pyscf.gw package#

Submodules#

pyscf.gw.gw_ac module#

Spin-restricted G0W0 approximation with analytic continuation This implementation has N^4 scaling, and is faster than GW-CD (N^4) and analytic GW (N^6) methods. GW-AC is recommended for valence states only, and is inaccurate for core states.

Method:: See T. Zhu and G.K.-L. Chan, arxiv:2007.03148 (2020) for details Compute Sigma on imaginary frequency with density fitting, then analytically continued to real frequency
Useful References:: J. Chem. Theory Comput. 12, 3623-3635 (2016) New J. Phys. 14, 053020 (2012)

pyscf.gw.gw_ac.AC_pade_thiele_diag(sigma, omega)[source]#: Analytic continuation to real axis using a Pade approximation from Thiele’s reciprocal difference method Reference: J. Low Temp. Phys. 29, 179 (1977) Returns:

coeff: 2D array (ncoeff, norbs) omega: 2D array (norbs, npade)

pyscf.gw.gw_ac.AC_twopole_diag(sigma, omega, orbs, nocc)[source]#: Analytic continuation to real axis using a two-pole model Returns:

coeff: 2D array (ncoeff, norbs)

class pyscf.gw.gw_ac.GWAC(mf, frozen=None)[source]#

Bases: StreamObject

ac = 'pade'#

ao2mo(mo_coeff=None)[source]#

dump_flags()[source]#

get_frozen_mask()#

Get boolean mask for the restricted reference orbitals.

In the returned boolean (mask) array of frozen orbital indices, the element is False if it corresponds to the frozen orbital.

get_nmo()#

get_nocc()#

kernel(mo_energy=None, mo_coeff=None, Lpq=None, orbs=None, nw=100, vhf_df=False)[source]#

Input:: orbs: self-energy orbs nw: grid number vhf_df: whether using density fitting for HF exchange
Output:: mo_energy: GW quasiparticle energy

linearized = False#

property nmo#

property nocc#

pyscf.gw.gw_ac.get_rho_response(omega, mo_energy, Lpq)[source]#: Compute density response function in auxiliary basis at freq iw

pyscf.gw.gw_ac.get_sigma_diag(gw, orbs, Lpq, freqs, wts, iw_cutoff=None)[source]#: Compute GW correlation self-energy (diagonal elements) in MO basis on imaginary axis

pyscf.gw.gw_ac.kernel(gw, mo_energy, mo_coeff, Lpq=None, orbs=None, nw=None, vhf_df=False, verbose=3)[source]#: GW-corrected quasiparticle orbital energies Returns:

A list : converged, mo_energy, mo_coeff

pyscf.gw.gw_ac.pade_thiele(freqs, zn, coeff)[source]#

pyscf.gw.gw_ac.thiele(fn, zn)[source]#

pyscf.gw.gw_ac.two_pole(freqs, coeff)[source]#

pyscf.gw.gw_ac.two_pole_fit(coeff, omega, sigma)[source]#

pyscf.gw.gw_cd module#

Spin-restricted G0W0 approximation with contour deformation

This implementation has the same scaling (N^4) as GW-AC, more robust but slower. GW-CD is particularly recommended for accurate core and high-energy states.

Method:

See T. Zhu and G.K.-L. Chan, arxiv:2007.03148 (2020) for details Compute Sigma directly on real axis with density fitting through a contour deformation method

Useful References:

Chem. Theory Comput. 14, 4856-4869 (2018)

class pyscf.gw.gw_cd.GWCD(mf, frozen=None)[source]#

Bases: StreamObject

ao2mo(mo_coeff=None)[source]#

dump_flags()[source]#

eta = 0.001#

get_frozen_mask()#

Get boolean mask for the restricted reference orbitals.

In the returned boolean (mask) array of frozen orbital indices, the element is False if it corresponds to the frozen orbital.

get_nmo()#

get_nocc()#

kernel(mo_energy=None, mo_coeff=None, Lpq=None, orbs=None, nw=100, vhf_df=False)[source]#

Input:: orbs: self-energy orbs nw: grid number
Output:: mo_energy: GW quasiparticle energy

linearized = False#

property nmo#

property nocc#

pyscf.gw.gw_cd.get_WmnI_diag(gw, orbs, Lpq, freqs)[source]#: Compute W_mn(iw) on imarginary axis grids Return:

