Hubbard correction (DFT+U)

In this example, we'll plot the DOS and projected DOS of Nickel Oxide with and without the Hubbard term correction.

using DFTK
using PseudoPotentialData
using Unitful
using UnitfulAtomic
using Plots

Define the geometry and pseudopotential

a = 7.9  # Nickel Oxide lattice constant in Bohr
lattice = a * [[ 1.0  0.5  0.5];
               [ 0.5  1.0  0.5];
               [ 0.5  0.5  1.0]]
pseudopotentials = PseudoFamily("dojo.nc.sr.pbe.v0_4_1.standard.upf")
Ni = ElementPsp(:Ni, pseudopotentials)
O  = ElementPsp(:O, pseudopotentials)
atoms = [Ni, O, Ni, O]
positions = [zeros(3), ones(3) / 4, ones(3) / 2, ones(3) * 3 / 4]
magnetic_moments = [2, 0, -1, 0]

4-element Vector{Int64}:
  2
  0
 -1
  0

First, we run an SCF and band computation without the Hubbard term

model = model_DFT(lattice, atoms, positions; temperature=5e-3,
                  functionals=PBE(), magnetic_moments)
basis = PlaneWaveBasis(model; Ecut=20, kgrid=[2, 2, 2])
scfres = self_consistent_field(basis; tol=1e-6, ρ=guess_density(basis, magnetic_moments))
bands = compute_bands(scfres, MonkhorstPack(4, 4, 4))
lowest_unocc_band = findfirst(ε -> ε-bands.εF > 0, bands.eigenvalues[1])
band_gap = bands.eigenvalues[1][lowest_unocc_band] - bands.eigenvalues[1][lowest_unocc_band-1]

0.08219271482621016

Then we plot the DOS and the PDOS for the relevant 3D (pseudo)atomic projector

εF = bands.εF
width = 5.0u"eV"
εrange = (εF - austrip(width), εF + austrip(width))
p = plot_dos(bands; εrange, colors=[:red, :red])
plot_pdos(bands; p, iatom=1, label="3D", colors=[:yellow, :orange], εrange)

To perform and Hubbard computation, we have to define the Hubbard manifold and associated constant.

In DFTK there are a few ways to construct the OrbitalManifold. Here, we will apply the Hubbard correction on the 3D orbital of all nickel atoms.

Note that "manifold" is the standard term used in the literature for the set of atomic orbitals used to compute the Hubbard correction, but it is not meant in the mathematical sense.

U = 10u"eV"
manifold = OrbitalManifold(atoms, Ni, "3D")

OrbitalManifold(PspUpf{Float64, Interpolations.Extrapolation{Float64, 1, Interpolations.GriddedInterpolation{Float64, 1, Vector{Float64}, Interpolations.Gridded{Interpolations.Linear{Interpolations.Throw{Interpolations.OnGrid}}}, Tuple{Vector{Float64}}}, Interpolations.Gridded{Interpolations.Linear{Interpolations.Throw{Interpolations.OnGrid}}}, Interpolations.Throw{Nothing}}}(18, 2, [0.0, 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09  …  13.62, 13.63, 13.64, 13.65, 13.66, 13.67, 13.68, 13.69, 13.7, 13.71], [0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01  …  0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01], [-30.7606040365, -30.7593739845, -30.755682951, -30.7495283205, -30.740905647, -30.7298085375, -30.716228498, -30.700154752, -30.681574037, -30.660470406  …  -1.3215850272, -1.3206154187, -1.3196472319, -1.3186804636, -1.31771511075, -1.31675117025, -1.31578863895, -1.31482751375, -1.31386779165, -1.31290946955], [[[-0.0, 0.0005217795003000001, 0.0020831601089999997, 0.0046723025154, 0.0082695886268, 0.012847791100500001, 0.018372307510799997, 0.0248014560444, 0.0320868288388, 0.04017369836115  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [-0.0, 0.00028922418401, 0.0011509529034, 0.00256749292695, 0.0045098131016, 0.006938219141500001, 0.009803275499699999, 0.013046952142, 0.0166039686152, 0.02040330304755  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], [[0.0, 7.8037391715e-6, 6.2367815898e-5, 0.00021014258838, 0.00049696081846, 0.0009677347417000001, 0.0016661600746800001, 0.0026344291007300005, 0.00391295483348, 0.00554010808725  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [-0.0, -8.660111850500001e-6, -6.905143214e-5, -0.00023176402578, -0.00054513429178, -0.0010541889172, -0.00179967164997, -0.0028171770128950003, -0.0041364122088, -0.005780605017599999  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], [[0.0, 1.5464858854e-7, 2.4717230303999998e-6, 1.2490731494549999e-5, 3.937811459200001e-5, 9.582878665e-5, 0.000197929587672, 0.00036498592298000006, 0.00061931320804, 0.000985995059265  …  0.005090920716645, 0.0028433923676649997, 0.001234928893802, 0.00031278601398825, -5.859709123050999e-5, -8.369209057265e-5, 4.421824089984e-6, 2.5655702737015e-5, -6.07884920211e-7, -5.0078592404775e-6], [-0.0, -8.963316422e-8, -1.4313025747e-6, -7.22215646955e-6, -2.2720540228000002e-5, -5.51417012075e-5, -0.000113513874429, -0.00020849681132350002, -0.00035216535126, -0.00055776113523  …  -0.01766690779761, -0.00983409528922, -0.004293974434816, -0.00114969821175, 0.00012000798693809999, 0.0002450364669611, -1.335466494936e-5, -7.8567691750925e-5, 1.8202693242099999e-6, 1.5111426717225001e-5]]], [[25.01813916 0.0; 0.0 -1.00698946204], [-11.3608362698 0.0; 0.0 -1.55042267544], [-28.89375713 0.0; 0.0 -10.1777566916]], [[[-0.0, 0.00027294903406, 0.00109160842824, 0.0024554138733, 0.0043634209180000005, 0.006814299107500001, 0.0098063238612, 0.013337366169400003, 0.017404880222400002, 0.0220058890884  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 6.8646807342e-5, 0.00027453709056000003, 0.0006175195142699999, 0.00109733880272, 0.0017136312077000002, 0.00246591824922, 0.0033535988122000006, 0.00437593970584, 0.0055320648111  …  -0.016003109683488, -0.015912392467138003, -0.01582217938664, -0.015732467718240002, -0.015643254754670002, -0.015554537799784999, -0.015466314172751999, -0.015378581205412, -0.01529133624648, -0.015204576654795]], [[0.0, 7.7353207428e-6, 6.1837537246e-5, 0.00020844864918, 0.00049326202792, 0.0009613010095, 0.0016567009596, 0.0026224959398400004, 0.00390041108072, 0.00553066173567  …  3.4207753363979996e-12, 2.9580211617234e-12, 2.5030031035504e-12, 2.0596655044875e-12, 1.6318817906438002e-12, 1.2234048413374e-12, 8.378180416015201e-13, 4.7848739224029e-13, 1.485150599799e-13, -1.0284648499172701e-13]], [[0.0, 9.7474246874e-8, 1.5584805266599999e-6, 7.880471791199999e-6, 2.48649312524e-5, 6.0576154519999996e-5, 0.000125283923376, 0.00023139044704300002, 0.00039334204984800005, 0.000627526183959  …  0.00028610476879614, 0.0002839650496067, 0.0002818412291926, 0.00027973319038665, 0.00027764081686498, 0.00027556399313817, 0.00027350260461071995, 0.00027145653747648, 0.0002694256787643, 0.00026740991634273]]], [[2.0, 2.0], [6.0], [8.0]], [[-8.162710468, -0.4147552231], [-5.246920661], [-0.6522360711]], [["3S", "4S"], ["3P"], ["3D"]], [0.0, 0.00012635804776325816, 0.0005086834426636858, 0.0011567007365190021, 0.0020865202992691695, 0.0033204929328059505, 0.004887007214543443, 0.006820230474506866, 0.009159794593235451, 0.011950428106775853  …  2.2000348856820538e-7, 2.1719621546743513e-7, 2.144247240663934e-7, 2.1168855897504148e-7, 2.0898727060453842e-7, 2.0632041506379014e-7, 2.0368755409578763e-7, 2.0108825499802936e-7, 1.9852209059069028e-7, 1.959886386277487e-7], [0.0, 0.0011510748749, 0.0045942353996, 0.010299392244, 0.0182167385264, 0.028277258525000005, 0.0403934313564, 0.05446012122950001, 0.0703556437056, 0.0879429953196  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], 1372-element extrapolate(interpolate((::Vector{Float64},), ::Vector{Float64}, Gridded(Linear())), Throw()) with element type Float64:
 -30.7606040365
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   ⋮
  -1.3206154187
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  -1.3186804636
  -1.31771511075
  -1.31675117025
  -1.31578863895
  -1.31482751375
  -1.31386779165
  -1.31290946955, Vector{Interpolations.Extrapolation{Float64, 1, Interpolations.GriddedInterpolation{Float64, 1, Vector{Float64}, Interpolations.Gridded{Interpolations.Linear{Interpolations.Throw{Interpolations.OnGrid}}}, Tuple{Vector{Float64}}}, Interpolations.Gridded{Interpolations.Linear{Interpolations.Throw{Interpolations.OnGrid}}}, Interpolations.Throw{Nothing}}}[[172-element extrapolate(interpolate((::Vector{Float64},), ::Vector{Float64}, Gridded(Linear())), Throw()) with element type Float64:
 0.0
 0.0005217795003000001
 0.0020831601089999997
 0.0046723025154
 0.0082695886268
 0.012847791100500001
 0.018372307510799997
 0.0248014560444
 0.0320868288388
 0.04017369836115
 ⋮
 0.0
 0.0
 0.0
 0.0
 0.0
 0.0
 0.0
 0.0
 0.0, 172-element extrapolate(interpolate((::Vector{Float64},), ::Vector{Float64}, Gridded(Linear())), Throw()) with element type Float64:
 0.0
 0.00028922418401
 0.0011509529034
 0.00256749292695
 0.0045098131016
 0.006938219141500001
 0.009803275499699999
 0.013046952142
 0.0166039686152
 0.02040330304755
 ⋮
 0.0
 0.0
 0.0
 0.0
 0.0
 0.0
 0.0
 0.0
 0.0], [172-element extrapolate(interpolate((::Vector{Float64},), ::Vector{Float64}, Gridded(Linear())), Throw()) with element type Float64:
 0.0
 7.8037391715e-6
 6.2367815898e-5
 0.00021014258838
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 0.0009677347417000001
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 0.0026344291007300005
 0.00391295483348
 0.00554010808725
 ⋮
 0.0
 0.0
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 0.0
 0.0
 0.0
 0.0
 0.0
 0.0, 172-element extrapolate(interpolate((::Vector{Float64},), ::Vector{Float64}, Gridded(Linear())), Throw()) with element type Float64:
 -0.0
 -8.660111850500001e-6
 -6.905143214e-5
 -0.00023176402578
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 -0.0010541889172
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 -0.0028171770128950003
 -0.0041364122088
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  ⋮
  0.0
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  0.0], [172-element extrapolate(interpolate((::Vector{Float64},), ::Vector{Float64}, Gridded(Linear())), Throw()) with element type Float64:
  0.0
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  ⋮
  0.0028433923676649997
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  4.421824089984e-6
  2.5655702737015e-5
 -6.07884920211e-7
 -5.0078592404775e-6, 172-element extrapolate(interpolate((::Vector{Float64},), ::Vector{Float64}, Gridded(Linear())), Throw()) with element type Float64:
 -0.0
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 -1.4313025747e-6
 -7.22215646955e-6
 -2.2720540228000002e-5
 -5.51417012075e-5
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  ⋮
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  0.00012000798693809999
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  1.5111426717225001e-5]], 1372-element extrapolate(interpolate((::Vector{Float64},), ::Vector{Float64}, Gridded(Linear())), Throw()) with element type Float64:
 0.0
 0.00012635804776325816
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 0.0033204929328059505
 0.004887007214543443
 0.006820230474506866
 0.009159794593235451
 0.011950428106775853
 ⋮
 2.1719621546743513e-7
 2.144247240663934e-7
 2.1168855897504148e-7
 2.0898727060453842e-7
 2.0632041506379014e-7
 2.0368755409578763e-7
 2.0108825499802936e-7
 1.9852209059069028e-7
 1.959886386277487e-7, 1372-element extrapolate(interpolate((::Vector{Float64},), ::Vector{Float64}, Gridded(Linear())), Throw()) with element type Float64:
 0.0
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 0.0045942353996
 0.010299392244
 0.0182167385264
 0.028277258525000005
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 ⋮
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 0.0, 10.0, 1001, "/home/runner/.julia/artifacts/6629fcfbb53461928968115342cb8b4a0d27d33c/Ni.upf", ""), [1, 3], 2, 1)

Run SCF with a DFT+U setup, notice the extra_terms keyword argument, setting up the Hubbard +U term.

model = model_DFT(lattice, atoms, positions; extra_terms=[Hubbard(manifold, U)],
                  functionals=PBE(), temperature=5e-3, magnetic_moments)
basis = PlaneWaveBasis(model; Ecut=20, kgrid=[2, 2, 2])
scfres = self_consistent_field(basis; tol=1e-6, ρ=guess_density(basis, magnetic_moments))

