def set_folding(self, folding, width):
BaseInducedField.set_folding(self, folding, width)
if self.folding is None:
self.folder = Folder(None, None)
else:
if self.folding == 'Gauss':
self.folder = Folder(self.width, 'ComplexGauss')
elif self.folding == 'Lorentz':
self.folder = Folder(self.width, 'ComplexLorentz')
else:
raise RuntimeError('unknown folding "' + self.folding + '"')
def rotatory_spectrum(exlist=None,
filename=None,
emin=None,
emax=None,
de=None,
energyunit='eV',
folding='Gauss',
width=0.08, # Gauss/Lorentz width
comment=None
):
"""Write out a folded rotatory spectrum.
See spectrum() for explanation of the parameters.
"""
# output
out = sys.stdout
if filename is not None:
out = open(filename, 'w')
if comment:
print('#', comment, file=out)
print('# Rotatory spectrum from linear response TD-DFT', file=out)
print('# GPAW version:', version, file=out)
if folding is not None: # fold the spectrum
print('# %s folded, width=%g [%s]' % (folding, width,
energyunit), file=out)
print('# om [%s] R [cgs]'
% energyunit, file=out)
x = []
y = []
for ex in exlist:
x.append(ex.get_energy() * Hartree)
y.append(ex.get_rotatory_strength())
if energyunit == 'nm':
# transform to experimentally used wavelength [nm]
x = 1.e+9 * 2 * np.pi * _hbar * _c / _e / np.array(x)
y = np.array(y)
elif energyunit != 'eV':
raise RuntimeError('currently only eV and nm are supported')
energies, values = Folder(width, folding).fold(x, y, de, emin, emax)
for e, val in zip(energies, values):
print('%10.5f %12.7e' %
(e, val), file=out)
if filename is not None:
out.close()
def get_folded_spectrum(
exlist=None,
emin=None,
emax=None,
de=None,
energyunit='eV',
folding='Gauss',
width=0.08, # Gauss/Lorentz width
form='r'):
"""Return folded spectrum."""
x = []
y = []
for ex in exlist:
x.append(ex.get_energy() * Hartree)
y.append(ex.get_oscillator_strength(form))
if energyunit == 'nm':
# transform to experimentally used wavelength [nm]
x = 1.e+9 * 2 * np.pi * _hbar * _c / _e / np.array(x)
elif energyunit != 'eV':
raise RuntimeError('currently only eV and nm are supported')
return Folder(width, folding).fold(x, y, de, emin, emax)
from gpaw.test import equal
from gpaw.utilities.folder import Folder, Lorentz, Voigt # noqa
# Gauss and Lorentz functions
width = 0.5
x = 1.5
equal(Gauss(width).get(x),
exp(- x**2 / 2 / width**2) / sqrt(2 * pi) / width,
1.e-15)
equal(Gauss(width).fwhm, width * np.sqrt(8 * np.log(2)), 1.e-15)
equal(Lorentz(width).get(x),
width / (x**2 + width**2) / pi,
1.e-15)
equal(Lorentz(width).fwhm, width * 2, 1.e-15)
# folder function
for func in [Gauss, Lorentz, Voigt]:
folder = Folder(width, func(width).__class__.__name__)
x = [0, 2]
y = [[2, 0, 1], [1, 1, 1]]
xl, yl = folder.fold(x, y, dx=.7)
# check first value
yy = np.dot(np.array(y)[:, 0], func(width).get(xl[0] - np.array(x)))
equal(yl[0, 0], yy, 1.e-15)
def spectrum(
exlist=None,
filename=None,
emin=None,
emax=None,
de=None,
energyunit='eV',
folding='Gauss',
width=0.08, # Gauss/Lorentz width
comment=None):
"""Write out a folded spectrum.
