def test_franck_condon(testdir):
# FCOverlap
fco = FranckCondonOverlap()
fcr = FranckCondonRecursive()
# check factorial
assert (fco.factorial(8) == factorial(8))
# the second test is useful according to the implementation
assert (fco.factorial(5) == factorial(5))
assert (fco.factorial.inv(5) == 1. / factorial(5))
# check T=0 and n=0 equality
S = np.array([1, 2.1, 34])
m = 5
assert (((fco.directT0(m, S) - fco.direct(0, m, S)) / fco.directT0(m, S) <
1e-15).all())
# check symmetry
S = 2
n = 3
assert (fco.direct(n, m, S) == fco.direct(m, n, S))
# ---------------------------
# specials
S = np.array([0, 1.5])
delta = np.sqrt(2 * S)
for m in [2, 7]:
equal(
fco.direct0mm1(m, S)**2,
fco.direct(1, m, S) * fco.direct(m, 0, S), 1.e-17)
equal(fco.direct0mm1(m, S), fcr.ov0mm1(m, delta), 1.e-15)
equal(fcr.ov0mm1(m, delta),
fcr.ov0m(m, delta) * fcr.ov1m(m, delta), 1.e-15)
equal(fcr.ov0mm1(m, -delta), fcr.direct0mm1(m, -delta), 1.e-15)
equal(fcr.ov0mm1(m, delta), -fcr.direct0mm1(m, -delta), 1.e-15)
equal(
fco.direct0mm2(m, S)**2,
fco.direct(2, m, S) * fco.direct(m, 0, S), 1.e-17)
equal(fco.direct0mm2(m, S), fcr.ov0mm2(m, delta), 1.e-15)
equal(fcr.ov0mm2(m, delta),
fcr.ov0m(m, delta) * fcr.ov2m(m, delta), 1.e-15)
equal(fco.direct0mm2(m, S), fcr.direct0mm2(m, delta), 1.e-15)
equal(fcr.direct0mm3(m, delta),
fcr.ov0m(m, delta) * fcr.ov3m(m, delta), 1.e-15)
equal(fcr.ov1mm2(m, delta),
fcr.ov1m(m, delta) * fcr.ov2m(m, delta), 1.e-15)
equal(fcr.direct1mm2(m, delta), fcr.ov1mm2(m, delta), 1.e-15)
def test_franck_condon():
import sys
import numpy as np
from ase.vibrations.franck_condon import FranckCondonOverlap, FranckCondonRecursive
from math import factorial
def equal(x, y, tolerance=0, fail=True, msg=''):
"""Compare x and y."""
if not np.isfinite(x - y).any() or (np.abs(x - y) > tolerance).any():
msg = (msg + '%s != %s (error: |%s| > %.9g)' %
(x, y, x - y, tolerance))
if fail:
raise AssertionError(msg)
else:
sys.stderr.write('WARNING: %s\n' % msg)
# FCOverlap
fco = FranckCondonOverlap()
fcr = FranckCondonRecursive()
# check factorial
assert(fco.factorial(8) == factorial(8))
# the second test is useful according to the implementation
assert(fco.factorial(5) == factorial(5))
assert(fco.factorial.inv(5) == 1. / factorial(5))
# check T=0 and n=0 equality
S = np.array([1, 2.1, 34])
m = 5
assert(((fco.directT0(m, S) - fco.direct(0, m, S)) / fco.directT0(m, S) <
1e-15).all())
# check symmetry
S = 2
n = 3
assert(fco.direct(n, m, S) == fco.direct(m, n, S))
# ---------------------------
# specials
S = np.array([0, 1.5])
delta = np.sqrt(2 * S)
for m in [2, 7]:
equal(fco.direct0mm1(m, S)**2,
fco.direct(1, m, S) * fco.direct(m, 0, S), 1.e-17)
equal(fco.direct0mm1(m, S), fcr.ov0mm1(m, delta), 1.e-15)
equal(fcr.ov0mm1(m, delta),
fcr.ov0m(m, delta) * fcr.ov1m(m, delta), 1.e-15)
equal(fcr.ov0mm1(m, -delta), fcr.direct0mm1(m, -delta), 1.e-15)
equal(fcr.ov0mm1(m, delta), - fcr.direct0mm1(m, -delta), 1.e-15)
equal(fco.direct0mm2(m, S)**2,
fco.direct(2, m, S) * fco.direct(m, 0, S), 1.e-17)
equal(fco.direct0mm2(m, S), fcr.ov0mm2(m, delta), 1.e-15)
equal(fcr.ov0mm2(m, delta),
fcr.ov0m(m, delta) * fcr.ov2m(m, delta), 1.e-15)
equal(fco.direct0mm2(m, S), fcr.direct0mm2(m, delta), 1.e-15)
equal(fcr.direct0mm3(m, delta),
fcr.ov0m(m, delta) * fcr.ov3m(m, delta), 1.e-15)
equal(fcr.ov1mm2(m, delta),
fcr.ov1m(m, delta) * fcr.ov2m(m, delta), 1.e-15)
equal(fcr.direct1mm2(m, delta), fcr.ov1mm2(m, delta), 1.e-15)
m = 5
assert (((fco.directT0(m, S) - fco.direct(0, m, S)) / fco.directT0(m, S) <
1e-15).all())
# check symmetry
S = 2
n = 3
assert (fco.direct(n, m, S) == fco.direct(m, n, S))
# ---------------------------
# specials
S = np.array([0, 1.5])
delta = np.sqrt(2 * S)
for m in [2, 7]:
equal(
fco.direct0mm1(m, S)**2,
fco.direct(1, m, S) * fco.direct(m, 0, S), 1.e-17)
equal(fco.direct0mm1(m, S), fcr.ov0mm1(m, delta), 1.e-15)
equal(fcr.ov0mm1(m, delta),
fcr.ov0m(m, delta) * fcr.ov1m(m, delta), 1.e-15)
equal(fcr.ov0mm1(m, -delta), fcr.direct0mm1(m, -delta), 1.e-15)
equal(fcr.ov0mm1(m, delta), -fcr.direct0mm1(m, -delta), 1.e-15)
equal(
fco.direct0mm2(m, S)**2,
fco.direct(2, m, S) * fco.direct(m, 0, S), 1.e-17)
equal(fco.direct0mm2(m, S), fcr.ov0mm2(m, delta), 1.e-15)
equal(fcr.ov0mm2(m, delta),
fcr.ov0m(m, delta) * fcr.ov2m(m, delta), 1.e-15)
equal(fco.direct0mm2(m, S), fcr.direct0mm2(m, delta), 1.e-15)
class ResonantRaman(Vibrations):
"""Class for calculating vibrational modes and
resonant Raman intensities using finite difference.
