fcdmft.rpa.mol.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 fcdmft.rpa.mol.rpa.RPA(mf, frozen=None, auxbasis=None)

Bases: StreamObject

Attributes:

nmo

nocc

Methods

__call__(*args, **kwargs)	Update the attributes of the current object.
ao2mo([mo_coeff])	Transform density-fitting integral from AO to MO.
apply(fn, *args, **kwargs)	Apply the fn to rest arguments: return fn(*args, **kwargs). The return value of method set is the object itself. This allows a series of functions/methods to be executed in pipe.
as_scanner()	Generating a scanner/solver for RPA PES.
check_sanity()	Check input of class/object attributes, check whether a class method is overwritten.
copy()	Returns a shallow copy
get_ehf()	Get Hartree-Fock energy.
get_frozen_mask()	Get boolean mask for the restricted reference orbitals.
get_grids([alg, nw, mo_energy])	Generate grids for integration.
initialize_df([auxbasis])	Initialize density fitting.
kernel([mo_energy, mo_coeff, Lpq, nw])	RPA correlation and total energy
loop_ao2mo([mo_coeff, ijslice])	Transform density-fitting integral from AO to MO by block.
post_kernel(envs)	A hook to be run after the main body of the kernel function.
pre_kernel(envs)	A hook to be run before the main body of kernel function is executed.
run(*args, **kwargs)	Call the kernel function of current object.
set(*args, **kwargs)	Update the attributes of the current object.
view(cls)	New view of object with the same attributes.

dump_flags
get_nmo
get_nocc

ao2mo(mo_coeff=None)

Transform density-fitting integral from AO to MO.

Parameters:

mo_coeffdouble 2d array, optional

coefficient from AO to MO, by default None

Returns:

Lpqdouble 3d array

three-center density-fitting matrix in MO

as_scanner()

Generating a scanner/solver for RPA PES.

dump_flags(verbose=None)

get_ehf()

Get Hartree-Fock energy.

Returns:

e_hfdouble

Hartree-Fock energy

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_grids(alg=None, nw=None, mo_energy=None)

Generate grids for integration.

Parameters:

algstr, optional

algorithm for generating grids, by default None

nwint, optional

number of grids, by default None

mo_energydouble 1d array, optional

orbital energy, used for minimax grids, by default None

Returns:

freqsdouble 1d array

frequency grid

wtsdouble 1d array

weight of grids

get_nmo()

get_nocc()

initialize_df(auxbasis=None)

Initialize density fitting.

Parameters:

auxbasisstr, optional

name of auxiliary basis set, by default None

kernel(mo_energy=None, mo_coeff=None, Lpq=None, nw=None)

RPA correlation and total energy

Calculated total energy, HF energy and RPA correlation energy are stored in self.e_tot, self.e_hf, self.e_corr

Parameters:

mo_energydouble 1d array

molecular orbital energies

mo_coeffdouble 2d ndarray

molecular orbital coefficients

Lpqdouble 3d array, optional

density fitting 3-center integral in MO basis, by default None

nwint, optional

number of frequency point on imaginary axis, by default None

Returns:

self.e_corrfloat

RPA correlation energy

loop_ao2mo(mo_coeff=None, ijslice=None)

Transform density-fitting integral from AO to MO by block.

Parameters:

mo_coeffdouble 2d array, optional

coefficient from AO to MO, by default None

ijslicetuple, optional

tuples for (1st idx start, 1st idx end, 2nd idx start, 2nd idx end), by default None

Returns:

eri_3ddouble 3d array

three-center density-fitting matrix in MO in a block

property nmo

property nocc

fcdmft.rpa.mol.rpa.as_scanner(rpa)

Generating a scanner/solver for RPA PES.

fcdmft.rpa.mol.rpa.get_idx_metal(mo_occ, threshold=1e-06)

Get index of occupied/virtual/fractional orbitals of metals.

Parameters:

mo_occdouble 1d array

occupation number

thresholddouble, optional

threshold to determine fractionally occupied orbitals, by default 1.0e-6

Returns:

idx_occlist

list of occupied orbital indexes

idx_fraclist

list of fractionally occupied orbital indexes

idx_virlist

list of virtual orbital indexes

fcdmft.rpa.mol.rpa.get_rho_response_metal(omega, mo_energy, Lpq, mo_occ, out=None)

Compute density response function in auxiliary basis at freq iw.

Parameters:

omegadouble

imaginary part of a frequency point

mo_energydouble 1d array

orbital energy

Lpqdouble 3d array

three-center density-fitting matrix in MO

mo_occdouble 1d array

occupation number

outdouble ndarray, optional

a location into which the result is stored, by default None

Returns:

Pidouble 2d array

density-density response function in auxiliary basis at freq iw

fcdmft.rpa.mol.rpa.get_rpa_ecorr(rpa, Lpq, freqs, wts)

Compute RPA correlation energy.

Parameters:

rpaRPA

rpa object

Lpqdouble 3d array

density fitting 3-center integral in MO basis

freqsdouble 1d array

frequency grid

wtsdouble 1d array

weight of grids

Returns:

e_corrdouble

RPA correlation energy

fcdmft.rpa.mol.rpa.get_rpa_ecorr_outcore(rpa, mo_coeff, freqs, wts)

Low-memory routine to compute RPA correlation energy.

Parameters:

rpaRPA

rpa object

mo_coeffdouble 2d array

orbital coefficient

freqsdouble 1d array

frequency grid

wtsdouble 1d array

weight of grids

Returns:

e_corrdouble

RPA correlation energy

fcdmft.rpa.mol.rpa.kernel(rpa, mo_energy, mo_coeff, Lpq=None, nw=None)

RPA correlation and total energy.

Parameters:

rpaRPA

rpa object

mo_energydouble 1d array

molecular orbital energies

mo_coeffdouble 2d array

molecular orbital coefficients

Lpqdouble 3d array, optional

density fitting 3-center integral in MO basis, by default None

nwint, optional

number of frequency point on imaginary axis, by default None

Returns:

e_totfloat

RPA total energy

e_hffloat

HF energy (exact exchange for given mo_coeff)

e_corrfloat

RPA correlation energy