Wmn: (Nmo, Norbs, Nw)

pyscf.gw.gw_cd.get_rho_response(omega, mo_energy, Lpq)[source]#: Compute density response function in auxiliary basis at freq iw

pyscf.gw.gw_cd.get_rho_response_R(gw, omega, Lpq)[source]#: Compute density response function in auxiliary basis at poles

pyscf.gw.gw_cd.get_sigmaI_diag(gw, omega, Wmn, sign, freqs, wts)[source]#: Compute self-energy by integrating on imaginary axis

pyscf.gw.gw_cd.get_sigmaR_diag(gw, omega, orbp, ef, Lpq)[source]#: Compute self-energy for poles inside contour (more and more expensive away from Fermi surface)

pyscf.gw.gw_cd.get_sigma_diag(gw, ep, p, Lpq, Wmn, freqs, wts)[source]#: Compute self-energy on real axis using contour deformation

pyscf.gw.gw_cd.kernel(gw, mo_energy, mo_coeff, Lpq=None, orbs=None, nw=None, vhf_df=False, verbose=3)[source]#

GW-corrected quasiparticle orbital energies

Returns:: A list : converged, mo_energy, mo_coeff

pyscf.gw.gw_exact module#

Spin-restricted G0W0 approximation with exact frequency integration

class pyscf.gw.gw_exact.GWExact(mf, frozen=None, tdmf=None)[source]#

Bases: StreamObject

non-relativistic restricted GW

Saved results

mo_energy :
Orbital energies

mo_coeff
Orbital coefficients

ao2mo(mo_coeff=None)[source]#

dump_flags(verbose=None)[source]#

eta = 1e-08#

get_frozen_mask()#

Get boolean mask for the restricted reference orbitals.

In the returned boolean (mask) array of frozen orbital indices, the element is False if it corresponds to the frozen orbital.

get_g(omega, eta=None)[source]#

get_g0(omega, eta=None)[source]#

get_nmo()#

get_nocc()#

kernel(mo_energy=None, mo_coeff=None, td_e=None, td_xy=None, eris=None, orbs=None)[source]#: Kernel function is the main driver of a method. Every method should define the kernel function as the entry of the calculation. Note the return value of kernel function is not strictly defined. It can be anything related to the method (such as the energy, the wave-function, the DFT mesh grids etc.).

linearized = False#

property nmo#

property nocc#

reset(mol=None)[source]#

pyscf.gw.gw_exact.get_g(omega, mo_energy, mo_occ, eta)[source]#

pyscf.gw.gw_exact.get_sigma_deriv_element(gw, omega, tdm_p, tdm_q, td_e, eta=None, vir_sgn=1)[source]#

pyscf.gw.gw_exact.get_sigma_element(gw, omega, tdm_p, tdm_q, td_e, eta=None, vir_sgn=1)[source]#

pyscf.gw.gw_exact.kernel(gw, mo_energy, mo_coeff, td_e, td_xy, eris=None, orbs=None, verbose=3)[source]#

GW-corrected quasiparticle orbital energies

Returns:: A list : converged, mo_energy, mo_coeff

pyscf.gw.gw_slow module#

This module implements the G0W0 approximation on top of pyscf.tdscf.rhf_slow and pyscf.tdscf.proxy TD implementations. Unlike gw.py, all integrals are stored in memory. Several variants of GW are available:

(this module) pyscf.gw_slow: the molecular implementation;

pyscf.pbc.gw.gw_slow: single-kpoint PBC (periodic boundary condition) implementation;

pyscf.pbc.gw.kgw_slow_supercell: a supercell approach to PBC implementation with multiple k-points. Runs the molecular code for a model with several k-points for the cost of discarding momentum conservation and using dense instead of sparse matrixes;

pyscf.pbc.gw.kgw_slow: a PBC implementation with multiple k-points;

class pyscf.gw.gw_slow.AbstractIMDS(td, eri=None)[source]#

Bases: object

entire_space()[source]#: The entire orbital space. Returns:

An iterable of the entire orbital space.

get_rhs(p)[source]#

The right-hand side of the quasiparticle equation. Args:

p (int, tuple): the orbital;

Returns:: Right-hand sides of the quasiparticle equation

get_sigma_element(omega, p, **kwargs)[source]#

The diagonal matrix element of the self-energy matrix. Args:

omega (float): the energy value; p (int, tuple): the orbital;

Returns:: The diagonal matrix element.

initial_guess(p)[source]#

Retrieves the initial guess for the quasiparticle energy for orbital p. Args:

p (int, tuple): the orbital;

Returns:: The value of initial guess (float).

orb_dims = 1#

quasiparticle_eq(p, **kwargs)[source]#

The quasiparticle equation f(omega) = 0. Args:

p (int, tuple): the orbital; **kwargs: keyword arguments to get_sigma_element;

Returns:: A callable function of one parameter.

class pyscf.gw.gw_slow.GW(td, eri=None)[source]#

Bases: object

base_imds#: alias of IMDS

kernel()[source]#

Calculates GW roots.

