from __future__ import annotations
import pickle
import warnings
from math import pi
from pathlib import Path
import numpy as np
from ase.parallel import paropen
from ase.units import Ha
from gpaw import GPAW, debug
import gpaw.mpi as mpi
from gpaw.hybrids.eigenvalues import non_self_consistent_eigenvalues
from gpaw.pw.descriptor import (count_reciprocal_vectors, PWMapping)
from gpaw.utilities.progressbar import ProgressBar
from gpaw.response import ResponseContext, ResponseGroundStateAdapter
from gpaw.response.chi0 import Chi0Calculator, get_frequency_descriptor
from gpaw.response.pair import phase_shifted_fft_indices
from gpaw.response.pair_functions import SingleQPWDescriptor
from gpaw.response.pw_parallelization import Blocks1D
from gpaw.response.screened_interaction import initialize_w_calculator
from gpaw.response.coulomb_kernels import CoulombKernel
from gpaw.response import timer
from ase.utils.filecache import MultiFileJSONCache as FileCache
from contextlib import ExitStack
from ase.parallel import broadcast
def compare_dicts(dict1, dict2, rel_tol=1e-14, abs_tol=1e-14):
"""
Compare each key-value pair within dictionaries that contain nested data
structures of arbitrary depth. If a kvp contains floats, you may specify
the tolerance (abs or rel) to which the floats are compared. Individual
elements within lists are not compared to floating point precision.
:params dict1: Dictionary containing kvp to compare with other dictionary.
:params dict2: Second dictionary.
:params rel_tol: Maximum difference for being considered "close",
relative to the magnitude of the input values as defined by math.isclose().
:params abs_tol: Maximum difference for being considered "close",
regardless of the magnitude of the input values as defined by
math.isclose().
:returns: bool indicating kvp's don't match (False) or do match (True)
"""
from math import isclose
if dict1.keys() != dict2.keys():
return False
for key in dict1.keys():
val1 = dict1[key]
val2 = dict2[key]
if isinstance(val1, dict) and isinstance(val2, dict):
# recursive func call to ensure nested structures are also compared
if not compare_dicts(val1, val2, rel_tol, abs_tol):
return False
elif isinstance(val1, float) and isinstance(val2, float):
if not isclose(val1, val2, rel_tol=rel_tol, abs_tol=abs_tol):
return False
else:
if val1 != val2:
return False
return True
class Sigma:
def __init__(self, iq, q_c, fxc, esknshape, **inputs):
"""Inputs are used for cache invalidation, and are stored for each
file.
"""
self.iq = iq
self.q_c = q_c
self.fxc = fxc
self._buf = np.zeros((2, *esknshape))
# self-energies and derivatives:
self.sigma_eskn, self.dsigma_eskn = self._buf
self.inputs = inputs
def sum(self, comm):
comm.sum(self._buf)
def __iadd__(self, other):
self.validate_inputs(other.inputs)
self._buf += other._buf
return self
def validate_inputs(self, inputs):
equals = compare_dicts(inputs, self.inputs, rel_tol=1e-14,
abs_tol=1e-14)
if not equals:
raise RuntimeError('There exists a cache with mismatching input '
f'parameters: {inputs} != {self.inputs}.')
@classmethod
def fromdict(cls, dct):
instance = cls(dct['iq'], dct['q_c'], dct['fxc'],
dct['sigma_eskn'].shape, **dct['inputs'])
instance.sigma_eskn[:] = dct['sigma_eskn']
instance.dsigma_eskn[:] = dct['dsigma_eskn']
return instance
def todict(self):
return {'iq': self.iq,
'q_c': self.q_c,
'fxc': self.fxc,
'sigma_eskn': self.sigma_eskn,
'dsigma_eskn': self.dsigma_eskn,
'inputs': self.inputs}
class G0W0Outputs:
def __init__(self, context, shape, ecut_e, sigma_eskn, dsigma_eskn,
eps_skn, vxc_skn, exx_skn, f_skn):
self.extrapolate(context, shape, ecut_e, sigma_eskn, dsigma_eskn)
self.Z_skn = 1 / (1 - self.dsigma_skn)
