pyscf.pbc.dft.multigrid package

Submodules

pyscf.pbc.dft.multigrid.multigrid module

Multigrid to compute DFT integrals

class pyscf.pbc.dft.multigrid.multigrid.MultiGridFFTDF(cell, kpts=array([[0., 0., 0.]]))

Bases: FFTDF

build()

get_jk(dm, hermi=1, kpts=None, kpts_band=None, with_j=True, with_k=True, exxdiv='ewald', **kwargs)

get_nuc(kpts=None)

get_pp(kpts=None, max_memory=4000)

Get the periodic pseudotential nuc-el AO matrix, with G=0 removed.

get_rho(dm, kpts=array([[0., 0., 0.]]))

Density in real space

reset(cell=None)

pyscf.pbc.dft.multigrid.multigrid.cache_xc_kernel(mydf, xc_code, mo_coeff, mo_occ, spin=0, kpts=None)

pyscf.pbc.dft.multigrid.multigrid.cache_xc_kernel1(mydf, xc_code, dm, spin=0, kpts=None)

Compute the 0th order density, Vxc and fxc. They can be used in TDDFT, DFT hessian module etc.

pyscf.pbc.dft.multigrid.multigrid.eval_mat(cell, weights, shls_slice=None, comp=1, hermi=0, xctype='LDA', kpts=None, mesh=None, offset=None, submesh=None)

pyscf.pbc.dft.multigrid.multigrid.eval_rho(cell, dm, shls_slice=None, hermi=0, xctype='LDA', kpts=None, mesh=None, offset=None, submesh=None, ignore_imag=False, out=None)

Collocate the real density (opt. gradients) on the real-space grid.

Kwargs:

ignore_image :

The output density is assumed to be real if ignore_imag=True.

pyscf.pbc.dft.multigrid.multigrid.get_j_kpts(mydf, dm_kpts, hermi=1, kpts=array([[0., 0., 0.]]), kpts_band=None)

Get the Coulomb (J) AO matrix at sampled k-points.

Args:

dm_kpts(nkpts, nao, nao) ndarray or a list of (nkpts,nao,nao) ndarray

Density matrix at each k-point. If a list of k-point DMs, eg, UHF alpha and beta DM, the alpha and beta DMs are contracted separately.

kpts : (nkpts, 3) ndarray

Kwargs:

kpts_band(3,) ndarray or (*,3) ndarray

A list of arbitrary “band” k-points at which to evalute the matrix.

Returns:

vj : (nkpts, nao, nao) ndarray or list of vj if the input dm_kpts is a list of DMs

pyscf.pbc.dft.multigrid.multigrid.get_nuc(mydf, kpts=None)

pyscf.pbc.dft.multigrid.multigrid.get_pp(mydf, kpts=None, max_memory=4000)

Get the periodic pseudotential nuc-el AO matrix, with G=0 removed.

pyscf.pbc.dft.multigrid.multigrid.get_rho(mydf, dm, kpts=array([[0., 0., 0.]]))

Density in real space

pyscf.pbc.dft.multigrid.multigrid.multi_grids_tasks(cell, fft_mesh=None, verbose=None)

pyscf.pbc.dft.multigrid.multigrid.multi_grids_tasks_for_ke_cut(cell, fft_mesh=None, verbose=None)

pyscf.pbc.dft.multigrid.multigrid.multi_grids_tasks_for_rcut(cell, fft_mesh=None, verbose=None)

pyscf.pbc.dft.multigrid.multigrid.multigrid(mf)

Use MultiGridFFTDF to replace the default FFTDF integration method in the DFT object.

pyscf.pbc.dft.multigrid.multigrid.multigrid_fftdf(mf)

Use MultiGridFFTDF to replace the default FFTDF integration method in the DFT object.

pyscf.pbc.dft.multigrid.multigrid.nr_rks(mydf, xc_code, dm_kpts, hermi=1, kpts=None, kpts_band=None, with_j=False, return_j=False, verbose=None)

Compute the XC energy and RKS XC matrix at sampled k-points. multigrid version of function pbc.dft.numint.nr_rks.

Args:

dm_kpts(nkpts, nao, nao) ndarray or a list of (nkpts,nao,nao) ndarray

Density matrix at each k-point.

kpts : (nkpts, 3) ndarray

Kwargs:

kpts_band(3,) ndarray or (*,3) ndarray

A list of arbitrary “band” k-points at which to evalute the matrix.