atoms:
Atoms object
Excitations:
Class to calculate the excitations. The class object is
initialized as::
Excitations(atoms.get_calculator())
or by reading form a file as::
Excitations('filename', **exkwargs)
The file is written by calling the method
Excitations.write('filename').
Excitations should work like a list of ex obejects, where:
ex.get_dipole_me(form='v'):
gives the dipole matrix element in |e| * Angstrom
ex.energy:
is the transition energy in Hartrees
"""
def __init__(
self,
atoms,
Excitations,
indices=None,
gsname='rraman', # name for ground state calculations
exname=None, # name for excited state calculations
delta=0.01,
nfree=2,
directions=None,
approximation='Profeta',
observation={'geometry': '-Z(XX)Z'},
exkwargs={}, # kwargs to be passed to Excitations
exext='.ex.gz', # extension for Excitation names
txt='-',
verbose=False,
):
assert (nfree == 2)
Vibrations.__init__(self, atoms, indices, gsname, delta, nfree)
self.name = gsname + '-d%.3f' % delta
if exname is None:
exname = gsname
self.exname = exname + '-d%.3f' % delta
self.exext = exext
if directions is None:
self.directions = np.array([0, 1, 2])
else:
self.directions = np.array(directions)
self.approximation = approximation
self.observation = observation
self.exobj = Excitations
self.exkwargs = exkwargs
self.timer = Timer()
self.txt = convert_string_to_fd(txt)
self.verbose = verbose
@staticmethod
def m2(z):
return (z * z.conj()).real
def log(self, message, pre='# ', end='\n'):
if self.verbose:
self.txt.write(pre + message + end)
self.txt.flush()
def calculate(self, filename, fd):
"""Call ground and excited state calculation"""
self.timer.start('Ground state')
forces = self.atoms.get_forces()
if rank == 0:
pickle.dump(forces, fd, protocol=2)
fd.close()
self.timer.stop('Ground state')
self.timer.start('Excitations')
basename, _ = os.path.splitext(filename)
excitations = self.exobj(self.atoms.get_calculator(), **self.exkwargs)
excitations.write(basename + self.exext)
self.timer.stop('Excitations')
def read_excitations(self):
self.timer.start('read excitations')
self.timer.start('really read')
self.log('reading ' + self.exname + '.eq' + self.exext)
ex0_object = self.exobj(self.exname + '.eq' + self.exext,
**self.exkwargs)
self.timer.stop('really read')
self.timer.start('index')
matching = frozenset(ex0_object)
self.timer.stop('index')
def append(lst, exname, matching):
self.timer.start('really read')
self.log('reading ' + exname, end=' ')
exo = self.exobj(exname, **self.exkwargs)
lst.append(exo)
self.timer.stop('really read')
self.timer.start('index')
matching = matching.intersection(exo)
self.log('len={0}, matching={1}'.format(len(exo), len(matching)),
pre='')
self.timer.stop('index')
return matching
exm_object_list = []
exp_object_list = []
for a in self.indices:
for i in 'xyz':
name = '%s.%d%s' % (self.exname, a, i)
matching = append(exm_object_list, name + '-' + self.exext,
matching)
matching = append(exp_object_list, name + '+' + self.exext,
matching)
self.ndof = 3 * len(self.indices)
self.nex = len(matching)
self.timer.stop('read excitations')
self.timer.start('select')
def select(exl, matching):
mlst = [ex for ex in exl if ex in matching]
assert (len(mlst) == len(matching))
return mlst
ex0 = select(ex0_object, matching)
exm = []
exp = []
r = 0
for a in self.indices:
for i in 'xyz':
exm.append(select(exm_object_list[r], matching))
exp.append(select(exp_object_list[r], matching))
r += 1
self.timer.stop('select')
self.timer.start('me and energy')
eu = units.Hartree
self.ex0E_p = np.array([ex.energy * eu for ex in ex0])
self.ex0m_pc = np.array([ex.get_dipole_me(form='v') for ex in ex0])
exmE_rp = []
expE_rp = []
exF_rp = []
exmm_rpc = []
expm_rpc = []
r = 0
for a in self.indices:
for i in 'xyz':
exmE_rp.append([em.energy for em in exm[r]])
expE_rp.append([ep.energy for ep in exp[r]])
exF_rp.append([(ep.energy - em.energy)
for ep, em in zip(exp[r], exm[r])])
exmm_rpc.append([ex.get_dipole_me(form='v') for ex in exm[r]])
expm_rpc.append([ex.get_dipole_me(form='v') for ex in exp[r]])
r += 1
self.exmE_rp = np.array(exmE_rp) * eu
self.expE_rp = np.array(expE_rp) * eu
self.exF_rp = np.array(exF_rp) * eu / 2 / self.delta
self.exmm_rpc = np.array(exmm_rpc)
self.expm_rpc = np.array(expm_rpc)
self.timer.stop('me and energy')
def read(self, method='standard', direction='central'):
"""Read data from a pre-performed calculation."""
