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

Bases: RPA

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 unrestricted 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 3d array, optional

coefficient from AO to MO, by default None

Returns:

Lpqdouble 4d 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 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_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 2d 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()

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 2d array

molecular orbital energies

mo_coeffdouble 3d array

molecular orbital coefficients

Lpqdouble 4d 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

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

Generating a scanner/solver for RPA PES.

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

Compute RPA correlation energy.

Parameters:

rpaURPA

rpa object

Lpqdouble 4d 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.urpa.kernel(rpa, mo_energy, mo_coeff, Lpq=None, nw=None)

RPA correlation and total energy

Parameters:

rpaRPA

rpa object

mo_energydouble 2d array

molecular orbital energies

mo_coeffdouble 3d array

molecular orbital coefficients

Lpqdouble 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