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#781"{DFTK.var"#anderson#780#782"{Base.Pairs{Symbol, Int64, Tuple{Symbol}, @NamedTuple{m::Int64}}}}) (generic function with 1 method)All keyword arguments are passed through to
DFTK.AndersonAcceleration.Try increasing convergence for for the bands in each SCF step by increasing the
ratio_ρdiffparameter of theAdaptiveDiagtolalgorithm. For example:diagtolalg = AdaptiveDiagtol(; ratio_ρdiff=0.05)AdaptiveDiagtol(0.05, nothing, 0.005, 0.03)Increase the number of bands, which are fully converged in each SCF step by tweaking the
AdaptiveBandsalgorithm. For example:nbandsalg = AdaptiveBands(model; temperature_factor_converge=1.1)AdaptiveBands(4, 7, 1.0e-6, 0.01)Try the adaptive damping algorithm by using
DFTK.scf_potential_mixing_adaptiveinstead ofself_consistent_field:DFTK.scf_potential_mixing_adaptive(basis; tol=1e-10)(ham = Hamiltonian(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), HamiltonianBlock[DFTK.DftHamiltonianBlock(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749), DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749), [0.0, 0.5624107360872233, 2.249642944348893, 5.061696624785009, 8.998571777395572, 14.06026840218058, 14.06026840218058, 8.998571777395572, 5.061696624785009, 2.249642944348893 … 0.7498809814496308, 2.062172698986485, 4.499285888697785, 8.061220550583531, 12.747976684643724, 11.060744476382055, 6.748928833046679, 3.561934661885747, 1.499761962899262, 0.5624107360872233]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749), ComplexF64[0.11162114718647566 + 0.0im 0.17292273765511482 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.10094779392345996 + 0.0im 0.14590894423989453 + 0.0im … -0.05030254922547522 - 0.0im 0.0503025492254752 + 0.0im; … ; 0.08537828309138949 + 0.0im 0.10863402648960857 + 0.0im … -0.0 + 0.08075097926136235im 0.0 + 0.0im; 0.10094779392345996 + 0.0im 0.14590894423989453 + 0.0im … 0.05030254922547522 + 0.0im 0.0503025492254752 + 0.0im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0, 0, 0], spin = 1, num. G vectors = 749), [-12.247569668723362 -11.100308396742287 … -8.2898457724124 -11.100308396742346; -11.100308396742285 -9.130057825947773 … -9.130057795896482 -11.10030835675931; … ; -8.2898457724124 -9.130057795896482 … -4.149589921643215 -6.287956198199211; -11.100308396742346 -11.10030835675931 … -6.287956198199212 -9.111848223577335;;; -11.100308396742289 -9.130057825947771 … -9.130057795896484 -11.100308356759312; -9.130057825947773 -6.9031594819821445 … -9.130057827297456 -10.053883826552095; … ; -9.130057795896482 -9.130057827297456 … -5.294353669214334 -7.547399206521581; -11.10030835675931 -10.053883826552095 … -7.5473992065215825 -10.0538838265522;;; -8.289845772412699 -6.3076219315167235 … -8.289845781011653 -9.111848193526004; -6.307621931516725 -4.516655665815764 … -7.547399237611413 -7.547399206521814; … ; -8.289845781011651 -7.547399237611412 … -5.768969083581177 -7.547399237611484; -9.111848193526003 -7.5473992065218125 … -7.547399237611486 -9.111848224927241;;; … ;;; -5.301031718249762 -6.307621955788931 … -2.5497035732760023 -3.849582179387786; -6.307621955788932 -6.903159495208973 … -3.3290606985462565 -4.878419358630623; … ; -2.5497035732760014 -3.329060698546257 … -1.256798470902507 -1.8141947460410646; -3.8495821793877845 -4.878419358630625 … -1.8141947460410641 -2.7147673353225956;;; -8.289845772412402 -9.13005779589648 … -4.149589921643217 -6.287956198199209; -9.130057795896482 -9.130057827297453 … -5.294353669214332 -7.54739920652158; … ; -4.149589921643217 -5.294353669214333 … -1.909449239915301 -2.894612367852225; -6.28795619819921 -7.547399206521582 … -2.8946123678522246 -4.485542759371942;;; -11.100308396742346 -11.100308356759312 … -6.287956198199212 -9.111848223577333; -11.10030835675931 -10.053883826552095 … -7.547399206521583 -10.0538838265522; … ; -6.28795619819921 -7.547399206521583 … -2.8946123678522246 -4.485542759371942; -9.111848223577335 -10.0538838265522 … -4.485542759371943 -6.871104500135123])], 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), [-12.247569668723362 -11.100308396742287 … -8.2898457724124 -11.100308396742346; -11.100308396742285 -9.130057825947773 … -9.130057795896482 -11.10030835675931; … ; -8.2898457724124 -9.130057795896482 … -4.149589921643215 -6.287956198199211; -11.100308396742346 -11.10030835675931 … -6.287956198199212 -9.111848223577335;;; -11.100308396742289 -9.130057825947771 … -9.130057795896484 -11.100308356759312; -9.130057825947773 -6.9031594819821445 … -9.130057827297456 -10.053883826552095; … ; -9.130057795896482 -9.130057827297456 … -5.294353669214334 -7.547399206521581; -11.10030835675931 -10.053883826552095 … -7.5473992065215825 -10.0538838265522;;; -8.289845772412699 -6.3076219315167235 … -8.289845781011653 -9.111848193526004; -6.307621931516725 -4.516655665815764 … -7.547399237611413 -7.547399206521814; … ; -8.289845781011651 -7.547399237611412 … -5.768969083581177 -7.547399237611484; -9.111848193526003 -7.5473992065218125 … -7.547399237611486 -9.111848224927241;;; … ;;; -5.301031718249762 -6.307621955788931 … -2.5497035732760023 -3.849582179387786; -6.307621955788932 -6.903159495208973 … -3.3290606985462565 -4.878419358630623; … ; -2.5497035732760014 -3.329060698546257 … -1.256798470902507 -1.8141947460410646; -3.8495821793877845 -4.878419358630625 … -1.8141947460410641 -2.7147673353225956;;; -8.289845772412402 -9.13005779589648 … -4.149589921643217 -6.287956198199209; -9.130057795896482 -9.130057827297453 … -5.294353669214332 -7.54739920652158; … ; -4.149589921643217 -5.294353669214333 … -1.909449239915301 -2.894612367852225; -6.28795619819921 -7.547399206521582 … -2.8946123678522246 -4.485542759371942;;; -11.100308396742346 -11.100308356759312 … -6.287956198199212 -9.111848223577333; -11.10030835675931 -10.053883826552095 … -7.547399206521583 -10.0538838265522; … ; -6.28795619819921 -7.547399206521583 … -2.8946123678522246 -4.485542759371942; -9.111848223577335 -10.0538838265522 … -4.485542759371943 -6.871104500135123]), 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 = [0.0016734728661811542 - 0.004352397216935177im 0.044391955128515424 + 0.00019831066290279488im … -0.018661538558586654 - 0.035082284456473795im -0.030989731706858273 - 0.010819175801883445im; -0.0017776310030698298 - 0.031241138353261415im -0.019591207872783137 - 0.02475129006668124im … -0.04632465236935042 + 0.01396341391494938im -0.005260020717721678 + 0.00515907995861645im; … ; 0.032925340365608596 - 0.04177061751384238im 0.036539126508816855 + 0.009021965223941518im … 0.0448649759887718 + 0.0388687828633562im 0.07908634800195842 - 0.04005078002112873im; 0.027007899969595798 - 0.008984902458939688im 0.05102843075144245 + 0.01714829433284954im … 0.04913858485228192 + 0.008581028814937077im 0.017220761880406006 - 0.03285316160470154im;;; 0.07499072827076365 - 0.021537197902525985im 0.07249793120142495 - 0.07950791274080307im … -0.06339267376636556 + 0.14071282787383638im 0.043182578721045486 + 0.06947298670452497im; -0.07486015846202415 + 0.021689199330737964im -0.014542454616053843 - 0.031439570026504784im … 0.035898104344860716 + 0.09106189819879432im -0.007489330828220137 - 0.015864641084074323im; … ; 0.04046443734179429 - 0.037729056943565896im 0.08041829007451484 + 0.0023903488637629887im … 0.09790047155387438 - 0.028406876135719097im 0.04958342471920883 - 0.07618422441897893im; 0.06590236275266521 + 0.0026556748889115037im 0.1398896674353096 - 0.04128297269819087im … -0.033012975612002005 - 0.011788968416094524im -0.003377613728228597 + 0.04342978828837771im;;; 0.013534632248741258 - 0.02581065044929834im 0.03344649390127006 - 0.10357246237630131im … 0.06365395267325073 + 0.09870735584542381im 0.03953257035143909 - 0.013694457062485937im; -0.004374549502350122 + 0.0912899688535673im 0.012741571822675712 - 0.03551189271785246im … -0.030933260118736487 + 0.0035833523166260758im -0.125672016861095 + 0.0892517453835108im; … ; 0.0847523045543485 + 0.009659636089508287im 0.12826733766278325 - 0.04232086790612204im … 0.00027511525977242345 - 0.03459428504514088im 0.013732086140491463 + 0.004851759855563072im; 0.1365865223303941 - 0.045210661054557094im 0.12877439524626294 - 0.1340776942805078im … -0.022429652472687134 + 0.09603133468573571im 0.09068350909000089 + 0.05810734361565984im;;; … ;;; -0.05837223207508168 - 0.011256627421478125im -0.08001284150310578 + 0.06032617811420364im … 0.024432954082954407 - 0.1725867590814285im -0.03495130268636544 - 0.06865636231375605im; -0.015603516958243472 - 0.007649491257099303im -0.013523232073205509 + 0.07190828667704442im … -0.014508969010773823 - 0.06698560340803604im 0.023667471827298874 - 0.03102570165189071im; … ; 0.016047536010886515 + 0.10904567228789258im 0.027609874575944552 + 0.038465570071637846im … -0.13929916064028536 + 0.014409079318362758im -0.07529699543212294 + 0.11911984995524627im; -0.007198434222176489 - 0.005878995549730773im -0.049209834206682054 + 0.00902620412616384im … 0.056094373392776634 - 0.031699691686583056im 0.022243871718591428 - 0.017705894423763708im;;; -0.05057545008662202 + 0.040042478438632206im -0.016064579457417107 + 0.11939346356219825im … -0.10590256106097472 - 0.11991391248402253im -0.06721763135073977 - 0.012912028178511586im; -0.014496839928170968 - 0.02551491269953183im 0.02226690331178091 + 0.03243442515090536im … 0.055731602684370996 - 0.03467581059454415im 0.0633521338242148 - 0.10463336702096745im; … ; 0.008207179354959238 - 0.012736257335145456im -0.03985789518873144 + 0.012476653393309278im … 0.028040115495843787 + 0.006520552842942128im 0.03763015979627859 + 0.02094857286158402im; -0.11803999379754149 + 0.014864776510879103im -0.08935836216222158 + 0.10440872805926674im … 0.004747586023524658 - 0.18784468643029356im -0.08386767623587049 - 0.0921605317135297im;;; -0.013015714069307304 - 0.01514038130803478im -0.0037357770422441275 + 0.027848312989184644im … 0.00799709086434782 - 0.013357384395131955im 0.05355475795044799 - 0.0900187027860611im; -0.05034873578259036 - 0.03677666100345966im -0.02702306790314747 - 0.0074740222701787234im … 0.06351079446834876 - 0.12485488435431691im -0.03279077001199261 - 0.12863928652341822im; … ; -0.01812119863963521 - 0.017200045235476157im -0.025443643299607688 + 0.04732268149448925im … 0.0057479277772285245 - 0.04278035652662718im 0.026119099556756856 - 0.0179472217452881im; -0.012468424105132558 + 0.036608883890964415im 0.014901383863362788 + 0.0810745791758158im … -0.06696781433000465 - 0.03801400730895006im -0.03673529091636072 + 0.0026929357180470077im],)]), DFTK.DftHamiltonianBlock(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757), DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757), [0.062490081787469245, 0.9998413085995079, 3.062014007585993, 6.249008178746925, 10.5608238220823, 12.248056030343973, 7.561299896283778, 3.9993652343980317, 1.5622520446867312, 0.24996032714987704 … 2.7495635986486464, 5.561617279084762, 9.498492431695325, 14.560189056480333, 14.560189056480338, 9.498492431695329, 5.561617279084762, 2.7495635986486464, 1.0623313903869773, 0.49992065429975385]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757), ComplexF64[0.11038155824020969 + 0.0im 0.1697292679710574 + 0.0im … -0.009426647060181403 - 0.016327431653253982im 0.009426647060181401 + 0.01632743165325398im; 0.09335704685777356 + 0.0im 0.12740009431942179 + 0.0im … -0.052421044862493965 + 0.030265304362562334im 0.05242104486249396 - 0.030265304362562327im; … ; 0.09232028665365559 + 0.0im 0.12492048143428733 + 0.0im … 0.03728123116232768 + 0.06457298654187171im 0.007456246232465533 + 0.012914597308374338im; 0.10208144135055229 + 0.0im 0.14872488279907023 + 0.0im … 0.029470953026436673 - 0.01701506266308801im 0.05894190605287333 - 0.03403012532617602im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757), [-12.247569668723362 -11.100308396742287 … -8.2898457724124 -11.100308396742346; -11.100308396742285 -9.130057825947773 … -9.130057795896482 -11.10030835675931; … ; -8.2898457724124 -9.130057795896482 … -4.149589921643215 -6.287956198199211; -11.100308396742346 -11.10030835675931 … -6.287956198199212 -9.111848223577335;;; -11.100308396742289 -9.130057825947771 … -9.130057795896484 -11.100308356759312; -9.130057825947773 -6.9031594819821445 … -9.130057827297456 -10.053883826552095; … ; -9.130057795896482 -9.130057827297456 … -5.294353669214334 -7.547399206521581; -11.10030835675931 -10.053883826552095 … -7.5473992065215825 -10.0538838265522;;; -8.289845772412699 -6.3076219315167235 … -8.289845781011653 -9.111848193526004; -6.307621931516725 -4.516655665815764 … -7.547399237611413 -7.547399206521814; … ; -8.289845781011651 -7.547399237611412 … -5.768969083581177 -7.547399237611484; -9.111848193526003 -7.5473992065218125 … -7.547399237611486 -9.111848224927241;;; … ;;; -5.301031718249762 -6.307621955788931 … -2.5497035732760023 -3.849582179387786; -6.307621955788932 -6.903159495208973 … -3.3290606985462565 -4.878419358630623; … ; -2.5497035732760014 -3.329060698546257 … -1.256798470902507 -1.8141947460410646; -3.8495821793877845 -4.878419358630625 … -1.8141947460410641 -2.7147673353225956;;; -8.289845772412402 -9.13005779589648 … -4.149589921643217 -6.287956198199209; -9.130057795896482 -9.130057827297453 … -5.294353669214332 -7.54739920652158; … ; -4.149589921643217 -5.294353669214333 … -1.909449239915301 -2.894612367852225; -6.28795619819921 -7.547399206521582 … -2.8946123678522246 -4.485542759371942;;; -11.100308396742346 -11.100308356759312 … -6.287956198199212 -9.111848223577333; -11.10030835675931 -10.053883826552095 … -7.547399206521583 -10.0538838265522; … ; -6.28795619819921 -7.547399206521583 … -2.8946123678522246 -4.485542759371942; -9.111848223577335 -10.0538838265522 … -4.485542759371943 -6.871104500135123])], DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757), [0.062490081787469245, 0.9998413085995079, 3.062014007585993, 6.249008178746925, 10.5608238220823, 12.248056030343973, 7.561299896283778, 3.9993652343980317, 1.5622520446867312, 0.24996032714987704 … 2.7495635986486464, 5.561617279084762, 9.498492431695325, 14.560189056480333, 14.560189056480338, 9.498492431695329, 5.561617279084762, 2.7495635986486464, 1.0623313903869773, 0.49992065429975385]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757), [-12.247569668723362 -11.100308396742287 … -8.2898457724124 -11.100308396742346; -11.100308396742285 -9.130057825947773 … -9.130057795896482 -11.10030835675931; … ; -8.2898457724124 -9.130057795896482 … -4.149589921643215 -6.287956198199211; -11.100308396742346 -11.10030835675931 … -6.287956198199212 -9.111848223577335;;; -11.100308396742289 -9.130057825947771 … -9.130057795896484 -11.100308356759312; -9.130057825947773 -6.9031594819821445 … -9.130057827297456 -10.053883826552095; … ; -9.130057795896482 -9.130057827297456 … -5.294353669214334 -7.547399206521581; -11.10030835675931 -10.053883826552095 … -7.5473992065215825 -10.0538838265522;;; -8.289845772412699 -6.3076219315167235 … -8.289845781011653 -9.111848193526004; -6.307621931516725 -4.516655665815764 … -7.547399237611413 -7.547399206521814; … ; -8.289845781011651 -7.547399237611412 … -5.768969083581177 -7.547399237611484; -9.111848193526003 -7.5473992065218125 … -7.547399237611486 -9.111848224927241;;; … ;;; -5.301031718249762 -6.307621955788931 … -2.5497035732760023 -3.849582179387786; -6.307621955788932 -6.903159495208973 … -3.3290606985462565 -4.878419358630623; … ; -2.5497035732760014 -3.329060698546257 … -1.256798470902507 -1.8141947460410646; -3.8495821793877845 -4.878419358630625 … -1.8141947460410641 -2.7147673353225956;;; -8.289845772412402 -9.13005779589648 … -4.149589921643217 -6.287956198199209; -9.130057795896482 -9.130057827297453 … -5.294353669214332 -7.54739920652158; … ; -4.149589921643217 -5.294353669214333 … -1.909449239915301 -2.894612367852225; -6.28795619819921 -7.547399206521582 … -2.8946123678522246 -4.485542759371942;;; -11.100308396742346 -11.100308356759312 … -6.287956198199212 -9.111848223577333; -11.10030835675931 -10.053883826552095 … -7.547399206521583 -10.0538838265522; … ; -6.28795619819921 -7.547399206521583 … -2.8946123678522246 -4.485542759371942; -9.111848223577335 -10.0538838265522 … -4.485542759371943 -6.871104500135123]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0, 0], spin = 1, num. G vectors = 757), ComplexF64[0.11038155824020969 + 0.0im 0.1697292679710574 + 0.0im … -0.009426647060181403 - 0.016327431653253982im 0.009426647060181401 + 0.01632743165325398im; 0.09335704685777356 + 0.0im 0.12740009431942179 + 0.0im … -0.052421044862493965 + 0.030265304362562334im 0.05242104486249396 - 0.030265304362562327im; … ; 0.09232028665365559 + 0.0im 0.12492048143428733 + 0.0im … 0.03728123116232768 + 0.06457298654187171im 0.007456246232465533 + 0.012914597308374338im; 0.10208144135055229 + 0.0im 0.14872488279907023 + 0.0im … 0.029470953026436673 - 0.01701506266308801im 0.05894190605287333 - 0.03403012532617602im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, @NamedTuple{ψ_reals::Array{ComplexF64, 3}}[(ψ_reals = [0.0016734728661811542 - 0.004352397216935177im 0.044391955128515424 + 0.00019831066290279488im … -0.018661538558586654 - 0.035082284456473795im -0.030989731706858273 - 0.010819175801883445im; -0.0017776310030698298 - 0.031241138353261415im -0.019591207872783137 - 0.02475129006668124im … -0.04632465236935042 + 0.01396341391494938im -0.005260020717721678 + 0.00515907995861645im; … ; 0.032925340365608596 - 0.04177061751384238im 0.036539126508816855 + 0.009021965223941518im … 0.0448649759887718 + 0.0388687828633562im 0.07908634800195842 - 0.04005078002112873im; 0.027007899969595798 - 0.008984902458939688im 0.05102843075144245 + 0.01714829433284954im … 0.04913858485228192 + 0.008581028814937077im 0.017220761880406006 - 0.03285316160470154im;;; 0.07499072827076365 - 0.021537197902525985im 0.07249793120142495 - 0.07950791274080307im … -0.06339267376636556 + 0.14071282787383638im 0.043182578721045486 + 0.06947298670452497im; -0.07486015846202415 + 0.021689199330737964im -0.014542454616053843 - 