if not hasattr(self, 'modes'):
self.timer.start('read vibrations')
Vibrations.read(self, method, direction)
# we now have:
# self.H : Hessian matrix
# self.im : 1./sqrt(masses)
# self.modes : Eigenmodes of the mass weighted H
self.om_r = self.hnu.real # energies in eV
self.timer.stop('read vibrations')
if not hasattr(self, 'ex0E_p'):
self.read_excitations()
def get_Huang_Rhys_factors(self, forces_r):
"""Evaluate Huang-Rhys factors derived from forces."""
self.timer.start('Huang-Rhys')
assert (len(forces_r.flat) == self.ndof)
# solve the matrix equation for the equilibrium displacements
# XXX why are the forces mass weighted ???
X_r = np.linalg.solve(self.im[:, None] * self.H * self.im,
forces_r.flat * self.im)
d_r = np.dot(self.modes, X_r)
# Huang-Rhys factors S
s = 1.e-20 / units.kg / units.C / units._hbar**2 # SI units
self.timer.stop('Huang-Rhys')
return s * d_r**2 * self.om_r / 2.
def get_matrix_element_AlbrechtA(self, omega, gamma=0.1, ml=range(16)):
"""Evaluate Albrecht A term.
Unit: |e|^2Angstrom^2/eV
"""
self.read()
self.timer.start('AlbrechtA')
if not hasattr(self, 'fco'):
self.fco = FranckCondonOverlap()
# excited state forces
F_pr = self.exF_rp.T
m_rcc = np.zeros((self.ndof, 3, 3), dtype=complex)
for p, energy in enumerate(self.ex0E_p):
S_r = self.get_Huang_Rhys_factors(F_pr[p])
me_cc = np.outer(self.ex0m_pc[p], self.ex0m_pc[p].conj())
for m in ml:
self.timer.start('0mm1')
fco_r = self.fco.direct0mm1(m, S_r)
self.timer.stop('0mm1')
self.timer.start('einsum')
m_rcc += np.einsum(
'a,bc->abc',
fco_r / (energy + m * self.om_r - omega - 1j * gamma),
me_cc)
m_rcc += np.einsum(
'a,bc->abc', fco_r /
(energy + (m - 1) * self.om_r + omega + 1j * gamma), me_cc)
self.timer.stop('einsum')
self.timer.stop('AlbrechtA')
return m_rcc
def get_matrix_element_AlbrechtBC(self,
omega,
gamma=0.1,
ml=[1],
term='BC'):
"""Evaluate Albrecht B and/or C term(s)."""
self.read()
self.timer.start('AlbrechtBC')
if not hasattr(self, 'fco'):
self.fco = FranckCondonOverlap()
# excited state forces
F_pr = self.exF_rp.T
m_rcc = np.zeros((self.ndof, 3, 3), dtype=complex)
for p, energy in enumerate(self.ex0E_p):
S_r = self.get_Huang_Rhys_factors(F_pr[p])
for m in ml:
self.timer.start('Franck-Condon overlaps')
fc1mm1_r = self.fco.direct(1, m, S_r)
fc0mm02_r = self.fco.direct(0, m, S_r)
fc0mm02_r += np.sqrt(2) * self.fco.direct0mm2(m, S_r)
# XXXXX
fc1mm1_r[-1] = 1
fc0mm02_r[-1] = 1
print(m, fc1mm1_r[-1], fc0mm02_r[-1])
self.timer.stop('Franck-Condon overlaps')
self.timer.start('me dervivatives')
dm_rc = []
r = 0
for a in self.indices:
for i in 'xyz':
dm_rc.append(
(self.expm_rpc[r, p] - self.exmm_rpc[r, p]) *
self.im[r])
print('pm=', self.expm_rpc[r, p], self.exmm_rpc[r, p])
r += 1
dm_rc = np.array(dm_rc) / (2 * self.delta)
self.timer.stop('me dervivatives')
self.timer.start('map to modes')
# print('dm_rc[2], dm_rc[5]', dm_rc[2], dm_rc[5])
print('dm_rc=', dm_rc)
dm_rc = np.dot(dm_rc.T, self.modes.T).T
print('dm_rc[-1][2]', dm_rc[-1][2])
self.timer.stop('map to modes')
self.timer.start('multiply')
# me_cc = np.outer(self.ex0m_pc[p], self.ex0m_pc[p].conj())
for r in range(self.ndof):
if 'B' in term:
# XXXX
denom = (1. / (energy + m * 0 * self.om_r[r] - omega -
1j * gamma))
# ok print('denom=', denom)
m_rcc[r] += (
np.outer(dm_rc[r], self.ex0m_pc[p].conj()) *
fc1mm1_r[r] * denom)
if r == 5:
print('m_rcc[r]=', m_rcc[r][2, 2])
m_rcc[r] += (
np.outer(self.ex0m_pc[p], dm_rc[r].conj()) *
fc0mm02_r[r] * denom)
if 'C' in term:
denom = (1. /
(energy +
(m - 1) * self.om_r[r] + omega + 1j * gamma))
m_rcc[r] += (
np.outer(self.ex0m_pc[p], dm_rc[r].conj()) *
fc1mm1_r[r] * denom)
m_rcc[r] += (
