Source code for pyscf.pbc.tdscf.krhf_slow_supercell

#  Author: Artem Pulkin
"""
This and other `_slow` modules implement the time-dependent Hartree-Fock procedure. The primary performance drawback is
that, unlike other 'fast' routines with an implicit construction of the eigenvalue problem, these modules construct
TDHF matrices explicitly via an AO-MO transformation, i.e. with a O(N^5) complexity scaling. As a result, regular
`numpy.linalg.eig` can be used to retrieve TDHF roots in a reliable fashion without any issues related to the Davidson
procedure. Several variants of TDHF are available:

 * `pyscf.tdscf.rhf_slow`: the molecular implementation;
 * `pyscf.pbc.tdscf.rhf_slow`: PBC (periodic boundary condition) implementation for RHF objects of `pyscf.pbc.scf`
   modules;
 * (this module) `pyscf.pbc.tdscf.krhf_slow_supercell`: PBC implementation for KRHF objects of `pyscf.pbc.scf` modules.
   Works with an arbitrary number of k-points but has a overhead due to an effective construction of a supercell.
 * `pyscf.pbc.tdscf.krhf_slow_gamma`: A Gamma-point calculation resembling the original `pyscf.pbc.tdscf.krhf`
   module. Despite its name, it accepts KRHF objects with an arbitrary number of k-points but finds only few TDHF roots
   corresponding to collective oscillations without momentum transfer;
 * `pyscf.pbc.tdscf.krhf_slow`: PBC implementation for KRHF objects of `pyscf.pbc.scf` modules. Works with
   an arbitrary number of k-points and employs k-point conservation (diagonalizes matrix blocks separately).
"""

from pyscf.tdscf.common_slow import TDERIMatrixBlocks, PeriodicMFMixin
from pyscf.tdscf import rhf_slow

from pyscf.pbc.lib.kpts_helper import loop_kkk
from pyscf.lib import logger

import numpy
import scipy
from itertools import product


# Convention for these modules:
# * PhysERI, PhysERI4, PhysERI8 are 2-electron integral routines computed directly (for debug purposes), with a 4-fold
#   symmetry and with an 8-fold symmetry
# * vector_to_amplitudes reshapes and normalizes the solution
# * TDRHF provides a container


class PhysERI(PeriodicMFMixin, TDERIMatrixBlocks):

    def __init__(self, model, frozen=None):
        """
        The TDHF ERI implementation performing a full transformation of integrals to Bloch functions. No symmetries are
        employed in this class.

        Args:
            model (KRHF): the base model;
            frozen (int, Iterable): the number of frozen valence orbitals or the list of frozen orbitals for all
            k-points or multiple lists of frozen orbitals for each k-point;
        """
        TDERIMatrixBlocks.__init__(self)
        PeriodicMFMixin.__init__(self, model, frozen=frozen)
        # Phys representation
        self.__full_eri_k__ = {}
        for k in loop_kkk(len(model.kpts)):
            k = k + (self.kconserv[k],)
            self.__full_eri_k__[k] = self.ao2mo_k(tuple(self.mo_coeff[j] for j in k), k)

    def ao2mo_k(self, coeff, k):
        """
        Phys ERI in MO basis.
        Args:
            coeff (Iterable): MO orbitals;
            k (Iterable): the 4 k-points MOs correspond to;

        Returns:
            ERI in MO basis.
        """
        coeff = (coeff[0], coeff[2], coeff[1], coeff[3])
        k = (k[0], k[2], k[1], k[3])
        result = self.model.with_df.ao2mo(coeff, tuple(self.model.kpts[i] for i in k), compact=False)
        return result.reshape(
            tuple(i.shape[1] for i in coeff)
        ).swapaxes(1, 2)

    def __get_mo_energies__(self, k1, k2):
        """This routine collects occupied and virtual MO energies."""
        return self.mo_energy[k1][:self.nocc[k1]], self.mo_energy[k2][self.nocc[k2]:]

    def tdhf_diag_k(self, k1, k2):
        """
        Retrieves the diagonal block.
        Args:
            k1 (int): first k-index (row);
            k2 (int): second k-index (column);

        Returns:
            The diagonal block.
        """
        # Everything is already implemented in molecular code
        return super(PhysERI, self).tdhf_diag(k1, k2)

    def tdhf_diag(self, pairs=None):
        """
        Retrieves the merged diagonal block with specified or all possible k-index pairs.
        Args:
            pairs (Iterable): pairs of k-points to assmble;

        Returns:
            The diagonal block.
        """
        if pairs is None:
            pairs = product(range(len(self.model.kpts)), range(len(self.model.kpts)))
        result = []
        for k1, k2 in pairs:
            result.append(self.tdhf_diag_k(k1, k2))
        return scipy.linalg.block_diag(*result)

    def __calc_block__(self, item, k):
        if k in self.__full_eri_k__:
            slc = tuple(slice(self.nocc[_k]) if i == 'o' else slice(self.nocc[_k], None) for i, _k in zip(item, k))
            return self.__full_eri_k__[k][slc]
        else:
            return numpy.zeros(tuple(
                self.nocc[_k] if i == 'o' else self.nmo[_k] - self.nocc[_k]
                for i, _k in zip(item, k)
            ))

    def eri_mknj_k(self, item, k):
        """
        Retrieves ERI block using 'mknj' notation.
        Args:
            item (str): a 4-character string of 'mknj' letters;
            k (Iterable): k indexes;

