lumeq.embedding package

Submodules

lumeq.embedding.fragment_entangle module

class EmbeddingMeanField(mf, frgm_list, method='pipek_mezey', extra_orb=0, min_weight=0.8)[source]

Bases: object

Embedding system class of mean field ground-state

emb_basis_dmet(mf, ifrgm, embed_method=0)[source]

Build embedding basis for a given fragment

Parameters:

  • mf – Converged PySCF mean-field object. This should be the same object passed during initialization.

  • ifrgm (int) – Index of the fragment chosen as the impurity.

  • embed_method (int) – Embedding method selector. 0 corresponds to DMET.

Returns:

Embedding-orbital coefficients in the AO basis and density matrix in the EO basis.

Return type:

tuple

get_eomf(mf)[source]

Build the embedded mean-field object with reduced MO space, ready to be used for excited-state calculations

Parameters:

mf – Mean-field object, the same class used previously.

Returns:

Embedded mean-field object.

Return type:

object

fragment_localization(mf, frgm_list, method='pipek_mezey', extra_orb=0, min_weight=0.8)[source]

Get the localized orbitals and density matrix for fragment analysis

Parameters:

  • mf – PySCF mean-field object such as HF/DFT.

  • frgm_list (list) – Atom indices in each fragment.

  • method (str) – Localization method.

  • extra_orb (int) – Number of virtual orbitals added in the density-matrix build.

  • min_weight (float) – Threshold for the fragment LO partition.

Returns:

Localized-orbital basis coefficients C^{AO,LO}. dm_lo_in_ao: Density matrix in the LO basis. frgm_lo_idx (list): Local-orbital indices for each fragment.

Return type:

coeff_lo_in_ao

get_embedding_energy(mf, coeff_eo_in_ao, dm_eo_in_ao, neo_imp, extra_orb=0)[source]

Calculate electronic energy of the impurity in the embedding orbital basis

Parameters:

  • mf – Converged PySCF mean-field object.

  • coeff_eo_in_ao – Embedding-orbital coefficients C^{AO,EO} in AO basis.

  • dm_eo_in_ao – Density matrix P^{EO,EO} in the EO basis.

  • neo_imp (int) – Number of impurity embedding orbitals.

  • extra_orb (int) – Number of virtual MO orbitals in the top-level SCF.

Returns:

Embedded-system energy, occupied EO count, EO energies, and EO coefficients.

Return type:

tuple

get_embedding_orbital(dm_lo_in_ao, coeff_lo_in_ao, ovlp_ao, imp_lo_idx, env_lo_idx, method=0, threshold=1e-12)[source]

Embedding orbital construction from the density matrix in localized orbital basis

Parameters:

  • dm_lo_in_ao (numpy.ndarray) – Density matrix in the localized-orbital basis.

  • coeff_lo_in_ao (numpy.ndarray) – Localized-orbital basis coefficients.

  • ovlp_ao (numpy.ndarray) – Overlap matrix in the AO basis.

  • imp_lo_idx (list) – Impurity localized-orbital indices from frgm_lo_idx.

  • env_lo_idx (list) – Environment localized-orbital indices from frgm_lo_idx.

  • method (int) – Bath-orbital selection method. 0 uses singular vectors of the off-diagonal block of the density matrix in the LO basis, and 1 uses eigenvectors of the environment diagonal block of the density matrix in the LO basis.

  • threshold (float) – Cutoff for singular values or eigenvalues.

Returns:

Embedding-orbital coefficients C^{AO,EO} in the AO basis and density matrix P^{EO,EO} in the EO basis.

Return type:

tuple

get_embedding_system(mf, frgm_idx, ifrgm=0, extra_orb=0)[source]

Embedding energy calculation for a given fragment

Parameters:

  • mf – PySCF mean-field object.

  • frgm_idx (list) – Atomic indices for each fragment.

  • ifrgm (int) – Fragment index treated as the impurity. If -1, loop over all fragments.

  • extra_orb (int) – Number of extra orbitals to include in the density matrix.

Returns:

For a chosen fragment, returns the values from

get_embedding_energy. Otherwise computes the whole-system energy.

Return type:

tuple or None

get_localized_orbital(mol, coeff, method='pipek_mezey', **kwargs)[source]
get_localized_orbital_rdm(coeff_lo_in_ao, coeff_mo_in_ao, ovlp_ao, nocc, scale=2.0, extra_orb=0)[source]

Compute total density matrix alpha+beta in localized orbital (LO) basis S^{1/2} P S^{1/2} = C_lo^T S C_mo occ C_mo occ^T S C_lo

Parameters:

  • coeff_lo_in_ao – LO basis coefficients C^{AO,LO}.

  • coeff_mo_in_ao – MO coefficients C^{AO,MO} in AO basis.

  • ovlp_ao – AO overlap matrix S.

  • nocc (int) – Number of occupied orbitals.

  • scale (float) – Scaling factor, 2 for the restricted case.