np.outer(dm_rc[r], self.ex0m_pc[p].conj()) *
fc0mm02_r[r] * denom)
self.timer.stop('multiply')
print('m_rcc[-1]=', m_rcc[-1][2, 2])
self.timer.start('pre_r')
with np.errstate(divide='ignore'):
pre_r = np.where(self.om_r > 0,
np.sqrt(units._hbar**2 / 2. / self.om_r), 0)
# print('BC: pre_r=', pre_r)
for r, p in enumerate(pre_r):
m_rcc[r] *= p
self.timer.stop('pre_r')
self.timer.stop('AlbrechtBC')
return m_rcc
def get_matrix_element_Profeta(self,
omega,
gamma=0.1,
energy_derivative=False):
"""Evaluate Albrecht B+C term in Profeta and Mauri approximation"""
self.read()
self.timer.start('amplitudes')
self.timer.start('init')
V_rcc = np.zeros((self.ndof, 3, 3), dtype=complex)
pre = 1. / (2 * self.delta)
self.timer.stop('init')
def kappa(me_pc, e_p, omega, gamma, form='v'):
"""Kappa tensor after Profeta and Mauri
PRB 63 (2001) 245415"""
me_ccp = np.empty((3, 3, len(e_p)), dtype=complex)
for p, me_c in enumerate(me_pc):
me_ccp[:, :, p] = np.outer(me_pc[p], me_pc[p].conj())
# print('kappa: me_ccp=', me_ccp[2,2,0])
# ok print('kappa: den=', 1./(e_p - omega - 1j * gamma))
kappa_ccp = (me_ccp / (e_p - omega - 1j * gamma) + me_ccp.conj() /
(e_p + omega + 1j * gamma))
return kappa_ccp.sum(2)
self.timer.start('kappa')
r = 0
for a in self.indices:
for i in 'xyz':
if not energy_derivative < 0:
V_rcc[r] = pre * self.im[r] * (
kappa(self.expm_rpc[r], self.ex0E_p, omega, gamma) -
kappa(self.exmm_rpc[r], self.ex0E_p, omega, gamma))
if energy_derivative:
V_rcc[r] += pre * self.im[r] * (
kappa(self.ex0m_pc, self.expE_rp[r], omega, gamma) -
kappa(self.ex0m_pc, self.exmE_rp[r], omega, gamma))
r += 1
self.timer.stop('kappa')
# print('V_rcc[2], V_rcc[5]=', V_rcc[2,2,2], V_rcc[5,2,2])
self.timer.stop('amplitudes')
# map to modes
self.timer.start('pre_r')
with np.errstate(divide='ignore'):
pre_r = np.where(self.om_r > 0,
np.sqrt(units._hbar**2 / 2. / self.om_r), 0)
V_rcc = np.dot(V_rcc.T, self.modes.T).T
# looks ok print('self.modes.T[-1]',self.modes.T)
# looks ok print('V_rcc[-1]=', V_rcc[-1][2,2])
# ok print('Profeta: pre_r=', pre_r)
for r, p in enumerate(pre_r):
V_rcc[r] *= p
self.timer.stop('pre_r')
return V_rcc
def get_matrix_element(self, omega, gamma):
self.read()
V_rcc = np.zeros((self.ndof, 3, 3), dtype=complex)
if self.approximation.lower() == 'profeta':
V_rcc += self.get_matrix_element_Profeta(omega, gamma)
elif self.approximation.lower() == 'placzek':
V_rcc += self.get_matrix_element_Profeta(omega, gamma, True)
elif self.approximation.lower() == 'p-p':
V_rcc += self.get_matrix_element_Profeta(omega, gamma, -1)
elif self.approximation.lower() == 'albrecht a':
V_rcc += self.get_matrix_element_AlbrechtA(omega, gamma)
elif self.approximation.lower() == 'albrecht b':
raise NotImplementedError('not working')
V_rcc += self.get_matrix_element_AlbrechtBC(omega, gamma, term='B')
elif self.approximation.lower() == 'albrecht c':
raise NotImplementedError('not working')
V_rcc += self.get_matrix_element_AlbrechtBC(omega, gamma, term='C')
elif self.approximation.lower() == 'albrecht bc':
raise NotImplementedError('not working')
V_rcc += self.get_matrix_element_AlbrechtBC(omega, gamma)
elif self.approximation.lower() == 'albrecht':
raise NotImplementedError('not working')
V_rcc += self.get_matrix_element_AlbrechtA(omega, gamma)
V_rcc += self.get_matrix_element_AlbrechtBC(omega, gamma)
elif self.approximation.lower() == 'albrecht+profeta':
V_rcc += self.get_matrix_element_AlbrechtA(omega, gamma)
V_rcc += self.get_matrix_element_Profeta(omega, gamma)
else:
raise NotImplementedError(
'Approximation {0} not implemented. '.format(
self.approximation) +
'Please use "Profeta", "Albrecht A/B/C/BC", ' +
'or "Albrecht".')