(ham = Hamiltonian(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), HamiltonianBlock[DFTK.GenericHamiltonianBlock(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 1, num. G vectors =  1075), Any[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 1, num. G vectors =  1075), [0.0, 0.8697776671365403, 3.479110668546161, 7.827999004228862, 13.916442674184644, 13.916442674184644, 7.827999004228862, 3.479110668546161, 0.8697776671365403, 0.8697776671365403  …  1.265131152198604, 0.9488483641489529, 3.400039971533748, 7.590786913191624, 13.521089189122582, 14.78622034132119, 8.53963527734058, 4.03260554763305, 1.265131152198604, 0.23721209103723823]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 1, num. G vectors =  1075), [-19.69293028378679 -19.127691055462872 … -17.172460520653278 -19.127691055462872; -19.127691055462876 -17.402291367764306 … -18.721733773909865 -19.50894133358841; … ; -17.172460520653278 -18.721733773909865 … -10.245935170367524 -14.130197210981127; -19.127691055462872 -19.508941333588407 … -14.130197210981125 -17.402291367764303;;; -19.127691055462876 -17.402291367764303 … -18.72173377390986 -19.50894133358841; -17.402291367764303 -14.359308164945631 … -19.125807118069726 -18.92715469613527; … ; -18.721733773909865 -19.125807118069723 … -13.677457054305759 -16.940214173578532; -19.50894133358841 -18.92715469613527 … -16.940214173578532 -18.927154696135265;;; -17.172460520653278 -14.130197210981125 … -18.92628169003941 -18.721733773909865; -14.130197210981125 -10.423976117759622 … -18.297379847683594 -16.940214173578532; … ; -18.92628169003941 -18.297379847683594 … -16.235670612963965 -18.29737984768359; -18.72173377390986 -16.940214173578532 … -18.297379847683587 -19.125807118069723;;; … ;;; -13.677837405304386 -16.472166305707145 … -6.690325178037546 -10.071186579504449; -16.472166305707145 -18.079038283637747 … -9.730069757032524 -13.454546643596201; … ; -6.690325178037547 -9.730069757032522 … -2.391416851902863 -4.231026654525081; -10.071186579504452 -13.454546643596197 … -4.231026654525081 -6.802550458542525;;; -17.172460520653274 -18.72173377390986 … -10.245935170367522 -14.130197210981125; -18.72173377390986 -19.125807118069723 … -13.677457054305755 -16.940214173578532; … ; -10.245935170367522 -13.677457054305755 … -4.298952176788824 -6.916318157831658; -14.130197210981128 -16.940214173578532 … -6.916318157831658 -10.423976117759619;;; -19.127691055462876 -19.508941333588407 … -14.130197210981125 -17.402291367764303; -19.508941333588407 -18.92715469613527 … -16.940214173578536 -18.927154696135265; … ; -14.130197210981128 -16.940214173578536 … -6.91631815783166 -10.423976117759619; -17.402291367764303 -18.927154696135265 … -10.423976117759617 -14.359308164945627]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 1, num. G vectors =  1075), ComplexF64[0.0006002260183055469 + 0.0im 0.07505547926746237 + 0.0im … -0.0 + 0.0im -0.0 + 0.0im; 0.0038095861649428834 + 0.0im 0.0575940500481257 + 0.0im … -0.0 - 0.002199873402472219im 0.0 + 0.002933164536629625im; … ; 0.005099332415993166 + 0.0im 0.050624187347729784 + 0.0im … -0.0 + 0.0im 0.0057490967761396235 + 0.0im; 0.001528456059177435 + 0.0im 0.0699878067058058 + 0.0im … 0.0 + 0.0007557958658307776im 0.0 + 0.0im], [25.01813916 0.0 … 0.0 0.0; 0.0 -1.00698946204 … 0.0 0.0; … ; 0.0 0.0 … -5.327819979 0.0; 0.0 0.0 … 0.0 -5.327819979]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 1, num. G vectors =  1075)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 1, num. G vectors =  1075)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 1, num. G vectors =  1075), [10.877593800343199 10.729889422350716 … 10.09940572538798 10.729889422350716; 10.729889422350716 10.189012190068507 … 10.605300714277549 10.832545389614797; … ; 10.09940572538798 10.605300714277549 … 7.154147988494096 8.94385400564696; 10.729889422350716 10.832545389614799 … 8.94385400564696 10.189012190068507;;; 10.729889422350716 10.189012190068507 … 10.60530071427755 10.832545389614797; 10.189012190068507 9.048105173582577 … 10.729328157888629 10.67229949577574; … ; 10.60530071427755 10.729328157888629 … 8.743132050613442 10.01666945353644; 10.832545389614797 10.672299495775741 … 10.01666945353644 10.672299495775741;;; 10.09940572538798 8.94385400564696 … 10.671694823038989 10.605300714277547; 8.94385400564696 7.25124113554755 … 10.478405847429542 10.01666945353644; … ; 10.671694823038989 10.478405847429542 … 9.758036639158725 10.478405847429542; 10.605300714277547 10.016669453536442 … 10.478405847429542 10.729328157888629;;; … ;;; 8.72960061203429 9.823313976208432 … 5.125906964733587 7.053967661259478; 9.82331397620843 10.38731254842216 … 6.86950217921741 8.633221178530908; … ; 5.125906964733589 6.86950217921741 … 2.064083067041997 3.453936462414575; 7.053967661259478 8.63322117853091 … 3.453936462414576 5.199760967953645;;; 10.09940572538798 10.605300714277547 … 7.154147988494096 8.94385400564696; 10.605300714277549 10.729328157888627 … 8.74313205061344 10.01666945353644; … ; 7.154147988494096 8.743132050613442 … 3.5057692413610893 5.2767073984394965; 8.94385400564696 10.01666945353644 … 5.276707398439497 7.25124113554755;;; 10.729889422350716 10.832545389614795 … 8.94385400564696 10.189012190068505; 10.832545389614797 10.67229949577574 … 10.01666945353644 10.67229949577574; … ; 8.94385400564696 10.01666945353644 … 5.276707398439497 7.25124113554755; 10.189012190068507 10.672299495775741 … 7.25124113554755 9.048105173582577]), DFTK.RealSpaceMultiplication{Float64, SubArray{Float64, 3, Array{Float64, 4}, Tuple{Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Int64}, true}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 1, num. G vectors =  1075), [-2.4486276320726303 -2.245992751112004 … -1.921671638081339 -2.245992751112051; -2.2459927511119857 -1.9541866390021723 … -2.1547727578222857 -2.400027684647741; … ; -1.9216716380813312 -2.1547727578223577 … -1.482585280489783 -1.6409267226498647; -2.2459927511119577 -2.400027684647778 … -1.6409267226497974 -1.9541866390020664;;; -2.2459927511120097 -1.9541866390020397 … -2.154772757822387 -2.4000276846477115; -1.9541866390020215 -1.6481092867546645 … -2.2960282380160675 -2.199699159653614; … ; -2.154772757822308 -2.2960282380161257 … -1.62013007963383 -1.8893785023188108; -2.400027684647722 -2.1996991596536146 … -1.8893785023186933 -2.1996991596536217;;; -1.9216716380813477 -1.6409267226498856 … -2.2427869006357986 -2.154772757822358; -1.6409267226498383 -1.4868345497116555 … -2.0695956826905464 -1.8893785023187788; … ; -2.242786900635731 -2.0695956826907134 … -1.811427666975934 -2.0695956826906547; -2.154772757822319 -1.88937850231873 … -2.0695956826905832 -2.2960282380161012;;; … ;;; -1.6299162872836042 -1.837752996498007 … -1.182859739476749 -1.4739850738953066; -1.8377529964980406 -2.0362474009576084 … -1.4642490217052808 -1.6162359687281103; … ; -1.1828597394768299 -1.46424902170512 … -0.577711036558847 -0.8271490178127838; -1.4739850738953382 -1.6162359687281525 … -0.8271490178128423 -1.2013353171417838;;; -1.9216716380813612 -2.154772757822337 … -1.4825852804898552 -1.6409267226498436; -2.1547727578223688 -2.296028238016138 … -1.6201300796337874 -1.889378502318735; … ; -1.4825852804897763 -1.6201300796338678 … -0.8310516413648759 -1.2189685233576244; -1.6409267226497901 -1.889378502318788 … -1.2189685233575387 -1.486834549711634;;; -2.245992751112092 -2.400027684647719 … -1.6409267226498299 -1.9541866390019784; -2.4000276846476503 -2.199699159653522 … -1.8893785023188043 -2.1996991596536377; … ; -1.640926722649979 -1.8893785023186878 … -1.218968523357663 -1.486834549711493; -1.95418663900202 -2.1996991596535627 … -1.4868345497116486 -1.6481092867547376]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{ComplexF64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 1, num. G vectors =  1075), ComplexF64[-8.859292477751685e-17 - 1.7074042659338244e-16im -4.783566607446491e-17 + 5.663324065062725e-17im … 9.861795881045906e-17 + 2.672442082471657e-16im -1.5974197588400363e-17 - 7.633240274996076e-17im; 0.0899547666901153 - 1.413144577113148e-15im -0.026697568337758607 + 3.0801362819085753e-17im … -0.08995476669011464 + 3.4822917796892204e-16im 0.10617545164788754 - 2.821017445726888e-16im; … ; 9.632346948129199e-17 - 1.3057865978428654e-16im -3.146022294998665e-17 - 4.835959214516585e-17im … 1.3209920794091407e-16 + 1.5024841307910963e-16im -0.16771615563505324 - 1.968999427913288e-16im; -0.05314794173232918 - 1.4572633601693817e-16im -0.05314794173232926 - 2.365957523638594e-17im … 0.053147941732329236 - 2.0193733144987457e-16im -3.001564680560613e-16 - 3.6601892425188467e-16im], ComplexF64[-0.18117993655143472 + 2.6562463293377237e-20im -2.200140701945268e-5 + 4.781243376975576e-19im … -0.0 - 0.0im -0.0 - 0.0im; -2.200140701945268e-5 + 4.7812434086405e-19im -0.18117993655143783 + 2.6562463293380917e-20im … -0.0 - 0.0im -0.0 - 0.0im; … ; -0.0 - 0.0im -0.0 - 0.0im … -0.1804137822512097 - 7.224990015798813e-18im -0.0033087208230130525 + 1.1337570115769357e-8im; -0.0 - 0.0im -0.0 - 0.0im … -0.003308720823013052 - 1.1337570116279256e-8im 0.13303982008815268 + 1.1874349130312374e-27im]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 1, num. G vectors =  1075))], DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 1, num. G vectors =  1075), [0.0, 0.8697776671365403, 3.479110668546161, 7.827999004228862, 13.916442674184644, 13.916442674184644, 7.827999004228862, 3.479110668546161, 0.8697776671365403, 0.8697776671365403  …  1.265131152198604, 0.9488483641489529, 3.400039971533748, 7.590786913191624, 13.521089189122582, 14.78622034132119, 8.53963527734058, 4.03260554763305, 1.265131152198604, 0.23721209103723823]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 1, num. G vectors =  1075), ComplexF64[0.0006002260183055469 + 0.0im 0.07505547926746237 + 0.0im … -0.0 + 0.0im -0.0 + 0.0im; 0.0038095861649428834 + 0.0im 0.0575940500481257 + 0.0im … -0.0 - 0.002199873402472219im 0.0 + 0.002933164536629625im; … ; 0.005099332415993166 + 0.0im 0.050624187347729784 + 0.0im … -0.0 + 0.0im 0.0057490967761396235 + 0.0im; 0.001528456059177435 + 0.0im 0.0699878067058058 + 0.0im … 0.0 + 0.0007557958658307776im 0.0 + 0.0im], [25.01813916 0.0 … 0.0 0.0; 0.0 -1.00698946204 … 0.0 0.0; … ; 0.0 0.0 … -5.327819979 0.0; 0.0 0.0 … 0.0 -5.327819979]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{ComplexF64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 1, num. G vectors =  1075), ComplexF64[-8.859292477751685e-17 - 1.7074042659338244e-16im -4.783566607446491e-17 + 5.663324065062725e-17im … 9.861795881045906e-17 + 2.672442082471657e-16im -1.5974197588400363e-17 - 7.633240274996076e-17im; 0.0899547666901153 - 1.413144577113148e-15im -0.026697568337758607 + 3.0801362819085753e-17im … -0.08995476669011464 + 3.4822917796892204e-16im 0.10617545164788754 - 2.821017445726888e-16im; … ; 9.632346948129199e-17 - 1.3057865978428654e-16im -3.146022294998665e-17 - 4.835959214516585e-17im … 1.3209920794091407e-16 + 1.5024841307910963e-16im -0.16771615563505324 - 1.968999427913288e-16im; -0.05314794173232918 - 1.4572633601693817e-16im -0.05314794173232926 - 2.365957523638594e-17im … 0.053147941732329236 - 2.0193733144987457e-16im -3.001564680560613e-16 - 3.6601892425188467e-16im], ComplexF64[-0.18117993655143472 + 2.6562463293377237e-20im -2.200140701945268e-5 + 4.781243376975576e-19im … -0.0 - 0.0im -0.0 - 0.0im; -2.200140701945268e-5 + 4.7812434086405e-19im -0.18117993655143783 + 2.6562463293380917e-20im … -0.0 - 0.0im -0.0 - 0.0im; … ; -0.0 - 0.0im -0.0 - 0.0im … -0.1804137822512097 - 7.224990015798813e-18im -0.0033087208230130525 + 1.1337570115769357e-8im; -0.0 - 0.0im -0.0 - 0.0im … -0.003308720823013052 - 1.1337570116279256e-8im 0.13303982008815268 + 1.1874349130312374e-27im]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 1, num. G vectors =  1075), [-11.263964115516222 -10.64379438422416 … -8.994726433346637 -10.643794384224208; -10.643794384224146 -9.167465816697971 … -10.271205817454602 -11.076423628621354; … ; -8.99472643334663 -10.271205817454673 … -4.57437246236321 -6.827269927984031; -10.643794384224114 -11.076423628621386 … -6.827269927983962 -9.167465816697863;;; -10.643794384224169 -9.167465816697835 … -10.271205817454698 -11.076423628621324; -9.167465816697817 -6.959312278117718 … -10.692507198197164 -10.454554360013143; … ; -10.271205817454621 -10.69250719819722 … -6.554455083326147 -8.812923222360903; -11.076423628621335 -10.454554360013141 … -8.812923222360785 -10.454554360013145;;; -8.994726433346646 -6.82726992798405 … -10.497373767636219 -10.271205817454675; -6.827269927984003 -4.659569531923728 … -9.888569682944599 -8.81292322236087; … ; -10.497373767636152 -9.888569682944766 … -8.289061640781174 -9.888569682944702; -10.271205817454632 -8.81292322236082 … -9.888569682944627 -10.692507198197195;;; … ;;; -6.578153080553701 -8.48660532599672 … -2.747277952780708 -4.491203992140277; -8.486605325996756 -9.727973136173194 … -4.324816599520395 -6.4375614337934035; … ; -2.747277952780788 -4.324816599520233 … -0.905044821419713 -1.6042392099232898; -4.491203992140312 -6.43756143379344 … -1.6042392099233473 -2.804124807730664;;; -8.994726433346656 -10.27120581745465 … -4.57437246236328 -6.827269927984008; -10.271205817454682 -10.692507198197234 … -6.554455083326102 -8.812923222360826; … ; -4.574372462363202 -6.554455083326181 … -1.624234576792611 -2.858579282749786; -6.827269927983958 -8.81292322236088 … -2.8585792827497 -4.659569531923703;;; -10.64379438422425 -11.076423628621331 … -6.827269927983995 -9.167465816697776; -11.07642362862126 -10.45455436001305 … -8.812923222360899 -10.454554360013162; … ; -6.827269927984148 -8.812923222360784 … -2.858579282749826 -4.6595695319235615; -9.167465816697815 -10.454554360013086 … -4.659569531923715 -6.959312278117787])], nothing), DFTK.GenericHamiltonianBlock(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 1, num. G vectors =  1058), Any[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 1, num. G vectors =  1058), [0.21744441678413506, 0.21744441678413506, 1.9569997510572155, 5.436110419603376, 10.654776422422616, 17.61299775951494, 17.61299775951494, 10.654776422422616, 5.436110419603376, 1.9569997510572155  …  0.3755858108089606, 1.9569997510572157, 5.277969025578551, 10.338493634372968, 17.138573577440457, 18.561846123663894, 11.44548339254675, 6.0686759957026775, 2.431423933131692, 0.5337272048337861]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 1, num. G vectors =  1058), [-19.69293028378679 -19.127691055462872 … -17.172460520653278 -19.127691055462872; -19.127691055462876 -17.402291367764306 … -18.721733773909865 -19.50894133358841; … ; -17.172460520653278 -18.721733773909865 … -10.245935170367524 -14.130197210981127; -19.127691055462872 -19.508941333588407 … -14.130197210981125 -17.402291367764303;;; -19.127691055462876 -17.402291367764303 … -18.72173377390986 -19.50894133358841; -17.402291367764303 -14.359308164945631 … -19.125807118069726 -18.92715469613527; … ; -18.721733773909865 -19.125807118069723 … -13.677457054305759 -16.940214173578532; -19.50894133358841 -18.92715469613527 … -16.940214173578532 -18.927154696135265;;; -17.172460520653278 -14.130197210981125 … -18.92628169003941 -18.721733773909865; -14.130197210981125 -10.423976117759622 … -18.297379847683594 -16.940214173578532; … ; -18.92628169003941 -18.297379847683594 … -16.235670612963965 -18.29737984768359; -18.72173377390986 -16.940214173578532 … -18.297379847683587 -19.125807118069723;;; … ;;; -13.677837405304386 -16.472166305707145 … -6.690325178037546 -10.071186579504449; -16.472166305707145 -18.079038283637747 … -9.730069757032524 -13.454546643596201; … ; -6.690325178037547 -9.730069757032522 … -2.391416851902863 -4.231026654525081; -10.071186579504452 -13.454546643596197 … -4.231026654525081 -6.802550458542525;;; -17.172460520653274 -18.72173377390986 … -10.245935170367522 -14.130197210981125; -18.72173377390986 -19.125807118069723 … -13.677457054305755 -16.940214173578532; … ; -10.245935170367522 -13.677457054305755 … -4.298952176788824 -6.916318157831658; -14.130197210981128 -16.940214173578532 … -6.916318157831658 -10.423976117759619;;; -19.127691055462876 -19.508941333588407 … -14.130197210981125 -17.402291367764303; -19.508941333588407 -18.92715469613527 … -16.940214173578536 -18.927154696135265; … ; -14.130197210981128 -16.940214173578536 … -6.91631815783166 -10.423976117759619; -17.402291367764303 -18.927154696135265 … -10.423976117759617 -14.359308164945627]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 1, num. G vectors =  1058), ComplexF64[0.0014526620565169196 + 0.0im 0.07040107498680777 + 0.0im … 0.0004011832434853789 - 0.0004011832434853788im -0.0005349109913138384 + 0.0005349109913138384im; 0.0014526620565169196 + 0.0im 0.07040107498680777 + 0.0im … 0.0004011832434853789 + 0.0004011832434853788im -0.0005349109913138384 - 0.0005349109913138384im; … ; 0.008349144389251885 + 0.0im 0.033173443134468926 + 0.0im … 0.0013093410302517496 - 0.0013093410302517493im -0.007141860165009543 + 0.007141860165009542im; 0.0026321132587078 + 0.0im 0.0639807860468336 + 0.0im … -0.0006588486948450427 - 0.0006588486948450426im -0.0015812368676281026 - 0.0015812368676281024im], [25.01813916 0.0 … 0.0 0.0; 0.0 -1.00698946204 … 0.0 0.0; … ; 0.0 0.0 … -5.327819979 0.0; 0.0 0.0 … 0.0 -5.327819979]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 1, num. G vectors =  1058)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 1, num. G vectors =  1058)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 1, num. G vectors =  1058), [10.877593800343199 10.729889422350716 … 10.09940572538798 10.729889422350716; 10.729889422350716 10.189012190068507 … 10.605300714277549 10.832545389614797; … ; 10.09940572538798 10.605300714277549 … 7.154147988494096 8.94385400564696; 10.729889422350716 10.832545389614799 … 8.94385400564696 10.189012190068507;;; 10.729889422350716 10.189012190068507 … 10.60530071427755 10.832545389614797; 10.189012190068507 