Exact exchange and Hybrid DFT

This is a quick sketch how to run a simple hybrid DFT calculation using DFTK.

Preliminary implementation

Hybrid-DFT in DFTK is still in its early stages. MPI parallelisation does not work and $k$-point symmetry cannot yet be used to reduce the $k$-point grid when using exact exchange terms, hence the use_symmetries_for_kpoint_reduction=false argument below. We appreciate any issues, bug reports or PRs.

using AtomsBuilder
using DFTK
using PseudoPotentialData

pseudopotentials = PseudoFamily("dojo.nc.sr.pbe.v0_5.stringent.upf")
system = bulk(:Si)

FlexibleSystem(Si₂, periodicity = TTT):
    cell_vectors      : [       0    2.715    2.715;
                            2.715        0    2.715;
                            2.715    2.715        0]u"Å"

    Atom(Si, [       0,        0,        0]u"Å")
    Atom(Si, [  1.3575,   1.3575,   1.3575]u"Å")

First perform a PBE calculation to get a good starting point.

model  = model_DFT(system; pseudopotentials, functionals=PBE())
basis  = PlaneWaveBasis(model; Ecut=15, kgrid=[2, 2, 2],
                        use_symmetries_for_kpoint_reduction=false)
scfres = self_consistent_field(basis; tol=1e-6);
nothing  # hide

n     Energy            log10(ΔE)   log10(Δρ)   Diag   Δtime 
---   ---------------   ---------   ---------   ----   ------
  1   -8.363770346505                   -0.82    5.6    173ms
  2   -8.367889225248       -2.39       -1.67    1.0   99.4ms
  3   -8.368236126074       -3.46       -2.62    2.0    140ms
  4   -8.368255041379       -4.72       -3.20    2.5    127ms
  5   -8.368255333679       -6.53       -3.90    1.6    110ms
  6   -8.368255354959       -7.67       -4.69    2.1    123ms
  7   -8.368255355759       -9.10       -5.94    2.0    117ms
  8   -8.368255355781      -10.65       -6.01    3.4    146ms

Then run PBE0, see also PBE0 and HybridFunctional for more documentation.

model  = model_DFT(system; pseudopotentials, functionals=PBE0())
basis  = PlaneWaveBasis(model; basis.Ecut, basis.kgrid,
                        use_symmetries_for_kpoint_reduction=false)
scfres = self_consistent_field(basis; tol=1e-4, scfres.ρ, scfres.ψ, scfres.occupation,
                               scfres.eigenvalues, solver=DFTK.scf_damping_solver());
nothing  # hide

n     Energy            log10(ΔE)   log10(Δρ)   Diag   Δtime 
---   ---------------   ---------   ---------   ----   ------
  1   -8.229516108819                   -2.20    1.0    7.73s
  2   -8.229646579596       -3.88       -2.66    1.0    3.92s
  3   -8.229683858915       -4.43       -2.79    6.0    2.61s
  4   -8.229684369474       -6.29       -3.34    5.0    2.59s
  5   -8.229684382995       -7.87       -4.03    4.6    2.56s

See also HSE and model_HF for setting up Hartree-Fock calculations and the example Hybrid DFT band structures how to compute band structures using DFTK and Hybrid functionals.