import re
import numpy as np
from gpaw import __version__ as version
from gpaw.mpi import world
from gpaw.tddft.units import au_to_as, au_to_fs, au_to_eV, rot_au_to_cgs
from gpaw.tddft.folding import FoldedFrequencies
from gpaw.tddft.folding import Folding
def calculate_fourier_transform(x_t, y_ti, foldedfrequencies):
ff = foldedfrequencies
X_w = ff.frequencies
envelope = ff.folding.envelope
# Construct integration weights:
# We use trapezoidal rule except the end point is accounted with
# full weight. This ensures better numerical compatibility
# with the on-the-fly Fourier integrators.
# This shouldn't affect in usual scenarios as the envelope
# should damp the data to zero at the end point in any case.
dx_t1 = x_t[1:] - x_t[:-1]
dx_t = 0.5 * (np.insert(dx_t1, 0, 0.0) + np.append(dx_t1, dx_t1[-1]))
# Integrate
f_wt = np.exp(1.0j * np.outer(X_w, x_t))
y_it = np.swapaxes(y_ti, 0, 1)
Y_wi = np.tensordot(f_wt, dx_t * envelope(x_t) * y_it, axes=(1, 1))
return Y_wi
def read_td_file_data(fname, remove_duplicates=True):
"""Read data from time-dependent data file.
Parameters
----------
fname
File path
remove_duplicates
If true, remove data from overlapping time values.
The first encountered values are kept.
Returns
-------
time_t
Array of time values
data_ti
Array of data values
"""
# Read data
data_tj = np.loadtxt(fname)
time_t = data_tj[:, 0]
data_ti = data_tj[:, 1:]
# Remove duplicates due to abruptly stopped and restarted calculation
if remove_duplicates:
flt_t = np.ones_like(time_t, dtype=bool)
maxtime = time_t[0]
for t in range(1, len(time_t)):
# Note about ">=" here:
# The equality is included here in order to
# retain step-like data (for example, the data both just before
# and just after the kick is kept).
if time_t[t] >= maxtime:
maxtime = time_t[t]
else:
flt_t[t] = False
time_t = time_t[flt_t]
data_ti = data_ti[flt_t]
ndup = len(flt_t) - flt_t.sum()
if ndup > 0:
print('Removed %d duplicates' % ndup)
return time_t, data_ti
def read_td_file_kicks(fname):
"""Read kicks from time-dependent data file.
Parameters
----------
fname
File path
Returns
-------
kick_i
List of kicks.
Each kick is a dictionary with keys
``strength_v`` and ``time``.
"""
def parse_kick_line(line):
# Kick
regexp = (r"Kick = \["
r"(?P<k0>[-+0-9\.e\ ]+), "
r"(?P<k1>[-+0-9\.e\ ]+), "
r"(?P<k2>[-+0-9\.e\ ]+)\]")
m = re.search(regexp, line)
assert m is not None, 'Kick not found'
kick_v = np.array([float(m.group('k%d' % v)) for v in range(3)])
# Time
regexp = r"Time = (?P<time>[-+0-9\.e\ ]+)"
m = re.search(regexp, line)
if m is None:
print('time not found')
time = 0.0
else:
time = float(m.group('time'))
return kick_v, time
# Search kicks
kick_i = []
with open(fname) as f:
for line in f:
if line.startswith('# Kick'):
kick_v, time = parse_kick_line(line)
kick_i.append({'strength_v': kick_v, 'time': time})
return kick_i
def clean_td_data(kick_i, time_t, data_ti):
"""Prune time-dependent data.
This function checks that there is only one kick
in the kick list and moves time zero to the kick
time (discarding all preceding data).
Parameters
----------
kick_i
List of kicks.
time_t
Array of time values
data_ti
Array of data values
Returns
-------
kick_i
List of kicks.
Each kick is a dictionary with keys
``strength_v`` and ``time``.
Raises
------
RuntimeError
If kick list contains multiple kicks.
