Electron–electron

Coulomb interaction from VASP.

class elphmod.elel.Model(uijkl=None, vijkl_full=None, vijkl_redu=None, nq=None, no=None, Wmat=None, a=None, r=None, angle=120)[source]

Localized model for electron-electron interaction.

Currently, only square and hexagonal Bravais lattices are supported.

Parameters:

uijklstr: File with Coulomb tensor in orbital basis on uniform q mesh.
vijkl_full, vijkl_redustr: Files with full and reduced bare Coulomb tensors. The difference is added as a correction to the Coulomb tensor provided via uijkl.
nqtuple of int or int: Number of q points per dimension. If an integer is given, a 2D mesh with nq points in both the first and the second dimension is assumed (for backward compatibility). If omitted or None, lattice vectors and corresponding interactions from Wmat are used unmodified.
noint: Number of orbitals. Ignored if Wmat is used.
Wmatstr: File with density-density Coulomb matrix in orbitals basis for different lattice vectors.
andarray, optional: Bravais lattice vectors. By default, a 2D lattice with angle between the first and the second basis vector is assumed.
rndarray, optional: Positions of orbital centers. By default, all orbitals are assumed to be located at the origin of the unit cell.
anglenumber, default 120: Angle between lattice vectors in degrees.

Attributes:

Rndarray: Lattice vectors \(\vec R\) of Wigner-Seitz supercell.
datandarray: Corresponding density-density interaction in orbital basis.
sizeint: Number of Wannier functions.
cellslist of tuple of int, optional: Lattice vectors of unit cells if the model describes a supercell.
Nlist of tuple of int, optional: Primitive vectors of supercell if the model describes a supercell.

W(q1=0, q2=0, q3=0)[source]

Set up density-density Coulomb matrix for arbitrary q point.

Parameters:

q1, q2, q3float, default 0.0: q point in crystal coordinates with period \(2 \pi\).

Returns:

ndarray: Fourier transform of data.

WR(R1=0, R2=0, R3=0)[source]

Get density-density Coulomb matrix for arbitrary lattice vector.

Parameters:

R1, R2, R3int, default 0: Lattice vector in units of primitive vectors.

Returns:

ndarray: Element of data or zero.

standardize(eps=0.0)[source]

Standardize real-space interaction data.

Keep only nonzero matrix elements.
Sum over repeated lattice vectors.
Sort lattice vectors.

Parameters:

epsfloat: Threshold for “nonzero” matrix elements in units of the maximum matrix element.

supercell(N1=1, N2=1, N3=1)[source]

Map localized model for electron-electron interaction onto supercell.

Parameters:

N1, N2, N3tuple of int or int, default 1: Supercell lattice vectors in units of primitive lattice vectors. Multiples of single primitive vector can be defined via a scalar integer, linear combinations via a 3-tuple of integers.

Returns:

object: Localized model for electron-electron interaction for supercell.

elphmod.elel.hartree_energy(rho_g, g_vect, ngm_g, uc_volume, a=1.0)[source]

Calculate the Hartree energy in units of Rydberg.

This function is basically a copy of Quantum ESPRESSO’s subroutine v_h from v_of_rho.f90.

All input parameters can be obtained from reading the formatted charge-density output. Use elphmod.el.read_rhoG_density() for this purpose.

Parameters:

rho_gndarray: Electronic charge density \(\rho(\vec G)\) on reciprocal-space grid points.
g_vectndarray: Reciprocal lattice vectors \(\vec G\).
ngm_ginteger: Number of reciprocal lattice vectors.
uc_volume: float: Unit-cell volume.

Returns:

ehartfloat: Hartree energy in units of Rydberg.

elphmod.elel.orbital2band(U, H, nq, nk, band=0, status=False, share=False, dd=False)[source]: Transform Coulomb interaction from orbital basis onto single band.

elphmod.elel.q2r(elel, W, a, r, fft=True)[source]

Interpolate electron-electron interaction on uniform q-point mesh.

Parameters:

elelelphmod.elel.Model: Localized model for electron-electron interaction.
Wndarray: Density-density interaction matrices on complete uniform q-point mesh.
andarray: Bravais lattice vectors.
rndarray: Positions of orbital centers.
fftbool: Perform Fourier transform? If False, only the mapping to the Wigner-Seitz cell is performed.

elphmod.elel.read_band_Coulomb_interaction(filename, nQ, nk, binary=False, share=False)[source]: Read Coulomb interaction for single band in band basis.

elphmod.elel.read_local_Coulomb_tensor(filename, no, dd=False)[source]: Read local Coulomb tensor from VASP.

elphmod.elel.read_orbital_Coulomb_interaction(filename, nq, no, dd=False)[source]: Read Coulomb interaction in orbital basis.

elphmod.elel.write_band_Coulomb_interaction(filename, U, binary=False)[source]: Write Coulomb interaction for single band in band basis.