momentGW.pbc.ints

Integral helpers with periodic boundary conditions.

Module Contents

class momentGW.pbc.ints.KIntegrals(with_df, kpts, mo_coeff, mo_occ, compression='ia', compression_tol=1e-10, store_full=False, input_path=None)

Bases: momentGW.ints.Integrals

Container for the integrals required for KGW methods.

Parameters:

  • with_df (pyscf.pbc.df.DF) – Density fitting object.

  • mo_coeff (numpy.ndarray) – Molecular orbital coefficients at each k-point.

  • mo_occ (numpy.ndarray) – Molecular orbital occupations at each k-point.

  • compression (str, optional) – Compression scheme to use. Default value is ‘ia’. See momentGW.gw for more details.

  • compression_tol (float, optional) – Compression tolerance. Default value is 1e-10. See momentGW.gw for more details.

  • store_full (bool, optional) – Store the full MO integrals in memory. Default value is False.

property madelung

Return the Madelung constant for the lattice.

property Lai

Get the full uncompressed (aux, MO, MO) integrals.

property nmo

Get the number of MOs.

property nocc

Get the number of occupied MOs.

property nvir

Get the number of virtual MOs.

property nmo_g

Get the number of MOs for the Green’s function.

property nmo_w

Get the number of MOs for the screened Coulomb interaction.

property nocc_w

Get the number of occupied MOs for the screened Coulomb interaction.

property nvir_w

Get the number of virtual MOs for the screened Coulomb interaction.

property naux

Get the number of auxiliary basis functions, after the compression.

property naux_full

Get the number of auxiliary basis functions, before the compression.

property Lpq

Get the full uncompressed (aux, MO, MO) integrals.

property Lpx

Get the compressed (aux, MO, G) integrals.

property Lia

Get the compressed (aux, W occ, W vir) integrals.

property mo_coeff_g

Get the MO coefficients for the Green’s function.

property mo_coeff_w

Get the MO coefficients for the screened Coulomb interaction.

property mo_occ_w

Get the MO occupation numbers for the screened Coulomb interaction.

property nao

Get the number of AOs.

property is_bare

Get a boolean flag indicating whether the integrals have no self-consistencies.

property dtype

Get the dtype of the integrals.

get_compression_metric()

Return the compression metric.

Returns:

rot – Rotation matrix into the compressed auxiliary space.

Return type:

numpy.ndarray

transform(do_Lpq=None, do_Lpx=True, do_Lia=True)

Transform the integrals in-place.

Parameters:

  • do_Lpq (bool, optional) – Whether to compute the full (aux, MO, MO) array. Default value is True if store_full is True, False otherwise.

  • do_Lpx (bool, optional) – Whether to compute the compressed (aux, MO, MO) array. Default value is True.

  • do_Lia (bool, optional) – Whether to compute the compressed (aux, occ, vir) array. Default value is True.

get_cderi_from_thc()

Build CDERIs using THC integrals imported from a h5py file. It must contain a ‘collocation_matrix’ and a ‘coulomb_matrix’.

update_coeffs(mo_coeff_g=None, mo_coeff_w=None, mo_occ_w=None)

Update the MO coefficients in-place for the Green’s function and the screened Coulomb interaction.

Parameters:

  • mo_coeff_g (numpy.ndarray, optional) – Coefficients corresponding to the Green’s function at each k-point. Default value is None.

  • mo_coeff_w (numpy.ndarray, optional) – Coefficients corresponding to the screened Coulomb interaction at each k-point. Default value is None.

  • mo_occ_w (numpy.ndarray, optional) – Occupations corresponding to the screened Coulomb interaction at each k-point. Default value is None.

Notes

If mo_coeff_g is None, the Green’s function is assumed to remain in the basis in which it was originally defined, and vice-versa for mo_coeff_w and mo_occ_w. At least one of mo_coeff_g and mo_coeff_w must be provided.

get_j(dm, basis='mo', other=None)

Build the J matrix.

Parameters:

  • dm (numpy.ndarray) – Density matrix at each k-point.

  • basis (str, optional) – Basis in which to build the J matrix. One of (“ao”, “mo”). Default value is “mo”.

  • other (Integrals, optional) – Integrals object for the ket side. Allows inheritence for mixed-spin evaluations. If None, use self. Default value is None.

Returns:

vj – J matrix.

Return type:

numpy.ndarray

Notes

The contraction is J[p, q] = self[p, q] * other[r, s] * dm[r, s], and the bases must reflect shared indices.

get_k(dm, basis='mo', ewald=False)

Build the K matrix.

Parameters:

  • dm (numpy.ndarray) – Density matrix at each k-point.

  • basis (str, optional) – Basis in which to build the K matrix. One of (“ao”, “mo”). Default value is “mo”.

Returns:

vk – K matrix at each k-point.

Return type:

numpy.ndarray

Notes

The contraction is K[p, q] = self[r, q] * self[p, r] * dm[q, s], and the bases must reflect shared indices.

get_ewald(dm, basis='mo')

Build the Ewald exchange divergence matrix.

Parameters:

  • dm (numpy.ndarray) – Density matrix at each k-point.

  • basis (str, optional) – Basis in which to build the K matrix. One of (“ao”, “mo”). Default value is “mo”.

Returns:

ew – Ewald exchange divergence matrix at each k-point.

Return type:

numpy.ndarray

get_jk(dm, **kwargs)

Build the J and K matrices.

Returns:

  • vj (numpy.ndarray) – J matrix at each k-point.

  • vk (numpy.ndarray) – K matrix at each k-point.

Notes

See get_j and get_k for more information.

get_veff(dm, j=None, k=None, **kwargs)

Build the effective potential.

Returns:

  • veff (numpy.ndarray) – Effective potential at each k-point.

  • j (numpy.ndarray, optional) – J matrix at each k-point. If None, compute it. Default value is None.

  • k (numpy.ndarray, optional) – K matrix at each k-point. If None, compute it. Default value is None.

Notes

See get_jk for more information.

get_fock(dm, h1e, **kwargs)

Build the Fock matrix.

Parameters:

  • dm (numpy.ndarray) – Density matrix at each k-point.

  • h1e (numpy.ndarray) – Core Hamiltonian matrix at each k-point.

  • **kwargs (dict, optional) – Additional keyword arguments for get_jk.

Returns:

fock – Fock matrix at each k-point.

Return type:

numpy.ndarray

Notes

See get_jk for more information. The basis of h1e must be the same as dm.