# G0W0 single-step.
# If we want GW0 again, we need to grab the expressions
# from e.g. e73917fca5b9dc06c899f00b26a7c46e7d6fa749
# or earlier and use qp correctly.
self.qp_skn = eps_skn + self.Z_skn * (
-vxc_skn + exx_skn + self.sigma_skn)
self.sigma_eskn = sigma_eskn
self.dsigma_eskn = dsigma_eskn
self.eps_skn = eps_skn
self.vxc_skn = vxc_skn
self.exx_skn = exx_skn
self.f_skn = f_skn
def extrapolate(self, context, shape, ecut_e, sigma_eskn, dsigma_eskn):
if len(ecut_e) == 1:
self.sigma_skn = sigma_eskn[0]
self.dsigma_skn = dsigma_eskn[0]
self.sigr2_skn = None
self.dsigr2_skn = None
return
from scipy.stats import linregress
# Do linear fit of selfenergy vs. inverse of number of plane waves
# to extrapolate to infinite number of plane waves
context.print('', flush=False)
context.print('Extrapolating selfenergy to infinite energy cutoff:',
flush=False)
context.print(' Performing linear fit to %d points' % len(ecut_e))
self.sigr2_skn = np.zeros(shape)
self.dsigr2_skn = np.zeros(shape)
self.sigma_skn = np.zeros(shape)
self.dsigma_skn = np.zeros(shape)
invN_i = ecut_e**(-3. / 2)
for m in range(np.prod(shape)):
s, k, n = np.unravel_index(m, shape)
slope, intercept, r_value, p_value, std_err = \
linregress(invN_i, sigma_eskn[:, s, k, n])
self.sigr2_skn[s, k, n] = r_value**2
self.sigma_skn[s, k, n] = intercept
slope, intercept, r_value, p_value, std_err = \
linregress(invN_i, dsigma_eskn[:, s, k, n])
self.dsigr2_skn[s, k, n] = r_value**2
self.dsigma_skn[s, k, n] = intercept
if np.any(self.sigr2_skn < 0.9) or np.any(self.dsigr2_skn < 0.9):
context.print(' Warning: Bad quality of linear fit for some ('
'n,k). ', flush=False)
context.print(' Higher cutoff might be necessary.',
flush=False)
context.print(' Minimum R^2 = %1.4f. (R^2 Should be close to 1)' %
min(np.min(self.sigr2_skn), np.min(self.dsigr2_skn)))
def get_results_eV(self):
results = {
'f': self.f_skn,
'eps': self.eps_skn * Ha,
'vxc': self.vxc_skn * Ha,
'exx': self.exx_skn * Ha,
'sigma': self.sigma_skn * Ha,
'dsigma': self.dsigma_skn,
'Z': self.Z_skn,
'qp': self.qp_skn * Ha}
results.update(
sigma_eskn=self.sigma_eskn * Ha,
dsigma_eskn=self.dsigma_eskn)
if self.sigr2_skn is not None:
assert self.dsigr2_skn is not None
results['sigr2_skn'] = self.sigr2_skn
results['dsigr2_skn'] = self.dsigr2_skn
return results
class QSymmetryOp:
def __init__(self, symno, U_cc, sign):
self.symno = symno
self.U_cc = U_cc
self.sign = sign
def apply(self, q_c):
return self.sign * (self.U_cc @ q_c)
def check_q_Q_symmetry(self, Q_c, q_c):
d_c = self.apply(q_c) - Q_c
assert np.allclose(d_c.round(), d_c)
def get_M_vv(self, cell_cv):
# We'll be inverting these cells a lot.
# Should have an object with the cell and its inverse which does this.
return cell_cv.T @ self.U_cc.T @ np.linalg.inv(cell_cv).T
@classmethod
def get_symops(cls, qd, iq, q_c):
# Loop over all k-points in the BZ and find those that are
# related to the current IBZ k-point by symmetry
Q1 = qd.ibz2bz_k[iq]
done = set()
for Q2 in qd.bz2bz_ks[Q1]:
if Q2 >= 0 and Q2 not in done:
time_reversal = qd.time_reversal_k[Q2]
symno = qd.sym_k[Q2]
Q_c = qd.bzk_kc[Q2]
symop = cls(
symno=symno,
U_cc=qd.symmetry.op_scc[symno],
sign=1 - 2 * time_reversal)
symop.check_q_Q_symmetry(Q_c, q_c)
# Q_c, symop = QSymmetryOp.from_qd(qd, Q2, q_c)
yield Q_c, symop
done.add(Q2)
@classmethod
def get_symop_from_kpair(cls, kd, qd, kpt1, kpt2):
# from k-point pair kpt1, kpt2 get Q_c = kpt2-kpt1, corrsponding IBZ
# k-point q_c, indexes iQ, iq and symmetry transformation relating
# Q_c to q_c
Q_c = kd.bzk_kc[kpt2.K] - kd.bzk_kc[kpt1.K]
iQ = qd.where_is_q(Q_c, qd.bzk_kc)
iq = qd.bz2ibz_k[iQ]
q_c = qd.ibzk_kc[iq]
# Find symmetry that transforms Q_c into q_c
sym = qd.sym_k[iQ]
U_cc = qd.symmetry.op_scc[sym]
time_reversal = qd.time_reversal_k[iQ]
sign = 1 - 2 * time_reversal
symop = cls(sym, U_cc, sign)
symop.check_q_Q_symmetry(Q_c, q_c)
return symop, iq
def apply_symop_q(self, qpd, pawcorr, kpt1, kpt2):
# returns necessary quantities to get symmetry transformed
# density matrix
Q_G = phase_shifted_fft_indices(kpt1.k_c, kpt2.k_c, qpd,
coordinate_transformation=self.apply)
qG_Gv = qpd.get_reciprocal_vectors(add_q=True)
M_vv = self.get_M_vv(qpd.gd.cell_cv)
mypawcorr = pawcorr.remap_by_symop(self, qG_Gv, M_vv)
return mypawcorr, Q_G
def get_nmG(kpt1, kpt2, mypawcorr, n, qpd, I_G, pair_calc, timer=None):
if timer:
timer.start('utcc and pawcorr multiply')
ut1cc_R = kpt1.ut_nR[n].conj()
C1_aGi = mypawcorr.multiply(kpt1.P_ani, band=n)
if timer:
timer.stop('utcc and pawcorr multiply')
n_mG = pair_calc.calculate_pair_density(
ut1cc_R, C1_aGi, kpt2, qpd, I_G)
return n_mG
gw_logo = """\
___ _ _ _
| || | | |
| | || | | |
|__ ||_____|
|___|
"""
def get_max_nblocks(world, calc, ecut):
nblocks = world.size
if not isinstance(calc, (str, Path)):
raise Exception('Using a calulator is not implemented at '
'the moment, load from file!')
