pyscf.pbc.gto.pseudo package

Submodules

pyscf.pbc.gto.pseudo.pp module

PP with numeric integration. See also pyscf/pbc/gto/pesudo/pp_int.py

For GTH/HGH PPs, see:

Goedecker, Teter, Hutter, PRB 54, 1703 (1996) Hartwigsen, Goedecker, and Hutter, PRB 58, 3641 (1998)

pyscf.pbc.gto.pseudo.pp.Ylm_real(l, m, theta, phi)

Real spherical harmonics, if desired.

pyscf.pbc.gto.pseudo.pp.cart2polar(rvec)

pyscf.pbc.gto.pseudo.pp.get_alphas(cell)

alpha parameters from the non-divergent Hartree+Vloc G=0 term.

See ewald.pdf

Returns:

alphas : (natm,) ndarray

pyscf.pbc.gto.pseudo.pp.get_alphas_gth(cell)

alpha parameters for the local GTH pseudopotential.

pyscf.pbc.gto.pseudo.pp.get_gth_projG(cell, Gvs)

G space projectors from the FT of the real-space projectors.

int e^{iGr} p_j^l(r) Y_{lm}^*(theta,phi) = i^l p_j^l(G) Y_{lm}^*(thetaG, phiG)

See MH Eq.(4.80)

pyscf.pbc.gto.pseudo.pp.get_gth_vlocG(cell, Gv)

Local part of the GTH pseudopotential.

See MH (4.79).

Args:

Gv : (ngrids,3) ndarray

Returns:

(natm, ngrids) ndarray

pyscf.pbc.gto.pseudo.pp.get_jvloc_G0(cell, kpt=array([0., 0., 0.]))

Get the (separately divergent) Hartree + Vloc G=0 contribution.

pyscf.pbc.gto.pseudo.pp.get_pp(cell, kpt=array([0., 0., 0.]))

Get the periodic pseudopotential nuc-el AO matrix

pyscf.pbc.gto.pseudo.pp.get_projG(cell, kpt=array([0., 0., 0.]))

PP weight and projector for the nonlocal PP in G space.

Returns:

hslist( list( np.array( , ) ) )

• hs[atm][l][i,j]

projslist( list( list( list( np.array(ngrids) ) ) ) )

• projs[atm][l][m][i][ngrids]

pyscf.pbc.gto.pseudo.pp.get_vlocG(cell, Gv=None)

Local PP kernel in G space: Vloc(G)

Returns:

(natm, ngrids) ndarray

pyscf.pbc.gto.pseudo.pp.projG_li(G, l, i, rl)

pyscf.pbc.gto.pseudo.pp_int module

Analytic PP integrals. See also pyscf/pbc/gto/pesudo/pp.py

For GTH/HGH PPs, see:

Goedecker, Teter, Hutter, PRB 54, 1703 (1996) Hartwigsen, Goedecker, and Hutter, PRB 58, 3641 (1998)

pyscf.pbc.gto.pseudo.pp_int.fake_cell_vloc(cell, cn=0, atm_id=None)

Generate fake cell for V_{loc}.

Each term of V_{loc} (erf, C_1, C_2, C_3, C_4) is a gaussian type function. The integral over V_{loc} can be transfered to the 3-center integrals, in which the auxiliary basis is given by the fake cell.

The kwarg cn indiciates which term to generate for the fake cell. If cn = 0, the erf term is generated. C_1,..,C_4 are generated with cn = 1..4

pyscf.pbc.gto.pseudo.pp_int.fake_cell_vnl(cell)

Generate fake cell for V_{nl}.

gaussian function p_i^l Y_{lm}

pyscf.pbc.gto.pseudo.pp_int.get_gth_vlocG_part1(cell, Gv)

PRB, 58, 3641 Eq (5) first term

pyscf.pbc.gto.pseudo.pp_int.get_pp_loc_part1(cell, kpts=None)

PRB, 58, 3641 Eq (1), integrals associated to erf

pyscf.pbc.gto.pseudo.pp_int.get_pp_loc_part2(cell, kpts=None)

