momentGW.pbc.uhf.fock

Fock matrix and static self-energy parts with periodic boundary conditions and unrestricted references.

Module Contents

class momentGW.pbc.uhf.fock.FockLoop(gw, gf=None, se=None, **kwargs)

Bases: FockLoop

Self-consistent loop for the density matrix via the Hartree–Fock self-consistent field for spin-unrestricted periodic systems.

Parameters:

  • gw (BaseKUGW) – GW object.

  • gf (tuple of tuple of dyson.Lehmann, optional) – Initial Green’s function object at each k-point for each spin channel. If None, use gw.init_gf(). Default value is None.

  • se (tuple of tuple of dyson.Lehmann, optional) – Initial self-energy object at each k-point for each spin channel. If passed, use as dynamic part of the self-energy. If None, self-energy is assumed to be static and fully defined by the Fock matrix. Default value is None.

  • fock_diis_space (int, optional) – DIIS space size for the Fock matrix. Default value is 10.

  • fock_diis_min_space (int, optional) – Minimum DIIS space size for the Fock matrix. Default value is 1.

  • conv_tol_nelec (float, optional) – Convergence tolerance for the number of electrons. Default value is 1e-6.

  • conv_tol_rdm1 (float, optional) – Convergence tolerance for the density matrix. Default value is 1e-8.

  • max_cycle_inner (int, optional) – Maximum number of inner iterations. Default value is 100.

  • max_cycle_outer (int, optional) – Maximum number of outer iterations. Default value is 20.

property naux

Get the number of auxiliary states.

property nqmo

Get the number of quasiparticle MOs.

property nelec

Get the number of electrons.

property h1e

Get the core Hamiltonian.

property mo_coeff

Get the MO coefficients.

property nmo

Get the number of MOs.

property nocc

Get the number of occupied MOs.

property kpts

Get the k-points object.

auxiliary_shift(fock, se=None)

Optimise a shift in the auxiliary energies to best satisfy the electron number.

Parameters:

  • fock (numpy.ndarray) – Fock matrix at each k-point for each spin channel.

  • se (tuple of tuple of dyson.Lehmann, optional) – Self-energy at each k-point for each spin channel. If None, use self.se. Default value is None.

Returns:

se – Self-energy at each k-point for each spin channel.

Return type:

tuple of tuple of dyson.Lehmann

Notes

If there is no dynamic part of the self-energy (self.se is None), this method returns None.

search_chempot(gf=None)

Search for a chemical potential for a given Green’s function.

Parameters:

gf (tuple of dyson.Lehmann, optional) – Green’s function for each spin channel. If None, use self.gf. Default value is None.

Returns:

  • chempot (tuple of float) – Chemical potential for each spin channel.

  • nerr (tuple of float) – Error in the number of electrons for each spin channel.

solve_dyson(fock, se=None)

Solve the Dyson equation for a given Fock matrix.

Parameters:

  • fock (numpy.ndarray) – Fock matrix at each k-point for each spin channel.

  • se (tuple of dyson.Lehmann, optional) – Self-energy at each k-point. If None, use self.se. Default value is None.

Returns:

  • gf (tuple of dyson.Lehmann) – Green’s function at each k-point.

  • nerr (float) – Error in the number of electrons.

Notes

If there is no dynamic part of the self-energy (self.se is None), this method simply diagonalises the Fock matrix and returns the Lehmann representation of the resulting zeroth-order Green’s function.

kernel(integrals=None)

Driver for the Fock loop.

Parameters:

integrals (KUIntegrals, optional) – Integrals object. If None, generate from scratch. Default value is None.

Returns:

  • converged (bool) – Whether the loop has converged.

  • gf (tuple of tuple of dyson.Lehmann) – Green’s function object at each k-point for each spin channel.

  • se (tuple of tuple of dyson.Lehmann) – Self-energy object at each k-point for each spin channel.

make_rdm1(gf=None)

Get the first-order reduced density matrix.

Parameters:

gf (dyson.Lehmann, optional) – Green’s function object. If None, use either self.gf, or the mean-field Green’s function. Default value is None.

Returns:

rdm1 – First-order reduced density matrix.

Return type:

numpy.ndarray

get_fock(integrals, rdm1, h1e=None)

Get the Fock matrix.

Parameters:

  • integrals (BaseIntegrals) – Integrals object.

  • rdm1 (numpy.ndarray) – First-order reduced density matrix.

  • h1e (numpy.ndarray, optional) – Core Hamiltonian. If None, use self.h1e. Default value is None.

Returns:

fock – Fock matrix.

Return type:

numpy.ndarray