# nblocks_calc = calc
else:
nblocks_calc = GPAW(calc)
ngmax = []
for q_c in nblocks_calc.wfs.kd.bzk_kc:
qpd = SingleQPWDescriptor.from_q(q_c, np.min(ecut) / Ha,
nblocks_calc.wfs.gd)
ngmax.append(qpd.ngmax)
nG = np.min(ngmax)
while nblocks > nG**0.5 + 1 or world.size % nblocks != 0:
nblocks -= 1
mynG = (nG + nblocks - 1) // nblocks
assert mynG * (nblocks - 1) < nG
return nblocks
def get_frequencies(frequencies: dict | None,
domega0: float | None, omega2: float | None):
if domega0 is not None or omega2 is not None:
assert frequencies is None
frequencies = {'type': 'nonlinear',
'domega0': 0.025 if domega0 is None else domega0,
'omega2': 10.0 if omega2 is None else omega2}
warnings.warn(f'Please use frequencies={frequencies}')
elif frequencies is None:
frequencies = {'type': 'nonlinear',
'domega0': 0.025,
'omega2': 10.0}
else:
assert frequencies['type'] == 'nonlinear'
return frequencies
def choose_ecut_things(ecut, ecut_extrapolation):
if ecut_extrapolation is True:
pct = 0.8
necuts = 3
ecut_e = ecut * (1 + (1. / pct - 1) * np.arange(necuts)[::-1] /
(necuts - 1))**(-2 / 3)
elif isinstance(ecut_extrapolation, (list, np.ndarray)):
ecut_e = np.array(np.sort(ecut_extrapolation))
if not np.allclose(ecut, ecut_e[-1]):
raise ValueError('ecut parameter must be the largest value'
'of ecut_extrapolation, when it is a list.')
ecut = ecut_e[-1]
else:
ecut_e = np.array([ecut])
return ecut, ecut_e
def select_kpts(kpts, kd):
"""Function to process input parameters that take a list of k-points given
in different format and returns a list of indices of the corresponding
k-points in the IBZ."""
if kpts is None:
# Do all k-points in the IBZ:
return np.arange(kd.nibzkpts)
if np.asarray(kpts).ndim == 1:
return kpts
# Find k-points:
bzk_Kc = kd.bzk_kc
indices = []
for k_c in kpts:
d_Kc = bzk_Kc - k_c
d_Kc -= d_Kc.round()
K = abs(d_Kc).sum(1).argmin()
if not np.allclose(d_Kc[K], 0):
raise ValueError('Could not find k-point: {k_c}'
.format(k_c=k_c))
k = kd.bz2ibz_k[K]
indices.append(k)
return indices
class PairDistribution:
def __init__(self, kptpair_factory, blockcomm, mysKn1n2):
self.get_k_point = kptpair_factory.get_k_point
self.kd = kptpair_factory.gs.kd
self.blockcomm = blockcomm
self.mysKn1n2 = mysKn1n2
self.mykpts = [self.get_k_point(s, K, n1, n2)
for s, K, n1, n2 in self.mysKn1n2]
def kpt_pairs_by_q(self, q_c, m1, m2):
mykpts = self.mykpts
for u, kpt1 in enumerate(mykpts):
progress = u / len(mykpts)
K2 = self.kd.find_k_plus_q(q_c, [kpt1.K])[0]
kpt2 = self.get_k_point(kpt1.s, K2, m1, m2,
blockcomm=self.blockcomm)
yield progress, kpt1, kpt2
def distribute_k_points_and_bands(chi0_body_calc, band1, band2, kpts=None):
"""Distribute spins, k-points and bands.
The attribute self.mysKn1n2 will be set to a list of (s, K, n1, n2)
tuples that this process handles.
"""
gs = chi0_body_calc.gs
blockcomm = chi0_body_calc.blockcomm
kncomm = chi0_body_calc.kncomm
if kpts is None:
kpts = np.arange(gs.kd.nbzkpts)
# nbands is the number of bands for each spin/k-point combination.
nbands = band2 - band1
size = kncomm.size
rank = kncomm.rank
ns = gs.nspins
nk = len(kpts)
n = (ns * nk * nbands + size - 1) // size
i1 = min(rank * n, ns * nk * nbands)
i2 = min(i1 + n, ns * nk * nbands)
mysKn1n2 = []
i = 0
for s in range(ns):
for K in kpts:
n1 = min(max(0, i1 - i), nbands)
n2 = min(max(0, i2 - i), nbands)
if n1 != n2:
mysKn1n2.append((s, K, n1 + band1, n2 + band1))
i += nbands
p = chi0_body_calc.context.print
p('BZ k-points:', gs.kd, flush=False)
p('Distributing spins, k-points and bands (%d x %d x %d)' %
(ns, nk, nbands), 'over %d process%s' %
(kncomm.size, ['es', ''][kncomm.size == 1]),
flush=False)
p('Number of blocks:', blockcomm.size)
return PairDistribution(
chi0_body_calc.kptpair_factory, blockcomm, mysKn1n2)
class G0W0Calculator:
def __init__(self, filename='gw', *,
wd,
chi0calc,
wcalc,
kpts, bands, nbands=None,
fxc_modes,
eta,
ecut_e,
frequencies=None,
exx_vxc_calculator,
qcache,
ppa=False):
"""G0W0 calculator, initialized through G0W0 object.