9.048105173582577 … 10.729328157888629 10.67229949577574; … ; 10.60530071427755 10.729328157888629 … 8.743132050613442 10.01666945353644; 10.832545389614797 10.672299495775741 … 10.01666945353644 10.672299495775741;;; 10.09940572538798 8.94385400564696 … 10.671694823038989 10.605300714277547; 8.94385400564696 7.25124113554755 … 10.478405847429542 10.01666945353644; … ; 10.671694823038989 10.478405847429542 … 9.758036639158725 10.478405847429542; 10.605300714277547 10.016669453536442 … 10.478405847429542 10.729328157888629;;; … ;;; 8.72960061203429 9.823313976208432 … 5.125906964733587 7.053967661259478; 9.82331397620843 10.38731254842216 … 6.86950217921741 8.633221178530908; … ; 5.125906964733589 6.86950217921741 … 2.064083067041997 3.453936462414575; 7.053967661259478 8.63322117853091 … 3.453936462414576 5.199760967953645;;; 10.09940572538798 10.605300714277547 … 7.154147988494096 8.94385400564696; 10.605300714277549 10.729328157888627 … 8.74313205061344 10.01666945353644; … ; 7.154147988494096 8.743132050613442 … 3.5057692413610893 5.2767073984394965; 8.94385400564696 10.01666945353644 … 5.276707398439497 7.25124113554755;;; 10.729889422350716 10.832545389614795 … 8.94385400564696 10.189012190068505; 10.832545389614797 10.67229949577574 … 10.01666945353644 10.67229949577574; … ; 8.94385400564696 10.01666945353644 … 5.276707398439497 7.25124113554755; 10.189012190068507 10.672299495775741 … 7.25124113554755 9.048105173582577]), DFTK.RealSpaceMultiplication{Float64, SubArray{Float64, 3, Array{Float64, 4}, Tuple{Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Int64}, true}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 1, num. G vectors =  1058), [-2.4486276320726303 -2.245992751112004 … -1.921671638081339 -2.245992751112051; -2.2459927511119857 -1.9541866390021723 … -2.1547727578222857 -2.400027684647741; … ; -1.9216716380813312 -2.1547727578223577 … -1.482585280489783 -1.6409267226498647; -2.2459927511119577 -2.400027684647778 … -1.6409267226497974 -1.9541866390020664;;; -2.2459927511120097 -1.9541866390020397 … -2.154772757822387 -2.4000276846477115; -1.9541866390020215 -1.6481092867546645 … -2.2960282380160675 -2.199699159653614; … ; -2.154772757822308 -2.2960282380161257 … -1.62013007963383 -1.8893785023188108; -2.400027684647722 -2.1996991596536146 … -1.8893785023186933 -2.1996991596536217;;; -1.9216716380813477 -1.6409267226498856 … -2.2427869006357986 -2.154772757822358; -1.6409267226498383 -1.4868345497116555 … -2.0695956826905464 -1.8893785023187788; … ; -2.242786900635731 -2.0695956826907134 … -1.811427666975934 -2.0695956826906547; -2.154772757822319 -1.88937850231873 … -2.0695956826905832 -2.2960282380161012;;; … ;;; -1.6299162872836042 -1.837752996498007 … -1.182859739476749 -1.4739850738953066; -1.8377529964980406 -2.0362474009576084 … -1.4642490217052808 -1.6162359687281103; … ; -1.1828597394768299 -1.46424902170512 … -0.577711036558847 -0.8271490178127838; -1.4739850738953382 -1.6162359687281525 … -0.8271490178128423 -1.2013353171417838;;; -1.9216716380813612 -2.154772757822337 … -1.4825852804898552 -1.6409267226498436; -2.1547727578223688 -2.296028238016138 … -1.6201300796337874 -1.889378502318735; … ; -1.4825852804897763 -1.6201300796338678 … -0.8310516413648759 -1.2189685233576244; -1.6409267226497901 -1.889378502318788 … -1.2189685233575387 -1.486834549711634;;; -2.245992751112092 -2.400027684647719 … -1.6409267226498299 -1.9541866390019784; -2.4000276846476503 -2.199699159653522 … -1.8893785023188043 -2.1996991596536377; … ; -1.640926722649979 -1.8893785023186878 … -1.218968523357663 -1.486834549711493; -1.95418663900202 -2.1996991596535627 … -1.4868345497116486 -1.6481092867547376]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{ComplexF64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 1, num. G vectors =  1058), ComplexF64[0.0456169904168819 + 5.256995280119557e-17im -0.005769056936983059 - 3.7269078237974735e-17im … -7.735188675374558e-17 + 0.04561699041688176im -6.849128483095165e-17 - 0.06204498655219164im; 0.045616990416881865 - 7.86928762928864e-17im -0.0057690569369830205 + 9.336541693261431e-18im … 1.5419256198164503e-17 - 0.04561699041688183im -9.488344932578529e-17 + 0.06204498655219174im; … ; 0.021965357246362498 + 2.2464498668511797e-18im -0.002934802628982521 + 8.536727290997887e-17im … 1.9479992462911396e-18 + 0.021965357246362494im 8.64310917551173e-17 - 0.1335397161269563im; -0.059772984378440364 - 3.7392872748683694e-17im -0.007492120784271785 + 3.665094057581889e-17im … 6.887202895609839e-18 + 0.059772984378440246im -1.3882455122011876e-17 + 0.11270080613749778im], ComplexF64[-0.18117993655143472 + 2.6562463293377237e-20im -2.200140701945268e-5 + 4.781243376975576e-19im … -0.0 - 0.0im -0.0 - 0.0im; -2.200140701945268e-5 + 4.7812434086405e-19im -0.18117993655143783 + 2.6562463293380917e-20im … -0.0 - 0.0im -0.0 - 0.0im; … ; -0.0 - 0.0im -0.0 - 0.0im … -0.1804137822512097 - 7.224990015798813e-18im -0.0033087208230130525 + 1.1337570115769357e-8im; -0.0 - 0.0im -0.0 - 0.0im … -0.003308720823013052 - 1.1337570116279256e-8im 0.13303982008815268 + 1.1874349130312374e-27im]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 1, num. G vectors =  1058))], DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 1, num. G vectors =  1058), [0.21744441678413506, 0.21744441678413506, 1.9569997510572155, 5.436110419603376, 10.654776422422616, 17.61299775951494, 17.61299775951494, 10.654776422422616, 5.436110419603376, 1.9569997510572155  …  0.3755858108089606, 1.9569997510572157, 5.277969025578551, 10.338493634372968, 17.138573577440457, 18.561846123663894, 11.44548339254675, 6.0686759957026775, 2.431423933131692, 0.5337272048337861]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 1, num. G vectors =  1058), ComplexF64[0.0014526620565169196 + 0.0im 0.07040107498680777 + 0.0im … 0.0004011832434853789 - 0.0004011832434853788im -0.0005349109913138384 + 0.0005349109913138384im; 0.0014526620565169196 + 0.0im 0.07040107498680777 + 0.0im … 0.0004011832434853789 + 0.0004011832434853788im -0.0005349109913138384 - 0.0005349109913138384im; … ; 0.008349144389251885 + 0.0im 0.033173443134468926 + 0.0im … 0.0013093410302517496 - 0.0013093410302517493im -0.007141860165009543 + 0.007141860165009542im; 0.0026321132587078 + 0.0im 0.0639807860468336 + 0.0im … -0.0006588486948450427 - 0.0006588486948450426im -0.0015812368676281026 - 0.0015812368676281024im], [25.01813916 0.0 … 0.0 0.0; 0.0 -1.00698946204 … 0.0 0.0; … ; 0.0 0.0 … -5.327819979 0.0; 0.0 0.0 … 0.0 -5.327819979]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{ComplexF64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 1, num. G vectors =  1058), ComplexF64[0.0456169904168819 + 5.256995280119557e-17im -0.005769056936983059 - 3.7269078237974735e-17im … -7.735188675374558e-17 + 0.04561699041688176im -6.849128483095165e-17 - 0.06204498655219164im; 0.045616990416881865 - 7.86928762928864e-17im -0.0057690569369830205 + 9.336541693261431e-18im … 1.5419256198164503e-17 - 0.04561699041688183im -9.488344932578529e-17 + 0.06204498655219174im; … ; 0.021965357246362498 + 2.2464498668511797e-18im -0.002934802628982521 + 8.536727290997887e-17im … 1.9479992462911396e-18 + 0.021965357246362494im 8.64310917551173e-17 - 0.1335397161269563im; -0.059772984378440364 - 3.7392872748683694e-17im -0.007492120784271785 + 3.665094057581889e-17im … 6.887202895609839e-18 + 0.059772984378440246im -1.3882455122011876e-17 + 0.11270080613749778im], ComplexF64[-0.18117993655143472 + 2.6562463293377237e-20im -2.200140701945268e-5 + 4.781243376975576e-19im … -0.0 - 0.0im -0.0 - 0.0im; -2.200140701945268e-5 + 4.7812434086405e-19im -0.18117993655143783 + 2.6562463293380917e-20im … -0.0 - 0.0im -0.0 - 0.0im; … ; -0.0 - 0.0im -0.0 - 0.0im … -0.1804137822512097 - 7.224990015798813e-18im -0.0033087208230130525 + 1.1337570115769357e-8im; -0.0 - 0.0im -0.0 - 0.0im … -0.003308720823013052 - 1.1337570116279256e-8im 0.13303982008815268 + 1.1874349130312374e-27im]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 1, num. G vectors =  1058), [-11.263964115516222 -10.64379438422416 … -8.994726433346637 -10.643794384224208; -10.643794384224146 -9.167465816697971 … -10.271205817454602 -11.076423628621354; … ; -8.99472643334663 -10.271205817454673 … -4.57437246236321 -6.827269927984031; -10.643794384224114 -11.076423628621386 … -6.827269927983962 -9.167465816697863;;; -10.643794384224169 -9.167465816697835 … -10.271205817454698 -11.076423628621324; -9.167465816697817 -6.959312278117718 … -10.692507198197164 -10.454554360013143; … ; -10.271205817454621 -10.69250719819722 … -6.554455083326147 -8.812923222360903; -11.076423628621335 -10.454554360013141 … -8.812923222360785 -10.454554360013145;;; -8.994726433346646 -6.82726992798405 … -10.497373767636219 -10.271205817454675; -6.827269927984003 -4.659569531923728 … -9.888569682944599 -8.81292322236087; … ; -10.497373767636152 -9.888569682944766 … -8.289061640781174 -9.888569682944702; -10.271205817454632 -8.81292322236082 … -9.888569682944627 -10.692507198197195;;; … ;;; -6.578153080553701 -8.48660532599672 … -2.747277952780708 -4.491203992140277; -8.486605325996756 -9.727973136173194 … -4.324816599520395 -6.4375614337934035; … ; -2.747277952780788 -4.324816599520233 … -0.905044821419713 -1.6042392099232898; -4.491203992140312 -6.43756143379344 … -1.6042392099233473 -2.804124807730664;;; -8.994726433346656 -10.27120581745465 … -4.57437246236328 -6.827269927984008; -10.271205817454682 -10.692507198197234 … -6.554455083326102 -8.812923222360826; … ; -4.574372462363202 -6.554455083326181 … -1.624234576792611 -2.858579282749786; -6.827269927983958 -8.81292322236088 … -2.8585792827497 -4.659569531923703;;; -10.64379438422425 -11.076423628621331 … -6.827269927983995 -9.167465816697776; -11.07642362862126 -10.45455436001305 … -8.812923222360899 -10.454554360013162; … ; -6.827269927984148 -8.812923222360784 … -2.858579282749826 -4.6595695319235615; -9.167465816697815 -10.454554360013086 … -4.659569531923715 -6.959312278117787])], nothing), DFTK.GenericHamiltonianBlock(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 1, num. G vectors =  1068), Any[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 1, num. G vectors =  1068), [0.23721209103723823, 0.632565576099302, 2.767474395434446, 6.641938549042671, 12.255958036923975, 19.60953285907836, 16.05135149351979, 9.48848364148953, 4.665171123732353, 1.581413940248255  …  0.8697776671365403, 2.846545092446859, 6.562867852030259, 12.01874594588674, 19.214179374016293, 17.07927055468115, 10.358261308626071, 5.376807396844065, 2.1349088193351444, 0.632565576099302]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 1, num. G vectors =  1068), [-19.69293028378679 -19.127691055462872 … -17.172460520653278 -19.127691055462872; -19.127691055462876 -17.402291367764306 … -18.721733773909865 -19.50894133358841; … ; -17.172460520653278 -18.721733773909865 … -10.245935170367524 -14.130197210981127; -19.127691055462872 -19.508941333588407 … -14.130197210981125 -17.402291367764303;;; -19.127691055462876 -17.402291367764303 … -18.72173377390986 -19.50894133358841; -17.402291367764303 -14.359308164945631 … -19.125807118069726 -18.92715469613527; … ; -18.721733773909865 -19.125807118069723 … -13.677457054305759 -16.940214173578532; -19.50894133358841 -18.92715469613527 … -16.940214173578532 -18.927154696135265;;; -17.172460520653278 -14.130197210981125 … -18.92628169003941 -18.721733773909865; -14.130197210981125 -10.423976117759622 … -18.297379847683594 -16.940214173578532; … ; -18.92628169003941 -18.297379847683594 … -16.235670612963965 -18.29737984768359; -18.72173377390986 -16.940214173578532 … -18.297379847683587 -19.125807118069723;;; … ;;; -13.677837405304386 -16.472166305707145 … -6.690325178037546 -10.071186579504449; -16.472166305707145 -18.079038283637747 … -9.730069757032524 -13.454546643596201; … ; -6.690325178037547 -9.730069757032522 … -2.391416851902863 -4.231026654525081; -10.071186579504452 -13.454546643596197 … -4.231026654525081 -6.802550458542525;;; -17.172460520653274 -18.72173377390986 … -10.245935170367522 -14.130197210981125; -18.72173377390986 -19.125807118069723 … -13.677457054305755 -16.940214173578532; … ; -10.245935170367522 -13.677457054305755 … -4.298952176788824 -6.916318157831658; -14.130197210981128 -16.940214173578532 … -6.916318157831658 -10.423976117759619;;; -19.127691055462876 -19.508941333588407 … -14.130197210981125 -17.402291367764303; -19.508941333588407 -18.92715469613527 … -16.940214173578536 -18.927154696135265; … ; -14.130197210981128 -16.940214173578536 … -6.91631815783166 -10.423976117759619; -17.402291367764303 -18.927154696135265 … -10.423976117759617 -14.359308164945627]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 1, num. G vectors =  1068), ComplexF64[0.001528456059177435 + 0.0im 0.0699878067058058 + 0.0im … 0.0 + 0.0007557958658307776im 0.0 - 0.0im; 0.0029863830726715615 + 0.0im 0.06205679930112999 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0075972732146966145 + 0.0im 0.03719800266440645 + 0.0im … 0.0 + 0.003425530158349149im 0.0 - 0.008221272380037958im; 0.0029863830726715615 + 0.0im 0.06205679930112999 + 0.0im … -0.0 + 0.0im 0.0 + 0.0im], [25.01813916 0.0 … 0.0 0.0; 0.0 -1.00698946204 … 0.0 0.0; … ; 0.0 0.0 … -5.327819979 0.0; 0.0 0.0 … 0.0 -5.327819979]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 1, num. G vectors =  1068)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 1, num. G vectors =  1068)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 1, num. G vectors =  1068), [10.877593800343199 10.729889422350716 … 10.09940572538798 10.729889422350716; 10.729889422350716 10.189012190068507 … 10.605300714277549 10.832545389614797; … ; 10.09940572538798 10.605300714277549 … 7.154147988494096 8.94385400564696; 10.729889422350716 10.832545389614799 … 8.94385400564696 10.189012190068507;;; 10.729889422350716 10.189012190068507 … 10.60530071427755 10.832545389614797; 10.189012190068507 9.048105173582577 … 10.729328157888629 10.67229949577574; … ; 10.60530071427755 10.729328157888629 … 8.743132050613442 10.01666945353644; 10.832545389614797 10.672299495775741 … 10.01666945353644 10.672299495775741;;; 10.09940572538798 8.94385400564696 … 10.671694823038989 10.605300714277547; 8.94385400564696 7.25124113554755 … 10.478405847429542 10.01666945353644; … ; 10.671694823038989 10.478405847429542 … 9.758036639158725 10.478405847429542; 10.605300714277547 10.016669453536442 … 10.478405847429542 10.729328157888629;;; … ;;; 8.72960061203429 9.823313976208432 … 5.125906964733587 7.053967661259478; 9.82331397620843 10.38731254842216 … 6.86950217921741 8.633221178530908; … ; 5.125906964733589 6.86950217921741 … 2.064083067041997 3.453936462414575; 7.053967661259478 8.63322117853091 … 3.453936462414576 5.199760967953645;;; 10.09940572538798 10.605300714277547 … 7.154147988494096 8.94385400564696; 10.605300714277549 10.729328157888627 … 8.74313205061344 10.01666945353644; … ; 7.154147988494096 8.743132050613442 … 3.5057692413610893 5.2767073984394965; 8.94385400564696 10.01666945353644 … 5.276707398439497 7.25124113554755;;; 10.729889422350716 10.832545389614795 … 8.94385400564696 10.189012190068505; 10.832545389614797 10.67229949577574 … 10.01666945353644 10.67229949577574; … ; 8.94385400564696 10.01666945353644 … 5.276707398439497 7.25124113554755; 10.189012190068507 10.672299495775741 … 7.25124113554755 9.048105173582577]), DFTK.RealSpaceMultiplication{Float64, SubArray{Float64, 3, Array{Float64, 4}, Tuple{Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Int64}, true}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 1, num. G vectors =  1068), [-2.4486276320726303 -2.245992751112004 … -1.921671638081339 -2.245992751112051; -2.2459927511119857 -1.9541866390021723 … -2.1547727578222857 -2.400027684647741; … ; -1.9216716380813312 -2.1547727578223577 … -1.482585280489783 -1.6409267226498647; -2.2459927511119577 -2.400027684647778 … -1.6409267226497974 -1.9541866390020664;;; -2.2459927511120097 -1.9541866390020397 … -2.154772757822387 -2.4000276846477115; -1.9541866390020215 -1.6481092867546645 … -2.2960282380160675 -2.199699159653614; … ; -2.154772757822308 -2.2960282380161257 … -1.62013007963383 -1.8893785023188108; -2.400027684647722 -2.1996991596536146 … -1.8893785023186933 -2.1996991596536217;;; -1.9216716380813477 -1.6409267226498856 … -2.2427869006357986 -2.154772757822358; -1.6409267226498383 -1.4868345497116555 … -2.0695956826905464 -1.8893785023187788; … ; -2.242786900635731 -2.0695956826907134 … -1.811427666975934 -2.0695956826906547; -2.154772757822319 -1.88937850231873 … -2.0695956826905832 -2.2960282380161012;;; … ;;; -1.6299162872836042 -1.837752996498007 … -1.182859739476749 -1.4739850738953066; -1.8377529964980406 -2.0362474009576084 … -1.4642490217052808 -1.6162359687281103; … ; -1.1828597394768299 -1.46424902170512 … -0.577711036558847 -0.8271490178127838; -1.4739850738953382 -1.6162359687281525 … -0.8271490178128423 -1.2013353171417838;;; -1.9216716380813612 -2.154772757822337 … -1.4825852804898552 -1.6409267226498436; -2.1547727578223688 -2.296028238016138 … -1.6201300796337874 -1.889378502318735; … ; -1.4825852804897763 -1.6201300796338678 … -0.8310516413648759 -1.2189685233576244; -1.6409267226497901 -1.889378502318788 … -1.2189685233575387 -1.486834549711634;;; -2.245992751112092 -2.400027684647719 … -1.6409267226498299 -1.9541866390019784; -2.4000276846476503 -2.199699159653522 … -1.8893785023188043 -2.1996991596536377; … ; -1.640926722649979 -1.8893785023186878 … -1.218968523357663 -1.486834549711493; -1.95418663900202 -2.1996991596535627 … -1.4868345497116486 -1.6481092867547376]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{ComplexF64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 1, num. G vectors =  1068), ComplexF64[-0.053147941732329174 - 3.217765983632577e-16im 0.053147941732329194 + 1.1163342355645655e-16im … -0.05314794173232953 + 4.1286694451800125e-16im 3.335876085490484e-15 + 1.0671530155115488e-14im; 0.17147037220597233 - 2.7208438931753915e-16im -8.964348940144319e-18 + 2.67355757645808e-16im … 7.249454759992234e-17 - 2.83871374430065e-16im 3.86283921755773e-16 - 9.963933479287324e-17im; … ; -0.0505260746971852 - 1.438770091830379e-16im 0.009908285858871735 - 3.398411462321443e-17im … -0.05052607469718487 - 3.672370556104554e-17im 0.13525754331904807 - 2.6399712700320597e-15im; -0.17147037220597228 + 3.373089203076437e-16im -2.2759767045522606e-17 - 2.833625285936374e-16im … 1.4925393575239546e-16 + 3.4015816928299227e-16im 4.542859638316812e-16 + 3.914375309655923e-17im], ComplexF64[-0.18117993655143472 + 2.6562463293377237e-20im -2.200140701945268e-5 + 4.781243376975576e-19im … -0.0 - 0.0im -0.0 - 0.0im; -2.200140701945268e-5 + 4.7812434086405e-19im -0.18117993655143783 + 2.6562463293380917e-20im … -0.0 - 0.0im -0.0 - 0.0im; … ; -0.0 - 0.0im -0.0 - 0.0im … -0.1804137822512097 - 7.224990015798813e-18im -0.0033087208230130525 + 1.1337570115769357e-8im; -0.0 - 0.0im -0.0 - 0.0im … -0.003308720823013052 - 1.1337570116279256e-8im 0.13303982008815268 + 1.1874349130312374e-27im]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 1, num. G vectors =  1068))], DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 1, num. G vectors =  1068), [0.23721209103723823, 0.632565576099302, 2.767474395434446, 6.641938549042671, 12.255958036923975, 19.60953285907836, 16.05135149351979, 9.48848364148953, 4.665171123732353, 1.581413940248255  …  0.8697776671365403, 2.846545092446859, 6.562867852030259, 12.01874594588674, 19.214179374016293, 17.07927055468115, 10.358261308626071, 5.376807396844065, 2.1349088193351444, 0.632565576099302]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 1, num. G vectors =  1068), ComplexF64[0.001528456059177435 + 0.0im 0.0699878067058058 + 0.0im … 0.0 + 0.0007557958658307776im 0.0 - 0.0im; 0.0029863830726715615 + 0.0im 0.06205679930112999 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0075972732146966145 + 0.0im 0.03719800266440645 + 0.0im … 0.0 + 0.003425530158349149im 0.0 - 0.008221272380037958im; 0.0029863830726715615 + 0.0im 0.06205679930112999 + 0.0im … -0.0 + 0.0im 0.0 + 0.0im], [25.01813916 0.0 … 0.0 0.0; 0.0 -1.00698946204 … 0.0 0.0; … ; 0.0 0.0 … -5.327819979 0.0; 0.0 0.0 … 0.0 -5.327819979]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{ComplexF64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 1, num. G vectors =  1068), ComplexF64[-0.053147941732329174 - 3.217765983632577e-16im 0.053147941732329194 + 1.1163342355645655e-16im … -0.05314794173232953 + 4.1286694451800125e-16im 3.335876085490484e-15 + 1.0671530155115488e-14im; 0.17147037220597233 - 2.7208438931753915e-16im -8.964348940144319e-18 + 2.67355757645808e-16im … 7.249454759992234e-17 - 2.83871374430065e-16im 3.86283921755773e-16 - 9.963933479287324e-17im; … ; -0.0505260746971852 - 1.438770091830379e-16im 0.009908285858871735 - 3.398411462321443e-17im … -0.05052607469718487 - 3.672370556104554e-17im 0.13525754331904807 - 2.6399712700320597e-15im; -0.17147037220597228 + 3.373089203076437e-16im -2.2759767045522606e-17 - 2.833625285936374e-16im … 1.4925393575239546e-16 + 3.4015816928299227e-16im 4.542859638316812e-16 + 3.914375309655923e-17im], ComplexF64[-0.18117993655143472 + 2.6562463293377237e-20im -2.200140701945268e-5 + 4.781243376975576e-19im … -0.0 - 0.0im -0.0 - 0.0im; -2.200140701945268e-5 + 4.7812434086405e-19im -0.18117993655143783 + 2.6562463293380917e-20im … -0.0 - 0.0im -0.0 - 0.0im; … ; -0.0 - 0.0im -0.0 - 0.0im … -0.1804137822512097 - 7.224990015798813e-18im -0.0033087208230130525 + 1.1337570115769357e-8im; -0.0 - 0.0im -0.0 - 0.0im … -0.003308720823013052 - 1.1337570116279256e-8im 0.13303982008815268 + 1.1874349130312374e-27im]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 1, num. G vectors =  1068), [-11.263964115516222 -10.64379438422416 … -8.994726433346637 -10.643794384224208; -10.643794384224146 -9.167465816697971 … -10.271205817454602 -11.076423628621354; … ; -8.99472643334663 -10.271205817454673 … -4.57437246236321 -6.827269927984031; -10.643794384224114 -11.076423628621386 … -6.827269927983962 -9.167465816697863;;; -10.643794384224169 -9.167465816697835 … -10.271205817454698 -11.076423628621324; -9.167465816697817 -6.959312278117718 … -10.692507198197164 -10.454554360013143; … ; -10.271205817454621 -10.69250719819722 … -6.554455083326147 -8.812923222360903; -11.076423628621335 -10.454554360013141 … -8.812923222360785 -10.454554360013145;;; -8.994726433346646 -6.82726992798405 … -10.497373767636219 -10.271205817454675; -6.827269927984003 -4.659569531923728 … -9.888569682944599 -8.81292322236087; … ; -10.497373767636152 -9.888569682944766 … -8.289061640781174 -9.888569682944702; -10.271205817454632 -8.81292322236082 … -9.888569682944627 -10.692507198197195;;; … ;;; -6.578153080553701 -8.48660532599672 … -2.747277952780708 -4.491203992140277; -8.486605325996756 -9.727973136173194 … -4.324816599520395 -6.4375614337934035; … ; -2.747277952780788 -4.324816599520233 … -0.905044821419713 -1.6042392099232898; -4.491203992140312 -6.43756143379344 … -1.6042392099233473 -2.804124807730664;;; -8.994726433346656 -10.27120581745465 … -4.57437246236328 -6.827269927984008; -10.271205817454682 -10.692507198197234 … -6.554455083326102 -8.812923222360826; … ; -4.574372462363202 -6.554455083326181 … -1.624234576792611 -2.858579282749786; -6.827269927983958 -8.81292322236088 … -2.8585792827497 -4.659569531923703;;; -10.64379438422425 -11.076423628621331 … -6.827269927983995 -9.167465816697776; -11.07642362862126 -10.45455436001305 … -8.812923222360899 -10.454554360013162; … ; -6.827269927984148 -8.812923222360784 … -2.858579282749826 -4.6595695319235615; -9.167465816697815 -10.454554360013086 … -4.659569531923715 -6.959312278117787])], nothing), DFTK.GenericHamiltonianBlock(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 1, num. G vectors =  1062), Any[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 1, num. G vectors =  1062), [0.05930302275930956, 0.850009992883437, 3.3802722972806456, 7.650089935950932, 13.6594629088943, 14.292028484993606, 8.12451411802541, 3.6965550853302975, 1.0081513869082626, 0.850009992883437  …  1.6407169630075644, 1.1662927809330879, 3.5384136913054705, 7.650089935950933, 13.50132151486948, 15.39901824316738, 9.073362482174362, 4.487262055454421, 1.6407169630075644, 0.533727204833786]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 1, num. G vectors =  1062), [-19.69293028378679 -19.127691055462872 … -17.172460520653278 -19.127691055462872; -19.127691055462876 -17.402291367764306 … -18.721733773909865 -19.50894133358841; … ; -17.172460520653278 -18.721733773909865 … -10.245935170367524 -14.130197210981127; -19.127691055462872 -19.508941333588407 … -14.130197210981125 -17.402291367764303;;; -19.127691055462876 -17.402291367764303 … -18.72173377390986 -19.50894133358841; -17.402291367764303 -14.359308164945631 … -19.125807118069726 -18.92715469613527; … ; -18.721733773909865 -19.125807118069723 … -13.677457054305759 -16.940214173578532; -19.50894133358841 -18.92715469613527 … -16.940214173578532 -18.927154696135265;;; -17.172460520653278 -14.130197210981125 … -18.92628169003941 -18.721733773909865; -14.130197210981125 -10.423976117759622 … -18.297379847683594 -16.940214173578532; … ; -18.92628169003941 -18.297379847683594 … -16.235670612963965 -18.29737984768359; -18.72173377390986 -16.940214173578532 … -18.297379847683587 -19.125807118069723;;; … ;;; -13.677837405304386 -16.472166305707145 … -6.690325178037546 -10.071186579504449; -16.472166305707145 -18.079038283637747 … -9.730069757032524 -13.454546643596201; … ; -6.690325178037547 -9.730069757032522 … -2.391416851902863 -4.231026654525081; -10.071186579504452 -13.454546643596197 … -4.231026654525081 -6.802550458542525;;; -17.172460520653274 -18.72173377390986 … -10.245935170367522 -14.130197210981125; -18.72173377390986 -19.125807118069723 … -13.677457054305755 -16.940214173578532; … ; -10.245935170367522 -13.677457054305755 … -4.298952176788824 -6.916318157831658; -14.130197210981128 -16.940214173578532 … -6.916318157831658 -10.423976117759619;;; -19.127691055462876 -19.508941333588407 … -14.130197210981125 -17.402291367764303; -19.508941333588407 -18.92715469613527 … -16.940214173578536 -18.927154696135265; … ; -14.130197210981128 -16.940214173578536 … -6.91631815783166 -10.423976117759619; -17.402291367764303 -18.927154696135265 … -10.423976117759617 -14.359308164945627]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 1, num. G vectors =  1062), ComplexF64[0.0008361342694689059 + 0.0im 0.07376620221926404 + 0.0im … 0.00013468431164408555 + 0.00013468431164408555im 0.0 + 0.0im; 0.0037424247587792016 + 0.0im 0.05795773062060897 + 0.0im … 0.001946345118023464 - 0.0019463451180234635im -0.0010380507296125138 + 0.0010380507296125136im; … ; 0.006233363233366942 + 0.0im 0.04451750272603676 + 0.0im … 0.0011206236616205692 + 0.001120623661620569im 0.0049805496072025295 + 0.004980549607202529im; 0.0026321132587077975 + 0.0im 0.0639807860468336 + 0.0im … -0.001185927650721078 + 0.0011859276507210777im 0.0 + 0.0im], [25.01813916 0.0 … 0.0 0.0; 0.0 -1.00698946204 … 0.0 0.0; … ; 0.0 0.0 … -5.327819979 0.0; 0.0 0.0 … 0.0 -5.327819979]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 1, num. G vectors =  1062)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 1, num. G vectors =  1062)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 1, num. G vectors =  1062), [10.877593800343199 10.729889422350716 … 10.09940572538798 10.729889422350716; 10.729889422350716 10.189012190068507 … 10.605300714277549 10.832545389614797; … ; 10.09940572538798 10.605300714277549 … 7.154147988494096 8.94385400564696; 10.729889422350716 10.832545389614799 … 8.94385400564696 10.189012190068507;;; 10.729889422350716 10.189012190068507 … 10.60530071427755 10.832545389614797; 10.189012190068507 9.048105173582577 … 10.729328157888629 10.67229949577574; … ; 10.60530071427755 10.729328157888629 … 8.743132050613442 10.01666945353644; 10.832545389614797 10.672299495775741 … 10.01666945353644 10.672299495775741;;; 10.09940572538798 8.94385400564696 … 10.671694823038989 10.605300714277547; 8.94385400564696 7.25124113554755 … 10.478405847429542 10.01666945353644; … ; 10.671694823038989 10.478405847429542 … 9.758036639158725 10.478405847429542; 10.605300714277547 10.016669453536442 … 10.478405847429542 10.729328157888629;;; … ;;; 8.72960061203429 9.823313976208432 … 5.125906964733587 7.053967661259478; 9.82331397620843 10.38731254842216 … 6.86950217921741 8.633221178530908; … ; 5.125906964733589 6.86950217921741 … 2.064083067041997 3.453936462414575; 7.053967661259478 8.63322117853091 … 3.453936462414576 5.199760967953645;;; 10.09940572538798 10.605300714277547 … 7.154147988494096 8.94385400564696; 10.605300714277549 10.729328157888627 … 8.74313205061344 10.01666945353644; … ; 7.154147988494096 8.743132050613442 … 3.5057692413610893 5.2767073984394965; 8.94385400564696 10.01666945353644 … 5.276707398439497 7.25124113554755;;; 10.729889422350716 10.832545389614795 … 8.94385400564696 10.189012190068505; 10.832545389614797 10.67229949577574 … 10.01666945353644 10.67229949577574; … ; 8.94385400564696 10.01666945353644 … 5.276707398439497 7.25124113554755; 10.189012190068507 10.672299495775741 … 7.25124113554755 9.048105173582577]), DFTK.RealSpaceMultiplication{Float64, SubArray{Float64, 3, Array{Float64, 4}, Tuple{Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Int64}, true}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 1, num. G vectors =  1062), [-2.4486276320726303 -2.245992751112004 … -1.921671638081339 -2.245992751112051; -2.2459927511119857 -1.9541866390021723 … -2.1547727578222857 -2.400027684647741; … ; -1.9216716380813312 -2.1547727578223577 … -1.482585280489783 -1.6409267226498647; -2.2459927511119577 -2.400027684647778 … -1.6409267226497974 -1.9541866390020664;;; -2.2459927511120097 -1.9541866390020397 … -2.154772757822387 -2.4000276846477115; -1.9541866390020215 -1.6481092867546645 … -2.2960282380160675 -2.199699159653614; … ; -2.154772757822308 -2.2960282380161257 … -1.62013007963383 -1.8893785023188108; -2.400027684647722 -2.1996991596536146 … -1.8893785023186933 -2.1996991596536217;;; -1.9216716380813477 -1.6409267226498856 … -2.2427869006357986 -2.154772757822358; -1.6409267226498383 -1.4868345497116555 … -2.0695956826905464 -1.8893785023187788; … ; -2.242786900635731 -2.0695956826907134 … -1.811427666975934 -2.0695956826906547; -2.154772757822319 -1.88937850231873 … -2.0695956826905832 -2.2960282380161012;;; … ;;; -1.6299162872836042 -1.837752996498007 … -1.182859739476749 -1.4739850738953066; -1.8377529964980406 -2.0362474009576084 … -1.4642490217052808 -1.6162359687281103; … ; -1.1828597394768299 -1.46424902170512 … -0.577711036558847 -0.8271490178127838; -1.4739850738953382 -1.6162359687281525 … -0.8271490178128423 -1.2013353171417838;;; -1.9216716380813612 -2.154772757822337 … -1.4825852804898552 -1.6409267226498436; -2.1547727578223688 -2.296028238016138 … -1.6201300796337874 -1.889378502318735; … ; -1.4825852804897763 -1.6201300796338678 … -0.8310516413648759 -1.2189685233576244; -1.6409267226497901 -1.889378502318788 … -1.2189685233575387 -1.486834549711634;;; -2.245992751112092 -2.400027684647719 … -1.6409267226498299 -1.9541866390019784; -2.4000276846476503 -2.199699159653522 … -1.8893785023188043 -2.1996991596536377; … ; -1.640926722649979 -1.8893785023186878 … -1.218968523357663 -1.486834549711493; -1.95418663900202 -2.1996991596535627 … -1.4868345497116486 -1.6481092867547376]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{ComplexF64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 1, num. G vectors =  1062), ComplexF64[-0.012306510152407416 + 8.66503947247771e-17im -0.012306510152407354 + 2.0444870790939625e-17im … -1.3080345152670957e-16 + 0.012306510152407333im 1.3703939864966026e-16 - 2.051166158440309e-17im; 0.12191225909305085 + 1.8370881862396167e-16im -0.06662978048669259 + 1.550512978349806e-17im … 4.235462497063209e-17 + 0.12191225909305088im -2.2290612952231276e-17 - 0.04951021313498459im; … ; -0.030676718659148398 - 3.188442971770381e-17im -0.0033251636058130598 + 5.2143093254116074e-17im … 4.487444041001481e-17 + 0.03067671865914838im 4.3049148233430525e-17 + 0.1590928808831705im; -0.10276141274450667 + 1.311556505659984e-16im -0.10276141274450659 + 1.2754573952389513e-16im … -8.762988110877603e-17 - 0.10276141274450663im 2.145514056873749e-16 + 4.7381574593839345e-17im], ComplexF64[-0.18117993655143472 + 2.6562463293377237e-20im -2.200140701945268e-5 + 4.781243376975576e-19im … -0.0 - 0.0im -0.0 - 0.0im; -2.200140701945268e-5 + 4.7812434086405e-19im -0.18117993655143783 + 2.6562463293380917e-20im … -0.0 - 0.0im -0.0 - 0.0im; … ; -0.0 - 0.0im -0.0 - 0.0im … -0.1804137822512097 - 7.224990015798813e-18im -0.0033087208230130525 + 1.1337570115769357e-8im; -0.0 - 0.0im -0.0 - 0.0im … -0.003308720823013052 - 1.1337570116279256e-8im 0.13303982008815268 + 1.1874349130312374e-27im]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 1, num. G vectors =  1062))], DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 1, num. G vectors =  1062), [0.05930302275930956, 0.850009992883437, 3.3802722972806456, 7.650089935950932, 13.6594629088943, 14.292028484993606, 8.12451411802541, 3.6965550853302975, 1.0081513869082626, 0.850009992883437  …  1.6407169630075644, 1.1662927809330879, 3.5384136913054705, 7.650089935950933, 13.50132151486948, 15.39901824316738, 9.073362482174362, 4.487262055454421, 1.6407169630075644, 0.533727204833786]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 1, num. G vectors =  1062), ComplexF64[0.0008361342694689059 + 0.0im 0.07376620221926404 + 0.0im … 0.00013468431164408555 + 0.00013468431164408555im 0.0 + 0.0im; 0.0037424247587792016 + 0.0im 0.05795773062060897 + 0.0im … 0.001946345118023464 - 0.0019463451180234635im -0.0010380507296125138 + 0.0010380507296125136im; … ; 0.006233363233366942 + 0.0im 0.04451750272603676 + 0.0im … 0.0011206236616205692 + 0.001120623661620569im 0.0049805496072025295 + 0.004980549607202529im; 0.0026321132587077975 + 0.0im 0.0639807860468336 + 0.0im … -0.001185927650721078 + 0.0011859276507210777im 0.0 + 0.0im], [25.01813916 0.0 … 0.0 0.0; 0.0 -1.00698946204 … 0.0 0.0; … ; 0.0 0.0 … -5.327819979 0.0; 0.0 0.0 … 0.0 -5.327819979]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{ComplexF64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 1, num. G vectors =  1062), ComplexF64[-0.012306510152407416 + 8.66503947247771e-17im -0.012306510152407354 + 2.0444870790939625e-17im … -1.3080345152670957e-16 + 0.012306510152407333im 1.3703939864966026e-16 - 2.051166158440309e-17im; 0.12191225909305085 + 1.8370881862396167e-16im -0.06662978048669259 + 1.550512978349806e-17im … 4.235462497063209e-17 + 0.12191225909305088im -2.2290612952231276e-17 - 0.04951021313498459im; … ; -0.030676718659148398 - 3.188442971770381e-17im -0.0033251636058130598 + 5.2143093254116074e-17im … 4.487444041001481e-17 + 0.03067671865914838im 4.3049148233430525e-17 + 0.1590928808831705im; -0.10276141274450667 + 1.311556505659984e-16im -0.10276141274450659 + 1.2754573952389513e-16im … -8.762988110877603e-17 - 0.10276141274450663im 2.145514056873749e-16 + 4.7381574593839345e-17im], ComplexF64[-0.18117993655143472 + 2.6562463293377237e-20im -2.200140701945268e-5 + 4.781243376975576e-19im … -0.0 - 0.0im -0.0 - 0.0im; -2.200140701945268e-5 + 4.7812434086405e-19im -0.18117993655143783 + 2.6562463293380917e-20im … -0.0 - 0.0im -0.0 - 0.0im; … ; -0.0 - 0.0im -0.0 - 0.0im … -0.1804137822512097 - 7.224990015798813e-18im -0.0033087208230130525 + 1.1337570115769357e-8im; -0.0 - 0.0im -0.0 - 0.0im … -0.003308720823013052 - 1.1337570116279256e-8im 0.13303982008815268 + 1.1874349130312374e-27im]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 1, num. G vectors =  1062), [-11.263964115516222 -10.64379438422416 … -8.994726433346637 -10.643794384224208; -10.643794384224146 -9.167465816697971 … -10.271205817454602 -11.076423628621354; … ; -8.99472643334663 -10.271205817454673 … -4.57437246236321 -6.827269927984031; -10.643794384224114 -11.076423628621386 … -6.827269927983962 -9.167465816697863;;; -10.643794384224169 -9.167465816697835 … -10.271205817454698 -11.076423628621324; -9.167465816697817 -6.959312278117718 … -10.692507198197164 -10.454554360013143; … ; -10.271205817454621 -10.69250719819722 … -6.554455083326147 -8.812923222360903; -11.076423628621335 -10.454554360013141 … -8.812923222360785 -10.454554360013145;;; -8.994726433346646 -6.82726992798405 … -10.497373767636219 -10.271205817454675; -6.827269927984003 -4.659569531923728 … -9.888569682944599 -8.81292322236087; … ; -10.497373767636152 -9.888569682944766 … -8.289061640781174 -9.888569682944702; -10.271205817454632 -8.81292322236082 … -9.888569682944627 -10.692507198197195;;; … ;;; -6.578153080553701 -8.48660532599672 … -2.747277952780708 -4.491203992140277; -8.486605325996756 -9.727973136173194 … -4.324816599520395 -6.4375614337934035; … ; -2.747277952780788 -4.324816599520233 … -0.905044821419713 -1.6042392099232898; -4.491203992140312 -6.43756143379344 … -1.6042392099233473 -2.804124807730664;;; -8.994726433346656 -10.27120581745465 … -4.57437246236328 -6.827269927984008; -10.271205817454682 -10.692507198197234 … -6.554455083326102 -8.812923222360826; … ; -4.574372462363202 -6.554455083326181 … -1.624234576792611 -2.858579282749786; -6.827269927983958 -8.81292322236088 … -2.8585792827497 -4.659569531923703;;; -10.64379438422425 -11.076423628621331 … -6.827269927983995 -9.167465816697776; -11.07642362862126 -10.45455436001305 … -8.812923222360899 -10.454554360013162; … ; -6.827269927984148 -8.812923222360784 … -2.858579282749826 -4.6595695319235615; -9.167465816697815 -10.454554360013086 … -4.659569531923715 -6.959312278117787])], nothing), DFTK.GenericHamiltonianBlock(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 2, num. G vectors =  1075), Any[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 2, num. G vectors =  1075), [0.0, 0.8697776671365403, 3.479110668546161, 7.827999004228862, 13.916442674184644, 13.916442674184644, 7.827999004228862, 3.479110668546161, 0.8697776671365403, 0.8697776671365403  …  1.265131152198604, 0.9488483641489529, 3.400039971533748, 7.590786913191624, 13.521089189122582, 14.78622034132119, 8.53963527734058, 4.03260554763305, 1.265131152198604, 0.23721209103723823]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 2, num. G vectors =  1075), [-19.69293028378679 -19.127691055462872 … -17.172460520653278 -19.127691055462872; -19.127691055462876 -17.402291367764306 … -18.721733773909865 -19.50894133358841; … ; -17.172460520653278 -18.721733773909865 … -10.245935170367524 -14.130197210981127; -19.127691055462872 -19.508941333588407 … -14.130197210981125 -17.402291367764303;;; -19.127691055462876 -17.402291367764303 … -18.72173377390986 -19.50894133358841; -17.402291367764303 -14.359308164945631 … -19.125807118069726 -18.92715469613527; … ; -18.721733773909865 -19.125807118069723 … -13.677457054305759 -16.940214173578532; -19.50894133358841 -18.92715469613527 … -16.940214173578532 -18.927154696135265;;; -17.172460520653278 -14.130197210981125 … -18.92628169003941 -18.721733773909865; -14.130197210981125 -10.423976117759622 … -18.297379847683594 -16.940214173578532; … ; -18.92628169003941 -18.297379847683594 … -16.235670612963965 -18.29737984768359; -18.72173377390986 -16.940214173578532 … -18.297379847683587 -19.125807118069723;;; … ;;; -13.677837405304386 -16.472166305707145 … -6.690325178037546 -10.071186579504449; -16.472166305707145 -18.079038283637747 … -9.730069757032524 -13.454546643596201; … ; -6.690325178037547 -9.730069757032522 … -2.391416851902863 -4.231026654525081; -10.071186579504452 -13.454546643596197 … -4.231026654525081 -6.802550458542525;;; -17.172460520653274 -18.72173377390986 … -10.245935170367522 -14.130197210981125; -18.72173377390986 -19.125807118069723 … -13.677457054305755 -16.940214173578532; … ; -10.245935170367522 -13.677457054305755 … -4.298952176788824 -6.916318157831658; -14.130197210981128 -16.940214173578532 … -6.916318157831658 -10.423976117759619;;; -19.127691055462876 -19.508941333588407 … -14.130197210981125 -17.402291367764303; -19.508941333588407 -18.92715469613527 … -16.940214173578536 -18.927154696135265; … ; -14.130197210981128 -16.940214173578536 … -6.91631815783166 -10.423976117759619; -17.402291367764303 -18.927154696135265 … -10.423976117759617 -14.359308164945627]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 2, num. G vectors =  1075), ComplexF64[0.0006002260183055469 + 0.0im 0.07505547926746237 + 0.0im … -0.0 + 0.0im -0.0 + 0.0im; 0.0038095861649428834 + 0.0im 0.0575940500481257 + 0.0im … -0.0 - 0.002199873402472219im 0.0 + 0.002933164536629625im; … ; 0.005099332415993166 + 0.0im 0.050624187347729784 + 0.0im … -0.0 + 0.0im 0.0057490967761396235 + 0.0im; 0.001528456059177435 + 0.0im 0.0699878067058058 + 0.0im … 0.0 + 0.0007557958658307776im 0.0 + 0.0im], [25.01813916 0.0 … 0.0 0.0; 0.0 -1.00698946204 … 0.0 0.0; … ; 0.0 0.0 … -5.327819979 0.0; 0.0 0.0 … 0.0 -5.327819979]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 2, num. G vectors =  1075)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 2, num. G vectors =  1075)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 2, num. G vectors =  1075), [10.877593800343199 10.729889422350716 … 10.09940572538798 10.729889422350716; 10.729889422350716 10.189012190068507 … 10.605300714277549 10.832545389614797; … ; 10.09940572538798 10.605300714277549 … 7.154147988494096 8.94385400564696; 10.729889422350716 10.832545389614799 … 8.94385400564696 10.189012190068507;;; 10.729889422350716 10.189012190068507 … 10.60530071427755 10.832545389614797; 10.189012190068507 9.048105173582577 … 10.729328157888629 10.67229949577574; … ; 10.60530071427755 10.729328157888629 … 8.743132050613442 10.01666945353644; 10.832545389614797 10.672299495775741 … 10.01666945353644 10.672299495775741;;; 10.09940572538798 8.94385400564696 … 10.671694823038989 10.605300714277547; 8.94385400564696 7.25124113554755 … 10.478405847429542 10.01666945353644; … ; 10.671694823038989 10.478405847429542 … 9.758036639158725 10.478405847429542; 10.605300714277547 10.016669453536442 … 10.478405847429542 10.729328157888629;;; … ;;; 8.72960061203429 9.823313976208432 … 5.125906964733587 7.053967661259478; 9.82331397620843 10.38731254842216 … 6.86950217921741 8.633221178530908; … ; 5.125906964733589 6.86950217921741 … 2.064083067041997 3.453936462414575; 7.053967661259478 8.63322117853091 … 3.453936462414576 5.199760967953645;;; 10.09940572538798 10.605300714277547 … 7.154147988494096 8.94385400564696; 10.605300714277549 10.729328157888627 … 8.74313205061344 10.01666945353644; … ; 7.154147988494096 8.743132050613442 … 3.5057692413610893 5.2767073984394965; 8.94385400564696 10.01666945353644 … 5.276707398439497 7.25124113554755;;; 10.729889422350716 10.832545389614795 … 8.94385400564696 10.189012190068505; 10.832545389614797 10.67229949577574 … 10.01666945353644 10.67229949577574; … ; 8.94385400564696 10.01666945353644 … 5.276707398439497 7.25124113554755; 10.189012190068507 10.672299495775741 … 7.25124113554755 9.048105173582577]), DFTK.RealSpaceMultiplication{Float64, SubArray{Float64, 3, Array{Float64, 4}, Tuple{Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Int64}, true}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 2, num. G vectors =  1075), [-2.448526913033643 -2.249023512194019 … -1.9268729604384136 -2.249023512194006; -2.2490235121941 -1.9702042500427028 … -2.1544595935164588 -2.4012800624968156; … ; -1.9268729604384407 -2.154459593516325 … -1.5016310959745591 -1.6549903266627528; -2.249023512194015 -2.40128006249684 … -1.654990326662806 -1.9702042500427335;;; -2.249023512194022 -1.9702042500426165 … -2.154459593516411 -2.4012800624966784; -1.970204250042618 -1.6727393911863497 … -2.299589943887216 -2.204222842893198; … ; -2.1544595935163993 -2.2995899438872525 … -1.6240586150423488 -1.890440066911896; -2.4012800624967694 -2.2042228428931563 … -1.8904400669119645 -2.2042228428932207;;; -1.9268729604385157 -1.6549903266627917 … -2.247179097295615 -2.1544595935164357; -1.6549903266628367 -1.5175444904221198 … -2.0779407590889676 -1.8904400669119292; … ; -2.247179097295677 -2.0779407590888286 … -1.8038334456714262 -2.077940759088921; -2.1544595935163726 -1.8904400669119936 … -2.077940759088931 -2.2995899438871956;;; … ;;; -1.610168471352356 -1.8085679269828476 … -1.1951576411201699 -1.4741991328378998; -1.8085679269828059 -2.019900802227582 … -1.4571028957773198 -1.5972138336823307; … ; -1.1951576411201115 -1.457102895777457 … -0.6054904395176082 -0.8475258868687711; -1.4741991328379298 -1.5972138336823127 … -0.8475258868687339 -1.2242192324998638;;; -1.9268729604384263 -2.1544595935164557 … -1.5016310959745502 -1.6549903266628203; -2.1544595935164783 -2.2995899438872027 … -1.6240586150424043 -1.890440066911978; … ; -1.501631095974519 -1.6240586150423826 … -0.8513905328875382 -1.2499060725784203; -1.654990326662895 -1.890440066911878 … -1.2499060725784918 -1.5175444904220317;;; -2.2490235121940056 -2.4012800624966757 … -1.6549903266628792 -1.970204250042576; -2.4012800624967676 -2.20422284289318 … -1.8904400669119061 -2.204222842893172; … ; -1.654990326662741 -1.8904400669119756 … -1.2499060725784168 -1.5175444904220647; -1.9702042500427435 -2.2042228428931523 … -1.5175444904220923 -1.6727393911863622]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{ComplexF64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 2, num. G vectors =  1075), ComplexF64[-8.859292477751685e-17 - 1.7074042659338244e-16im -4.783566607446491e-17 + 5.663324065062725e-17im … 9.861795881045906e-17 + 2.672442082471657e-16im -1.5974197588400363e-17 - 7.633240274996076e-17im; 0.0899547666901153 - 1.413144577113148e-15im -0.026697568337758607 + 3.0801362819085753e-17im … -0.08995476669011464 + 3.4822917796892204e-16im 0.10617545164788754 - 2.821017445726888e-16im; … ; 9.632346948129199e-17 - 1.3057865978428654e-16im -3.146022294998665e-17 - 4.835959214516585e-17im … 1.3209920794091407e-16 + 1.5024841307910963e-16im -0.16771615563505324 - 1.968999427913288e-16im; -0.05314794173232918 - 1.4572633601693817e-16im -0.05314794173232926 - 2.365957523638594e-17im … 0.053147941732329236 - 2.0193733144987457e-16im -3.001564680560613e-16 - 3.6601892425188467e-16im], ComplexF64[-0.18041386462540418 + 2.762496182511301e-18im -4.77981535127589e-5 - 7.898169367276841e-19im … -0.0 - 0.0im -0.0 - 0.0im; -4.77981535127589e-5 - 7.898195522503882e-19im -0.1804138646254073 + 2.7624961825113176e-18im … -0.0 - 0.0im -0.0 - 0.0im; … ; -0.0 - 0.0im -0.0 - 0.0im … -0.181179949759701 + 8.499988253880949e-19im 5.0674722534505665e-5 - 1.0365811865687846e-12im; -0.0 - 0.0im -0.0 - 0.0im … 5.0674722534506214e-5 + 1.0365780638962131e-12im -0.18129360079367485 + 6.374991190014906e-18im]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 2, num. G vectors =  1075))], DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 2, num. G vectors =  1075), [0.0, 0.8697776671365403, 3.479110668546161, 7.827999004228862, 13.916442674184644, 13.916442674184644, 7.827999004228862, 3.479110668546161, 0.8697776671365403, 0.8697776671365403  …  1.265131152198604, 0.9488483641489529, 3.400039971533748, 7.590786913191624, 13.521089189122582, 14.78622034132119, 8.53963527734058, 4.03260554763305, 1.265131152198604, 0.23721209103723823]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 2, num. G vectors =  1075), ComplexF64[0.0006002260183055469 + 0.0im 0.07505547926746237 + 0.0im … -0.0 + 0.0im -0.0 + 0.0im; 0.0038095861649428834 + 0.0im 0.0575940500481257 + 0.0im … -0.0 - 0.002199873402472219im 0.0 + 0.002933164536629625im; … ; 0.005099332415993166 + 0.0im 0.050624187347729784 + 0.0im … -0.0 + 0.0im 0.0057490967761396235 + 0.0im; 0.001528456059177435 + 0.0im 0.0699878067058058 + 0.0im … 0.0 + 0.0007557958658307776im 0.0 + 0.0im], [25.01813916 0.0 … 0.0 0.0; 0.0 -1.00698946204 … 0.0 0.0; … ; 0.0 0.0 … -5.327819979 0.0; 0.0 0.0 … 0.0 -5.327819979]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{ComplexF64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 2, num. G vectors =  1075), ComplexF64[-8.859292477751685e-17 - 1.7074042659338244e-16im -4.783566607446491e-17 + 5.663324065062725e-17im … 9.861795881045906e-17 + 2.672442082471657e-16im -1.5974197588400363e-17 - 7.633240274996076e-17im; 0.0899547666901153 - 1.413144577113148e-15im -0.026697568337758607 + 3.0801362819085753e-17im … -0.08995476669011464 + 3.4822917796892204e-16im 0.10617545164788754 - 2.821017445726888e-16im; … ; 9.632346948129199e-17 - 1.3057865978428654e-16im -3.146022294998665e-17 - 4.835959214516585e-17im … 1.3209920794091407e-16 + 1.5024841307910963e-16im -0.16771615563505324 - 1.968999427913288e-16im; -0.05314794173232918 - 1.4572633601693817e-16im -0.05314794173232926 - 2.365957523638594e-17im … 0.053147941732329236 - 2.0193733144987457e-16im -3.001564680560613e-16 - 3.6601892425188467e-16im], ComplexF64[-0.18041386462540418 + 2.762496182511301e-18im -4.77981535127589e-5 - 7.898169367276841e-19im … -0.0 - 0.0im -0.0 - 0.0im; -4.77981535127589e-5 - 7.898195522503882e-19im -0.1804138646254073 + 2.7624961825113176e-18im … -0.0 - 0.0im -0.0 - 0.0im; … ; -0.0 - 0.0im -0.0 - 0.0im … -0.181179949759701 + 8.499988253880949e-19im 5.0674722534505665e-5 - 1.0365811865687846e-12im; -0.0 - 0.0im -0.0 - 0.0im … 5.0674722534506214e-5 + 1.0365780638962131e-12im -0.18129360079367485 + 6.374991190014906e-18im]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([     0,      0,      0], spin = 2, num. G vectors =  1075), [-11.263863396477234 -10.646825145306174 … -8.999927755703713 -10.646825145306162; -10.64682514530626 -9.183483427738501 … -10.270892653148774 -11.07767600647043; … ; -8.99992775570374 -10.27089265314864 … -4.593418277847986 -6.841333531996919; -10.64682514530617 -11.077676006470448 … -6.841333531996971 -9.18348342773853;;; -10.646825145306181 -9.183483427738413 … -10.27089265314872 -11.077676006470291; -9.183483427738414 -6.983942382549404 … -10.696068904068314 -10.459078043252727; … ; -10.270892653148714 -10.696068904068346 … -6.558383618734666 -8.813984786953988; -11.077676006470384 -10.459078043252683 … -8.813984786954055 -10.459078043252745;;; -8.999927755703814 -6.841333531996956 … -10.501765964296037 -10.270892653148753; -6.841333531997002 -4.690279472634192 … -9.89691475934302 -8.81398478695402; … ; -10.501765964296098 -9.89691475934288 … -8.281467419476666 -9.89691475934297; -10.270892653148687 -8.813984786954084 … -9.896914759342977 -10.696068904068289;;; … ;;; -6.558405264622452 -8.45742025648156 … -2.759575854424129 -4.491418051082871; -8.45742025648152 -9.711626537443168 … -4.317670473592434 -6.418539298747623; … ; -2.75957585442407 -4.317670473592569 … -0.9328242243784741 -1.624616078979277; -4.491418051082904 -6.4185392987476 … -1.624616078979239 -2.8270087230887437;;; -8.999927755703721 -10.27089265314877 … -4.5934182778479755 -6.841333531996985; -10.27089265314879 -10.696068904068298 … -6.5583836187347195 -8.81398478695407; … ; -4.593418277847944 -6.558383618734696 … -1.6445734683152733 -2.889516831970582; -6.841333531997063 -8.81398478695397 … -2.889516831970653 -4.6902794726341;;; -10.646825145306165 -11.077676006470288 … -6.841333531997044 -9.183483427738373; -11.077676006470377 -10.45907804325271 … -8.813984786954002 -10.459078043252697; … ; -6.841333531996909 -8.813984786954071 … -2.8895168319705795 -4.690279472634133; -9.183483427738539 -10.459078043252676 … -4.690279472634159 -6.9839423825494125])], nothing), DFTK.GenericHamiltonianBlock(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 2, num. G vectors =  1058), Any[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 2, num. G vectors =  1058), [0.21744441678413506, 0.21744441678413506, 1.9569997510572155, 5.436110419603376, 10.654776422422616, 17.61299775951494, 17.61299775951494, 10.654776422422616, 5.436110419603376, 1.9569997510572155  …  0.3755858108089606, 1.9569997510572157, 5.277969025578551, 10.338493634372968, 17.138573577440457, 18.561846123663894, 11.44548339254675, 6.0686759957026775, 2.431423933131692, 0.5337272048337861]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 2, num. G vectors =  1058), [-19.69293028378679 -19.127691055462872 … -17.172460520653278 -19.127691055462872; -19.127691055462876 -17.402291367764306 … -18.721733773909865 -19.50894133358841; … ; -17.172460520653278 -18.721733773909865 … -10.245935170367524 -14.130197210981127; -19.127691055462872 -19.508941333588407 … -14.130197210981125 -17.402291367764303;;; -19.127691055462876 -17.402291367764303 … -18.72173377390986 -19.50894133358841; -17.402291367764303 -14.359308164945631 … -19.125807118069726 -18.92715469613527; … ; -18.721733773909865 -19.125807118069723 … -13.677457054305759 -16.940214173578532; -19.50894133358841 -18.92715469613527 … -16.940214173578532 -18.927154696135265;;; -17.172460520653278 -14.130197210981125 … -18.92628169003941 -18.721733773909865; -14.130197210981125 -10.423976117759622 … -18.297379847683594 -16.940214173578532; … ; -18.92628169003941 -18.297379847683594 … -16.235670612963965 -18.29737984768359; -18.72173377390986 -16.940214173578532 … -18.297379847683587 -19.125807118069723;;; … ;;; -13.677837405304386 -16.472166305707145 … -6.690325178037546 -10.071186579504449; -16.472166305707145 -18.079038283637747 … -9.730069757032524 -13.454546643596201; … ; -6.690325178037547 -9.730069757032522 … -2.391416851902863 -4.231026654525081; -10.071186579504452 -13.454546643596197 … -4.231026654525081 -6.802550458542525;;; -17.172460520653274 -18.72173377390986 … -10.245935170367522 -14.130197210981125; -18.72173377390986 -19.125807118069723 … -13.677457054305755 -16.940214173578532; … ; -10.245935170367522 -13.677457054305755 … -4.298952176788824 -6.916318157831658; -14.130197210981128 -16.940214173578532 … -6.916318157831658 -10.423976117759619;;; -19.127691055462876 -19.508941333588407 … -14.130197210981125 -17.402291367764303; -19.508941333588407 -18.92715469613527 … -16.940214173578536 -18.927154696135265; … ; -14.130197210981128 -16.940214173578536 … -6.91631815783166 -10.423976117759619; -17.402291367764303 -18.927154696135265 … -10.423976117759617 -14.359308164945627]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 2, num. G vectors =  1058), ComplexF64[0.0014526620565169196 + 0.0im 0.07040107498680777 + 0.0im … 0.0004011832434853789 - 0.0004011832434853788im -0.0005349109913138384 + 0.0005349109913138384im; 0.0014526620565169196 + 0.0im 0.07040107498680777 + 0.0im … 0.0004011832434853789 + 0.0004011832434853788im -0.0005349109913138384 - 0.0005349109913138384im; … ; 0.008349144389251885 + 0.0im 0.033173443134468926 + 0.0im … 0.0013093410302517496 - 0.0013093410302517493im -0.007141860165009543 + 0.007141860165009542im; 0.0026321132587078 + 0.0im 0.0639807860468336 + 0.0im … -0.0006588486948450427 - 0.0006588486948450426im -0.0015812368676281026 - 0.0015812368676281024im], [25.01813916 0.0 … 0.0 0.0; 0.0 -1.00698946204 … 0.0 0.0; … ; 0.0 0.0 … -5.327819979 0.0; 0.0 0.0 … 0.0 -5.327819979]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 2, num. G vectors =  1058)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 2, num. G vectors =  1058)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 2, num. G vectors =  1058), [10.877593800343199 10.729889422350716 … 10.09940572538798 10.729889422350716; 10.729889422350716 10.189012190068507 … 10.605300714277549 10.832545389614797; … ; 10.09940572538798 10.605300714277549 … 7.154147988494096 8.94385400564696; 10.729889422350716 10.832545389614799 … 8.94385400564696 10.189012190068507;;; 10.729889422350716 10.189012190068507 … 10.60530071427755 10.832545389614797; 10.189012190068507 9.048105173582577 … 10.729328157888629 10.67229949577574; … ; 10.60530071427755 10.729328157888629 … 8.743132050613442 10.01666945353644; 10.832545389614797 10.672299495775741 … 10.01666945353644 10.672299495775741;;; 10.09940572538798 8.94385400564696 … 10.671694823038989 10.605300714277547; 8.94385400564696 7.25124113554755 … 10.478405847429542 10.01666945353644; … ; 10.671694823038989 10.478405847429542 … 9.758036639158725 10.478405847429542; 10.605300714277547 10.016669453536442 … 10.478405847429542 10.729328157888629;;; … ;;; 8.72960061203429 9.823313976208432 … 5.125906964733587 7.053967661259478; 9.82331397620843 10.38731254842216 … 6.86950217921741 8.633221178530908; … ; 5.125906964733589 6.86950217921741 … 2.064083067041997 3.453936462414575; 7.053967661259478 8.63322117853091 … 3.453936462414576 5.199760967953645;;; 10.09940572538798 10.605300714277547 … 7.154147988494096 8.94385400564696; 10.605300714277549 10.729328157888627 … 8.74313205061344 10.01666945353644; … ; 7.154147988494096 8.743132050613442 … 3.5057692413610893 5.2767073984394965; 8.94385400564696 10.01666945353644 … 5.276707398439497 7.25124113554755;;; 10.729889422350716 10.832545389614795 … 8.94385400564696 10.189012190068505; 10.832545389614797 10.67229949577574 … 10.01666945353644 10.67229949577574; … ; 8.94385400564696 10.01666945353644 … 5.276707398439497 7.25124113554755; 10.189012190068507 10.672299495775741 … 7.25124113554755 9.048105173582577]), DFTK.RealSpaceMultiplication{Float64, SubArray{Float64, 3, Array{Float64, 4}, Tuple{Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Int64}, true}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 2, num. G vectors =  1058), [-2.448526913033643 -2.249023512194019 … -1.9268729604384136 -2.249023512194006; -2.2490235121941 -1.9702042500427028 … -2.1544595935164588 -2.4012800624968156; … ; -1.9268729604384407 -2.154459593516325 … -1.5016310959745591 -1.6549903266627528; -2.249023512194015 -2.40128006249684 … -1.654990326662806 -1.9702042500427335;;; -2.249023512194022 -1.9702042500426165 … -2.154459593516411 -2.4012800624966784; -1.970204250042618 -1.6727393911863497 … -2.299589943887216 -2.204222842893198; … ; -2.1544595935163993 -2.2995899438872525 … -1.6240586150423488 -1.890440066911896; -2.4012800624967694 -2.2042228428931563 … -1.8904400669119645 -2.2042228428932207;;; -1.9268729604385157 -1.6549903266627917 … -2.247179097295615 -2.1544595935164357; -1.6549903266628367 -1.5175444904221198 … -2.0779407590889676 -1.8904400669119292; … ; -2.247179097295677 -2.0779407590888286 … -1.8038334456714262 -2.077940759088921; -2.1544595935163726 -1.8904400669119936 … -2.077940759088931 -2.2995899438871956;;; … ;;; -1.610168471352356 -1.8085679269828476 … -1.1951576411201699 -1.4741991328378998; -1.8085679269828059 -2.019900802227582 … -1.4571028957773198 -1.5972138336823307; … ; -1.1951576411201115 -1.457102895777457 … -0.6054904395176082 -0.8475258868687711; -1.4741991328379298 -1.5972138336823127 … -0.8475258868687339 -1.2242192324998638;;; -1.9268729604384263 -2.1544595935164557 … -1.5016310959745502 -1.6549903266628203; -2.1544595935164783 -2.2995899438872027 … -1.6240586150424043 -1.890440066911978; … ; -1.501631095974519 -1.6240586150423826 … -0.8513905328875382 -1.2499060725784203; -1.654990326662895 -1.890440066911878 … -1.2499060725784918 -1.5175444904220317;;; -2.2490235121940056 -2.4012800624966757 … -1.6549903266628792 -1.970204250042576; -2.4012800624967676 -2.20422284289318 … -1.8904400669119061 -2.204222842893172; … ; -1.654990326662741 -1.8904400669119756 … -1.2499060725784168 -1.5175444904220647; -1.9702042500427435 -2.2042228428931523 … -1.5175444904220923 -1.6727393911863622]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{ComplexF64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 2, num. G vectors =  1058), ComplexF64[0.0456169904168819 + 5.256995280119557e-17im -0.005769056936983059 - 3.7269078237974735e-17im … -7.735188675374558e-17 + 0.04561699041688176im -6.849128483095165e-17 - 0.06204498655219164im; 0.045616990416881865 - 7.86928762928864e-17im -0.0057690569369830205 + 9.336541693261431e-18im … 1.5419256198164503e-17 - 0.04561699041688183im -9.488344932578529e-17 + 0.06204498655219174im; … ; 0.021965357246362498 + 2.2464498668511797e-18im -0.002934802628982521 + 8.536727290997887e-17im … 1.9479992462911396e-18 + 0.021965357246362494im 8.64310917551173e-17 - 0.1335397161269563im; -0.059772984378440364 - 3.7392872748683694e-17im -0.007492120784271785 + 3.665094057581889e-17im … 6.887202895609839e-18 + 0.059772984378440246im -1.3882455122011876e-17 + 0.11270080613749778im], ComplexF64[-0.18041386462540418 + 2.762496182511301e-18im -4.77981535127589e-5 - 7.898169367276841e-19im … -0.0 - 0.0im -0.0 - 0.0im; -4.77981535127589e-5 - 7.898195522503882e-19im -0.1804138646254073 + 2.7624961825113176e-18im … -0.0 - 0.0im -0.0 - 0.0im; … ; -0.0 - 0.0im -0.0 - 0.0im … -0.181179949759701 + 8.499988253880949e-19im 5.0674722534505665e-5 - 1.0365811865687846e-12im; -0.0 - 0.0im -0.0 - 0.0im … 5.0674722534506214e-5 + 1.0365780638962131e-12im -0.18129360079367485 + 6.374991190014906e-18im]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 2, num. G vectors =  1058))], DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 2, num. G vectors =  1058), [0.21744441678413506, 0.21744441678413506, 1.9569997510572155, 5.436110419603376, 10.654776422422616, 17.61299775951494, 17.61299775951494, 10.654776422422616, 5.436110419603376, 1.9569997510572155  …  0.3755858108089606, 1.9569997510572157, 5.277969025578551, 10.338493634372968, 17.138573577440457, 18.561846123663894, 11.44548339254675, 6.0686759957026775, 2.431423933131692, 0.5337272048337861]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 2, num. G vectors =  1058), ComplexF64[0.0014526620565169196 + 0.0im 0.07040107498680777 + 0.0im … 0.0004011832434853789 - 0.0004011832434853788im -0.0005349109913138384 + 0.0005349109913138384im; 0.0014526620565169196 + 0.0im 0.07040107498680777 + 0.0im … 0.0004011832434853789 + 0.0004011832434853788im -0.0005349109913138384 - 0.0005349109913138384im; … ; 0.008349144389251885 + 0.0im 0.033173443134468926 + 0.0im … 0.0013093410302517496 - 0.0013093410302517493im -0.007141860165009543 + 0.007141860165009542im; 0.0026321132587078 + 0.0im 0.0639807860468336 + 0.0im … -0.0006588486948450427 - 0.0006588486948450426im -0.0015812368676281026 - 0.0015812368676281024im], [25.01813916 0.0 … 0.0 0.0; 0.0 -1.00698946204 … 0.0 0.0; … ; 0.0 0.0 … -5.327819979 0.0; 0.0 0.0 … 0.0 -5.327819979]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{ComplexF64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 2, num. G vectors =  1058), ComplexF64[0.0456169904168819 + 5.256995280119557e-17im -0.005769056936983059 - 3.7269078237974735e-17im … -7.735188675374558e-17 + 0.04561699041688176im -6.849128483095165e-17 - 0.06204498655219164im; 0.045616990416881865 - 7.86928762928864e-17im -0.0057690569369830205 + 9.336541693261431e-18im … 1.5419256198164503e-17 - 0.04561699041688183im -9.488344932578529e-17 + 0.06204498655219174im; … ; 0.021965357246362498 + 2.2464498668511797e-18im -0.002934802628982521 + 8.536727290997887e-17im … 1.9479992462911396e-18 + 0.021965357246362494im 8.64310917551173e-17 - 0.1335397161269563im; -0.059772984378440364 - 3.7392872748683694e-17im -0.007492120784271785 + 3.665094057581889e-17im … 6.887202895609839e-18 + 0.059772984378440246im -1.3882455122011876e-17 + 0.11270080613749778im], ComplexF64[-0.18041386462540418 + 2.762496182511301e-18im -4.77981535127589e-5 - 7.898169367276841e-19im … -0.0 - 0.0im -0.0 - 0.0im; -4.77981535127589e-5 - 7.898195522503882e-19im -0.1804138646254073 + 2.7624961825113176e-18im … -0.0 - 0.0im -0.0 - 0.0im; … ; -0.0 - 0.0im -0.0 - 0.0im … -0.181179949759701 + 8.499988253880949e-19im 5.0674722534505665e-5 - 1.0365811865687846e-12im; -0.0 - 0.0im -0.0 - 0.0im … 5.0674722534506214e-5 + 1.0365780638962131e-12im -0.18129360079367485 + 6.374991190014906e-18im]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,      0,      0], spin = 2, num. G vectors =  1058), [-11.263863396477234 -10.646825145306174 … -8.999927755703713 -10.646825145306162; -10.64682514530626 -9.183483427738501 … -10.270892653148774 -11.07767600647043; … ; -8.99992775570374 -10.27089265314864 … -4.593418277847986 -6.841333531996919; -10.64682514530617 -11.077676006470448 … -6.841333531996971 -9.18348342773853;;; -10.646825145306181 -9.183483427738413 … -10.27089265314872 -11.077676006470291; -9.183483427738414 -6.983942382549404 … -10.696068904068314 -10.459078043252727; … ; -10.270892653148714 -10.696068904068346 … -6.558383618734666 -8.813984786953988; -11.077676006470384 -10.459078043252683 … -8.813984786954055 -10.459078043252745;;; -8.999927755703814 -6.841333531996956 … -10.501765964296037 -10.270892653148753; -6.841333531997002 -4.690279472634192 … -9.89691475934302 -8.81398478695402; … ; -10.501765964296098 -9.89691475934288 … -8.281467419476666 -9.89691475934297; -10.270892653148687 -8.813984786954084 … -9.896914759342977 -10.696068904068289;;; … ;;; -6.558405264622452 -8.45742025648156 … -2.759575854424129 -4.491418051082871; -8.45742025648152 -9.711626537443168 … -4.317670473592434 -6.418539298747623; … ; -2.75957585442407 -4.317670473592569 … -0.9328242243784741 -1.624616078979277; -4.491418051082904 -6.4185392987476 … -1.624616078979239 -2.8270087230887437;;; -8.999927755703721 -10.27089265314877 … -4.5934182778479755 -6.841333531996985; -10.27089265314879 -10.696068904068298 … -6.5583836187347195 -8.81398478695407; … ; -4.593418277847944 -6.558383618734696 … -1.6445734683152733 -2.889516831970582; -6.841333531997063 -8.81398478695397 … -2.889516831970653 -4.6902794726341;;; -10.646825145306165 -11.077676006470288 … -6.841333531997044 -9.183483427738373; -11.077676006470377 -10.45907804325271 … -8.813984786954002 -10.459078043252697; … ; -6.841333531996909 -8.813984786954071 … -2.8895168319705795 -4.690279472634133; -9.183483427738539 -10.459078043252676 … -4.690279472634159 -6.9839423825494125])], nothing), DFTK.GenericHamiltonianBlock(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 2, num. G vectors =  1068), Any[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 2, num. G vectors =  1068), [0.23721209103723823, 0.632565576099302, 2.767474395434446, 6.641938549042671, 12.255958036923975, 19.60953285907836, 16.05135149351979, 9.48848364148953, 4.665171123732353, 1.581413940248255  …  0.8697776671365403, 2.846545092446859, 6.562867852030259, 12.01874594588674, 19.214179374016293, 17.07927055468115, 10.358261308626071, 5.376807396844065, 2.1349088193351444, 0.632565576099302]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 2, num. G vectors =  1068), [-19.69293028378679 -19.127691055462872 … -17.172460520653278 -19.127691055462872; -19.127691055462876 -17.402291367764306 … -18.721733773909865 -19.50894133358841; … ; -17.172460520653278 -18.721733773909865 … -10.245935170367524 -14.130197210981127; -19.127691055462872 -19.508941333588407 … -14.130197210981125 -17.402291367764303;;; -19.127691055462876 -17.402291367764303 … -18.72173377390986 -19.50894133358841; -17.402291367764303 -14.359308164945631 … -19.125807118069726 -18.92715469613527; … ; -18.721733773909865 -19.125807118069723 … -13.677457054305759 -16.940214173578532; -19.50894133358841 -18.92715469613527 … -16.940214173578532 -18.927154696135265;;; -17.172460520653278 -14.130197210981125 … -18.92628169003941 -18.721733773909865; -14.130197210981125 -10.423976117759622 … -18.297379847683594 -16.940214173578532; … ; -18.92628169003941 -18.297379847683594 … -16.235670612963965 -18.29737984768359; -18.72173377390986 -16.940214173578532 … -18.297379847683587 -19.125807118069723;;; … ;;; -13.677837405304386 -16.472166305707145 … -6.690325178037546 -10.071186579504449; -16.472166305707145 -18.079038283637747 … -9.730069757032524 -13.454546643596201; … ; -6.690325178037547 -9.730069757032522 … -2.391416851902863 -4.231026654525081; -10.071186579504452 -13.454546643596197 … -4.231026654525081 -6.802550458542525;;; -17.172460520653274 -18.72173377390986 … -10.245935170367522 -14.130197210981125; -18.72173377390986 -19.125807118069723 … -13.677457054305755 -16.940214173578532; … ; -10.245935170367522 -13.677457054305755 … -4.298952176788824 -6.916318157831658; -14.130197210981128 -16.940214173578532 … -6.916318157831658 -10.423976117759619;;; -19.127691055462876 -19.508941333588407 … -14.130197210981125 -17.402291367764303; -19.508941333588407 -18.92715469613527 … -16.940214173578536 -18.927154696135265; … ; -14.130197210981128 -16.940214173578536 … -6.91631815783166 -10.423976117759619; -17.402291367764303 -18.927154696135265 … -10.423976117759617 -14.359308164945627]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 2, num. G vectors =  1068), ComplexF64[0.001528456059177435 + 0.0im 0.0699878067058058 + 0.0im … 0.0 + 0.0007557958658307776im 0.0 - 0.0im; 0.0029863830726715615 + 0.0im 0.06205679930112999 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0075972732146966145 + 0.0im 0.03719800266440645 + 0.0im … 0.0 + 0.003425530158349149im 0.0 - 0.008221272380037958im; 0.0029863830726715615 + 0.0im 0.06205679930112999 + 0.0im … -0.0 + 0.0im 0.0 + 0.0im], [25.01813916 0.0 … 0.0 0.0; 0.0 -1.00698946204 … 0.0 0.0; … ; 0.0 0.0 … -5.327819979 0.0; 0.0 0.0 … 0.0 -5.327819979]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 2, num. G vectors =  1068)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 2, num. G vectors =  1068)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 2, num. G vectors =  1068), [10.877593800343199 10.729889422350716 … 10.09940572538798 10.729889422350716; 10.729889422350716 10.189012190068507 … 10.605300714277549 10.832545389614797; … ; 10.09940572538798 10.605300714277549 … 7.154147988494096 8.94385400564696; 10.729889422350716 10.832545389614799 … 8.94385400564696 10.189012190068507;;; 10.729889422350716 10.189012190068507 … 10.60530071427755 10.832545389614797; 10.189012190068507 9.048105173582577 … 10.729328157888629 10.67229949577574; … ; 10.60530071427755 10.729328157888629 … 8.743132050613442 10.01666945353644; 10.832545389614797 10.672299495775741 … 10.01666945353644 10.672299495775741;;; 10.09940572538798 8.94385400564696 … 10.671694823038989 10.605300714277547; 8.94385400564696 7.25124113554755 … 10.478405847429542 10.01666945353644; … ; 10.671694823038989 10.478405847429542 … 9.758036639158725 10.478405847429542; 10.605300714277547 10.016669453536442 … 10.478405847429542 10.729328157888629;;; … ;;; 8.72960061203429 9.823313976208432 … 5.125906964733587 7.053967661259478; 9.82331397620843 10.38731254842216 … 6.86950217921741 8.633221178530908; … ; 5.125906964733589 6.86950217921741 … 2.064083067041997 3.453936462414575; 7.053967661259478 8.63322117853091 … 3.453936462414576 5.199760967953645;;; 10.09940572538798 10.605300714277547 … 7.154147988494096 8.94385400564696; 10.605300714277549 10.729328157888627 … 8.74313205061344 10.01666945353644; … ; 7.154147988494096 8.743132050613442 … 3.5057692413610893 5.2767073984394965; 8.94385400564696 10.01666945353644 … 5.276707398439497 7.25124113554755;;; 10.729889422350716 10.832545389614795 … 8.94385400564696 10.189012190068505; 10.832545389614797 10.67229949577574 … 10.01666945353644 10.67229949577574; … ; 8.94385400564696 10.01666945353644 … 5.276707398439497 7.25124113554755; 10.189012190068507 10.672299495775741 … 7.25124113554755 9.048105173582577]), DFTK.RealSpaceMultiplication{Float64, SubArray{Float64, 3, Array{Float64, 4}, Tuple{Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Int64}, true}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 2, num. G vectors =  1068), [-2.448526913033643 -2.249023512194019 … -1.9268729604384136 -2.249023512194006; -2.2490235121941 -1.9702042500427028 … -2.1544595935164588 -2.4012800624968156; … ; -1.9268729604384407 -2.154459593516325 … -1.5016310959745591 -1.6549903266627528; -2.249023512194015 -2.40128006249684 … -1.654990326662806 -1.9702042500427335;;; -2.249023512194022 -1.9702042500426165 … -2.154459593516411 -2.4012800624966784; -1.970204250042618 -1.6727393911863497 … -2.299589943887216 -2.204222842893198; … ; -2.1544595935163993 -2.2995899438872525 … -1.6240586150423488 -1.890440066911896; -2.4012800624967694 -2.2042228428931563 … -1.8904400669119645 -2.2042228428932207;;; -1.9268729604385157 -1.6549903266627917 … -2.247179097295615 -2.1544595935164357; -1.6549903266628367 -1.5175444904221198 … -2.0779407590889676 -1.8904400669119292; … ; -2.247179097295677 -2.0779407590888286 … -1.8038334456714262 -2.077940759088921; -2.1544595935163726 -1.8904400669119936 … -2.077940759088931 -2.2995899438871956;;; … ;;; -1.610168471352356 -1.8085679269828476 … -1.1951576411201699 -1.4741991328378998; -1.8085679269828059 -2.019900802227582 … -1.4571028957773198 -1.5972138336823307; … ; -1.1951576411201115 -1.457102895777457 … -0.6054904395176082 -0.8475258868687711; -1.4741991328379298 -1.5972138336823127 … -0.8475258868687339 -1.2242192324998638;;; -1.9268729604384263 -2.1544595935164557 … -1.5016310959745502 -1.6549903266628203; -2.1544595935164783 -2.2995899438872027 … -1.6240586150424043 -1.890440066911978; … ; -1.501631095974519 -1.6240586150423826 … -0.8513905328875382 -1.2499060725784203; -1.654990326662895 -1.890440066911878 … -1.2499060725784918 -1.5175444904220317;;; -2.2490235121940056 -2.4012800624966757 … -1.6549903266628792 -1.970204250042576; -2.4012800624967676 -2.20422284289318 … -1.8904400669119061 -2.204222842893172; … ; -1.654990326662741 -1.8904400669119756 … -1.2499060725784168 -1.5175444904220647; -1.9702042500427435 -2.2042228428931523 … -1.5175444904220923 -1.6727393911863622]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{ComplexF64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 2, num. G vectors =  1068), ComplexF64[-0.053147941732329174 - 3.217765983632577e-16im 0.053147941732329194 + 1.1163342355645655e-16im … -0.05314794173232953 + 4.1286694451800125e-16im 3.335876085490484e-15 + 1.0671530155115488e-14im; 0.17147037220597233 - 2.7208438931753915e-16im -8.964348940144319e-18 + 2.67355757645808e-16im … 7.249454759992234e-17 - 2.83871374430065e-16im 3.86283921755773e-16 - 9.963933479287324e-17im; … ; -0.0505260746971852 - 1.438770091830379e-16im 0.009908285858871735 - 3.398411462321443e-17im … -0.05052607469718487 - 3.672370556104554e-17im 0.13525754331904807 - 2.6399712700320597e-15im; -0.17147037220597228 + 3.373089203076437e-16im -2.2759767045522606e-17 - 2.833625285936374e-16im … 1.4925393575239546e-16 + 3.4015816928299227e-16im 4.542859638316812e-16 + 3.914375309655923e-17im], ComplexF64[-0.18041386462540418 + 2.762496182511301e-18im -4.77981535127589e-5 - 7.898169367276841e-19im … -0.0 - 0.0im -0.0 - 0.0im; -4.77981535127589e-5 - 7.898195522503882e-19im -0.1804138646254073 + 2.7624961825113176e-18im … -0.0 - 0.0im -0.0 - 0.0im; … ; -0.0 - 0.0im -0.0 - 0.0im … -0.181179949759701 + 8.499988253880949e-19im 5.0674722534505665e-5 - 1.0365811865687846e-12im; -0.0 - 0.0im -0.0 - 0.0im … 5.0674722534506214e-5 + 1.0365780638962131e-12im -0.18129360079367485 + 6.374991190014906e-18im]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 2, num. G vectors =  1068))], DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 2, num. G vectors =  1068), [0.23721209103723823, 0.632565576099302, 2.767474395434446, 6.641938549042671, 12.255958036923975, 19.60953285907836, 16.05135149351979, 9.48848364148953, 4.665171123732353, 1.581413940248255  …  0.8697776671365403, 2.846545092446859, 6.562867852030259, 12.01874594588674, 19.214179374016293, 17.07927055468115, 10.358261308626071, 5.376807396844065, 2.1349088193351444, 0.632565576099302]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 2, num. G vectors =  1068), ComplexF64[0.001528456059177435 + 0.0im 0.0699878067058058 + 0.0im … 0.0 + 0.0007557958658307776im 0.0 - 0.0im; 0.0029863830726715615 + 0.0im 0.06205679930112999 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0075972732146966145 + 0.0im 0.03719800266440645 + 0.0im … 0.0 + 0.003425530158349149im 0.0 - 0.008221272380037958im; 0.0029863830726715615 + 0.0im 0.06205679930112999 + 0.0im … -0.0 + 0.0im 0.0 + 0.0im], [25.01813916 0.0 … 0.0 0.0; 0.0 -1.00698946204 … 0.0 0.0; … ; 0.0 0.0 … -5.327819979 0.0; 0.0 0.0 … 0.0 -5.327819979]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{ComplexF64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 2, num. G vectors =  1068), ComplexF64[-0.053147941732329174 - 3.217765983632577e-16im 0.053147941732329194 + 1.1163342355645655e-16im … -0.05314794173232953 + 4.1286694451800125e-16im 3.335876085490484e-15 + 1.0671530155115488e-14im; 0.17147037220597233 - 2.7208438931753915e-16im -8.964348940144319e-18 + 2.67355757645808e-16im … 7.249454759992234e-17 - 2.83871374430065e-16im 3.86283921755773e-16 - 9.963933479287324e-17im; … ; -0.0505260746971852 - 1.438770091830379e-16im 0.009908285858871735 - 3.398411462321443e-17im … -0.05052607469718487 - 3.672370556104554e-17im 0.13525754331904807 - 2.6399712700320597e-15im; -0.17147037220597228 + 3.373089203076437e-16im -2.2759767045522606e-17 - 2.833625285936374e-16im … 1.4925393575239546e-16 + 3.4015816928299227e-16im 4.542859638316812e-16 + 3.914375309655923e-17im], ComplexF64[-0.18041386462540418 + 2.762496182511301e-18im -4.77981535127589e-5 - 7.898169367276841e-19im … -0.0 - 0.0im -0.0 - 0.0im; -4.77981535127589e-5 - 7.898195522503882e-19im -0.1804138646254073 + 2.7624961825113176e-18im … -0.0 - 0.0im -0.0 - 0.0im; … ; -0.0 - 0.0im -0.0 - 0.0im … -0.181179949759701 + 8.499988253880949e-19im 5.0674722534505665e-5 - 1.0365811865687846e-12im; -0.0 - 0.0im -0.0 - 0.0im … 5.0674722534506214e-5 + 1.0365780638962131e-12im -0.18129360079367485 + 6.374991190014906e-18im]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,      0], spin = 2, num. G vectors =  1068), [-11.263863396477234 -10.646825145306174 … -8.999927755703713 -10.646825145306162; -10.64682514530626 -9.183483427738501 … -10.270892653148774 -11.07767600647043; … ; -8.99992775570374 -10.27089265314864 … -4.593418277847986 -6.841333531996919; -10.64682514530617 -11.077676006470448 … -6.841333531996971 -9.18348342773853;;; -10.646825145306181 -9.183483427738413 … -10.27089265314872 -11.077676006470291; -9.183483427738414 -6.983942382549404 … -10.696068904068314 -10.459078043252727; … ; -10.270892653148714 -10.696068904068346 … -6.558383618734666 -8.813984786953988; -11.077676006470384 -10.459078043252683 … -8.813984786954055 -10.459078043252745;;; -8.999927755703814 -6.841333531996956 … -10.501765964296037 -10.270892653148753; -6.841333531997002 -4.690279472634192 … -9.89691475934302 -8.81398478695402; … ; -10.501765964296098 -9.89691475934288 … -8.281467419476666 -9.89691475934297; -10.270892653148687 -8.813984786954084 … -9.896914759342977 -10.696068904068289;;; … ;;; -6.558405264622452 -8.45742025648156 … -2.759575854424129 -4.491418051082871; -8.45742025648152 -9.711626537443168 … -4.317670473592434 -6.418539298747623; … ; -2.75957585442407 -4.317670473592569 … -0.9328242243784741 -1.624616078979277; -4.491418051082904 -6.4185392987476 … -1.624616078979239 -2.8270087230887437;;; -8.999927755703721 -10.27089265314877 … -4.5934182778479755 -6.841333531996985; -10.27089265314879 -10.696068904068298 … -6.5583836187347195 -8.81398478695407; … ; -4.593418277847944 -6.558383618734696 … -1.6445734683152733 -2.889516831970582; -6.841333531997063 -8.81398478695397 … -2.889516831970653 -4.6902794726341;;; -10.646825145306165 -11.077676006470288 … -6.841333531997044 -9.183483427738373; -11.077676006470377 -10.45907804325271 … -8.813984786954002 -10.459078043252697; … ; -6.841333531996909 -8.813984786954071 … -2.8895168319705795 -4.690279472634133; -9.183483427738539 -10.459078043252676 … -4.690279472634159 -6.9839423825494125])], nothing), DFTK.GenericHamiltonianBlock(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 2, num. G vectors =  1062), Any[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 2, num. G vectors =  1062), [0.05930302275930956, 0.850009992883437, 3.3802722972806456, 7.650089935950932, 13.6594629088943, 14.292028484993606, 8.12451411802541, 3.6965550853302975, 1.0081513869082626, 0.850009992883437  …  1.6407169630075644, 1.1662927809330879, 3.5384136913054705, 7.650089935950933, 13.50132151486948, 15.39901824316738, 9.073362482174362, 4.487262055454421, 1.6407169630075644, 0.533727204833786]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 2, num. G vectors =  1062), [-19.69293028378679 -19.127691055462872 … -17.172460520653278 -19.127691055462872; -19.127691055462876 -17.402291367764306 … -18.721733773909865 -19.50894133358841; … ; -17.172460520653278 -18.721733773909865 … -10.245935170367524 -14.130197210981127; -19.127691055462872 -19.508941333588407 … -14.130197210981125 -17.402291367764303;;; -19.127691055462876 -17.402291367764303 … -18.72173377390986 -19.50894133358841; -17.402291367764303 -14.359308164945631 … -19.125807118069726 -18.92715469613527; … ; -18.721733773909865 -19.125807118069723 … -13.677457054305759 -16.940214173578532; -19.50894133358841 -18.92715469613527 … -16.940214173578532 -18.927154696135265;;; -17.172460520653278 -14.130197210981125 … -18.92628169003941 -18.721733773909865; -14.130197210981125 -10.423976117759622 … -18.297379847683594 -16.940214173578532; … ; -18.92628169003941 -18.297379847683594 … -16.235670612963965 -18.29737984768359; -18.72173377390986 -16.940214173578532 … -18.297379847683587 -19.125807118069723;;; … ;;; -13.677837405304386 -16.472166305707145 … -6.690325178037546 -10.071186579504449; -16.472166305707145 -18.079038283637747 … -9.730069757032524 -13.454546643596201; … ; -6.690325178037547 -9.730069757032522 … -2.391416851902863 -4.231026654525081; -10.071186579504452 -13.454546643596197 … -4.231026654525081 -6.802550458542525;;; -17.172460520653274 -18.72173377390986 … -10.245935170367522 -14.130197210981125; -18.72173377390986 -19.125807118069723 … -13.677457054305755 -16.940214173578532; … ; -10.245935170367522 -13.677457054305755 … -4.298952176788824 -6.916318157831658; -14.130197210981128 -16.940214173578532 … -6.916318157831658 -10.423976117759619;;; -19.127691055462876 -19.508941333588407 … -14.130197210981125 -17.402291367764303; -19.508941333588407 -18.92715469613527 … -16.940214173578536 -18.927154696135265; … ; -14.130197210981128 -16.940214173578536 … -6.91631815783166 -10.423976117759619; -17.402291367764303 -18.927154696135265 … -10.423976117759617 -14.359308164945627]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 2, num. G vectors =  1062), ComplexF64[0.0008361342694689059 + 0.0im 0.07376620221926404 + 0.0im … 0.00013468431164408555 + 0.00013468431164408555im 0.0 + 0.0im; 0.0037424247587792016 + 0.0im 0.05795773062060897 + 0.0im … 0.001946345118023464 - 0.0019463451180234635im -0.0010380507296125138 + 0.0010380507296125136im; … ; 0.006233363233366942 + 0.0im 0.04451750272603676 + 0.0im … 0.0011206236616205692 + 0.001120623661620569im 0.0049805496072025295 + 0.004980549607202529im; 0.0026321132587077975 + 0.0im 0.0639807860468336 + 0.0im … -0.001185927650721078 + 0.0011859276507210777im 0.0 + 0.0im], [25.01813916 0.0 … 0.0 0.0; 0.0 -1.00698946204 … 0.0 0.0; … ; 0.0 0.0 … -5.327819979 0.0; 0.0 0.0 … 0.0 -5.327819979]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 2, num. G vectors =  1062)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 2, num. G vectors =  1062)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 2, num. G vectors =  1062), [10.877593800343199 10.729889422350716 … 10.09940572538798 10.729889422350716; 10.729889422350716 10.189012190068507 … 10.605300714277549 10.832545389614797; … ; 10.09940572538798 10.605300714277549 … 7.154147988494096 8.94385400564696; 10.729889422350716 10.832545389614799 … 8.94385400564696 10.189012190068507;;; 10.729889422350716 10.189012190068507 … 10.60530071427755 10.832545389614797; 10.189012190068507 9.048105173582577 … 10.729328157888629 10.67229949577574; … ; 10.60530071427755 10.729328157888629 … 8.743132050613442 10.01666945353644; 10.832545389614797 10.672299495775741 … 10.01666945353644 10.672299495775741;;; 10.09940572538798 8.94385400564696 … 10.671694823038989 10.605300714277547; 8.94385400564696 7.25124113554755 … 10.478405847429542 10.01666945353644; … ; 10.671694823038989 10.478405847429542 … 9.758036639158725 10.478405847429542; 10.605300714277547 10.016669453536442 … 10.478405847429542 10.729328157888629;;; … ;;; 8.72960061203429 9.823313976208432 … 5.125906964733587 7.053967661259478; 9.82331397620843 10.38731254842216 … 6.86950217921741 8.633221178530908; … ; 5.125906964733589 6.86950217921741 … 2.064083067041997 3.453936462414575; 7.053967661259478 8.63322117853091 … 3.453936462414576 5.199760967953645;;; 10.09940572538798 10.605300714277547 … 7.154147988494096 8.94385400564696; 10.605300714277549 10.729328157888627 … 8.74313205061344 10.01666945353644; … ; 7.154147988494096 8.743132050613442 … 3.5057692413610893 5.2767073984394965; 8.94385400564696 10.01666945353644 … 5.276707398439497 7.25124113554755;;; 10.729889422350716 10.832545389614795 … 8.94385400564696 10.189012190068505; 10.832545389614797 10.67229949577574 … 10.01666945353644 10.67229949577574; … ; 8.94385400564696 10.01666945353644 … 5.276707398439497 7.25124113554755; 10.189012190068507 10.672299495775741 … 7.25124113554755 9.048105173582577]), DFTK.RealSpaceMultiplication{Float64, SubArray{Float64, 3, Array{Float64, 4}, Tuple{Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Int64}, true}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 2, num. G vectors =  1062), [-2.448526913033643 -2.249023512194019 … -1.9268729604384136 -2.249023512194006; -2.2490235121941 -1.9702042500427028 … -2.1544595935164588 -2.4012800624968156; … ; -1.9268729604384407 -2.154459593516325 … -1.5016310959745591 -1.6549903266627528; -2.249023512194015 -2.40128006249684 … -1.654990326662806 -1.9702042500427335;;; -2.249023512194022 -1.9702042500426165 … -2.154459593516411 -2.4012800624966784; -1.970204250042618 -1.6727393911863497 … -2.299589943887216 -2.204222842893198; … ; -2.1544595935163993 -2.2995899438872525 … -1.6240586150423488 -1.890440066911896; -2.4012800624967694 -2.2042228428931563 … -1.8904400669119645 -2.2042228428932207;;; -1.9268729604385157 -1.6549903266627917 … -2.247179097295615 -2.1544595935164357; -1.6549903266628367 -1.5175444904221198 … -2.0779407590889676 -1.8904400669119292; … ; -2.247179097295677 -2.0779407590888286 … -1.8038334456714262 -2.077940759088921; -2.1544595935163726 -1.8904400669119936 … -2.077940759088931 -2.2995899438871956;;; … ;;; -1.610168471352356 -1.8085679269828476 … -1.1951576411201699 -1.4741991328378998; -1.8085679269828059 -2.019900802227582 … -1.4571028957773198 -1.5972138336823307; … ; -1.1951576411201115 -1.457102895777457 … -0.6054904395176082 -0.8475258868687711; -1.4741991328379298 -1.5972138336823127 … -0.8475258868687339 -1.2242192324998638;;; -1.9268729604384263 -2.1544595935164557 … -1.5016310959745502 -1.6549903266628203; -2.1544595935164783 -2.2995899438872027 … -1.6240586150424043 -1.890440066911978; … ; -1.501631095974519 -1.6240586150423826 … -0.8513905328875382 -1.2499060725784203; -1.654990326662895 -1.890440066911878 … -1.2499060725784918 -1.5175444904220317;;; -2.2490235121940056 -2.4012800624966757 … -1.6549903266628792 -1.970204250042576; -2.4012800624967676 -2.20422284289318 … -1.8904400669119061 -2.204222842893172; … ; -1.654990326662741 -1.8904400669119756 … -1.2499060725784168 -1.5175444904220647; -1.9702042500427435 -2.2042228428931523 … -1.5175444904220923 -1.6727393911863622]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{ComplexF64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 2, num. G vectors =  1062), ComplexF64[-0.012306510152407416 + 8.66503947247771e-17im -0.012306510152407354 + 2.0444870790939625e-17im … -1.3080345152670957e-16 + 0.012306510152407333im 1.3703939864966026e-16 - 2.051166158440309e-17im; 0.12191225909305085 + 1.8370881862396167e-16im -0.06662978048669259 + 1.550512978349806e-17im … 4.235462497063209e-17 + 0.12191225909305088im -2.2290612952231276e-17 - 0.04951021313498459im; … ; -0.030676718659148398 - 3.188442971770381e-17im -0.0033251636058130598 + 5.2143093254116074e-17im … 4.487444041001481e-17 + 0.03067671865914838im 4.3049148233430525e-17 + 0.1590928808831705im; -0.10276141274450667 + 1.311556505659984e-16im -0.10276141274450659 + 1.2754573952389513e-16im … -8.762988110877603e-17 - 0.10276141274450663im 2.145514056873749e-16 + 4.7381574593839345e-17im], ComplexF64[-0.18041386462540418 + 2.762496182511301e-18im -4.77981535127589e-5 - 7.898169367276841e-19im … -0.0 - 0.0im -0.0 - 0.0im; -4.77981535127589e-5 - 7.898195522503882e-19im -0.1804138646254073 + 2.7624961825113176e-18im … -0.0 - 0.0im -0.0 - 0.0im; … ; -0.0 - 0.0im -0.0 - 0.0im … -0.181179949759701 + 8.499988253880949e-19im 5.0674722534505665e-5 - 1.0365811865687846e-12im; -0.0 - 0.0im -0.0 - 0.0im … 5.0674722534506214e-5 + 1.0365780638962131e-12im -0.18129360079367485 + 6.374991190014906e-18im]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 2, num. G vectors =  1062))], DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 2, num. G vectors =  1062), [0.05930302275930956, 0.850009992883437, 3.3802722972806456, 7.650089935950932, 13.6594629088943, 14.292028484993606, 8.12451411802541, 3.6965550853302975, 1.0081513869082626, 0.850009992883437  …  1.6407169630075644, 1.1662927809330879, 3.5384136913054705, 7.650089935950933, 13.50132151486948, 15.39901824316738, 9.073362482174362, 4.487262055454421, 1.6407169630075644, 0.533727204833786]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 2, num. G vectors =  1062), ComplexF64[0.0008361342694689059 + 0.0im 0.07376620221926404 + 0.0im … 0.00013468431164408555 + 0.00013468431164408555im 0.0 + 0.0im; 0.0037424247587792016 + 0.0im 0.05795773062060897 + 0.0im … 0.001946345118023464 - 0.0019463451180234635im -0.0010380507296125138 + 0.0010380507296125136im; … ; 0.006233363233366942 + 0.0im 0.04451750272603676 + 0.0im … 0.0011206236616205692 + 0.001120623661620569im 0.0049805496072025295 + 0.004980549607202529im; 0.0026321132587077975 + 0.0im 0.0639807860468336 + 0.0im … -0.001185927650721078 + 0.0011859276507210777im 0.0 + 0.0im], [25.01813916 0.0 … 0.0 0.0; 0.0 -1.00698946204 … 0.0 0.0; … ; 0.0 0.0 … -5.327819979 