Returns:: GW roots.

class pyscf.gw.gw_slow.IMDS(td, eri=None)[source]#

Bases: AbstractIMDS

construct_tdm()[source]#

property entire_space#: The entire orbital space. Returns:

An iterable of the entire orbital space.

get_rhs(p)[source]#

The right-hand side of the quasiparticle equation. Args:

p (int, tuple): the orbital;

Returns:: Right-hand sides of the quasiparticle equation

get_sigma_element(omega, p, eta, vir_sgn=1)[source]#

The diagonal matrix element of the self-energy matrix. Args:

omega (float): the energy value; p (int, tuple): the orbital;

Returns:: The diagonal matrix element.

initial_guess(p)[source]#

Retrieves the initial guess for the quasiparticle energy for orbital p. Args:

p (int, tuple): the orbital;

Returns:: The value of initial guess (float).

class pyscf.gw.gw_slow.LoggingFunction(m)[source]#

Bases: object

plot_call_history(title='')[source]#: Plots calls to this function. Args:

title (str): plot title;

property x#

property y#

pyscf.gw.gw_slow.corrected_moe(eri, p)[source]#

Calculates the corrected orbital energy. Args:

eri (PhysERI): a container with electron repulsion integrals; p (int): orbital;

Returns:: The corrected orbital energy.

pyscf.gw.gw_slow.kernel(imds, orbs=None, linearized=False, eta=0.001, tol=1e-09, method='fallback')[source]#

Calculates GW energies. Args:

imds (AbstractIMDS): GW intermediates; orbs (Iterable): indexes of MO orbitals to correct; linearized (bool): whether to apply a single-step linearized correction to energies instead of iterative procedure; eta (float): imaginary energy for the Green’s function; tol (float): tolerance for the search of zero; method (str): ‘bisect’ finds roots no matter what but, potentially, wrong ones, ‘newton’ finding roots close to the correct one but, potentially, failing during iterations, or ‘fallback’ using ‘newton’ and proceeding to ‘bisect’ in case of failure;

Returns:: Corrected orbital energies.

pyscf.gw.rpa module#

Spin-restricted random phase approximation (direct RPA/dRPA in chemistry) with N^4 scaling

Method:: Main routines are based on GW-AC method described in: T. Zhu and G.K.-L. Chan, J. Chem. Theory. Comput. 17, 727-741 (2021) X. Ren et al., New J. Phys. 14, 053020 (2012)

class pyscf.gw.rpa.DirectRPA(mf, frozen=None, auxbasis=None)[source]#

Bases: StreamObject

ao2mo(mo_coeff=None, blksize=None)[source]#

dump_flags()[source]#

get_frozen_mask()#

Get boolean mask for the restricted reference orbitals.

In the returned boolean (mask) array of frozen orbital indices, the element is False if it corresponds to the frozen orbital.

get_nmo()#

get_nocc()#

kernel(mo_energy=None, mo_coeff=None, cderi_ov=None, nw=40, x0=0.5)[source]#: The kernel function for direct RPA

make_dielectric_matrix(omega, e_ov=None, cderi_ov=None, blksize=None)[source]#

Args:: omega : float, frequency e_ov : 1D array (nocc * nvir), orbital energy differences mo_coeff : (nao, nmo), mean-field mo coefficient cderi_ov : (naux, nocc, nvir), Cholesky decomposed ERI in OV subspace.
Returns:: diel : 2D array (naux, naux), dielectric matrix

make_e_ov(mo_energy=None)[source]#: Compute orbital energy differences

property nmo#

property nocc#

pyscf.gw.rpa.RPA#: alias of DirectRPA

pyscf.gw.rpa.dRPA#: alias of DirectRPA

pyscf.gw.rpa.kernel(rpa, mo_energy, mo_coeff, cderi_ov=None, nw=40, x0=0.5, verbose=3)[source]#

RPA correlation and total energy

Args:

cderi_ov:: Array-like object, Cholesky decomposed ERI in OV subspace.
nw:: number of frequency point on imaginary axis.
x0:: scaling factor for frequency grid.