The G0W0 calculator is used to calculate the quasi
particle energies through the G0W0 approximation for a number
of states.
Parameters
----------
filename: str
Base filename of output files.
wcalc: WCalculator object
Defines the calculator for computing the screened interaction
kpts: list
List of indices of the IBZ k-points to calculate the quasi particle
energies for.
bands:
Range of band indices, like (n1, n2), to calculate the quasi
particle energies for. Bands n where n1<=n<n2 will be
calculated. Note that the second band index is not included.
frequencies:
Input parameters for frequency_grid.
Can be array of frequencies to evaluate the response function at
or dictionary of parameters for build-in nonlinear grid
(see :ref:`frequency grid`).
ecut_e: array(float)
Plane wave cut-off energies in eV. Defined with choose_ecut_things
nbands: int
Number of bands to use in the calculation. If None, the number will
be determined from :ecut: to yield a number close to the number of
plane waves used.
do_GW_too: bool
When carrying out a calculation including vertex corrections, it
is possible to get the standard GW results at the same time
(almost for free).
ppa: bool
Use Godby-Needs plasmon-pole approximation for screened interaction
and self-energy
"""
self.chi0calc = chi0calc
self.wcalc = wcalc
self.context = self.wcalc.context
self.ppa = ppa
self.qcache = qcache
# Note: self.wd should be our only representation of the frequencies.
# We should therefore get rid of self.frequencies.
# It is currently only used by the restart code,
# so should be easy to remove after some further adaptation.
self.wd = wd
self.frequencies = frequencies
self.ecut_e = ecut_e / Ha
self.context.print(gw_logo)
if self.chi0calc.gs.metallic:
self.context.print('WARNING: \n'
'The current GW implementation cannot'
' handle intraband screening. \n'
'This results in poor k-point'
' convergence for metals')
self.fxc_modes = fxc_modes
if self.fxc_modes[0] != 'GW':
assert self.wcalc.xckernel.xc != 'RPA'
if len(self.fxc_modes) == 2:
# With multiple fxc_modes, we previously could do only
# GW plus one other fxc_mode. Now we can have any set
# of modes, but whether things are consistent or not may
# depend on how wcalc is configured.
assert 'GW' in self.fxc_modes
assert self.wcalc.xckernel.xc != 'RPA'
self.filename = filename
self.eta = eta / Ha
self.kpts = kpts
self.bands = bands
b1, b2 = self.bands
self.shape = (self.wcalc.gs.nspins, len(self.kpts), b2 - b1)
self.nbands = nbands
if self.wcalc.gs.nspins != 1:
for fxc_mode in self.fxc_modes:
if fxc_mode != 'GW':
raise RuntimeError('Including a xc kernel does not '
'currently work for spin-polarized '
f'systems. Invalid fxc_mode {fxc_mode}.'
)
self.pair_distribution = distribute_k_points_and_bands(
self.chi0calc.chi0_body_calc, b1, b2,
self.chi0calc.gs.kd.ibz2bz_k[self.kpts])
self.print_parameters(kpts, b1, b2)
self.exx_vxc_calculator = exx_vxc_calculator
if self.ppa:
self.context.print('Using Godby-Needs plasmon-pole approximation:')
self.context.print(' Fitting energy: i*E0, E0 = %.3f Hartee'
% self.wd.omega_w[1].imag)
else:
self.context.print('Using full frequency integration')
def print_parameters(self, kpts, b1, b2):
isl = ['',
'Quasi particle states:']
if kpts is None:
isl.append('All k-points in IBZ')
else:
kptstxt = ', '.join([f'{k:d}' for k in self.kpts])
isl.append(f'k-points (IBZ indices): [{kptstxt}]')
isl.extend([f'Band range: ({b1:d}, {b2:d})',
'',
'Computational parameters:'])
if len(self.ecut_e) == 1:
isl.append(
'Plane wave cut-off: '
f'{self.chi0calc.chi0_body_calc.ecut * Ha:g} eV')
else:
assert len(self.ecut_e) > 1
isl.append('Extrapolating to infinite plane wave cut-off using '
'points at:')
for ec in self.ecut_e:
isl.append(f' {ec * Ha:.3f} eV')
isl.extend([f'Number of bands: {self.nbands:d}',
f'Coulomb cutoff: {self.wcalc.coulomb.truncation}',
f'Broadening: {self.eta * Ha:g} eV',
'',
f'fxc modes: {", ".join(sorted(self.fxc_modes))}',
f'Kernel: {self.wcalc.xckernel.xc}'])
self.context.print('\n'.join(isl))
def get_eps_and_occs(self):
eps_skn = np.empty(self.shape) # KS-eigenvalues
f_skn = np.empty(self.shape) # occupation numbers
nspins = self.wcalc.gs.nspins
b1, b2 = self.bands
for i, k in enumerate(self.kpts):
for s in range(nspins):
u = s + k * nspins
kpt = self.wcalc.gs.kpt_u[u]
eps_skn[s, i] = kpt.eps_n[b1:b2]
f_skn[s, i] = kpt.f_n[b1:b2] / kpt.weight
return eps_skn, f_skn
@timer('G0W0')
def calculate(self):
"""Starts the G0W0 calculation.