0.0; 0.0 0.0 … 0.0 -5.327819979]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{ComplexF64}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 2, num. G vectors =  1062), ComplexF64[-0.012306510152407416 + 8.66503947247771e-17im -0.012306510152407354 + 2.0444870790939625e-17im … -1.3080345152670957e-16 + 0.012306510152407333im 1.3703939864966026e-16 - 2.051166158440309e-17im; 0.12191225909305085 + 1.8370881862396167e-16im -0.06662978048669259 + 1.550512978349806e-17im … 4.235462497063209e-17 + 0.12191225909305088im -2.2290612952231276e-17 - 0.04951021313498459im; … ; -0.030676718659148398 - 3.188442971770381e-17im -0.0033251636058130598 + 5.2143093254116074e-17im … 4.487444041001481e-17 + 0.03067671865914838im 4.3049148233430525e-17 + 0.1590928808831705im; -0.10276141274450667 + 1.311556505659984e-16im -0.10276141274450659 + 1.2754573952389513e-16im … -8.762988110877603e-17 - 0.10276141274450663im 2.145514056873749e-16 + 4.7381574593839345e-17im], ComplexF64[-0.18041386462540418 + 2.762496182511301e-18im -4.77981535127589e-5 - 7.898169367276841e-19im … -0.0 - 0.0im -0.0 - 0.0im; -4.77981535127589e-5 - 7.898195522503882e-19im -0.1804138646254073 + 2.7624961825113176e-18im … -0.0 - 0.0im -0.0 - 0.0im; … ; -0.0 - 0.0im -0.0 - 0.0im … -0.181179949759701 + 8.499988253880949e-19im 5.0674722534505665e-5 - 1.0365811865687846e-12im; -0.0 - 0.0im -0.0 - 0.0im … 5.0674722534506214e-5 + 1.0365780638962131e-12im -0.18129360079367485 + 6.374991190014906e-18im]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), KPoint([  -0.5,   -0.5,   -0.5], spin = 2, num. G vectors =  1062), [-11.263863396477234 -10.646825145306174 … -8.999927755703713 -10.646825145306162; -10.64682514530626 -9.183483427738501 … -10.270892653148774 -11.07767600647043; … ; -8.99992775570374 -10.27089265314864 … -4.593418277847986 -6.841333531996919; -10.64682514530617 -11.077676006470448 … -6.841333531996971 -9.18348342773853;;; -10.646825145306181 -9.183483427738413 … -10.27089265314872 -11.077676006470291; -9.183483427738414 -6.983942382549404 … -10.696068904068314 -10.459078043252727; … ; -10.270892653148714 -10.696068904068346 … -6.558383618734666 -8.813984786953988; -11.077676006470384 -10.459078043252683 … -8.813984786954055 -10.459078043252745;;; -8.999927755703814 -6.841333531996956 … -10.501765964296037 -10.270892653148753; -6.841333531997002 -4.690279472634192 … -9.89691475934302 -8.81398478695402; … ; -10.501765964296098 -9.89691475934288 … -8.281467419476666 -9.89691475934297; -10.270892653148687 -8.813984786954084 … -9.896914759342977 -10.696068904068289;;; … ;;; -6.558405264622452 -8.45742025648156 … -2.759575854424129 -4.491418051082871; -8.45742025648152 -9.711626537443168 … -4.317670473592434 -6.418539298747623; … ; -2.75957585442407 -4.317670473592569 … -0.9328242243784741 -1.624616078979277; -4.491418051082904 -6.4185392987476 … -1.624616078979239 -2.8270087230887437;;; -8.999927755703721 -10.27089265314877 … -4.5934182778479755 -6.841333531996985; -10.27089265314879 -10.696068904068298 … -6.5583836187347195 -8.81398478695407; … ; -4.593418277847944 -6.558383618734696 … -1.6445734683152733 -2.889516831970582; -6.841333531997063 -8.81398478695397 … -2.889516831970653 -4.6902794726341;;; -10.646825145306165 -11.077676006470288 … -6.841333531997044 -9.183483427738373; -11.077676006470377 -10.45907804325271 … -8.813984786954002 -10.459078043252697; … ; -6.841333531996909 -8.813984786954071 … -2.8895168319705795 -4.690279472634133; -9.183483427738539 -10.459078043252676 … -4.690279472634159 -6.9839423825494125])], nothing)]), basis = PlaneWaveBasis(model = Model(gga_x_pbe+gga_c_pbe, spin_polarization = :collinear), Ecut = 20.0 Ha, kgrid = MonkhorstPack([2, 2, 2])), energies = Energies(total = -363.397710017851), converged = true, occupation_threshold = 1.0e-6, ρ = [0.753647990467732 1.0913288117538218 … 1.6758738979869303 1.0913288117538218; 1.091328811753822 1.634162389089641 … 1.2744320582485518 0.8755098005447598; … ; 1.6758738979869303 1.2744320582485518 … 1.302598529926866 1.7746459747755299; 1.091328811753822 0.8755098005447598 … 1.7746459747755297 1.6341623890896408;;; 1.091328811753822 1.6341623890896404 … 1.2744320582485518 0.8755098005447596; 1.6341623890896404 1.7833598623199818 … 1.0912193559386905 1.1857745478244126; … ; 1.2744320582485518 1.0912193559386907 … 1.7476603639985535 1.7085217971544648; 0.8755098005447598 1.1857745478244126 … 1.7085217971544646 1.1857745478244126;;; 1.6758738979869303 1.7746459747755297 … 1.1858688139563573 1.2744320582485515; 1.7746459747755297 1.3310851802698338 … 1.421090092474188 1.7085217971544648; … ; 1.1858688139563573 1.4210900924741883 … 1.777089480609852 1.4210900924741883; 1.2744320582485518 1.7085217971544648 … 1.4210900924741883 1.0912193559386907;;; … ;;; 1.7524861231110191 1.767787045449779 … 0.6465150988919633 1.2751925001964266; 1.7677870454497793 1.4932270216902672 … 1.2165658841225548 1.7345893683028657; … ; 0.6465150988919632 1.2165658841225548 … 0.09398510113808943 0.2561017738695366; 1.2751925001964268 1.734589368302866 … 0.2561017738695363 0.6667773588277822;;; 1.6758738979869303 1.274432058248552 … 1.302598529926866 1.7746459747755294; 1.274432058248552 1.0912193559386907 … 1.7476603639985535 1.7085217971544648; … ; 1.3025985299268659 1.7476603639985537 … 0.26452560081438614 0.6870845266235509; 1.7746459747755294 1.7085217971544648 … 0.6870845266235509 1.3310851802698338;;; 1.0913288117538218 0.8755098005447596 … 1.7746459747755294 1.6341623890896404; 0.8755098005447598 1.1857745478244126 … 1.7085217971544644 1.1857745478244126; … ; 1.7746459747755294 1.7085217971544644 … 0.6870845266235507 1.3310851802698338; 1.6341623890896408 1.1857745478244126 … 1.3310851802698338 1.7833598623199818;;;; 0.7626352657211872 1.0944037551904298 … 1.6172343918663317 1.0944037551904298; 1.0944037551904298 1.6287035476306075 … 1.237158826388528 0.8842030083895203; … ; 1.6172343918663319 1.237158826388528 … 1.266133562947392 1.729754149163248; 1.0944037551904295 0.8842030083895202 … 1.729754149163248 1.6287035476306073;;; 1.0944037551904295 1.6287035476306075 … 1.237158826388528 0.88420300838952; 1.6287035476306075 1.7827752168669022 … 1.0945240225024535 1.1848784667274903; … ; 1.237158826388528 1.0945240225024537 … 1.6565607230878001 1.642914824096311; 0.8842030083895198 1.18487846672749 … 1.6429148240963114 1.1848784667274903;;; 1.6172343918663317 1.729754149163248 … 1.1845480938640538 1.2371588263885278; 1.729754149163248 1.3172870306692224 … 1.4025701307577423 1.6429148240963112; … ; 1.184548093864054 1.4025701307577423 … 1.6903910391518329 1.402570130757742; 1.2371588263885278 1.6429148240963112 … 1.4025701307577423 1.0945240225024535;;; … ;;; 1.600034757957209 1.5744998393420233 … 0.6213751350509521 1.20239798363803; 1.5744998393420233 1.3596516732059885 … 1.1248574992472404 1.5797430110197703; … ; 0.6213751350509521 1.1248574992472402 … 0.09617913352736703 0.25489460607343234; 1.20239798363803 1.5797430110197703 … 0.2548946060734325 0.6487378911574722;;; 1.6172343918663317 1.237158826388528 … 1.266133562947392 1.729754149163248; 1.237158826388528 1.0945240225024535 … 1.6565607230878003 1.6429148240963112; … ; 1.266133562947392 1.6565607230878003 … 0.2671409222158729 0.6830783082332164; 1.729754149163248 1.642914824096311 … 0.6830783082332165 1.3172870306692221;;; 1.0944037551904295 0.88420300838952 … 1.729754149163248 1.6287035476306073; 0.88420300838952 1.1848784667274905 … 1.6429148240963112 1.1848784667274903; … ; 1.729754149163248 1.642914824096311 … 0.6830783082332165 1.3172870306692221; 1.628703547630607 1.18487846672749 … 1.3172870306692221 1.7827752168669022], τ = nothing, hubbard_n = Matrix{ComplexF64}[[0.9930157233542988 - 7.228014483236491e-20im 5.986887843637405e-5 - 1.301042602674373e-18im … 5.986887843565698e-5 - 1.3010426285237672e-18im -9.62974817074469e-17 - 3.877409121342317e-26im; 5.986887843637405e-5 - 1.3010426112908376e-18im 0.9930157233543072 - 7.228014483237493e-20im … 5.986887843508024e-5 - 1.3010426069826053e-18im 0.00013782696012983235 + 4.340106360830873e-11im; … ; 5.986887843565699e-5 - 1.3010425854414435e-18im 5.9868878435080234e-5 - 1.3010426069826053e-18im … 0.9930157233543033 - 7.228014483236748e-20im -0.00013782696012907736 - 4.340106360830868e-11im; -9.630651672555095e-17 + 3.6619975034899665e-26im 0.000137826960129839 - 4.340107105379903e-11im … -0.000137826960129084 + 4.340107105379897e-11im 0.9933251737908156 - 8.673617379884035e-18im] [0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 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+ 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im];;; [0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im] [0.9909309112955421 + 1.9660199394403747e-17im 0.00013022355649467521 - 6.216084959259258e-18im … 0.0001302235564939527 - 6.2161056129251774e-18im 2.1955093992831465e-16 - 2.933044588677611e-23im; 0.00013022355649467521 - 6.21609995190786e-18im 0.9909309112955503 + 1.9660199394403864e-17im … 0.00013022355649337276 - 6.216086484373512e-18im -0.009003488029548009 + 3.0851099951231636e-8im; … ; 0.0001302235564939527 - 6.2160792982419406e-18im 0.00013022355649337274 - 6.216098426793606e-18im … 0.9909309112955462 + 1.9660199394403815e-17im 0.009003488029548564 - 3.085109995123159e-8im; 2.1918953920415282e-16 + 2.908918487478147e-23im -0.009003488029548005 - 3.0851099952619136e-8im … 0.009003488029548562 + 3.0851099952619096e-8im 0.13798020694710875 - 3.2311750060584095e-27im]; [0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im] [0.993015759295818 - 2.3129646346357315e-18im 6.001639356399244e-5 - 1.3010426038187471e-18im … 6.001639356327539e-5 - 1.3010426042899602e-18im -9.62974817074469e-17 + 2.692645223154387e-27im; 6.001639356399244e-5 - 1.3010426101464635e-18im 0.9930157592958263 - 2.312964634635758e-18im … 6.001639356269863e-5 - 1.301042602674373e-18im 0.00013789294478073734 - 2.8206811043152513e-12im; … ; 6.001639356327539e-5 - 1.3010426096752505e-18im 6.001639356269863e-5 - 1.3010426112908376e-18im … 0.9930157592958223 - 2.3129646346357407e-18im -0.00013789294477998236 + 2.8206811043152436e-12im; -9.630425797102493e-17 - 2.692645223154387e-27im 0.00013789294478073883 + 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0.052429272786240294im 0.011150591103546862 + 0.10735514451561633im … -0.09407941666247294 + 0.07951422181113688im -0.006109940662306557 - 0.0041794559493673125im; 0.15010098250256151 - 0.08318767533003141im -0.01769407651844902 - 0.17035420779820265im … -0.32685268294654807 + 0.27625001946108696im 9.717355124453504e-6 - 5.148065613811395e-6im], [0.1706137242944239 - 0.13534100210169617im 0.12937844239042035 - 0.1764657349435718im … 5.078286738416802e-11 - 1.475243832707301e-11im 4.466874221200575e-10 + 5.169851974601622e-10im; -0.11651828544924207 + 0.09242926729107931im 0.08721696671613759 - 0.11895958747247416im … 0.08464622799439124 + 0.3543094533485675im -0.3904966772351827 + 0.030819633963575937im; … ; 0.0983200908755974 - 0.07799337170177982im 0.07451390005329256 - 0.1016332388183106im … 0.0012053336397961215 + 0.005045237236557649im -0.005560637211979229 + 0.00043884230188858493im; -0.1539518601477258 + 0.12212381574001403im 0.11524349416851919 - 0.15718637139197153im … 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3.7397520893839504e-5im; -0.009784545294800988 + 0.16309281340400417im -0.16477031918535318 + 0.0006021394126376319im … 6.9936888157980645e-6 - 9.660502042849322e-6im 0.2223547872987591 - 0.34673929372923007im; … ; 0.005367778855589855 - 0.089472340887082im -0.08866262278105969 + 0.000324010178938819im … 0.0005215023395417147 - 0.000692678948804726im 0.0007007354853059683 - 0.0010789446930665255im; -0.009785182525369073 + 0.16310343436869282im -0.16476358766772028 + 0.0006021148241763523im … -0.0007211325577737864 + 0.000953924998693747im -0.22201929638966322 + 0.3462592584352635im], [0.1617901933447258 - 0.1377632718501925im 0.14755500460713655 - 0.1524215743156523im … 0.015039470325099114 + 0.01817733090988323im -1.1465116642835306e-7 + 6.375288396012797e-6im; -0.11383044690019108 + 0.09692586729299574im 0.10380820850094173 - 0.10723194793243165im … -0.09319103887357716 - 0.1126345057402907im -0.07117046135342771 + 0.2550777372443229im; … ; 0.0823495842212976 - 0.0701201220663557im 0.07507191432492473 - 0.07754789067230416im … -0.07852280780325696 - 0.09490593718792034im 0.002059036956519484 - 0.006647495225617253im; -0.13066120698423436 + 0.11125714731387253im 0.11912624401243611 - 0.12305519359695738im … 0.2728077673756208 + 0.32972682934129993im -6.184031283771894e-6 + 1.2345403034354766e-5im]], residual_norms = [[3.5486452430141253e-8, 8.098078512350886e-8, 1.573944890177003e-8, 1.6270585090727066e-8, 1.1330460216239821e-8, 2.5493275368805557e-8, 2.543572178819504e-8, 2.5540920706645565e-8, 1.9763451760550795e-8, 1.7167645373168135e-8  …  1.610598849684721e-7, 3.560343215780385e-8, 3.820893296603387e-8, 4.76030611326565e-8, 2.1947466228414423e-7, 2.6216954492867005e-7, 1.247589374091952e-7, 1.6672764597825703e-7, 4.4545731478044215e-7, 4.128406822385174e-6], [3.679834997469076e-8, 8.002054268663206e-8, 1.988380374758453e-8, 1.4732241107975292e-8, 2.086349529393805e-8, 4.6492893865951654e-8, 2.7201519189751857e-8, 4.703523754732868e-8, 3.095173201725042e-8, 5.71513524889057e-8  …  1.6798654074868298e-7, 1.516703075037782e-7, 1.439593127788276e-7, 2.1953847905510707e-7, 3.035344796139516e-7, 6.385741144140704e-7, 8.452444725926619e-7, 9.149379323930399e-7, 2.005583337196439e-6, 0.0009497834038008974], [4.114044098413006e-8, 8.619866331589707e-8, 2.0347543657722157e-8, 2.2941387980766947e-8, 2.8010769528641423e-8, 2.915651864086961e-8, 5.675245393158727e-8, 6.17750624336319e-8, 7.038090914143308e-8, 2.2470794188194244e-8  …  1.1651817500445286e-7, 2.078573423373419e-7, 1.8698423311814384e-7, 3.0597353739347984e-7, 2.902134246864549e-7, 2.34177194666562e-7, 3.75425673481413e-7, 5.64373852729966e-6, 4.0412182575926354e-5, 0.00026149048971138735], [3.7131338470748194e-8, 8.384173746001674e-8, 1.508343855935931e-8, 1.5232192862464798e-8, 1.1531917791563476e-8, 2.4809571243632067e-8, 2.685187902032152e-8, 2.5501487974899364e-8, 2.131670360365451e-8, 2.0983968052214374e-8  …  2.3414227928757672e-7, 9.324575128097655e-8, 7.060847897087595e-8, 3.550757021199579e-7, 4.575353268408068e-7, 4.701955524762437e-8, 5.1945301475206235e-8, 3.9433740887963725e-7, 4.000256353542801e-7, 0.007070054005081115], [1.489774182364168e-7, 2.090336353273211e-8, 3.635807765726945e-8, 3.29945613362428e-8, 3.098786074086705e-8, 1.5159156476365996e-8, 1.3725859156463146e-8, 1.2618694109406652e-8, 1.929061327764346e-8, 2.689107689731307e-8  …  1.4549623539050477e-7, 2.806026412314141e-8, 4.217174237928619e-8, 4.163530007535526e-8, 2.2854578086456892e-7, 2.5943493640508874e-7, 1.1522829239955671e-7, 1.6571126005824673e-7, 3.8320786270330435e-7, 9.190566959635289e-7], [1.4871366265423995e-7, 2.1580041295637304e-8, 8.401945638877561e-8, 4.0428785623966885e-8, 8.843561402166818e-8, 1.608695034079984e-8, 1.3072760009716563e-8, 1.4644521938143865e-8, 4.8611045694255516e-8, 4.981000334425741e-8  …  1.5491864386330425e-7, 2.2831729438062323e-7, 1.6485430180769696e-7, 2.8787631813279e-7, 3.701907607334539e-7, 1.846626901546845e-7, 1.315484788893827e-7, 4.938245417984587e-7, 1.0872587402878112e-6, 0.0005954135902500954], [1.6461440877239793e-7, 2.1651338539565998e-8, 3.677409247085757e-8, 8.793385402839253e-8, 9.103651464334576e-8, 2.3533783875805966e-8, 1.8492357659331216e-8, 2.7647485229951682e-8, 7.082438733596385e-8, 2.2716273136934497e-8  …  6.819528683620649e-8, 5.425472792398536e-8, 1.0843298151124364e-7, 1.426105125679649e-7, 1.1490221859799955e-7, 1.2448017217280838e-7, 1.7955793146987166e-7, 7.112073064228782e-6, 3.24681760973504e-5, 0.00027541016633503425], [1.3064862558003065e-7, 2.3282351409724943e-8, 3.99459354415319e-8, 3.9624734995803406e-8, 3.263251448327655e-8, 1.147526782765384e-8, 1.3012494404721085e-8, 1.2111418944953348e-8, 2.1270975882277284e-8, 2.8485464661113545e-8  …  6.87456556458687e-8, 1.1512611614602044e-7, 1.1668594433651101e-7, 2.865517452810431e-7, 3.148216144234522e-7, 4.914112248961843e-8, 4.296019104463906e-8, 1.6249104099454517e-7, 2.009187190823661e-7, 0.0035642277172320508]], n_iter = [1, 1, 1, 1, 1, 1, 1, 1], converged = 1, n_matvec = 496)], stage = :finalize, history_Δρ = [1.1673571041111102, 0.6129203368376972, 0.2645981628430637, 0.0668765987761375, 0.021512299143855867, 0.009122462411979082, 0.005179653939570379, 0.0023985194837036717, 0.0010953691491687736, 0.0011648711622692328  …  6.945834693168646e-5, 3.822510325330539e-5, 2.3685439097600075e-5, 2.6059359412353888e-5, 3.7770601051380615e-5, 5.340167696423024e-6, 4.807829510502033e-6, 3.087444606078206e-6, 2.732435813545152e-6, 9.247807529545105e-7], history_Etot = [-361.38524245693634, -363.2389609562929, -363.3508956787811, -363.38897261362916, -363.3959878828338, -363.3973085072677, -363.39761165998567, -363.39769153017033, -363.39770650807856, -363.3977064233673  …  -363.3977100167612, -363.3977100174856, -363.3977100176807, -363.39771001773136, -363.3977100174418, -363.39771001776165, -363.39771001778803, -363.3977100178347, -363.3977100178489, -363.397710017851], timedout = false, mixing = LdosMixing(RPA=true, reltol=0.01), seed = 0xf2620d58d4f7d485, runtime_ns = 0x00000010ce171dea, algorithm = "SCF")

Run band computation

bands_hub = compute_bands(scfres, MonkhorstPack(4, 4, 4))
lowest_unocc_band = findfirst(ε -> ε-bands_hub.εF > 0, bands_hub.eigenvalues[1])
band_gap = bands_hub.eigenvalues[1][lowest_unocc_band] - bands_hub.eigenvalues[1][lowest_unocc_band-1]

0.11667618314414563

With the electron localization introduced by the Hubbard term, the band gap has now opened, reflecting the experimental insulating behaviour of Nickel Oxide.

εF = bands_hub.εF
εrange = (εF - austrip(width), εF + austrip(width))
p = plot_dos(bands_hub; p, colors=[:blue, :blue], εrange)
plot_pdos(bands_hub; p, iatom=1, label="3D", colors=[:green, :purple], εrange)