return V_rcc
def get_intensities(self, omega, gamma=0.1):
m2 = ResonantRaman.m2
alpha_rcc = self.get_matrix_element(omega, gamma)
if not self.observation: # XXXX remove
"""Simple sum, maybe too simple"""
return m2(alpha_rcc).sum(axis=1).sum(axis=1)
# XXX enable when appropraiate
# if self.observation['orientation'].lower() != 'random':
# raise NotImplementedError('not yet')
# random orientation of the molecular frame
# Woodward & Long,
# Guthmuller, J. J. Chem. Phys. 2016, 144 (6), 64106
m2 = ResonantRaman.m2
alpha2_r = m2(alpha_rcc[:, 0, 0] + alpha_rcc[:, 1, 1] +
alpha_rcc[:, 2, 2]) / 9.
delta2_r = 3 / 4. * (m2(alpha_rcc[:, 0, 1] - alpha_rcc[:, 1, 0]) +
m2(alpha_rcc[:, 0, 2] - alpha_rcc[:, 2, 0]) +
m2(alpha_rcc[:, 1, 2] - alpha_rcc[:, 2, 1]))
gamma2_r = (3 / 4. * (m2(alpha_rcc[:, 0, 1] + alpha_rcc[:, 1, 0]) +
m2(alpha_rcc[:, 0, 2] + alpha_rcc[:, 2, 0]) +
m2(alpha_rcc[:, 1, 2] + alpha_rcc[:, 2, 1])) +
(m2(alpha_rcc[:, 0, 0] - alpha_rcc[:, 1, 1]) +
m2(alpha_rcc[:, 0, 0] - alpha_rcc[:, 2, 2]) +
m2(alpha_rcc[:, 1, 1] - alpha_rcc[:, 2, 2])) / 2)
if self.observation['geometry'] == '-Z(XX)Z': # Porto's notation
return (45 * alpha2_r + 5 * delta2_r + 4 * gamma2_r) / 45.
elif self.observation['geometry'] == '-Z(XY)Z': # Porto's notation
return gamma2_r / 15.
elif self.observation['scattered'] == 'Z':
# scattered light in direction of incoming light
return (45 * alpha2_r + 5 * delta2_r + 7 * gamma2_r) / 45.
elif self.observation['scattered'] == 'parallel':
# scattered light perendicular and
# polarization in plane
return 6 * gamma2_r / 45.
elif self.observation['scattered'] == 'perpendicular':
# scattered light perendicular and
# polarization out of plane
return (45 * alpha2_r + 5 * delta2_r + 7 * gamma2_r) / 45.
else:
raise NotImplementedError
def get_cross_sections(self, omega, gamma=0.1):
I_r = self.get_intensities(omega, gamma)
pre = 1. / 16 / np.pi**2 / units.eps0**2 / units.c**4
# frequency of scattered light
omS_r = omega - self.hnu
return pre * omega * omS_r**3 * I_r
def get_spectrum(self,
omega,
gamma=0.1,
start=200.0,
end=4000.0,
npts=None,
width=4.0,
type='Gaussian',
method='standard',
direction='central',
intensity_unit='????',
normalize=False):
"""Get resonant Raman spectrum.
The method returns wavenumbers in cm^-1 with corresponding
Raman cross section.
Start and end point, and width of the Gaussian/Lorentzian should
be given in cm^-1.
"""
self.type = type.lower()
assert self.type in ['gaussian', 'lorentzian']
if not npts:
npts = int((end - start) / width * 10 + 1)
frequencies = self.get_frequencies(method, direction).real
intensities = self.get_cross_sections(omega, gamma)
prefactor = 1
if type == 'lorentzian':
intensities = intensities * width * np.pi / 2.
if normalize:
prefactor = 2. / width / np.pi
else:
sigma = width / 2. / np.sqrt(2. * np.log(2.))
if normalize:
prefactor = 1. / sigma / np.sqrt(2 * np.pi)
# Make array with spectrum data
spectrum = np.empty(npts)
energies = np.linspace(start, end, npts)
for i, energy in enumerate(energies):
energies[i] = energy
if type == 'lorentzian':
spectrum[i] = (intensities * 0.5 * width / np.pi / (
(frequencies - energy)**2 + 0.25 * width**2)).sum()
else:
spectrum[i] = (
intensities *
np.exp(-(frequencies - energy)**2 / 2. / sigma**2)).sum()
return [energies, prefactor * spectrum]
def write_spectrum(self,
omega,
gamma,
out='resonant-raman-spectra.dat',
start=200,
end=4000,
npts=None,
width=10,
type='Gaussian',
method='standard',
direction='central'):
"""Write out spectrum to file.
