PAOFLOW.basis_gen.atomic_potential#

Spherical Hartree potential and frozen-density effective potential.

For a spherically symmetric density n(r) the Hartree potential is

V_H(r) = 4 pi [ (1/r) integral_0^r n(r’) r’^2 dr’ + integral_r^inf n(r’) r’ dr’ ]

The UPF stores atrho(r) = 4 pi r^2 n(r) with int atrho dr = z_valence, which makes the integrals cumulative trapezoidal sums of atrho and atrho/r respectively.

Functions#

hartree_radial(atrho, r[, rab])

Compute V_H(r) from an atomic radial density.

vxc_radial(atrho, r[, rho_core, functional])

Spin-unpolarised V_xc(r) from atomic radial density.

frozen_effective_potential(upf)

Return V_eff(r) = V_loc(r) + V_H(r) + V_xc(r) on the UPF mesh.

Module Contents#

PAOFLOW.basis_gen.atomic_potential.hartree_radial(atrho, r, rab=None)[source]#

Compute V_H(r) from an atomic radial density.

Parameters:

  • atrho (ndarray, shape (N,)) – 4 pi r^2 n(r), as stored in PP_RHOATOM.

  • r (ndarray, shape (N,)) – Radial mesh (Bohr).

  • rab (ndarray, optional) – Mesh integration weights (dr/di). Defaults to centred differences on r.

Returns:

v_h – Hartree potential in Hartree.

Return type:

ndarray, shape (N,)

PAOFLOW.basis_gen.atomic_potential.vxc_radial(atrho, r, rho_core=None, functional='LDA')[source]#

Spin-unpolarised V_xc(r) from atomic radial density.

Parameters:

  • atrho (ndarray) – 4 pi r^2 n_val(r).

  • r (ndarray) – Radial mesh (Bohr).

  • rho_core (ndarray, optional) – True core density n_c(r) (Bohr^-3), not 4 pi r^2 n_c. When provided, the XC functional sees n_val(r) + n_c(r) – the non-linear core correction (NLCC) and PAW convention.

  • functional ({'LDA', 'PBE'}) – XC functional to use. 'LDA' -> PW92; 'PBE' -> PBE GGA.

Returns:

v_xc – XC potential in Hartree.

Return type:

ndarray

PAOFLOW.basis_gen.atomic_potential.frozen_effective_potential(upf)[source]#

Return V_eff(r) = V_loc(r) + V_H(r) + V_xc(r) on the UPF mesh.

The Hartree and XC contributions are evaluated from upf.atrho (frozen at the pseudopotential-generation density). When the UPF carries a non-linear core correction (upf.nlcc true and upf.rho_atc available) the smooth pseudo-core density is added to the valence density in the XC functional only; the Hartree term remains valence-only (standard USPP/PAW convention). The XC functional is auto-selected from upf.qexc via PAOFLOW.basis_gen.xc.select_functional(): LDA-PW92 for LDA pseudos, PBE for PBE pseudos, and PBE as a fallback for any other GGA flavour. All terms are in Hartree atomic units.

Raises ValueError if upf.atrho is missing.