Returns:

exc : XC energy nelec : number of electrons obtained from the numerical integration veff : (nkpts, nao, nao) ndarray

or list of veff if the input dm_kpts is a list of DMs

vj(nkpts, nao, nao) ndarray

or list of vj if the input dm_kpts is a list of DMs

pyscf.pbc.dft.multigrid.multigrid.nr_rks_fxc(mydf, xc_code, dm0, dms, hermi=0, with_j=False, rho0=None, vxc=None, fxc=None, kpts=None, verbose=None)

multigrid version of function pbc.dft.numint.nr_rks_fxc

pyscf.pbc.dft.multigrid.multigrid.nr_rks_fxc_st(mydf, xc_code, dm0, dms_alpha, singlet=True, rho0=None, vxc=None, fxc=None, kpts=None, verbose=None)

multigrid version of function pbc.dft.numint.nr_rks_fxc_st

pyscf.pbc.dft.multigrid.multigrid.nr_uks(mydf, xc_code, dm_kpts, hermi=1, kpts=None, kpts_band=None, with_j=False, return_j=False, verbose=None)

Compute the XC energy and UKS XC matrix at sampled k-points. multigrid version of function pbc.dft.numint.nr_uks

Args:

dm_kpts(nkpts, nao, nao) ndarray or a list of (nkpts,nao,nao) ndarray

Density matrix at each k-point.

kpts : (nkpts, 3) ndarray

Kwargs:

kpts_band(3,) ndarray or (*,3) ndarray

A list of arbitrary “band” k-points at which to evalute the matrix.

Returns:

exc : XC energy nelec : number of electrons obtained from the numerical integration veff : (2, nkpts, nao, nao) ndarray

or list of veff if the input dm_kpts is a list of DMs

vj(nkpts, nao, nao) ndarray

or list of vj if the input dm_kpts is a list of DMs

pyscf.pbc.dft.multigrid.multigrid.nr_uks_fxc(mydf, xc_code, dm0, dms, hermi=0, with_j=False, rho0=None, vxc=None, fxc=None, kpts=None, verbose=None)

multigrid version of function pbc.dft.numint.nr_uks_fxc

pyscf.pbc.dft.multigrid.multigrid_pair module

class pyscf.pbc.dft.multigrid.multigrid_pair.GridLevel_Info

Bases: Structure

Info about the grid levels.

cutoff

Structure/Union member

mesh

Structure/Union member

nlevels

Structure/Union member

rel_cutoff

Structure/Union member

class pyscf.pbc.dft.multigrid.multigrid_pair.MultiGridFFTDF2(cell, kpts=array([[0., 0., 0.]]))

Bases: MultiGridFFTDF

Base class for multigrid DFT (version 2).

Attributes:

task_listTaskList instance

Task list recording which primitive basis function pairs need to be considered.

vpplocG_part1arrary

Short-range part of the local pseudopotential represented in the reciprocal space. It is cached to reduce cost.

rhoGarray

Electronic density represented in the reciprocal space. It is cached in nuclear gradient calculations to reduce cost.

get_pp(kpts=None)

Compute the GTH pseudopotential matrix, which includes the second part of the local potential and the non-local potential. The first part of the local potential is cached as vpplocG_part1, which is the reciprocal space representation, to be added to the electron density for computing the Coulomb matrix. In order to get the full PP matrix, the potential due to vpplocG_part1 needs to be added.

get_veff_ip1(dm, xc_code=None, kpts=None, kpts_band=None, spin=0)

ke_ratio = 3.0

ngrids = 4

rel_cutoff = 20.0

reset(cell=None)

vpploc_part1_nuc_grad(dm, kpts=array([[0., 0., 0.]]), atm_id=None, precision=None)

class pyscf.pbc.dft.multigrid.multigrid_pair.PGFPair

Bases: Structure

A primitive Gaussian function pair.

iL

Structure/Union member

ipgf

Structure/Union member

ish

Structure/Union member

jpgf

Structure/Union member

jsh

Structure/Union member

radius

Structure/Union member

class pyscf.pbc.dft.multigrid.multigrid_pair.RS_Grid

Bases: Structure

Values on real space multigrid.

comp

Structure/Union member

data

Structure/Union member

gridlevel_info

Structure/Union member

nlevels

Structure/Union member

class pyscf.pbc.dft.multigrid.multigrid_pair.Task

Bases: Structure

A single task.

buf_size

Structure/Union member

ntasks

Structure/Union member

pgfpairs

Structure/Union member

radius

Structure/Union member

class pyscf.pbc.dft.multigrid.multigrid_pair.TaskList

Bases: Structure

A task list.

gridlevel_info

Structure/Union member

hermi

Structure/Union member

nlevels

Structure/Union member

tasks

Structure/Union member

pyscf.pbc.dft.multigrid.multigrid_pair.build_task_list(cell, gridlevel_info, cell1=None, Ls=None, hermi=0, precision=None)

Build the task list for multigrid DFT calculations.

