momentGW.fock

Fock matrix self-consistent loop.

Module Contents

exception momentGW.fock.ChemicalPotentialError

Bases: ValueError

Exception raised when the chemical potential cannot be found.

add_note()

Exception.add_note(note) – add a note to the exception

with_traceback()

Exception.with_traceback(tb) – set self.__traceback__ to tb and return self.

momentGW.fock.search_chempot(w, v, nphys, nelec, occupancy=2)

Search for a chemical potential.

Parameters:

  • w (numpy.ndarray) – Eigenvalues.

  • v (numpy.ndarray) – Eigenvectors.

  • nphys (int) – Number of physical states.

  • nelec (int) – Number of electrons.

  • occupancy (int, optional) – Number of electrons per state. Default value is 2.

Returns:

  • chempot (float) – Chemical potential.

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

momentGW.fock.minimize_chempot(se, fock, nelec, occupancy=2, x0=0.0, tol=1e-06, maxiter=200)

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

Parameters:

  • se (dyson.Lehmann) – Self-energy object.

  • fock (numpy.ndarray) – Fock matrix.

  • nelec (int) – Number of electrons.

  • occupancy (int, optional) – Number of electrons per state. Default value is 2.

  • x0 (float, optional) – Initial guess value. Default value is 0.0.

  • tol (float, optional) – Threshold in the number of electrons. Default value is 1e-6.

  • maxiter (int, optional) – Maximum number of iterations. Default value is 200.

Returns:

  • se (dyson.Lehmann) – Self-energy object.

  • opt (scipy.optimize.OptimizeResult) – Result of the optimisation.

class momentGW.fock.BaseFockLoop(gw, gf=None, se=None, **kwargs)

Base class for Fock loops.

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.

abstract auxiliary_shift(fock=None, se=None)

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

abstract solve_dyson(fock=None, se=None, chempot=0.0)

Solve the Dyson equation for a given Fock matrix.

abstract search_chempot(gf=None)

Search for a chemical potential.

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

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

Bases: BaseFockLoop

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

Parameters:

  • gw (BaseGW) – GW object.

  • gf (dyson.Lehmann, optional) – Initial Green’s function object. If None, use gw.init_gf(). Default value is None.

  • se (dyson.Lehmann, optional) – Initial self-energy object. 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.

auxiliary_shift(fock, se=None)

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

Parameters:

  • fock (numpy.ndarray) – Fock matrix.

  • se (dyson.Lehmann, optional) – Self-energy. If None, use self.se. Default value is None.

Returns:

se – Self-energy.

Return type:

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 (dyson.Lehmann, optional) – Green’s function. If None, use self.gf. Default value is None.

Returns:

  • chempot (float) – Chemical potential.

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

solve_dyson(fock, se=None)

Solve the Dyson equation for a given Fock matrix.

Parameters:

  • fock (numpy.ndarray) – Fock matrix.

  • se (dyson.Lehmann, optional) – Self-energy. If None, use self.se. Default value is None.

Returns:

  • gf (dyson.Lehmann) – Green’s function.

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

Returns:

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

  • gf (dyson.Lehmann) – Green’s function object.

  • se (dyson.Lehmann) – Self-energy object.

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