Returns a dict with the results with the following key/value pairs:
=========== =============================================
key value
=========== =============================================
``f`` Occupation numbers
``eps`` Kohn-Sham eigenvalues in eV
``vxc`` Exchange-correlation
contributions in eV
``exx`` Exact exchange contributions in eV
``sigma`` Self-energy contributions in eV
``dsigma`` Self-energy derivatives
``sigma_e`` Self-energy contributions in eV
used for ecut extrapolation
``Z`` Renormalization factors
``qp`` Quasi particle (QP) energies in eV
``iqp`` GW0/GW: QP energies for each iteration in eV
=========== =============================================
All the values are ``ndarray``'s of shape
(spins, IBZ k-points, bands)."""
# Loop over q in the IBZ:
self.context.print('Summing all q:')
self.calculate_all_q_points()
sigmas = self.read_sigmas()
self.all_results = self.postprocess(sigmas)
# Note: self.results is a pointer pointing to one of the results,
# for historical reasons.
self.savepckl()
return self.results
def postprocess(self, sigmas):
all_results = {}
for fxc_mode, sigma in sigmas.items():
all_results[fxc_mode] = self.postprocess_single(fxc_mode, sigma)
self.print_results(all_results)
return all_results
def read_sigmas(self):
if self.context.comm.rank == 0:
sigmas = self._read_sigmas()
else:
sigmas = None
return broadcast(sigmas, comm=self.context.comm)
def _read_sigmas(self):
assert self.context.comm.rank == 0
# Integrate over all q-points, and accumulate the quasiparticle shifts
for iq, q_c in enumerate(self.wcalc.qd.ibzk_kc):
key = str(iq)
sigmas_contrib = self.get_sigmas_dict(key)
if iq == 0:
sigmas = sigmas_contrib
else:
for fxc_mode in self.fxc_modes:
sigmas[fxc_mode] += sigmas_contrib[fxc_mode]
return sigmas
def get_sigmas_dict(self, key):
assert self.context.comm.rank == 0
return {fxc_mode: Sigma.fromdict(sigma)
for fxc_mode, sigma in self.qcache[key].items()}
def postprocess_single(self, fxc_name, sigma):
output = self.calculate_g0w0_outputs(sigma)
return output.get_results_eV()
def savepckl(self):
"""Save outputs to pckl files and return paths to those files."""
# Note: this is always called, but the paths aren't returned
# to the caller. Calling it again then overwrites the files.
#
# TODO:
# * Replace with JSON
# * Save to different files or same file?
# * Move this functionality to g0w0 result object
paths = {}
for fxc_mode in self.fxc_modes:
path = Path(f'{self.filename}_results_{fxc_mode}.pckl')
with paropen(path, 'wb', comm=self.context.comm) as fd:
pickle.dump(self.all_results[fxc_mode], fd, 2)
paths[fxc_mode] = path
# Do not return paths to caller before we know they all exist:
self.context.comm.barrier()
return paths
def calculate_q(self, ie, k, kpt1, kpt2, qpd, Wdict,
*, symop, sigmas, blocks1d, pawcorr):
"""Calculates the contribution to the self-energy and its derivative
for a given set of k-points, kpt1 and kpt2."""
mypawcorr, I_G = symop.apply_symop_q(qpd, pawcorr, kpt1, kpt2)
if debug:
N_c = qpd.gd.N_c
i_cG = symop.apply(np.unravel_index(qpd.Q_qG[0], N_c))
bzk_kc = self.wcalc.gs.kd.bzk_kc
Q_c = bzk_kc[kpt2.K] - bzk_kc[kpt1.K]
shift0_c = Q_c - symop.apply(qpd.q_c)
self.check(ie, i_cG, shift0_c, N_c, Q_c, mypawcorr)
for n in range(kpt1.n2 - kpt1.n1):
eps1 = kpt1.eps_n[n]
n_mG = get_nmG(kpt1, kpt2, mypawcorr,
n, qpd, I_G, self.chi0calc.pair_calc)
if symop.sign == 1:
n_mG = n_mG.conj()
f_m = kpt2.f_n
deps_m = eps1 - kpt2.eps_n
nn = kpt1.n1 + n - self.bands[0]
assert set(Wdict) == set(sigmas)
for fxc_mode in self.fxc_modes:
sigma = sigmas[fxc_mode]
Wmodel = Wdict[fxc_mode]
# m is band index of all (both unoccupied and occupied) wave
# functions in G
for m, (deps, f, n_G) in enumerate(zip(deps_m, f_m, n_mG)):
# 2 * f - 1 will be used to select the branch of Hilbert
# transform, see get_HW of screened_interaction.py
# at FullFrequencyHWModel class.
S_GG, dSdw_GG = Wmodel.get_HW(deps, 2 * f - 1)
if S_GG is None:
continue
nc_G = n_G.conj()
# ie: ecut index for extrapolation
# kpt1.s: spin index of *
# k: k-point index of *
# nn: band index of *
# * wave function, where the sigma expectation value is
# evaluated
slot = ie, kpt1.s, k, nn
myn_G = n_G[blocks1d.myslice]
sigma.sigma_eskn[slot] += (myn_G @ S_GG @ nc_G).real
sigma.dsigma_eskn[slot] += (myn_G @ dSdw_GG @ nc_G).real
def check(self, ie, i_cG, shift0_c, N_c, Q_c, pawcorr):
# Can we delete this check? XXX
assert np.allclose(shift0_c.round(), shift0_c)
shift0_c = shift0_c.round().astype(int)
I0_G = np.ravel_multi_index(i_cG - shift0_c[:, None], N_c, 'wrap')
qpd = SingleQPWDescriptor.from_q(Q_c, self.ecut_e[ie],
self.wcalc.gs.gd)
G_I = np.empty(N_c.prod(), int)
G_I[:] = -1
I1_G = qpd.Q_qG[0]
G_I[I1_G] = np.arange(len(I0_G))
G_G = G_I[I0_G]