"""
# Check kicks
if len(kick_i) > 1:
raise RuntimeError('Multiple kicks')
kick = kick_i[0]
kick_v = kick['strength_v']
kick_time = kick['time']
# Discard times before kick
flt_t = time_t >= kick_time
time_t = time_t[flt_t]
data_ti = data_ti[flt_t]
# Move time zero to kick time
time_t -= kick_time
assert time_t[0] == 0.0
return kick_v, time_t, data_ti
def read_dipole_moment_file(fname, remove_duplicates=True):
"""Read time-dependent dipole moment data file.
Parameters
----------
fname
File path
remove_duplicates
If true, remove data from overlapping time values.
The first encountered values are kept.
Returns
-------
kick_i
List of kicks.
Each kick is a dictionary with keys
``strength_v`` and ``time``.
time_t
Array of time values
norm_t
Array of norm values
dm_tv
Array of dipole moment values
"""
time_t, data_ti = read_td_file_data(fname, remove_duplicates)
kick_i = read_td_file_kicks(fname)
norm_t = data_ti[:, 0]
dm_tv = data_ti[:, 1:]
return kick_i, time_t, norm_t, dm_tv
def calculate_polarizability(kick_v, time_t, dm_tv, foldedfrequencies):
dm_tv = dm_tv - dm_tv[0]
alpha_wv = calculate_fourier_transform(time_t, dm_tv, foldedfrequencies)
kick_magnitude = np.sqrt(np.sum(kick_v**2))
alpha_wv /= kick_magnitude
return alpha_wv
def calculate_photoabsorption(kick_v, time_t, dm_tv, foldedfrequencies):
omega_w = foldedfrequencies.frequencies
alpha_wv = calculate_polarizability(kick_v, time_t, dm_tv,
foldedfrequencies)
abs_wv = 2 / np.pi * omega_w[:, np.newaxis] * alpha_wv.imag
kick_magnitude = np.sqrt(np.sum(kick_v**2))
abs_wv *= kick_v / kick_magnitude
return abs_wv
def read_magnetic_moment_file(fname, remove_duplicates=True):
"""Read time-dependent magnetic moment data file.
Parameters
----------
fname
File path
remove_duplicates
If true, remove data from overlapping time values.
The first encountered values are kept.
Returns
-------
kick_i
List of kicks.
Each kick is a dictionary with keys
``strength_v`` and ``time``.
time_t
Array of time values
mm_tv
Array of magnetic moment values
"""
time_t, mm_tv = read_td_file_data(fname, remove_duplicates)
kick_i = read_td_file_kicks(fname)
return kick_i, time_t, mm_tv
def calculate_rotatory_strength_components(kick_v, time_t, mm_tv,
foldedfrequencies):
assert np.all(mm_tv[0] == 0.0)
mm_wv = calculate_fourier_transform(time_t, mm_tv, foldedfrequencies)
kick_magnitude = np.sqrt(np.sum(kick_v**2))
rot_wv = mm_wv.real / (np.pi * kick_magnitude)
return rot_wv
def write_spectrum(dipole_moment_file, spectrum_file,
folding, width, e_min, e_max, delta_e,
title, symbol, calculate):
def str_list(v_i, fmt='%g'):
return '[%s]' % ', '.join(map(lambda v: fmt % v, v_i))
kick_i, time_t, _, dm_tv = read_dipole_moment_file(dipole_moment_file)
kick_v, time_t, dm_tv = clean_td_data(kick_i, time_t, dm_tv)
dt_t = time_t[1:] - time_t[:-1]
freqs = np.arange(e_min, e_max + 0.5 * delta_e, delta_e)