First column is the wavenumber in cm^-1, the second column the
absolute infrared intensities, and
the third column the absorbance scaled so that data runs
from 1 to 0. Start and end
point, and width of the Gaussian/Lorentzian should be given
in cm^-1."""
energies, spectrum = self.get_spectrum(omega, gamma, start, end, npts,
width, type, method, direction)
# Write out spectrum in file. First column is absolute intensities.
outdata = np.empty([len(energies), 3])
outdata.T[0] = energies
outdata.T[1] = spectrum
fd = open(out, 'w')
fd.write('# Resonant Raman spectrum\n')
fd.write('# omega={0:g} eV, gamma={1:g} eV\n'.format(omega, gamma))
fd.write('# %s folded, width=%g cm^-1\n' % (type.title(), width))
fd.write('# [cm^-1] [a.u.]\n')
for row in outdata:
fd.write('%.3f %15.5g\n' % (row[0], row[1]))
fd.close()
def summary(self,
omega,
gamma=0.1,
method='standard',
direction='central',
log=sys.stdout):
"""Print summary for given omega [eV]"""
hnu = self.get_energies(method, direction)
s = 0.01 * units._e / units._c / units._hplanck
intensities = self.get_intensities(omega, gamma)
if isinstance(log, basestring):
log = paropen(log, 'a')
parprint('-------------------------------------', file=log)
parprint(' excitation at ' + str(omega) + ' eV', file=log)
parprint(' gamma ' + str(gamma) + ' eV', file=log)
parprint(' approximation:', self.approximation, file=log)
parprint(' observation:', self.observation, '\n', file=log)
parprint(' Mode Frequency Intensity', file=log)
parprint(' # meV cm^-1 [e^4A^4/eV^2]', file=log)
parprint('-------------------------------------', file=log)
for n, e in enumerate(hnu):
if e.imag != 0:
c = 'i'
e = e.imag
else:
c = ' '
e = e.real
parprint('%3d %6.1f%s %7.1f%s %9.3g' %
(n, 1000 * e, c, s * e, c, intensities[n]),
file=log)
parprint('-------------------------------------', file=log)
parprint('Zero-point energy: %.3f eV' % self.get_zero_point_energy(),
file=log)
def __del__(self):
self.timer.write(self.txt)
class ResonantRaman(Vibrations):
"""Class for calculating vibrational modes and
resonant Raman intensities using finite difference.
atoms:
Atoms object
Excitations:
Class to calculate the excitations. The class object is
initialized as::
Excitations(atoms.get_calculator())
or by reading form a file as::
Excitations('filename', **exkwargs)
The file is written by calling the method
Excitations.write('filename').
Excitations should work like a list of ex obejects, where:
ex.get_dipole_me(form='v'):
gives the dipole matrix element in |e| * Angstrom
ex.energy:
is the transition energy in Hartrees
"""
def __init__(self, atoms, Excitations,
indices=None,
gsname='rraman', # name for ground state calculations
exname=None, # name for excited state calculations
delta=0.01,
nfree=2,
directions=None,
approximation='Profeta',
observation={'geometry': '-Z(XX)Z'},
exkwargs={}, # kwargs to be passed to Excitations
exext='.ex.gz', # extension for Excitation names
txt='-',
verbose=False,):
assert(nfree == 2)
Vibrations.__init__(self, atoms, indices, gsname, delta, nfree)
self.name = gsname + '-d%.3f' % delta
if exname is None:
exname = gsname
self.exname = exname + '-d%.3f' % delta
self.exext = exext
if directions is None:
self.directions = np.array([0, 1, 2])
else:
self.directions = np.array(directions)
self.approximation = approximation
self.observation = observation
self.exobj = Excitations
self.exkwargs = exkwargs
self.timer = Timer()
self.txt = convert_string_to_fd(txt)
self.verbose = verbose
@staticmethod
def m2(z):
return (z * z.conj()).real
def log(self, message, pre='# ', end='\n'):
if self.verbose:
self.txt.write(pre + message + end)
self.txt.flush()
def calculate(self, filename, fd):
"""Call ground and excited state calculation"""
self.timer.start('Ground state')
forces = self.atoms.get_forces()
if rank == 0:
pickle.dump(forces, fd, protocol=2)
fd.close()
self.timer.stop('Ground state')
self.timer.start('Excitations')
basename, _ = os.path.splitext(filename)
excitations = self.exobj(
self.atoms.get_calculator(), **self.exkwargs)
excitations.write(basename + self.exext)
self.timer.stop('Excitations')
def read_excitations(self):
self.timer.start('read excitations')
self.timer.start('really read')
self.log('reading ' + self.exname + '.eq' + self.exext)
ex0_object = self.exobj(self.exname + '.eq' + self.exext,
**self.exkwargs)
self.timer.stop('really read')
self.timer.start('index')
matching = frozenset(ex0_object)
self.timer.stop('index')
def append(lst, exname, matching):
self.timer.start('really read')
self.log('reading ' + exname, end=' ')
exo = self.exobj(exname, **self.exkwargs)
lst.append(exo)
self.timer.stop('really read')
self.timer.start('index')
matching = matching.intersection(exo)
self.log('len={0}, matching={1}'.format(len(exo),
len(matching)), pre='')
self.timer.stop('index')
return matching
exm_object_list = []
exp_object_list = []
for a in self.indices:
for i in 'xyz':
name = '%s.%d%s' % (self.exname, a, i)
matching = append(exm_object_list,
name + '-' + self.exext, matching)
matching = append(exp_object_list,
name + '+' + self.exext, matching)
self.ndof = 3 * len(self.indices)
self.nex = len(matching)
self.timer.stop('read excitations')
self.timer.start('select')
def select(exl, matching):
mlst = [ex for ex in exl if ex in matching]
assert(len(mlst) == len(matching))
return mlst
ex0 = select(ex0_object, matching)
exm = []
exp = []
r = 0
for a in self.indices:
for i in 'xyz':
exm.append(select(exm_object_list[r], matching))
exp.append(select(exp_object_list[r], matching))
r += 1
self.timer.stop('select')
self.timer.start('me and energy')
eu = units.Hartree
self.ex0E_p = np.array([ex.energy * eu for ex in ex0])
self.ex0m_pc = np.array(
[ex.get_dipole_me(form='v') for ex in ex0])
exmE_rp = []
expE_rp = []
exF_rp = []
exmm_rpc = []
expm_rpc = []
r = 0
for a in self.indices:
for i in 'xyz':
exmE_rp.append([em.energy for em in exm[r]])
expE_rp.append([ep.energy for ep in exp[r]])
exF_rp.append(
[(ep.energy - em.energy)
for ep, em in zip(exp[r], exm[r])])
exmm_rpc.append(
[ex.get_dipole_me(form='v') for ex in exm[r]])
expm_rpc.append(
[ex.get_dipole_me(form='v') for ex in exp[r]])
r += 1
self.exmE_rp = np.array(exmE_rp) * eu
self.expE_rp = np.array(expE_rp) * eu
self.exF_rp = np.array(exF_rp) * eu / 2 / self.delta
self.exmm_rpc = np.array(exmm_rpc)
self.expm_rpc = np.array(expm_rpc)
self.timer.stop('me and energy')
def read(self, method='standard', direction='central'):
"""Read data from a pre-performed calculation."""