0.031439570026504784im … 0.035898104344860716 + 0.09106189819879432im -0.007489330828220137 - 0.015864641084074323im; … ; 0.04046443734179429 - 0.037729056943565896im 0.08041829007451484 + 0.0023903488637629887im … 0.09790047155387438 - 0.028406876135719097im 0.04958342471920883 - 0.07618422441897893im; 0.06590236275266521 + 0.0026556748889115037im 0.1398896674353096 - 0.04128297269819087im … -0.033012975612002005 - 0.011788968416094524im -0.003377613728228597 + 0.04342978828837771im;;; 0.013534632248741258 - 0.02581065044929834im 0.03344649390127006 - 0.10357246237630131im … 0.06365395267325073 + 0.09870735584542381im 0.03953257035143909 - 0.013694457062485937im; -0.004374549502350122 + 0.0912899688535673im 0.012741571822675712 - 0.03551189271785246im … -0.030933260118736487 + 0.0035833523166260758im -0.125672016861095 + 0.0892517453835108im; … ; 0.0847523045543485 + 0.009659636089508287im 0.12826733766278325 - 0.04232086790612204im … 0.00027511525977242345 - 0.03459428504514088im 0.013732086140491463 + 0.004851759855563072im; 0.1365865223303941 - 0.045210661054557094im 0.12877439524626294 - 0.1340776942805078im … -0.022429652472687134 + 0.09603133468573571im 0.09068350909000089 + 0.05810734361565984im;;; … ;;; -0.05837223207508168 - 0.011256627421478125im -0.08001284150310578 + 0.06032617811420364im … 0.024432954082954407 - 0.1725867590814285im -0.03495130268636544 - 0.06865636231375605im; -0.015603516958243472 - 0.007649491257099303im -0.013523232073205509 + 0.07190828667704442im … -0.014508969010773823 - 0.06698560340803604im 0.023667471827298874 - 0.03102570165189071im; … ; 0.016047536010886515 + 0.10904567228789258im 0.027609874575944552 + 0.038465570071637846im … -0.13929916064028536 + 0.014409079318362758im -0.07529699543212294 + 0.11911984995524627im; -0.007198434222176489 - 0.005878995549730773im -0.049209834206682054 + 0.00902620412616384im … 0.056094373392776634 - 0.031699691686583056im 0.022243871718591428 - 0.017705894423763708im;;; -0.05057545008662202 + 0.040042478438632206im -0.016064579457417107 + 0.11939346356219825im … -0.10590256106097472 - 0.11991391248402253im -0.06721763135073977 - 0.012912028178511586im; -0.014496839928170968 - 0.02551491269953183im 0.02226690331178091 + 0.03243442515090536im … 0.055731602684370996 - 0.03467581059454415im 0.0633521338242148 - 0.10463336702096745im; … ; 0.008207179354959238 - 0.012736257335145456im -0.03985789518873144 + 0.012476653393309278im … 0.028040115495843787 + 0.006520552842942128im 0.03763015979627859 + 0.02094857286158402im; -0.11803999379754149 + 0.014864776510879103im -0.08935836216222158 + 0.10440872805926674im … 0.004747586023524658 - 0.18784468643029356im -0.08386767623587049 - 0.0921605317135297im;;; -0.013015714069307304 - 0.01514038130803478im -0.0037357770422441275 + 0.027848312989184644im … 0.00799709086434782 - 0.013357384395131955im 0.05355475795044799 - 0.0900187027860611im; -0.05034873578259036 - 0.03677666100345966im -0.02702306790314747 - 0.0074740222701787234im … 0.06351079446834876 - 0.12485488435431691im -0.03279077001199261 - 0.12863928652341822im; … ; -0.01812119863963521 - 0.017200045235476157im -0.025443643299607688 + 0.04732268149448925im … 0.0057479277772285245 - 0.04278035652662718im 0.026119099556756856 - 0.0179472217452881im; -0.012468424105132558 + 0.036608883890964415im 0.014901383863362788 + 0.0810745791758158im … -0.06696781433000465 - 0.03801400730895006im -0.03673529091636072 + 0.0026929357180470077im],)]), DFTK.DftHamiltonianBlock(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749), DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749), [0.083320109049959, 0.8956911722870593, 2.8328837076986058, 5.8948977152846, 10.08173319504504, 12.893786875481156, 8.082050577846022, 4.395135752385337, 1.8330423990990978, 0.3957705179873052 … 0.8332010904995898, 2.3954531351863206, 5.082526652047498, 8.894421641083122, 13.83113810229319, 9.89426294968263, 5.832407633497128, 2.895373789486075, 1.083161417649467, 0.3957705179873052]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749), ComplexF64[0.10997142862853636 + 0.0im 0.1686758360708126 + 0.0im … -0.032495727623724026 - 0.018761417091069828im 5.710372280586092e-19 + 3.2968849733693577e-19im; 0.09511091805015323 + 0.0im 0.13162182200636915 + 0.0im … -0.03876707908042238 + 0.06714655062833207im 0.02326024744825342 - 0.04028793037699923im; … ; 0.09197726483082143 + 0.0im 0.12410271910068073 + 0.0im … 0.051406644402565774 + 0.029679639983956733im 0.0 - 0.0im; 0.10399921515860865 + 0.0im 0.15351809108742234 + 0.0im … 0.008717893888213726 - 0.015099835149380354im 0.02615368166464116 - 0.04529950544814103im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749), [-12.247569668723362 -11.100308396742287 … -8.2898457724124 -11.100308396742346; -11.100308396742285 -9.130057825947773 … -9.130057795896482 -11.10030835675931; … ; -8.2898457724124 -9.130057795896482 … -4.149589921643215 -6.287956198199211; -11.100308396742346 -11.10030835675931 … -6.287956198199212 -9.111848223577335;;; -11.100308396742289 -9.130057825947771 … -9.130057795896484 -11.100308356759312; -9.130057825947773 -6.9031594819821445 … -9.130057827297456 -10.053883826552095; … ; -9.130057795896482 -9.130057827297456 … -5.294353669214334 -7.547399206521581; -11.10030835675931 -10.053883826552095 … -7.5473992065215825 -10.0538838265522;;; -8.289845772412699 -6.3076219315167235 … -8.289845781011653 -9.111848193526004; -6.307621931516725 -4.516655665815764 … -7.547399237611413 -7.547399206521814; … ; -8.289845781011651 -7.547399237611412 … -5.768969083581177 -7.547399237611484; -9.111848193526003 -7.5473992065218125 … -7.547399237611486 -9.111848224927241;;; … ;;; -5.301031718249762 -6.307621955788931 … -2.5497035732760023 -3.849582179387786; -6.307621955788932 -6.903159495208973 … -3.3290606985462565 -4.878419358630623; … ; -2.5497035732760014 -3.329060698546257 … -1.256798470902507 -1.8141947460410646; -3.8495821793877845 -4.878419358630625 … -1.8141947460410641 -2.7147673353225956;;; -8.289845772412402 -9.13005779589648 … -4.149589921643217 -6.287956198199209; -9.130057795896482 -9.130057827297453 … -5.294353669214332 -7.54739920652158; … ; -4.149589921643217 -5.294353669214333 … -1.909449239915301 -2.894612367852225; -6.28795619819921 -7.547399206521582 … -2.8946123678522246 -4.485542759371942;;; -11.100308396742346 -11.100308356759312 … -6.287956198199212 -9.111848223577333; -11.10030835675931 -10.053883826552095 … -7.547399206521583 -10.0538838265522; … ; -6.28795619819921 -7.547399206521583 … -2.8946123678522246 -4.485542759371942; -9.111848223577335 -10.0538838265522 … -4.485542759371943 -6.871104500135123])], DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749), [0.083320109049959, 0.8956911722870593, 2.8328837076986058, 5.8948977152846, 10.08173319504504, 12.893786875481156, 8.082050577846022, 4.395135752385337, 1.8330423990990978, 0.3957705179873052 … 0.8332010904995898, 2.3954531351863206, 5.082526652047498, 8.894421641083122, 13.83113810229319, 9.89426294968263, 5.832407633497128, 2.895373789486075, 1.083161417649467, 0.3957705179873052]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749), [-12.247569668723362 -11.100308396742287 … -8.2898457724124 -11.100308396742346; -11.100308396742285 -9.130057825947773 … -9.130057795896482 -11.10030835675931; … ; -8.2898457724124 -9.130057795896482 … -4.149589921643215 -6.287956198199211; -11.100308396742346 -11.10030835675931 … -6.287956198199212 -9.111848223577335;;; -11.100308396742289 -9.130057825947771 … -9.130057795896484 -11.100308356759312; -9.130057825947773 -6.9031594819821445 … -9.130057827297456 -10.053883826552095; … ; -9.130057795896482 -9.130057827297456 … -5.294353669214334 -7.547399206521581; -11.10030835675931 -10.053883826552095 … -7.5473992065215825 -10.0538838265522;;; -8.289845772412699 -6.3076219315167235 … -8.289845781011653 -9.111848193526004; -6.307621931516725 -4.516655665815764 … -7.547399237611413 -7.547399206521814; … ; -8.289845781011651 -7.547399237611412 … -5.768969083581177 -7.547399237611484; -9.111848193526003 -7.5473992065218125 … -7.547399237611486 -9.111848224927241;;; … ;;; -5.301031718249762 -6.307621955788931 … -2.5497035732760023 -3.849582179387786; -6.307621955788932 -6.903159495208973 … -3.3290606985462565 -4.878419358630623; … ; -2.5497035732760014 -3.329060698546257 … -1.256798470902507 -1.8141947460410646; -3.8495821793877845 -4.878419358630625 … -1.8141947460410641 -2.7147673353225956;;; -8.289845772412402 -9.13005779589648 … -4.149589921643217 -6.287956198199209; -9.130057795896482 -9.130057827297453 … -5.294353669214332 -7.54739920652158; … ; -4.149589921643217 -5.294353669214333 … -1.909449239915301 -2.894612367852225; -6.28795619819921 -7.547399206521582 … -2.8946123678522246 -4.485542759371942;;; -11.100308396742346 -11.100308356759312 … -6.287956198199212 -9.111848223577333; -11.10030835675931 -10.053883826552095 … -7.547399206521583 -10.0538838265522; … ; -6.28795619819921 -7.547399206521583 … -2.8946123678522246 -4.485542759371942; -9.111848223577335 -10.0538838265522 … -4.485542759371943 -6.871104500135123]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([ 0.333, 0.333, 0], spin = 1, num. G vectors = 749), ComplexF64[0.10997142862853636 + 0.0im 0.1686758360708126 + 0.0im … -0.032495727623724026 - 0.018761417091069828im 5.710372280586092e-19 + 3.2968849733693577e-19im; 0.09511091805015323 + 0.0im 0.13162182200636915 + 0.0im … -0.03876707908042238 + 0.06714655062833207im 0.02326024744825342 - 0.04028793037699923im; … ; 0.09197726483082143 + 0.0im 0.12410271910068073 + 0.0im … 0.051406644402565774 + 0.029679639983956733im 0.0 - 0.0im; 0.10399921515860865 + 0.0im 0.15351809108742234 + 0.0im … 0.008717893888213726 - 0.015099835149380354im 0.02615368166464116 - 0.04529950544814103im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, @NamedTuple{ψ_reals::Array{ComplexF64, 3}}[(ψ_reals = [0.0016734728661811542 - 0.004352397216935177im 0.044391955128515424 + 0.00019831066290279488im … -0.018661538558586654 - 0.035082284456473795im -0.030989731706858273 - 0.010819175801883445im; -0.0017776310030698298 - 0.031241138353261415im -0.019591207872783137 - 0.02475129006668124im … -0.04632465236935042 + 0.01396341391494938im -0.005260020717721678 + 0.00515907995861645im; … ; 0.032925340365608596 - 0.04177061751384238im 0.036539126508816855 + 0.009021965223941518im … 0.0448649759887718 + 0.0388687828633562im 0.07908634800195842 - 0.04005078002112873im; 0.027007899969595798 - 0.008984902458939688im 0.05102843075144245 + 0.01714829433284954im … 0.04913858485228192 + 0.008581028814937077im 0.017220761880406006 - 0.03285316160470154im;;; 0.07499072827076365 - 0.021537197902525985im 0.07249793120142495 - 0.07950791274080307im … -0.06339267376636556 + 0.14071282787383638im 0.043182578721045486 + 0.06947298670452497im; -0.07486015846202415 + 0.021689199330737964im -0.014542454616053843 - 0.031439570026504784im … 0.035898104344860716 + 0.09106189819879432im -0.007489330828220137 - 0.015864641084074323im; … ; 0.04046443734179429 - 0.037729056943565896im 0.08041829007451484 + 0.0023903488637629887im … 0.09790047155387438 - 0.028406876135719097im 0.04958342471920883 - 0.07618422441897893im; 0.06590236275266521 + 0.0026556748889115037im 0.1398896674353096 - 0.04128297269819087im … -0.033012975612002005 - 0.011788968416094524im -0.003377613728228597 + 0.04342978828837771im;;; 0.013534632248741258 - 0.02581065044929834im 0.03344649390127006 - 0.10357246237630131im … 0.06365395267325073 + 0.09870735584542381im 0.03953257035143909 - 0.013694457062485937im; -0.004374549502350122 + 0.0912899688535673im 0.012741571822675712 - 0.03551189271785246im … -0.030933260118736487 + 0.0035833523166260758im -0.125672016861095 + 0.0892517453835108im; … ; 0.0847523045543485 + 0.009659636089508287im 0.12826733766278325 - 0.04232086790612204im … 0.00027511525977242345 - 0.03459428504514088im 0.013732086140491463 + 0.004851759855563072im; 0.1365865223303941 - 0.045210661054557094im 0.12877439524626294 - 0.1340776942805078im … -0.022429652472687134 + 