PRB, 58, 3641 Eq (1), integrals associated to C1, C2, C3, C4

pyscf.pbc.gto.pseudo.pp_int.get_pp_loc_part2_gamma(cell)

pyscf.pbc.gto.pseudo.pp_int.get_pp_nl(cell, kpts=None)

pyscf.pbc.gto.pseudo.pp_int.vpploc_part2_nuc_grad(cell, dm, kpts=None)

Nuclear gradients of the 2nd part of the local part of the GTH pseudo potential, contracted with the density matrix.

pyscf.pbc.gto.pseudo.pp_int.vppnl_nuc_grad(cell, dm, kpts=None)

Nuclear gradients of the non-local part of the GTH pseudo potential, contracted with the density matrix.

pyscf.pbc.gto.pseudo.ppnl_velgauge module

Analytic PP integrals for GTH/HGH PPs in velocity gauge.

For GTH/HGH PPs, see:

Goedecker, Teter, Hutter, PRB 54, 1703 (1996) Hartwigsen, Goedecker, and Hutter, PRB 58, 3641 (1998)

For the velocity gauge transformation, see: [1] Comparison of Length, Velocity, and Symmetric Gauges for the Calculation

of Absorption and Electric Circular Dichroism Spectra with Real-Time Time-Dependent Density Functional Theory, Johann Mattiat and Sandra Luber Journal of Chemical Theory and Computation 2022 18 (9), 5513-5526, DOI: 10.1021/acs.jctc.2c00644

class pyscf.pbc.gto.pseudo.ppnl_velgauge.VelGaugePPNLHelper(cell, kpts=None, intors=None, hl_max=3, origin=(0.0, 0.0, 0.0))

Bases: object

Helper class for evaluating velocity gauge pseudopotential non-local integrals. Useful to avoid recomputing data that only depends on the cell and k-points.

build()

int_vnl_ft(Gv, q=array([0., 0., 0.]), rc=False)

pyscf.pbc.gto.pseudo.ppnl_velgauge.ft_aopair_kpts_kern(cell, aosym='s1', kptjs=array([[0., 0., 0.]]), intor='GTO_ft_ovlp', comp=1, bvk_kmesh=None, origin=(0.0, 0.0, 0.0))

Fourier transform AO pair for a group of k-points sum_T exp(-i k_j * T) int exp(-i(G+q)r) i(r) j(r-T) dr^3

Modified version of pyscf.pbc.df.ft_ao.ft_aopair_kpts that returns the generated ft kernel.

pyscf.pbc.gto.pseudo.ppnl_velgauge.get_gth_pp_nl_velgauge(cell, q, kpts=None, vgppnl_helper=None)

Nonlocal part of GTH pseudopotential in velocity gauge.

Parameters

cellpyscf.pbc.gto.Cell

System cell

A_over_cnp.ndarray

Scaled magnetic vector potential. Shape is (3,)

kptsnp.ndarray, optional

k-point list.

vgppnl_helperVelGaugePPNLHelper, optional

Helper object for velocity gauge PP integrals. By default None which causes a new helper object to be created and built.

Returns

tuple

(ppnl, vgppnl_helper) where ppnl is an ndarray of shape (nkpts, nao, nao) and vgppnl_helper is the VelGaugePPNLHelper object used to compute the integrals.

pyscf.pbc.gto.pseudo.ppnl_velgauge.get_gth_pp_nl_velgauge_commutator(cell, q, kpts=None, vgppnl_helper=None)

pyscf.pbc.gto.pseudo.ppnl_velgauge.prepare_ppnl_ft_data(cell, fakecell, hl_idx, hl_blocks, kpts, intor, origin=(0.0, 0.0, 0.0), comp=1)

Prepare ft_kernel methods for fast evaluation of velocity gauge ppnl integrals

Parameters

cellpyscf.pbc.gto.Cell

System cell

fakecellpyscf.pbc.gto.Cell

Fake cell containing GTH projectors

hl_idxint

GTH projector angular momentum index

hl_blockslist

GTH hl blocks

kptsnp.ndarray

k-points

intorstr

GTO ft-ao integral name

compint, optional

Size of each integral (eg scalar=1, vector=3), by default 1

Returns

tuple

shls_slice, ft_kern, cell_conc_fakecell

pyscf.pbc.gto.pseudo.split_GTH_POTENTIALS module

pyscf.pbc.gto.pseudo.split_GTH_POTENTIALS.main()

Module contents