# This indexing magic should definitely be moved to a method.
# What on earth is it really?
assert len(I0_G) == len(I1_G)
assert (G_G >= 0).all()
pairden_paw_corr = self.wcalc.gs.pair_density_paw_corrections
pawcorr_wcalc1 = pairden_paw_corr(qpd)
assert pawcorr.almost_equal(pawcorr_wcalc1, G_G)
def calculate_all_q_points(self):
"""Main loop over irreducible Brillouin zone points.
Handles restarts of individual qpoints using FileCache from ASE,
and subsequently calls calculate_q."""
pb = ProgressBar(self.context.fd)
self.context.timer.start('W')
self.context.print('\nCalculating screened Coulomb potential')
self.context.print(self.wcalc.coulomb.description())
chi0calc = self.chi0calc
self.context.print(self.wd)
# Find maximum size of chi-0 matrices:
nGmax = max(count_reciprocal_vectors(chi0calc.chi0_body_calc.ecut,
self.wcalc.gs.gd, q_c)
for q_c in self.wcalc.qd.ibzk_kc)
nw = len(self.wd)
size = self.chi0calc.chi0_body_calc.integrator.blockcomm.size
mynGmax = (nGmax + size - 1) // size
mynw = (nw + size - 1) // size
# some memory sizes...
if self.context.comm.rank == 0:
siz = (nw * mynGmax * nGmax +
max(mynw * nGmax, nw * mynGmax) * nGmax) * 16
sizA = (nw * nGmax * nGmax + nw * nGmax * nGmax) * 16
self.context.print(
' memory estimate for chi0: local=%.2f MB, global=%.2f MB'
% (siz / 1024**2, sizA / 1024**2))
# Need to pause the timer in between iterations
self.context.timer.stop('W')
if self.context.comm.rank == 0:
for key, sigmas in self.qcache.items():
sigmas = {fxc_mode: Sigma.fromdict(sigma)
for fxc_mode, sigma in sigmas.items()}
for fxc_mode, sigma in sigmas.items():
sigma.validate_inputs(self.get_validation_inputs())
self.context.comm.barrier()
for iq, q_c in enumerate(self.wcalc.qd.ibzk_kc):
with ExitStack() as stack:
if self.context.comm.rank == 0:
qhandle = stack.enter_context(self.qcache.lock(str(iq)))
skip = qhandle is None
else:
skip = False
skip = broadcast(skip, comm=self.context.comm)
if skip:
continue
result = self.calculate_q_point(iq, q_c, pb, chi0calc)
if self.context.comm.rank == 0:
qhandle.save(result)
pb.finish()
def calculate_q_point(self, iq, q_c, pb, chi0calc):
# Reset calculation
sigmashape = (len(self.ecut_e), *self.shape)
sigmas = {fxc_mode: Sigma(iq, q_c, fxc_mode, sigmashape,
**self.get_validation_inputs())
for fxc_mode in self.fxc_modes}
chi0 = chi0calc.create_chi0(q_c)
m1 = chi0calc.gs.nocc1
for ie, ecut in enumerate(self.ecut_e):
self.context.timer.start('W')
# First time calculation
if ecut == chi0.qpd.ecut:
# Nothing to cut away:
m2 = self.nbands
else:
m2 = int(self.wcalc.gs.volume * ecut**1.5
* 2**0.5 / 3 / pi**2)
if m2 > self.nbands:
raise ValueError(f'Trying to extrapolate ecut to'
f'larger number of bands ({m2})'
f' than there are bands '
f'({self.nbands}).')
qpdi, Wdict, blocks1d, pawcorr = self.calculate_w(
chi0calc, q_c, chi0,
m1, m2, ecut, iq)
m1 = m2
self.context.timer.stop('W')
for nQ, (bzq_c, symop) in enumerate(QSymmetryOp.get_symops(
self.wcalc.qd, iq, q_c)):
for (progress, kpt1, kpt2)\
in self.pair_distribution.kpt_pairs_by_q(bzq_c, 0, m2):
pb.update((nQ + progress) / self.wcalc.qd.mynk)
k1 = self.wcalc.gs.kd.bz2ibz_k[kpt1.K]
i = self.kpts.index(k1)
self.calculate_q(ie, i, kpt1, kpt2, qpdi, Wdict,
symop=symop,
sigmas=sigmas,
blocks1d=blocks1d,
pawcorr=pawcorr)
for sigma in sigmas.values():
sigma.sum(self.context.comm)
return sigmas
def get_validation_inputs(self):
return {'kpts': self.kpts,
'bands': list(self.bands),
'nbands': self.nbands,
'ecut_e': list(self.ecut_e),
'frequencies': self.frequencies,
'fxc_modes': self.fxc_modes,
'integrate_gamma': self.wcalc.integrate_gamma}
@timer('calculate_w')
def calculate_w(self, chi0calc, q_c, chi0,
m1, m2, ecut,
iq):
"""Calculates the screened potential for a specified q-point."""