Returns:

e_tot:: RPA total energy
e_hf:: EXX energy
e_corr:: RPA correlation energy

pyscf.gw.rpa.make_dielectric_matrix(omega, e_ov, cderi_ov, blksize=None)[source]#

Compute dielectric matrix at a given frequency omega

Args:: omega : float, frequency e_ov : 1D array (nocc * nvir), orbital energy differences cderi_ov : 2D array (naux, nocc * nvir), Cholesky decomposed ERI

in OV subspace.
Returns:: diel : 2D array (naux, naux), dielectric matrix

pyscf.gw.ugw_ac module#

Spin-unrestricted G0W0 approximation with analytic continuation

This implementation has N^4 scaling, and is faster than GW-CD (N^4) and analytic GW (N^6) methods. GW-AC is recommended for valence states only, and is inaccurate for core states.

Method:: See T. Zhu and G.K.-L. Chan, arxiv:2007.03148 (2020) for details Compute Sigma on imaginary frequency with density fitting, then analytically continued to real frequency
Useful References:: J. Chem. Theory Comput. 12, 3623-3635 (2016) New J. Phys. 14, 053020 (2012)

pyscf.gw.ugw_ac.AC_pade_thiele_diag(sigma, omega)[source]#: Analytic continuation to real axis using a Pade approximation from Thiele’s reciprocal difference method Reference: J. Low Temp. Phys. 29, 179 (1977) Returns:

coeff: 2D array (ncoeff, norbs) omega: 2D array (norbs, npade)

pyscf.gw.ugw_ac.AC_twopole_diag(sigma, omega, orbs, nocc)[source]#: Analytic continuation to real axis using a two-pole model Returns:

coeff: 2D array (ncoeff, norbs)

class pyscf.gw.ugw_ac.UGWAC(mf, frozen=None)[source]#

Bases: StreamObject

ac = 'pade'#

ao2mo(mo_coeff=None)[source]#

dump_flags()[source]#

get_frozen_mask()#

Get boolean mask for the unrestricted reference orbitals.

In the returned boolean (mask) array of frozen orbital indices, the element is False if it corresponds to the frozen orbital.

get_nmo()#

get_nocc()#

kernel(mo_energy=None, mo_coeff=None, Lpq=None, orbs=None, nw=100, vhf_df=False)[source]#

Input:: orbs: self-energy orbs nw: grid number vhf_df: whether using density fitting for HF exchange
Output:: mo_energy: GW quasiparticle energy

linearized = False#

property nmo#

property nocc#

pyscf.gw.ugw_ac.get_rho_response(omega, mo_energy, Lpqa, Lpqb)[source]#: Compute density response function in auxiliary basis at freq iw

pyscf.gw.ugw_ac.get_sigma_diag(gw, orbs, Lpq, freqs, wts, iw_cutoff=None)[source]#: Compute GW correlation self-energy (diagonal elements) in MO basis on imaginary axis

pyscf.gw.ugw_ac.kernel(gw, mo_energy, mo_coeff, Lpq=None, orbs=None, nw=None, vhf_df=False, verbose=3)[source]#: GW-corrected quasiparticle orbital energies Returns:

A list : converged, mo_energy, mo_coeff

pyscf.gw.ugw_ac.pade_thiele(freqs, zn, coeff)[source]#

pyscf.gw.ugw_ac.thiele(fn, zn)[source]#

pyscf.gw.ugw_ac.two_pole(freqs, coeff)[source]#

pyscf.gw.ugw_ac.two_pole_fit(coeff, omega, sigma)[source]#

pyscf.gw.urpa module#

Spin-unrestricted random phase approximation (direct RPA/dRPA in chemistry) with N^4 scaling

Method:: Main routines are based on GW-AC method described in: T. Zhu and G.K.-L. Chan, J. Chem. Theory. Comput. 17, 727-741 (2021) X. Ren et al., New J. Phys. 14, 053020 (2012)

class pyscf.gw.urpa.URPA(mf, frozen=None, auxbasis=None)[source]#

Bases: DirectRPA

ao2mo(mo_coeff=None, blksize=None)[source]#

dump_flags()[source]#

get_frozen_mask()#

Get boolean mask for the unrestricted reference orbitals.

In the returned boolean (mask) array of frozen orbital indices, the element is False if it corresponds to the frozen orbital.

get_nmo()#

get_nocc()#

make_dielectric_matrix(omega, e_ov=None, cderi_ov=None, blksize=None)[source]#

Args:: omega : float, frequency mo_energy : (2, nmo), mean-field mo energy mo_coeff : (2, nao, nmo), mean-field mo coefficient cderi_ov : (2, naux, nocc, nvir), Cholesky decomposed ERI in OV subspace.
Returns:: diel : 2D array (naux, naux), dielectric matrix

make_e_ov(mo_energy=None)[source]#: Compute orbital energy differences

Module contents#

G0W0 approximation

pyscf.gw.GW(mf, freq_int='ac', frozen=None, tdmf=None)[source]#