0.09603133468573571im 0.09068350909000089 + 0.05810734361565984im;;; … ;;; -0.05837223207508168 - 0.011256627421478125im -0.08001284150310578 + 0.06032617811420364im … 0.024432954082954407 - 0.1725867590814285im -0.03495130268636544 - 0.06865636231375605im; -0.015603516958243472 - 0.007649491257099303im -0.013523232073205509 + 0.07190828667704442im … -0.014508969010773823 - 0.06698560340803604im 0.023667471827298874 - 0.03102570165189071im; … ; 0.016047536010886515 + 0.10904567228789258im 0.027609874575944552 + 0.038465570071637846im … -0.13929916064028536 + 0.014409079318362758im -0.07529699543212294 + 0.11911984995524627im; -0.007198434222176489 - 0.005878995549730773im -0.049209834206682054 + 0.00902620412616384im … 0.056094373392776634 - 0.031699691686583056im 0.022243871718591428 - 0.017705894423763708im;;; -0.05057545008662202 + 0.040042478438632206im -0.016064579457417107 + 0.11939346356219825im … -0.10590256106097472 - 0.11991391248402253im -0.06721763135073977 - 0.012912028178511586im; -0.014496839928170968 - 0.02551491269953183im 0.02226690331178091 + 0.03243442515090536im … 0.055731602684370996 - 0.03467581059454415im 0.0633521338242148 - 0.10463336702096745im; … ; 0.008207179354959238 - 0.012736257335145456im -0.03985789518873144 + 0.012476653393309278im … 0.028040115495843787 + 0.006520552842942128im 0.03763015979627859 + 0.02094857286158402im; -0.11803999379754149 + 0.014864776510879103im -0.08935836216222158 + 0.10440872805926674im … 0.004747586023524658 - 0.18784468643029356im -0.08386767623587049 - 0.0921605317135297im;;; -0.013015714069307304 - 0.01514038130803478im -0.0037357770422441275 + 0.027848312989184644im … 0.00799709086434782 - 0.013357384395131955im 0.05355475795044799 - 0.0900187027860611im; -0.05034873578259036 - 0.03677666100345966im -0.02702306790314747 - 0.0074740222701787234im … 0.06351079446834876 - 0.12485488435431691im -0.03279077001199261 - 0.12863928652341822im; … ; -0.01812119863963521 - 0.017200045235476157im -0.025443643299607688 + 0.04732268149448925im … 0.0057479277772285245 - 0.04278035652662718im 0.026119099556756856 - 0.0179472217452881im; -0.012468424105132558 + 0.036608883890964415im 0.014901383863362788 + 0.0810745791758158im … -0.06696781433000465 - 0.03801400730895006im -0.03673529091636072 + 0.0026929357180470077im],)]), DFTK.DftHamiltonianBlock(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740), DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740), [0.16664021809991797, 0.22913029988738726, 1.4164418538493029, 3.728574879985665, 7.1655293782964735, 11.72730534878173, 11.164894612694503, 6.72809880578419, 3.4161244710483185, 1.2289716084868951 … 0.41660054524979495, 1.228971608486895, 3.1661641438984414, 6.228178151484434, 10.415013631244872, 13.227067311680987, 8.415331014045858, 4.7284161885851725, 2.166322835298934, 0.729050954187141]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740), ComplexF64[0.1083460922901765 + 0.0im 0.16451669692939747 + 0.0im … 0.0 - 1.0213144005610526e-18im 0.0 - 0.03679672923035902im; 0.10714287388793554 + 0.0im 0.16145393303017874 + 0.0im … -0.054392079538503724 - 0.0im 0.01813069317950125 + 0.0im; … ; 0.07579045242767471 + 0.0im 0.08711041809792076 + 0.0im … -0.0 + 0.06906475263474504im 0.0 - 0.023021584211581677im; 0.09798590385967748 + 0.0im 0.13861415332258226 + 0.0im … 0.048374574773583326 + 0.0im 0.01612485825786111 + 0.0im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740), [-12.247569668723362 -11.100308396742287 … -8.2898457724124 -11.100308396742346; -11.100308396742285 -9.130057825947773 … -9.130057795896482 -11.10030835675931; … ; -8.2898457724124 -9.130057795896482 … -4.149589921643215 -6.287956198199211; -11.100308396742346 -11.10030835675931 … -6.287956198199212 -9.111848223577335;;; -11.100308396742289 -9.130057825947771 … -9.130057795896484 -11.100308356759312; -9.130057825947773 -6.9031594819821445 … -9.130057827297456 -10.053883826552095; … ; -9.130057795896482 -9.130057827297456 … -5.294353669214334 -7.547399206521581; -11.10030835675931 -10.053883826552095 … -7.5473992065215825 -10.0538838265522;;; -8.289845772412699 -6.3076219315167235 … -8.289845781011653 -9.111848193526004; -6.307621931516725 -4.516655665815764 … -7.547399237611413 -7.547399206521814; … ; -8.289845781011651 -7.547399237611412 … -5.768969083581177 -7.547399237611484; -9.111848193526003 -7.5473992065218125 … -7.547399237611486 -9.111848224927241;;; … ;;; -5.301031718249762 -6.307621955788931 … -2.5497035732760023 -3.849582179387786; -6.307621955788932 -6.903159495208973 … -3.3290606985462565 -4.878419358630623; … ; -2.5497035732760014 -3.329060698546257 … -1.256798470902507 -1.8141947460410646; -3.8495821793877845 -4.878419358630625 … -1.8141947460410641 -2.7147673353225956;;; -8.289845772412402 -9.13005779589648 … -4.149589921643217 -6.287956198199209; -9.130057795896482 -9.130057827297453 … -5.294353669214332 -7.54739920652158; … ; -4.149589921643217 -5.294353669214333 … -1.909449239915301 -2.894612367852225; -6.28795619819921 -7.547399206521582 … -2.8946123678522246 -4.485542759371942;;; -11.100308396742346 -11.100308356759312 … -6.287956198199212 -9.111848223577333; -11.10030835675931 -10.053883826552095 … -7.547399206521583 -10.0538838265522; … ; -6.28795619819921 -7.547399206521583 … -2.8946123678522246 -4.485542759371942; -9.111848223577335 -10.0538838265522 … -4.485542759371943 -6.871104500135123])], DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740), [0.16664021809991797, 0.22913029988738726, 1.4164418538493029, 3.728574879985665, 7.1655293782964735, 11.72730534878173, 11.164894612694503, 6.72809880578419, 3.4161244710483185, 1.2289716084868951 … 0.41660054524979495, 1.228971608486895, 3.1661641438984414, 6.228178151484434, 10.415013631244872, 13.227067311680987, 8.415331014045858, 4.7284161885851725, 2.166322835298934, 0.729050954187141]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740), [-12.247569668723362 -11.100308396742287 … -8.2898457724124 -11.100308396742346; -11.100308396742285 -9.130057825947773 … -9.130057795896482 -11.10030835675931; … ; -8.2898457724124 -9.130057795896482 … -4.149589921643215 -6.287956198199211; -11.100308396742346 -11.10030835675931 … -6.287956198199212 -9.111848223577335;;; -11.100308396742289 -9.130057825947771 … -9.130057795896484 -11.100308356759312; -9.130057825947773 -6.9031594819821445 … -9.130057827297456 -10.053883826552095; … ; -9.130057795896482 -9.130057827297456 … -5.294353669214334 -7.547399206521581; -11.10030835675931 -10.053883826552095 … -7.5473992065215825 -10.0538838265522;;; -8.289845772412699 -6.3076219315167235 … -8.289845781011653 -9.111848193526004; -6.307621931516725 -4.516655665815764 … -7.547399237611413 -7.547399206521814; … ; -8.289845781011651 -7.547399237611412 … -5.768969083581177 -7.547399237611484; -9.111848193526003 -7.5473992065218125 … -7.547399237611486 -9.111848224927241;;; … ;;; -5.301031718249762 -6.307621955788931 … -2.5497035732760023 -3.849582179387786; -6.307621955788932 -6.903159495208973 … -3.3290606985462565 -4.878419358630623; … ; -2.5497035732760014 -3.329060698546257 … -1.256798470902507 -1.8141947460410646; -3.8495821793877845 -4.878419358630625 … -1.8141947460410641 -2.7147673353225956;;; -8.289845772412402 -9.13005779589648 … -4.149589921643217 -6.287956198199209; -9.130057795896482 -9.130057827297453 … -5.294353669214332 -7.54739920652158; … ; -4.149589921643217 -5.294353669214333 … -1.909449239915301 -2.894612367852225; -6.28795619819921 -7.547399206521582 … -2.8946123678522246 -4.485542759371942;;; -11.100308396742346 -11.100308356759312 … -6.287956198199212 -9.111848223577333; -11.10030835675931 -10.053883826552095 … -7.547399206521583 -10.0538838265522; … ; -6.28795619819921 -7.547399206521583 … -2.8946123678522246 -4.485542759371942; -9.111848223577335 -10.0538838265522 … -4.485542759371943 -6.871104500135123]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), KPoint([-0.333, 0.333, 0], spin = 1, num. G vectors = 740), ComplexF64[0.1083460922901765 + 0.0im 0.16451669692939747 + 0.0im … 0.0 - 1.0213144005610526e-18im 0.0 - 0.03679672923035902im; 0.10714287388793554 + 0.0im 0.16145393303017874 + 0.0im … -0.054392079538503724 - 0.0im 0.01813069317950125 + 0.0im; … ; 0.07579045242767471 + 0.0im 0.08711041809792076 + 0.0im … -0.0 + 0.06906475263474504im 0.0 - 0.023021584211581677im; 0.09798590385967748 + 0.0im 0.13861415332258226 + 0.0im … 0.048374574773583326 + 0.0im 0.01612485825786111 + 0.0im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, @NamedTuple{ψ_reals::Array{ComplexF64, 3}}[(ψ_reals = [0.0016734728661811542 - 0.004352397216935177im 0.044391955128515424 + 0.00019831066290279488im … -0.018661538558586654 - 0.035082284456473795im -0.030989731706858273 - 0.010819175801883445im; -0.0017776310030698298 - 0.031241138353261415im -0.019591207872783137 - 0.02475129006668124im … -0.04632465236935042 + 0.01396341391494938im -0.005260020717721678 + 0.00515907995861645im; … ; 0.032925340365608596 - 0.04177061751384238im 0.036539126508816855 + 0.009021965223941518im … 0.0448649759887718 + 0.0388687828633562im 0.07908634800195842 - 0.04005078002112873im; 0.027007899969595798 - 0.008984902458939688im 0.05102843075144245 + 0.01714829433284954im … 0.04913858485228192 + 0.008581028814937077im 0.017220761880406006 - 0.03285316160470154im;;; 0.07499072827076365 - 0.021537197902525985im 0.07249793120142495 - 0.07950791274080307im … -0.06339267376636556 + 0.14071282787383638im 0.043182578721045486 + 0.06947298670452497im; -0.07486015846202415 + 0.021689199330737964im -0.014542454616053843 - 0.031439570026504784im … 0.035898104344860716 + 0.09106189819879432im -0.007489330828220137 - 0.015864641084074323im; … ; 0.04046443734179429 - 0.037729056943565896im 0.08041829007451484 + 0.0023903488637629887im … 0.09790047155387438 - 0.028406876135719097im 0.04958342471920883 - 0.07618422441897893im; 0.06590236275266521 + 0.0026556748889115037im 0.1398896674353096 - 0.04128297269819087im … -0.033012975612002005 - 0.011788968416094524im -0.003377613728228597 + 0.04342978828837771im;;; 0.013534632248741258 - 0.02581065044929834im 0.03344649390127006 - 0.10357246237630131im … 0.06365395267325073 + 0.09870735584542381im 0.03953257035143909 - 0.013694457062485937im; -0.004374549502350122 + 0.0912899688535673im 0.012741571822675712 - 0.03551189271785246im … -0.030933260118736487 + 0.0035833523166260758im -0.125672016861095 + 0.0892517453835108im; … ; 0.0847523045543485 + 0.009659636089508287im 0.12826733766278325 - 0.04232086790612204im … 0.00027511525977242345 - 0.03459428504514088im 0.013732086140491463 + 0.004851759855563072im; 0.1365865223303941 - 0.045210661054557094im 0.12877439524626294 - 0.1340776942805078im … -0.022429652472687134 + 0.09603133468573571im 0.09068350909000089 + 0.05810734361565984im;;; … ;;; -0.05837223207508168 - 0.011256627421478125im -0.08001284150310578 + 0.06032617811420364im … 0.024432954082954407 - 0.1725867590814285im -0.03495130268636544 - 0.06865636231375605im; -0.015603516958243472 - 0.007649491257099303im -0.013523232073205509 + 0.07190828667704442im … -0.014508969010773823 - 0.06698560340803604im 0.023667471827298874 - 0.03102570165189071im; … ; 0.016047536010886515 + 0.10904567228789258im 0.027609874575944552 + 0.038465570071637846im … -0.13929916064028536 + 0.014409079318362758im -0.07529699543212294 + 0.11911984995524627im; -0.007198434222176489 - 0.005878995549730773im -0.049209834206682054 + 0.00902620412616384im … 0.056094373392776634 - 0.031699691686583056im 0.022243871718591428 - 0.017705894423763708im;;; -0.05057545008662202 + 0.040042478438632206im -0.016064579457417107 + 0.11939346356219825im … -0.10590256106097472 - 0.11991391248402253im -0.06721763135073977 - 0.012912028178511586im; -0.014496839928170968 - 0.02551491269953183im 0.02226690331178091 + 0.03243442515090536im … 0.055731602684370996 - 0.03467581059454415im 0.0633521338242148 - 0.10463336702096745im; … ; 0.008207179354959238 - 0.012736257335145456im -0.03985789518873144 + 0.012476653393309278im … 0.028040115495843787 + 0.006520552842942128im 