Arguments:

cellpbc.gto.cell.Cell

The Cell instance for the bra basis functions.

gridlevel_infoctypes.POINTER

The C pointer of the GridLevel_Info structure.

cell1pbc.gto.cell.Cell, optional

The Cell instance for the ket basis functions. If not given, both bra and ket basis functions come from cell.

Ls(*,3) array, optional

The cartesian coordinates of the periodic images. Default is calculated by cell.get_lattice_Ls().

hermiint, optional

If \(hermi=1\), the task list is built only for the upper triangle of the matrix. Default is 0.

precisionfloat, optional

The integral precision. Default is cell.precision.

Returns: ctypes.POINTER

The C pointer of the TaskList structure.

pyscf.pbc.dft.multigrid.multigrid_pair.eval_mat(cell, weights, task_list, shls_slice=None, comp=1, hermi=0, deriv=0, xctype='LDA', kpts=None, grid_level=None, dimension=None, mesh=None, cell1=None, shls_slice1=None, Ls=None, a=None)

pyscf.pbc.dft.multigrid.multigrid_pair.eval_rho(cell, dm, task_list, shls_slice=None, hermi=0, xctype='LDA', kpts=None, dimension=None, cell1=None, shls_slice1=None, Ls=None, a=None, ignore_imag=False)

Collocate density (opt. gradients) on the real-space grid. The two sets of Gaussian functions can be different.

Returns:

rho: RS_Grid object

Densities on real space multigrids.

pyscf.pbc.dft.multigrid.multigrid_pair.free_gridlevel_info(gridlevel_info)

pyscf.pbc.dft.multigrid.multigrid_pair.free_rs_grid(rs_grid)

pyscf.pbc.dft.multigrid.multigrid_pair.free_task_list(task_list)

Note:

This will also free task_list.contents.gridlevel_info.

pyscf.pbc.dft.multigrid.multigrid_pair.get_veff_ip1(mydf, dm_kpts, xc_code=None, kpts=array([[0., 0., 0.]]), kpts_band=None, spin=0)

pyscf.pbc.dft.multigrid.multigrid_pair.gradient_gs(f_gs, Gv)

Compute the G-space components of \(\nabla f(r)\) given \(f(G)\) and \(G\), which is equivalent to einsum(‘np,px->nxp’, f_gs, 1j*Gv)

pyscf.pbc.dft.multigrid.multigrid_pair.init_gridlevel_info(cutoff, rel_cutoff, mesh)

pyscf.pbc.dft.multigrid.multigrid_pair.init_rs_grid(gridlevel_info, comp)

Initialize values on real space multigrid

pyscf.pbc.dft.multigrid.multigrid_pair.multi_grids_tasks(cell, ke_cutoff=None, hermi=0, ngrids=4, ke_ratio=3.0, rel_cutoff=20.0)

pyscf.pbc.dft.multigrid.multigrid_pair.nr_rks(mydf, xc_code, dm_kpts, hermi=1, kpts=None, kpts_band=None, with_j=False, return_j=False, verbose=None)

Same as multigrid.nr_rks, but considers Hermitian symmetry also for GGA

pyscf.pbc.dft.multigrid.multigrid_pair.nr_uks(mydf, xc_code, dm_kpts, hermi=1, kpts=None, kpts_band=None, with_j=False, return_j=False, verbose=None)

pyscf.pbc.dft.multigrid.pp module

pyscf.pbc.dft.multigrid.pp.fake_cell_vloc_part1(cell, atm_id=None, precision=None)

Generate fakecell for the non-local term of the local part of the GTH pseudo-potential. Also stores the atomic radii. Differs from pp_int.fake_cell_vloc(cell, cn=0) in the normalization factors.

pyscf.pbc.dft.multigrid.pp.get_pp_loc_part1_gs(cell, Gv)

pyscf.pbc.dft.multigrid.pp.get_vpploc_part1_ip1(mydf, kpts=array([[0., 0., 0.]]))

pyscf.pbc.dft.multigrid.pp.make_rho_core(cell, mesh=None, precision=None, atm_id=None)

pyscf.pbc.dft.multigrid.pp.vpploc_part1_nuc_grad(mydf, dm, kpts=array([[0., 0., 0.]]), atm_id=None, precision=None)

pyscf.pbc.dft.multigrid.utils module

Module contents

pyscf.pbc.dft.multigrid.nr_rks(mydf, xc_code, dm_kpts, hermi=1, kpts=None, kpts_band=None, with_j=False, return_j=False, verbose=None)

pyscf.pbc.dft.multigrid.nr_uks(mydf, xc_code, dm_kpts, hermi=1, kpts=None, kpts_band=None, with_j=False, return_j=False, verbose=None)