Parameters:
=============== ===================================================
``exlist`` ExcitationList
``filename`` File name for the output file, STDOUT if not given
``emin`` min. energy, set to cover all energies if not given
``emax`` max. energy, set to cover all energies if not given
``de`` energy spacing
``energyunit`` Energy unit 'eV' or 'nm', default 'eV'
``folding`` Gauss (default) or Lorentz
``width`` folding width in terms of the chosen energyunit
=============== ===================================================
all energies in [eV]
"""
# output
out = sys.stdout
if filename != None:
out = open(filename, 'w')
if comment:
print >> out, '#', comment
print >> out, '# Photoabsorption spectrum from linear response TD-DFT'
print >> out, '# GPAW version:', version
if folding is not None: # fold the spectrum
print >> out, '# %s folded, width=%g [%s]' % (folding, width,
energyunit)
print >> out,\
'# om [%s] osz osz x osz y osz z'\
% energyunit
x = []
y = []
for ex in exlist:
x.append(ex.get_energy() * Hartree)
y.append(ex.get_oscillator_strength())
if energyunit == 'nm':
# transform to experimentally used wavelength [nm]
x = 1.e+9 * 2 * np.pi * _hbar * _c / _e / np.array(x)
y = np.array(y)
elif energyunit != 'eV':
raise RuntimeError('currently only eV and nm are supported')
energies, values = Folder(width, folding).fold(x, y, de, emin, emax)
for e, val in zip(energies, values):
print >> out, "%10.5f %12.7e %12.7e %11.7e %11.7e" % \
(e,val[0],val[1],val[2],val[3])
if filename != None: out.close()
# Gauss and Lorentz functions
width = 0.5
x = 1.5
equal(Gauss(width).get(x),
exp(- x**2 / 2 / width**2) / sqrt(2 * pi) / width,
1.e-15)
equal(Lorentz(width).get(x),
width / (x**2 + width**2) / pi,
1.e-15)
# folder function
for name in ['Gauss', 'Lorentz']:
folder = Folder(width, name)
x = [0, 2]
y = [[2, 0, 1], [1, 1, 1]]
xl, yl = folder.fold(x, y, dx=.7)
# check first value
if name == 'Lorentz':
func = Lorentz(width)
else:
func = Gauss(width)
yy = np.dot(np.array(y)[:, 0], func.get(xl[0] - np.array(x)))
equal(yl[0, 0], yy, 1.e-15)
# write spectrum
plt.axis([-1000, 6000, 0, 1.05])
plt.ylabel('HR factors [a.u.]')
plt.xlabel('frequency [cm-1]')
plt.show()
#Plot Franck-Condon factors
FC, f = a.get_Franck_Condon_factors(n, T, F)
for l in range(len(FC)):
plt.vlines(f[l], 0, FC[l], color=colors[l], label=labels[l], linewidth=2.0)
#Fold the spectrum with a gaussian function
width = 300
folding = 'Gauss'
x = [j for j in chain(*f)]
y = [j for j in chain(*FC)]
X, Y = Folder(width, folding).fold(x, y)
plt.plot(X,
Y * 750,
color='black',
linewidth=2.0,
label='Temperature=' + str(T) + 'K, #quanta=' + str(n) +
', width of gaussian=' + str(width) + 'cm^-1',
linestyle='dashed')
plt.legend(loc='upper right')
plt.axis([-1000, 6000, 0, 0.6])
plt.ylabel('FC factors [a.u.]')
plt.xlabel('frequency [cm-1]')
plt.show()
def dielectric(
exlist,
volume,
filename=None,
emin=None,
emax=None,
de=None,
energyunit='eV',
width=0.08, # width in energyunit
comment=None,
form='v'):
"""Write out the dielectric function
Parameters:
=============== ===================================================
``exlist`` ExcitationList
``volume`` Unit cell volume in Angstrom**3
``filename`` File name for the output file, STDOUT if not given
``emin`` min. energy, set to cover all energies if not given
``emax`` max. energy, set to cover all energies if not given
``de`` energy spacing
``energyunit`` Energy unit 'eV' or 'nm', default 'eV'
``width`` folding width in terms of the chosen energyunit
=============== ===================================================
all energies in [eV]
"""
# output
out = sys.stdout
if filename is not None:
out = open(filename, 'w')
if comment:
print('#', comment, file=out)
print('# Dielec function', file=out)
print('# GPAW version:', gpaw.__version__, file=out)
print('# width={0} [{1}]'.format(width, energyunit), file=out)
if form == 'r':
print('# length form', file=out)
else:
assert (form == 'v')
print('# velocity form', file=out)
print(
'# om [{0}] eps1/eps0 eps2/eps0 n k R'.format(
energyunit),
file=out)
x = []
y = []
for ex in exlist:
x.append(ex.get_energy() * Hartree)
y.append(ex.get_oscillator_strength(form))
if energyunit != 'eV':
raise RuntimeError('currently only eV is supported')
pre = 4. * np.pi / volume * Bohr**3 * Hartree**2
energies, values = Folder(width,
'RealLorentzPole').fold(x, y, de, emin, emax)
eps1 = 1 + pre * values.T[0]
energies, values = Folder(width, 'ImaginaryLorentzPole').fold(
x, y, de, emin, emax)
eps2 = pre * values.T[0]
N = np.sqrt(0.5 * (np.sqrt(eps1**2 + eps2**2) + eps1))
K = np.sqrt(0.5 * (np.sqrt(eps1**2 + eps2**2) - eps1))
R = ((N - 1)**2 + K**2) / ((N + 1)**2 + K**2)
for e, e1, e2, n, k, r in zip(energies, eps1, eps2, N, K, R):
print('%10.5f %12.7e %12.7e %12.7e %12.7e %12.7e' %
(e, e1, e2, n, k, r),
file=out)
if filename is not None:
out.close()