0.03763015979627859 + 0.02094857286158402im; -0.11803999379754149 + 0.014864776510879103im -0.08935836216222158 + 0.10440872805926674im … 0.004747586023524658 - 0.18784468643029356im -0.08386767623587049 - 0.0921605317135297im;;; -0.013015714069307304 - 0.01514038130803478im -0.0037357770422441275 + 0.027848312989184644im … 0.00799709086434782 - 0.013357384395131955im 0.05355475795044799 - 0.0900187027860611im; -0.05034873578259036 - 0.03677666100345966im -0.02702306790314747 - 0.0074740222701787234im … 0.06351079446834876 - 0.12485488435431691im -0.03279077001199261 - 0.12863928652341822im; … ; -0.01812119863963521 - 0.017200045235476157im -0.025443643299607688 + 0.04732268149448925im … 0.0057479277772285245 - 0.04278035652662718im 0.026119099556756856 - 0.0179472217452881im; -0.012468424105132558 + 0.036608883890964415im 0.014901383863362788 + 0.0810745791758158im … -0.06696781433000465 - 0.03801400730895006im -0.03673529091636072 + 0.0026929357180470077im],)])]), basis = PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 15.0 Ha, kgrid = MonkhorstPack([3, 3, 3])), energies = Energies(total = -7.910594396488504), converged = true, ρ = [7.589784542567461e-5 0.0011262712728386517 … 0.006697037550090543 0.001126271272838662; 0.0011262712728386534 0.005274334457381303 … 0.005274334457381334 0.0011262712728386636; … ; 0.006697037550090552 0.005274334457381329 … 0.023244754191048215 0.01225898682524672; 0.0011262712728386671 0.0011262712728386636 … 0.012258986825246712 0.0037700086299027958;;; 0.0011262712728386537 0.005274334457381312 … 0.00527433445738134 0.0011262712728386658; 0.0052743344573813085 0.014620065304735502 … 0.005274334457381333 0.002588080874857377; … ; 0.005274334457381351 0.0052743344573813284 … 0.01810768664614617 0.008922003044755888; 0.0011262712728386695 0.002588080874857371 … 0.00892200304475588 0.002588080874857386;;; 0.00669703755009051 0.016412109101612383 … 0.006697037550090538 0.0037700086299027823; 0.016412109101612383 0.03127783931594172 … 0.008922003044755865 0.008922003044755844; … ; 0.006697037550090548 0.008922003044755858 … 0.016476756359456866 0.008922003044755888; 0.0037700086299027875 0.008922003044755844 … 0.00892200304475588 0.0037700086299027884;;; … ;;; 0.019853839853406795 0.01641210910161239 … 0.03715667363565941 0.027190800686576446; 0.016412109101612386 0.014620065304735506 … 0.03230127212644148 0.022322100931718918; … ; 0.03715667363565941 0.03230127212644147 … 0.046296980701432816 0.04263658273142514; 0.027190800686576446 0.022322100931718918 … 0.04263658273142514 0.034772229141986064;;; 0.006697037550090515 0.005274334457381311 … 0.02324475419104819 0.012258986825246688; 0.005274334457381311 0.005274334457381305 … 0.01810768664614613 0.008922003044755848; … ; 0.023244754191048198 0.018107686646146124 … 0.040371110335559963 0.03149160381137412; 0.012258986825246692 0.008922003044755848 … 0.031491603811374114 0.02004716343273181;;; 0.0011262712728386532 0.001126271272838662 … 0.012258986825246707 0.003770008629902788; 0.0011262712728386582 0.002588080874857367 … 0.008922003044755867 0.002588080874857379; … ; 0.012258986825246718 0.008922003044755865 … 0.03149160381137413 0.02004716343273184; 0.0037700086299027906 0.002588080874857372 … 0.020047163432731833 0.008952603496771853;;;;], eigenvalues = [[-0.1783683565395995, 0.2624919449911263, 0.2624919449911266, 0.2624919449911268, 0.3546921481675614, 0.35469214816756195, 0.35469214817267325], [-0.12755037617946607, 0.06475320594657258, 0.2254516651738499, 0.22545166517384999, 0.3219776496111841, 0.38922276908472164, 0.38922276908472203], [-0.10818729216535891, 0.07755003473406505, 0.17278328011443692, 0.17278328011443736, 0.28435185361973825, 0.3305476484330285, 0.5267232426395239], [-0.05777325374465118, 0.012724782205227818, 0.09766073750109311, 0.1841782533294447, 0.3152284179598256, 0.47203123646931744, 0.49791351855523147]], 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 = 0.27342189930543254, n_iter = 10, ψ = Matrix{ComplexF64}[[0.17897501258379692 + 0.9325618650244011im 3.494707438418179e-13 - 1.0216449398158559e-13im … -1.736664419940109e-11 - 5.945087066792047e-12im -7.90715866888256e-7 - 2.9379506804866644e-7im; 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-0.38769143829172337 - 0.05698901471334878im 0.035705984367171456 - 0.619743736838668im … 0.08917446657769641 - 0.15867966456217542im -1.1612125304065102e-7 + 5.311060536809534e-6im; … ; 0.007907663719564192 + 0.01063307443293805im -0.0001895474798674668 + 0.00016889607325992615im … 0.01255855516461551 - 0.003525001212481902im 0.006413316215226473 - 0.0456539103070839im; -0.06637812369223128 - 0.00975730566648896im -0.00030561537547695256 + 0.005304522986108195im … 0.07031195724520874 - 0.12514397172002087im -0.28363566556288616 - 0.3763079686412059im]], residual_norms = [[0.0, 2.6227785734210587e-12, 1.3244725920620039e-12, 2.3926511161945127e-12, 7.246451865587596e-12, 7.873335510814769e-11, 3.5414266470025033e-6], [0.0, 0.0, 3.5897457324095625e-12, 3.6137113206868593e-12, 5.500528940108615e-10, 1.2629720817167075e-8, 1.3052212358651764e-8], [1.142789074274719e-12, 1.4197171927151219e-12, 1.4409036492356846e-12, 1.4201611787796778e-12, 4.965929049695434e-11, 1.4535174790554939e-9, 1.2340664793848266e-6], [0.0, 0.0, 2.243579530464515e-12, 2.3001307936989633e-12, 7.667606686135136e-10, 0.0001228702771803448, 3.7374161853755996e-5]], n_iter = [5, 3, 3, 3], converged = 1, n_matvec = 119)], stage = :finalize, algorithm = "SCF", history_Δρ = [0.21069418705186088, 0.027611519786747456, 0.0023096677277025957, 0.00025785390274429, 9.301479304033525e-6, 8.924043503162435e-7, 4.2323057648630993e-8, 3.0051369661219165e-9, 1.603876075811974e-10, 1.7692007602539982e-11], history_Etot = [-7.905261869973346, -7.910544370303269, -7.910593452964777, -7.910594393412763, -7.910594396449799, -7.910594396488426, -7.910594396488505, -7.910594396488506, -7.910594396488506, -7.910594396488504], occupation_threshold = 1.0e-6, runtime_ns = 0x000000009f9f8b1b)