        Returns:
            The corresponding block of ERI (phys notation).
        """
        # Everything is already implemented in molecular code
        return super(PhysERI, self).eri_mknj(item, k)

    def eri_mknj(self, item, pairs_row=None, pairs_column=None):
        """
        Retrieves the merged ERI block using 'mknj' notation with all k-indexes.
        Args:
            item (str): a 4-character string of 'mknj' letters;
            pairs_row (Iterable): iterator for pairs of row k-points (first index in the output matrix);
            pairs_column (Iterable): iterator for pairs of column k-points (second index in the output matrix);

        Returns:
            The corresponding block of ERI (phys notation).
        """
        if pairs_row is None:
            pairs_row = product(range(len(self.model.kpts)), range(len(self.model.kpts)))
        if pairs_column is None:
            pairs_column = product(range(len(self.model.kpts)), range(len(self.model.kpts)))
        # Second index has to support re-iterations
        pairs_column = tuple(pairs_column)
        result = []
        for k1, k2 in pairs_row:
            result.append([])
            for k3, k4 in pairs_column:
                result[-1].append(self.eri_mknj_k(item, (k1, k2, k3, k4)))

        r = numpy.block(result)
        return r / len(self.model.kpts)


class PhysERI4(PhysERI):
    symmetries = [
        ((0, 1, 2, 3), False),
        ((1, 0, 3, 2), False),
        ((2, 3, 0, 1), True),
        ((3, 2, 1, 0), True),
    ]

    def __init__(self, model, frozen=None):
        """
        The TDHF ERI implementation performing a partial transformation of integrals to Bloch functions. A 4-fold
        symmetry of complex-valued wavefunctions is employed in this class.

        Args:
            model (KRHF): the base model;
            frozen (int, Iterable): the number of frozen valence orbitals or the list of frozen orbitals for all
            k-points or multiple lists of frozen orbitals for each k-point;
        """
        TDERIMatrixBlocks.__init__(self)
        PeriodicMFMixin.__init__(self, model, frozen=frozen)

    def __calc_block__(self, item, k):
        if self.kconserv[k[:3]] == k[3]:
            logger.info(self.model, "Computing {} {} ...".format(''.join(item), repr(k)))
            return self.ao2mo_k(tuple(
                self.mo_coeff[_k][:, :self.nocc[_k]] if i == "o" else self.mo_coeff[_k][:, self.nocc[_k]:]
                for i, _k in zip(item, k)
            ), k)
        else:
            return numpy.zeros(tuple(
                self.nocc[_k] if i == 'o' else self.nmo[_k] - self.nocc[_k]
                for i, _k in zip(item, k)
            ))


class PhysERI8(PhysERI4):
    symmetries = [
        ((0, 1, 2, 3), False),
        ((1, 0, 3, 2), False),
        ((2, 3, 0, 1), False),
        ((3, 2, 1, 0), False),

        ((2, 1, 0, 3), False),
        ((3, 0, 1, 2), False),
        ((0, 3, 2, 1), False),
        ((1, 2, 3, 0), False),
    ]

    def __init__(self, model, frozen=None):
        """
        The TDHF ERI implementation performing a partial transformation of integrals to Bloch functions. An 8-fold
        symmetry of real-valued wavefunctions is employed in this class.

        Args:
            model (KRHF): the base model;
            frozen (int, Iterable): the number of frozen valence orbitals or the list of frozen orbitals for all
            k-points or multiple lists of frozen orbitals for each k-point;
        """
        super(PhysERI8, self).__init__(model, frozen=frozen)


[docs]def vector_to_amplitudes(vectors, nocc, nmo): """ Transforms (reshapes) and normalizes vectors into amplitudes. Args: vectors (numpy.ndarray): raw eigenvectors to transform; nocc (tuple): numbers of occupied orbitals; nmo (tuple): the total numbers of AOs per k-point; Returns: Amplitudes with the following shape: (# of roots, 2 (x or y), # of kpts, # of kpts, # of occupied orbitals, # of virtual orbitals). """ if not all(i == nocc[0] for i in nocc): raise NotImplementedError("Varying occupation numbers are not implemented yet") nk = len(nocc) nocc = nocc[0] if not all(i == nmo[0] for i in nmo): raise NotImplementedError("Varying AO spaces are not implemented yet") nmo = nmo[0] vectors = numpy.asanyarray(vectors) vectors = vectors.reshape(2, nk, nk, nocc, nmo-nocc, vectors.shape[1]) norm = (abs(vectors) ** 2).sum(axis=(1, 2, 3, 4)) norm = 2 * (norm[0] - norm[1]) vectors /= norm ** .5 return vectors.transpose(5, 0, 1, 2, 3, 4)
class TDRHF(rhf_slow.TDRHF): eri4 = PhysERI4 eri8 = PhysERI8 v2a = staticmethod(vector_to_amplitudes)