folding = Folding(folding, width)
ff = FoldedFrequencies(freqs, folding)
omega_w = ff.frequencies
spec_wv = calculate(kick_v, time_t, dm_tv, ff)
# Write spectrum file header
with open(spectrum_file, 'w') as f:
def w(s):
f.write('%s\n' % s)
w('# %s spectrum from real-time propagation' % title)
w('# GPAW version: %s' % version)
w('# Total time = %.4f fs, Time steps = %s as' %
(dt_t.sum() * au_to_fs,
str_list(np.unique(np.around(dt_t, 6)) * au_to_as, '%.4f')))
w('# Kick = %s' % str_list(kick_v))
w('# %sian folding, Width = %.4f eV = %lf Hartree'
' <=> FWHM = %lf eV' %
(folding.folding, folding.width * au_to_eV, folding.width,
folding.fwhm * au_to_eV))
col_i = []
data_iw = [omega_w * au_to_eV]
for v in range(len(kick_v)):
h = '{}_{}'.format(symbol, 'xyz'[v])
if spec_wv.dtype == complex:
col_i.append('Re[%s]' % h)
data_iw.append(spec_wv[:, v].real)
col_i.append('Im[%s]' % h)
data_iw.append(spec_wv[:, v].imag)
else:
col_i.append(h)
data_iw.append(spec_wv[:, v])
w('# %10s %s' % ('om (eV)', ' '.join(['%20s' % s for s in col_i])))
# Write spectrum file data
with open(spectrum_file, 'ab') as f:
np.savetxt(f, np.array(data_iw).T,
fmt='%12.6lf' + (' %20.10le' * len(col_i)))
return folding.envelope(time_t[-1])
[docs]def photoabsorption_spectrum(dipole_moment_file: str,
spectrum_file: str,
folding: str = 'Gauss',
width: float = 0.2123,
e_min: float = 0.0,
e_max: float = 30.0,
delta_e: float = 0.05):
"""Calculates photoabsorption spectrum from the time-dependent
dipole moment.
The spectrum is represented as a dipole strength function
in units of 1/eV. Thus, the resulting spectrum should integrate
to the number of valence electrons in the system.
Parameters
----------
dipole_moment_file
Name of the time-dependent dipole moment file from which
the spectrum is calculated
spectrum_file
Name of the spectrum file
folding
Gaussian (``'Gauss'``) or Lorentzian (``'Lorentz'``) folding
width
Width of the Gaussian (sigma) or Lorentzian (Gamma)
Gaussian = 1/(sigma sqrt(2pi)) exp(-(1/2)(omega/sigma)^2)
Lorentzian = (1/pi) (1/2) Gamma / [omega^2 + ((1/2) Gamma)^2]
e_min
Minimum energy shown in the spectrum (eV)
e_max
Maximum energy shown in the spectrum (eV)
delta_e
Energy resolution (eV)
"""
if world.rank == 0:
print('Calculating photoabsorption spectrum from file "%s"'
% dipole_moment_file)
def calculate(*args):
return calculate_photoabsorption(*args) / au_to_eV
sinc = write_spectrum(dipole_moment_file, spectrum_file,
folding, width, e_min, e_max, delta_e,
'Photoabsorption', 'S', calculate)
print('Sinc contamination %.8f' % sinc)
print('Calculated photoabsorption spectrum saved to file "%s"'
% spectrum_file)
def polarizability_spectrum(dipole_moment_file, spectrum_file,
folding='Gauss', width=0.2123,
e_min=0.0, e_max=30.0, delta_e=0.05):
"""Calculates polarizability spectrum from the time-dependent
dipole moment.
