PseudopotentialGenerator.jl

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PseudopotentialGenerator.jl generates pseudopotential for plane-wave DFT.

Usage

Generating a pseudopotential requires first having reference states (from real all-electrons potential) and then construct the pseudopotential that can reproduce same scattering behavior.

The examples folder includes scripts of solving atomic Schrödinger equation and pseudizing to get pseudopotentials.

To solve the atomic Schrödinger equation under DFT framework, simply define the ionic configuration and call self_consistent_field function.

Z = 6
mesh = Mesh(1e-7, 50.0, 2.7e+6, 10000);
orbs = [Orbital(Z, 1, 0, 2), Orbital(Z, 2, 0, 2), Orbital(Z, 2, 1, 2)];

res = self_consistent_field(
    Z,
    mesh,
    orbs,
    mixing_beta = 0.2,
    abstol = 1e-7,
    maxiters_scf = 200,
    perturb = true,
)

ae_info = (ε_lst = res.ε_lst, ϕs = res.ϕs, vae = res.v_tot, occs = res.occs, xc = res.xc);

The ae_info contains eigenstates and self consistent potential.

The pseudopotential is then generated to have pseudo-states that meet the restriction with respect to the all-electrons reference. The Troullier-Martins (TM) is a one of the popular scheme to construct pseudopotential. To generate a TM type pseudopotential, call pseudize function,

v_pspot, ϕ_ps = pseudize(ae_info, mesh, rc; method = :TM, kbform = false)

The function returns the psudopotential and all pseudo-wavefunctions.

It is essential to check whether the generated pseudopotential is good enough for solid-state DFT calculations. One of the prevalent metric is logarithmic derivative (usually arctan of the derivative) of wavefunctions which reveal the discripancies between the all-electrons wavefunctions and pseudo-wavefunctions in both eigenstates and energies of scattering states. The arctan logarithmic derivative is computed for every angular momentum by calling compute_atanld in the given potential,

# For all-electrons potential
compute_atanld(l, Z, mesh, ae_info.vae, rcx, window = [-10.0, 10.0], δ = 0.05)

# For pseudo-potential which is semi-local (dependent on angular momentum l)
compute_atanld(l, Z, mesh, v_pspot.v[nl], rcx, window = [-10.0, 10.0], δ = 0.05)

Basic theory and package construction

You will find presentian that covers the thoretical background and the construction detials of this package.

DFT in atom, pseudopotential generation and its Julia implementation

For developers

To run tests, functions from DFTATOM are wrappered as reference which need to compiled first.

make -C deps all

Then run tests

julia --project=@. -e 'using Pkg; Pkg.test()'

TODOs

• Solving atomic DFT in radial coordination
• Migrate from self-crafted ODE solver to purely using NonlinearSolve.jl and OrdinaryDiffEq.jl as solver.
• pseudize using TM.
• pseudize using RRKJ.
• pseudize using BHS.
• compute logarithmic derivative plots.
• Kleinman-Bylander form and its logarithmic derivative by solving integ-ODE.
• full relativistic PP
• scalar relativistic PP
• Orbitals defined and constructed from atomic levels representation.
• Logger for SCF and eigensolver
• Support for semi-core states
• Support for ONCV NC pseudopotentials
• Support for US/PAW pseudopotentials
• meta-GGA PP generation
• ? Scattering states with good match