chi0calc.chi0_body_calc.print_info(chi0.qpd)
chi0calc.update_chi0(chi0, m1, m2, range(self.wcalc.gs.nspins))
Wdict = {}
for fxc_mode in self.fxc_modes:
rqpd = chi0.qpd.copy_with(ecut=ecut) # reduced qpd
rchi0 = chi0.copy_with_reduced_pd(rqpd)
Wdict[fxc_mode] = self.wcalc.get_HW_model(rchi0,
fxc_mode=fxc_mode)
if (chi0calc.chi0_body_calc.pawcorr is not None and
rqpd.ecut < chi0.qpd.ecut):
assert not self.ppa, """In previous master, PPA with ecut
extrapolation was not working. Now it would work, but
disabling it here still for sake of it is not tested."""
pw_map = PWMapping(rqpd, chi0.qpd)
# This is extremely bad behaviour! G0W0Calculator
# should not change properties on the
# Chi0BodyCalculator! Change in the future! XXX
chi0calc.chi0_body_calc.pawcorr = \
chi0calc.chi0_body_calc.pawcorr.reduce_ecut(pw_map.G2_G1)
# Create a blocks1d for the reduced plane-wave description
blocks1d = Blocks1D(chi0.body.blockdist.blockcomm, rqpd.ngmax)
return rqpd, Wdict, blocks1d, chi0calc.chi0_body_calc.pawcorr
@timer('calcualte_vxc_and_exx')
def calculate_vxc_and_exx(self):
return self.exx_vxc_calculator.calculate(
n1=self.bands[0], n2=self.bands[1],
kpt_indices=self.kpts)
def print_results(self, results):
description = ['f: Occupation numbers',
'eps: KS-eigenvalues [eV]',
'vxc: KS vxc [eV]',
'exx: Exact exchange [eV]',
'sigma: Self-energies [eV]',
'dsigma: Self-energy derivatives',
'Z: Renormalization factors',
'qp: QP-energies [eV]']
self.context.print('\nResults:')
for line in description:
self.context.print(line)
b1, b2 = self.bands
names = [line.split(':', 1)[0] for line in description]
ibzk_kc = self.wcalc.gs.kd.ibzk_kc
for s in range(self.wcalc.gs.nspins):
for i, ik in enumerate(self.kpts):
self.context.print(
'\nk-point ' + '{} ({}): ({:.3f}, {:.3f}, '
'{:.3f})'.format(i, ik, *ibzk_kc[ik]) +
' ' + self.fxc_modes[0])
self.context.print('band' + ''.join(f'{name:>8}'
for name in names))
def actually_print_results(resultset):
for n in range(b2 - b1):
self.context.print(
f'{n + b1:4}' +
''.join('{:8.3f}'.format(
resultset[name][s, i, n]) for name in names))
for fxc_mode in results:
self.context.print(fxc_mode.rjust(69))
actually_print_results(results[fxc_mode])
self.context.write_timer()
def calculate_g0w0_outputs(self, sigma):
eps_skn, f_skn = self.get_eps_and_occs()
vxc_skn, exx_skn = self.calculate_vxc_and_exx()
kwargs = dict(
context=self.context,
shape=self.shape,
ecut_e=self.ecut_e,
eps_skn=eps_skn,
vxc_skn=vxc_skn,
exx_skn=exx_skn,
f_skn=f_skn)
return G0W0Outputs(sigma_eskn=sigma.sigma_eskn,
dsigma_eskn=sigma.dsigma_eskn,
**kwargs)
def choose_bands(bands, relbands, nvalence, nocc):
if bands is not None and relbands is not None:
raise ValueError('Use bands or relbands!')
if relbands is not None:
bands = [nvalence // 2 + b for b in relbands]
if bands is None:
bands = [0, nocc]
return bands
[docs]class G0W0(G0W0Calculator):
def __init__(self, calc, filename='gw',
ecut=150.0,
ecut_extrapolation=False,
xc='RPA',
ppa=False,
E0=Ha,
eta=0.1,
nbands=None,
bands=None,
relbands=None,
frequencies=None,
domega0=None, # deprecated
omega2=None, # deprecated
nblocks=1,
nblocksmax=False,
kpts=None,
world=mpi.world,
timer=None,
fxc_mode='GW',
truncation=None,
integrate_gamma=0,
q0_correction=False,
do_GW_too=False,
**kwargs):
"""G0W0 calculator wrapper.
The G0W0 calculator is used to calculate the quasi
particle energies through the G0W0 approximation for a number
of states.
Parameters
----------
calc:
Filename of saved calculator object.
filename: str
Base filename of output files.
kpts: list
List of indices of the IBZ k-points to calculate the quasi particle
energies for.
bands:
Range of band indices, like (n1, n2), to calculate the quasi
particle energies for. Bands n where n1<=n<n2 will be
calculated. Note that the second band index is not included.
relbands:
Same as *bands* except that the numbers are relative to the
number of occupied bands.
E.g. (-1, 1) will use HOMO+LUMO.
frequencies:
Input parameters for the nonlinear frequency descriptor.
ecut: float
Plane wave cut-off energy in eV.
ecut_extrapolation: bool or list
If set to True an automatic extrapolation of the selfenergy to
infinite cutoff will be performed based on three points
for the cutoff energy.