if not hasattr(self, 'modes'):
self.timer.start('read vibrations')
Vibrations.read(self, method, direction)
# we now have:
# self.H : Hessian matrix
# self.im : 1./sqrt(masses)
# self.modes : Eigenmodes of the mass weighted H
self.om_r = self.hnu.real # energies in eV
self.timer.stop('read vibrations')
if not hasattr(self, 'ex0E_p'):
self.read_excitations()
def get_Huang_Rhys_factors(self, forces_r):
"""Evaluate Huang-Rhys factors derived from forces."""
self.timer.start('Huang-Rhys')
assert(len(forces_r.flat) == self.ndof)
# solve the matrix equation for the equilibrium displacements
# XXX why are the forces mass weighted ???
X_r = np.linalg.solve(self.im[:, None] * self.H * self.im,
forces_r.flat * self.im)
d_r = np.dot(self.modes, X_r)
# Huang-Rhys factors S
s = 1.e-20 / units.kg / units.C / units._hbar**2 # SI units
self.timer.stop('Huang-Rhys')
return s * d_r**2 * self.om_r / 2.
def get_matrix_element_AlbrechtA(self, omega, gamma=0.1, ml=range(16)):
"""Evaluate Albrecht A term.
Unit: |e|^2Angstrom^2/eV
"""
self.read()
self.timer.start('AlbrechtA')
if not hasattr(self, 'fco'):
self.fco = FranckCondonOverlap()
# excited state forces
F_pr = self.exF_rp.T
m_rcc = np.zeros((self.ndof, 3, 3), dtype=complex)
for p, energy in enumerate(self.ex0E_p):
S_r = self.get_Huang_Rhys_factors(F_pr[p])
me_cc = np.outer(self.ex0m_pc[p], self.ex0m_pc[p].conj())
for m in ml:
self.timer.start('0mm1')
fco_r = self.fco.direct0mm1(m, S_r)
self.timer.stop('0mm1')
self.timer.start('einsum')
m_rcc += np.einsum('a,bc->abc',
fco_r / (energy + m * self.om_r - omega -
1j * gamma),
me_cc)
m_rcc += np.einsum('a,bc->abc',
fco_r / (energy + (m - 1) * self.om_r +
omega + 1j * gamma),
me_cc)
self.timer.stop('einsum')
self.timer.stop('AlbrechtA')
return m_rcc
def get_matrix_element_AlbrechtBC(self, omega, gamma=0.1, ml=[1],
term='BC'):
"""Evaluate Albrecht B and/or C term(s)."""