Parameters:
dipole_moment_file: string
Name of the time-dependent dipole moment file from which
the spectrum is calculated
spectrum_file: string
Name of the spectrum file
folding: 'Gauss' or 'Lorentz'
Whether to use Gaussian or Lorentzian folding
width: float
Width of the Gaussian (sigma) or Lorentzian (Gamma)
Gaussian = 1/(sigma sqrt(2pi)) exp(-(1/2)(omega/sigma)^2)
Lorentzian = (1/pi) (1/2) Gamma / [omega^2 + ((1/2) Gamma)^2]
e_min: float
Minimum energy shown in the spectrum (eV)
e_max: float
Maximum energy shown in the spectrum (eV)
delta_e: float
Energy resolution (eV)
"""
if world.rank == 0:
print('Calculating polarizability spectrum from file "%s"'
% dipole_moment_file)
def calculate(*args):
return calculate_polarizability(*args) / au_to_eV**2
sinc = write_spectrum(dipole_moment_file, spectrum_file,
folding, width, e_min, e_max, delta_e,
'Polarizability', 'alpha', calculate)
print('Sinc contamination %.8f' % sinc)
print('Calculated polarizability spectrum saved to file "%s"'
% spectrum_file)
def rotatory_strength_spectrum(magnetic_moment_files, spectrum_file,
folding='Gauss', width=0.2123,
e_min=0.0, e_max=30.0, delta_e=0.05):
"""Calculates rotatory strength spectrum from the time-dependent
magnetic moment.
Parameters
----------
magnetic_moment_files: list of string
Time-dependent magnetic moment files for x, y, and z kicks
spectrum_file: string
Name of the spectrum file
folding: 'Gauss' or 'Lorentz'
Whether to use Gaussian or Lorentzian folding
width: float
Width of the Gaussian (sigma) or Lorentzian (Gamma)
Gaussian = 1/(sigma sqrt(2pi)) exp(-(1/2)(omega/sigma)^2)
Lorentzian = (1/pi) (1/2) Gamma / [omega^2 + ((1/2) Gamma)^2]
e_min: float
Minimum energy shown in the spectrum (eV)
e_max: float
Maximum energy shown in the spectrum (eV)
delta_e: float
Energy resolution (eV)
"""
if world.rank != 0:
return
freqs = np.arange(e_min, e_max + 0.5 * delta_e, delta_e)
folding = Folding(folding, width)
ff = FoldedFrequencies(freqs, folding)
omega_w = ff.frequencies * au_to_eV
rot_w = np.zeros_like(omega_w)
tot_time = np.inf
time_steps = []
kick_strength = None
for v, fpath in enumerate(magnetic_moment_files):
kick_i, time_t, mm_tv = read_magnetic_moment_file(fpath)
kick_v, time_t, mm_tv = clean_td_data(kick_i, time_t, mm_tv)
tot_time = min(tot_time, time_t[-1])
time_steps.append(np.around(time_t[1:] - time_t[:-1], 6))
# Check kicks
for v0 in range(3):
if v0 == v:
continue
if kick_v[v0] != 0.0:
raise RuntimeError('The magnetic moment files must be '
'for kicks in x, y, and z directions.')
if kick_strength is None:
kick_strength = np.sqrt(np.sum(kick_v**2))
if np.sqrt(np.sum(kick_v**2)) != kick_strength:
raise RuntimeError('The magnetic moment files must have '
'been calculated with the same kick strength.')
rot_wv = calculate_rotatory_strength_components(kick_v, time_t,
mm_tv, ff)
rot_w += rot_wv[:, v]
rot_w *= rot_au_to_cgs * 1e40 / au_to_eV
# Unique non-zero time steps
time_steps = np.unique(time_steps)
time_steps = time_steps[time_steps != 0]
with open(spectrum_file, 'w') as fd:
steps_str = ', '.join(f'{val:.4f}' for val in time_steps * au_to_as)
lines = ['Rotatory strength spectrum from real-time propagations',
f'Total time = {tot_time * au_to_fs:.4f} fs, '
f'Time steps = [{steps_str}] as',
f'Kick strength = {kick_strength}',
f'{folding.folding}ian folding, '
f'width = {folding.width * au_to_eV:.4f} eV '
f'<=> FWHM = {folding.fwhm * au_to_eV:.4f} eV']
fd.write('# ' + '\n# '.join(lines) + '\n')
fd.write(f'# {"Energy (eV)":>12} {"R (1e-40 cgs / eV)":>20}\n')
data_wi = np.vstack((omega_w, rot_w)).T
np.savetxt(fd, data_wi,
fmt='%14.6lf' + (' %20.10le' * (data_wi.shape[1] - 1)))