  • extra_orb (int) – Number of virtual orbitals added to the density matrix.

Returns:

Density matrix P^{LO,LO} in the LO basis.

Return type:

numpy.ndarray

lumeq.embedding.mol_lo_tools module

lo_weight_on_ao(mol: Mole = None, coeff_ao_lo: ndarray = None, ovlp_ao: ndarray = None)[source]

A function to calculate the weight of local orbitals on atomic orbitals.

Parameters:

  • mol (pyscf.gto.Mole) – The molecule object.

  • coeff_ao_lo (numpy.ndarray) – The coefficient matrix to transform atomic orbitals to local orbitals.

  • ovlp_ao (numpy.ndarray) – The overlap matrix of atomic orbitals.

Returns:

The weight of local orbitals on atomic orbitals.

Return type:

w2_ao_lo (numpy.ndarray)

lo_weight_on_atom(mol: Mole, coeff_ao_lo: ndarray = None, ovlp_ao: ndarray = None)[source]

A function to calculate the weight of local orbitals on atomic orbitals.

Parameters:

  • mol (pyscf.gto.Mole) – The molecule object.

  • coeff_ao_lo (numpy.ndarray) – The coefficient matrix to transform atomic orbitals to local orbitals.

  • ovlp_ao (numpy.ndarray) – The overlap matrix of atomic orbitals.

Returns:

The weight of local orbitals on each atom.

Return type:

w2_atm_lo (numpy.ndarray)

lo_weight_on_frag(frag_atms_list: list, mol: Mole, coeff_ao_lo: ndarray = None, ovlp_ao: ndarray = None)[source]

A function to calculate the weight of local orbitals on fragments.

Parameters:

  • frag_atms_list (list) – A list of atoms in each fragment.

  • mol (pyscf.gto.Mole) – The molecule object.

  • coeff_ao_lo (numpy.ndarray) – The coefficient matrix to transform atomic orbitals to local orbitals.

  • ovlp_ao (numpy.ndarray) – The overlap matrix of atomic orbitals.

Returns:

The weight of local orbitals on each fragment.

Return type:

w2_frag_lo (numpy.ndarray)

partition_lo_to_atms(mol: Mole = None, coeff_ao_lo: ndarray = None, w2_atm_lo: ndarray = None, min_weight: float = 0.9)[source]

A function to partition local orbitals to atoms.

Parameters:

  • mol (pyscf.gto.Mole) – The molecule object.

  • coeff_ao_lo (numpy.ndarray) – The coefficient matrix to transform atomic orbitals to local orbitals.

  • w2_atm_lo (numpy.ndarray) – The weight of local orbitals on each atom.

  • min_weight (float) – The minimum weight of local orbitals on each atom. If the max weight is smaller than min_weight, the local orbital will not be assigned to the atom.

Returns:

The list of local orbital indices on each atom.

Return type:

lo_idx_on_atm_list (list)

partition_lo_to_frags(frag_atms_list: list, mol: Mole = None, coeff_ao_lo: ndarray = None, w2_frag_lo: ndarray = None, min_weight: float = 0.9)[source]

A function to partition local orbitals to fragments.

Parameters:

  • frag_atms_list (list) – The list of atoms in each fragment.

  • mol (pyscf.gto.Mole) – The molecule object.

  • coeff_ao_lo (numpy.ndarray) – The coefficient matrix to transform atomic orbitals to local orbitals.

  • w2_frag_lo (numpy.ndarray) – The weight of local orbitals on each atom.

  • min_weight (float) – The minimum weight of local orbitals on each atom. If the max weight is smaller than min_weight, the local orbital will not be assigned to the atom.

Returns:

The list of local orbital indices on each fragment.

Return type:

lo_idx_on_frag_list (list)

partition_lo_to_imps(frag_atms_list: list, mol: Mole = None, coeff_ao_lo: ndarray = None, w2_frag_lo: ndarray = None, min_weight: float = 0.9)

A function to partition local orbitals to fragments.

Parameters:

  • frag_atms_list (list) – The list of atoms in each fragment.

  • mol (pyscf.gto.Mole) – The molecule object.

  • coeff_ao_lo (numpy.ndarray) – The coefficient matrix to transform atomic orbitals to local orbitals.

  • w2_frag_lo (numpy.ndarray) – The weight of local orbitals on each atom.

  • min_weight (float) – The minimum weight of local orbitals on each atom. If the max weight is smaller than min_weight, the local orbital will not be assigned to the atom.

Returns:

The list of local orbital indices on each fragment.

Return type:

lo_idx_on_frag_list (list)

lumeq.embedding.orbital_entropy module

get_1rdm(c0, c2)[source]
get_2rdm(c0, c2)[source]
get_orbital_entropy_info(s1, s2, imethod=0)[source]
get_rdm_entropy(rho)[source]
normalize_wf(t2)[source]

lumeq.embedding.td_embeddinng module

Module contents