If an array is given, the extrapolation will be performed based on
the cutoff energies given in the array.
nbands: int
Number of bands to use in the calculation. If None, the number will
be determined from :ecut: to yield a number close to the number of
plane waves used.
ppa: bool
Sets whether the Godby-Needs plasmon-pole approximation for the
dielectric function should be used.
xc: str
Kernel to use when including vertex corrections.
fxc_mode: str
Where to include the vertex corrections; polarizability and/or
self-energy. 'GWP': Polarizability only, 'GWS': Self-energy only,
'GWG': Both.
do_GW_too: bool
When carrying out a calculation including vertex corrections, it
is possible to get the standard GW results at the same time
(almost for free).
truncation: str
Coulomb truncation scheme. Can be either 2D, 1D, or 0D.
integrate_gamma: int
Method to integrate the Coulomb interaction. 1 is a numerical
integration at all q-points with G=[0,0,0] - this breaks the
symmetry slightly. 0 is analytical integration at q=[0,0,0] only -
this conserves the symmetry. integrate_gamma=2 is the same as 1,
but the average is only carried out in the non-periodic directions.
E0: float
Energy (in eV) used for fitting in the plasmon-pole approximation.
q0_correction: bool
Analytic correction to the q=0 contribution applicable to 2D
systems.
nblocks: int
Number of blocks chi0 should be distributed in so each core
does not have to store the entire matrix. This is to reduce
memory requirement. nblocks must be less than or equal to the
number of processors.
nblocksmax: bool
Cuts chi0 into as many blocks as possible to reduce memory
requirements as much as possible.
"""
# We pass a serial communicator because the parallel handling
# is somewhat wonky, we'd rather do that ourselves:
try:
qcache = FileCache(f'qcache_{filename}',
comm=mpi.SerialCommunicator())
except TypeError as err:
raise RuntimeError(
'File cache requires ASE master '
'from September 20 2022 or newer. '
'You may need to pull newest ASE.') from err
if world.rank == 0:
qcache.strip_empties()
mode = 'a' if qcache.filecount() > 1 else 'w'
# (calc can not actually be a calculator at all.)
gpwfile = Path(calc)
context = ResponseContext(txt=filename + '.txt',
comm=world, timer=timer)
gs = ResponseGroundStateAdapter.from_gpw_file(gpwfile)
# Check if nblocks is compatible, adjust if not
if nblocksmax:
nblocks = get_max_nblocks(context.comm, gpwfile, ecut)
kpts = list(select_kpts(kpts, gs.kd))
ecut, ecut_e = choose_ecut_things(ecut, ecut_extrapolation)
if nbands is None:
nbands = int(gs.volume * (ecut / Ha)**1.5 * 2**0.5 / 3 / pi**2)
else:
if ecut_extrapolation:
raise RuntimeError(
'nbands cannot be supplied with ecut-extrapolation.')
if ppa:
# use small imaginary frequency to avoid dividing by zero:
frequencies = [1e-10j, 1j * E0]
parameters = {'eta': 0,
'hilbert': False,
'timeordered': False}
else:
# use nonlinear frequency grid
frequencies = get_frequencies(frequencies, domega0, omega2)
parameters = {'eta': eta,
'hilbert': True,
'timeordered': True}
wd = get_frequency_descriptor(frequencies, gs=gs, nbands=nbands)
wcontext = context.with_txt(filename + '.w.txt', mode=mode)
chi0calc = Chi0Calculator(
gs, wcontext, nblocks=nblocks,
wd=wd,
nbands=nbands,
ecut=ecut,
intraband=False,
**parameters)
bands = choose_bands(bands, relbands, gs.nvalence, chi0calc.gs.nocc2)
coulomb = CoulombKernel.from_gs(gs, truncation=truncation)
# XXX eta needs to be converted to Hartree here,
# XXX and it is also converted to Hartree at superclass constructor
# XXX called below. This needs to be cleaned up.
wcalc = initialize_w_calculator(chi0calc, wcontext,
ppa=ppa,
xc=xc,
E0=E0, eta=eta / Ha, coulomb=coulomb,
integrate_gamma=integrate_gamma,
q0_correction=q0_correction)
fxc_modes = [fxc_mode]
if do_GW_too:
fxc_modes.append('GW')
exx_vxc_calculator = EXXVXCCalculator(
gpwfile,
snapshotfile_prefix=filename)
super().__init__(filename=filename,
wd=wd,
chi0calc=chi0calc,
wcalc=wcalc,
ecut_e=ecut_e,
eta=eta,
fxc_modes=fxc_modes,
nbands=nbands,
bands=bands,
frequencies=frequencies,
kpts=kpts,
exx_vxc_calculator=exx_vxc_calculator,
qcache=qcache,
ppa=ppa,
**kwargs)
@property
def results_GW(self):
# Compatibility with old "do_GW_too" behaviour
if 'GW' in self.fxc_modes and self.fxc_modes[0] != 'GW':
return self.all_results['GW']
@property
def results(self):
return self.all_results[self.fxc_modes[0]]
class EXXVXCCalculator:
"""EXX and Kohn-Sham XC contribution."""
def __init__(self, gpwfile, snapshotfile_prefix):
self._gpwfile = gpwfile
self._snapshotfile_prefix = snapshotfile_prefix
def calculate(self, n1, n2, kpt_indices):
_, vxc_skn, exx_skn = non_self_consistent_eigenvalues(
self._gpwfile,
'EXX',
n1, n2,
kpt_indices=kpt_indices,
snapshot=f'{self._snapshotfile_prefix}-vxc-exx.json',
)
return vxc_skn / Ha, exx_skn / Ha