940617585292im -0.02331711790602923 + 0.04524762833288322im; 0.1254021412638914 - 0.015854203489270767im 0.10264929491777663 - 0.10631082636089272im … -0.026308732858681384 + 0.007928928955662065im 0.004948544914000394 - 0.004849075379957632im; … ; -0.055348757821552685 + 0.02367612871848971im 0.005597471468215267 + 0.08760046283539846im … 0.04657981642804638 + 0.043470749546971346im -0.03954893729972981 - 0.038811240827002554im; -0.021935598714693208 + 0.07260699913105714im 0.09416640899678602 + 0.08433811907213358im … -0.04319220829794605 - 0.049164991930531164im -0.07182111596262165 - 0.004774211814860374im;;; 0.054786534093582376 - 0.040672389054100984im 0.015917141654862216 - 0.052194350938285526im … -0.0311364278448307 + 0.061609344163279976im 0.0361494452638602 + 0.015942055567380674im; 0.020183413422849752 - 0.04985513529529212im -0.005311695810131745 - 0.014368889436896787im … -0.017833950625652656 - 0.030429884752671242im -0.0180409037028693 - 0.03613168627676606im; … ; -0.028070402596879207 + 0.11870678813804157im 0.04544591251092166 + 0.036661105991430326im … -0.06140275852978085 - 0.061110178535139434im -0.14947911405248038 + 0.04629456847721384im; 0.04276506190900751 + 0.037950523579263054im 0.054978570130502336 - 0.0225567921574365im … -0.12754033911000087 + 0.015485410558384255im -0.034477423142400834 + 0.11687232548748214im],)])]), basis = PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), energies = Energies(total = -7.910594396488506), converged = true, ρ = [7.589784542011672e-5 0.001126271272850796 … 0.006697037550127159 0.0011262712728507995; 0.0011262712728507792 0.005274334457405435 … 0.005274334457405464 0.0011262712728507894; … ; 0.006697037550127163 0.005274334457405475 … 0.02324475419110745 0.012258986825303807; 0.0011262712728507978 0.0011262712728507826 … 0.01225898682530379 0.003770008629943259;;; 0.0011262712728507952 0.005274334457405452 … 0.00527433445740548 0.0011262712728508002; 0.005274334457405437 0.01462006530473962 … 0.00527433445740546 0.002588080874883084; … ; 0.005274334457405483 0.00527433445740547 … 0.018107686646193586 0.008922003044797655; 0.0011262712728507974 0.002588080874883076 … 0.008922003044797637 0.0025880808748830943;;; 0.006697037550127128 0.01641210910162484 … 0.0066970375501271525 0.003770008629943254; 0.016412109101624824 0.03127783931589509 … 0.008922003044797615 0.0089220030447976; … ; 0.006697037550127156 0.008922003044797623 … 0.016476756359498496 0.00892200304479765; 0.0037700086299432512 0.00892200304479759 … 0.008922003044797634 0.003770008629943254;;; … ;;; 0.01985383985343325 0.016412109101624845 … 0.037156673635702624 0.027190800686616237; 0.01641210910162483 0.014620065304739631 … 0.032301272126469195 0.022322100931744856; … ; 0.03715667363570262 0.0323012721264692 … 0.046296980701501796 0.04263658273148351; 0.027190800686616237 0.02232210093174485 … 0.0426365827314835 0.03477222914203778;;; 0.006697037550127137 0.005274334457405453 … 0.023244754191107418 0.01225898682530377; 0.0052743344574054385 0.00527433445740544 … 0.01810768664619353 0.008922003044797604; … ; 0.023244754191107418 0.01810768664619354 … 0.040371110335629574 0.03149160381144163; 0.012258986825303773 0.008922003044797597 … 0.031491603811441615 0.02004716343280139;;; 0.001126271272850797 0.001126271272850797 … 0.01225898682530379 0.0037700086299432565; 0.0011262712728507822 0.0025880808748830787 … 0.008922003044797615 0.0025880808748830865; … ; 0.01225898682530379 0.008922003044797627 … 0.03149160381144165 0.02004716343280142; 0.003770008629943256 0.002588080874883078 … 0.020047163432801402 0.008952603496837188;;;;], eigenvalues = [[-0.17836835653908206, 0.26249194499177864, 0.26249194499177875, 0.26249194499177925, 0.3546921481678885, 0.35469214816788913, 0.35469214816802036], [-0.12755037617893406, 0.06475320594709036, 0.22545166517443246, 0.22545166517443282, 0.32197764961164704, 0.3892227690850662, 0.38922276908506676], [-0.10818729216482516, 0.07755003473465251, 0.1727832801149502, 0.17278328011495042, 0.2843518536201166, 0.33054764843338674, 0.5267232426394169], [-0.05777325374409106, 0.012724782205785644, 0.09766073750153251, 0.1841782533299723, 0.3152284179601982, 0.4720312183635733, 0.49791351766660497]], 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 = 0.27342189930594796, n_iter = 10, ψ = Matrix{ComplexF64}[[0.9030025413957606 + 0.29375176162869815im -1.6276604008745865e-15 + 9.585303062663851e-14im … 2.3533391532982584e-11 + 7.49731929559234e-12im 7.780690588985925e-8 + 2.460992221778065e-8im; 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