self.read()
self.timer.start('AlbrechtBC')
if not hasattr(self, 'fco'):
self.fco = FranckCondonOverlap()
# excited state forces
F_pr = self.exF_rp.T
m_rcc = np.zeros((self.ndof, 3, 3), dtype=complex)
for p, energy in enumerate(self.ex0E_p):
S_r = self.get_Huang_Rhys_factors(F_pr[p])
for m in ml:
self.timer.start('Franck-Condon overlaps')
fc1mm1_r = self.fco.direct(1, m, S_r)
fc0mm02_r = self.fco.direct(0, m, S_r)
fc0mm02_r += np.sqrt(2) * self.fco.direct0mm2(m, S_r)
# XXXXX
fc1mm1_r[-1] = 1
fc0mm02_r[-1] = 1
print(m, fc1mm1_r[-1], fc0mm02_r[-1])
self.timer.stop('Franck-Condon overlaps')
self.timer.start('me dervivatives')
dm_rc = []
r = 0
for a in self.indices:
for i in 'xyz':
dm_rc.append(
(self.expm_rpc[r, p] - self.exmm_rpc[r, p]) *
self.im[r])
print('pm=', self.expm_rpc[r, p], self.exmm_rpc[r, p])
r += 1
dm_rc = np.array(dm_rc) / (2 * self.delta)
self.timer.stop('me dervivatives')
self.timer.start('map to modes')
# print('dm_rc[2], dm_rc[5]', dm_rc[2], dm_rc[5])
print('dm_rc=', dm_rc)
dm_rc = np.dot(dm_rc.T, self.modes.T).T
print('dm_rc[-1][2]', dm_rc[-1][2])
self.timer.stop('map to modes')
self.timer.start('multiply')
# me_cc = np.outer(self.ex0m_pc[p], self.ex0m_pc[p].conj())
for r in range(self.ndof):
if 'B' in term:
# XXXX
denom = (1. /
(energy + m * 0 * self.om_r[r] -
omega - 1j * gamma))
# ok print('denom=', denom)
m_rcc[r] += (np.outer(dm_rc[r],
self.ex0m_pc[p].conj()) *
fc1mm1_r[r] * denom)
if r == 5:
print('m_rcc[r]=', m_rcc[r][2, 2])
m_rcc[r] += (np.outer(self.ex0m_pc[p],
dm_rc[r].conj()) *
fc0mm02_r[r] * denom)
if 'C' in term:
denom = (1. /
(energy + (m - 1) * self.om_r[r] +
omega + 1j * gamma))
m_rcc[r] += (np.outer(self.ex0m_pc[p],
dm_rc[r].conj()) *
fc1mm1_r[r] * denom)
m_rcc[r] += (np.outer(dm_rc[r],
self.ex0m_pc[p].conj()) *
fc0mm02_r[r] * denom)
self.timer.stop('multiply')
print('m_rcc[-1]=', m_rcc[-1][2, 2])
self.timer.start('pre_r')
with np.errstate(divide='ignore'):
pre_r = np.where(self.om_r > 0,
np.sqrt(units._hbar**2 / 2. / self.om_r), 0)
# print('BC: pre_r=', pre_r)
for r, p in enumerate(pre_r):
m_rcc[r] *= p
self.timer.stop('pre_r')
self.timer.stop('AlbrechtBC')
return m_rcc
def get_matrix_element_Profeta(self, omega, gamma=0.1,
energy_derivative=False):
"""Evaluate Albrecht B+C term in Profeta and Mauri approximation"""
self.read()
self.timer.start('amplitudes')
self.timer.start('init')
V_rcc = np.zeros((self.ndof, 3, 3), dtype=complex)
pre = 1. / (2 * self.delta)
self.timer.stop('init')
def kappa(me_pc, e_p, omega, gamma, form='v'):
"""Kappa tensor after Profeta and Mauri
PRB 63 (2001) 245415"""
me_ccp = np.empty((3, 3, len(e_p)), dtype=complex)
for p, me_c in enumerate(me_pc):
me_ccp[:, :, p] = np.outer(me_pc[p], me_pc[p].conj())
# print('kappa: me_ccp=', me_ccp[2,2,0])
# ok print('kappa: den=', 1./(e_p - omega - 1j * gamma))
kappa_ccp = (me_ccp / (e_p - omega - 1j * gamma) +
me_ccp.conj() / (e_p + omega + 1j * gamma))
return kappa_ccp.sum(2)
self.timer.start('kappa')
r = 0
for a in self.indices:
for i in 'xyz':
if not energy_derivative < 0:
V_rcc[r] = pre * self.im[r] * (
kappa(self.expm_rpc[r], self.ex0E_p, omega, gamma) -
kappa(self.exmm_rpc[r], self.ex0E_p, omega, gamma))
if energy_derivative:
V_rcc[r] += pre * self.im[r] * (
kappa(self.ex0m_pc, self.expE_rp[r], omega, gamma) -
kappa(self.ex0m_pc, self.exmE_rp[r], omega, gamma))
r += 1
self.timer.stop('kappa')
# print('V_rcc[2], V_rcc[5]=', V_rcc[2,2,2], V_rcc[5,2,2])
self.timer.stop('amplitudes')
# map to modes
self.timer.start('pre_r')
with np.errstate(divide='ignore'):
pre_r = np.where(self.om_r > 0,
np.sqrt(units._hbar**2 / 2. / self.om_r), 0)
V_rcc = np.dot(V_rcc.T, self.modes.T).T
# looks ok print('self.modes.T[-1]',self.modes.T)
# looks ok print('V_rcc[-1]=', V_rcc[-1][2,2])
# ok print('Profeta: pre_r=', pre_r)
for r, p in enumerate(pre_r):
V_rcc[r] *= p
self.timer.stop('pre_r')
return V_rcc
def get_matrix_element(self, omega, gamma):
self.read()
V_rcc = np.zeros((self.ndof, 3, 3), dtype=complex)
if self.approximation.lower() == 'profeta':
V_rcc += self.get_matrix_element_Profeta(omega, gamma)
elif self.approximation.lower() == 'placzek':
V_rcc += self.get_matrix_element_Profeta(omega, gamma, True)
elif self.approximation.lower() == 'p-p':
V_rcc += self.get_matrix_element_Profeta(omega, gamma, -1)
elif self.approximation.lower() == 'albrecht a':
V_rcc += self.get_matrix_element_AlbrechtA(omega, gamma)
elif self.approximation.lower() == 'albrecht b':
raise NotImplementedError('not working')
V_rcc += self.get_matrix_element_AlbrechtBC(omega, gamma, term='B')
elif self.approximation.lower() == 'albrecht c':
raise NotImplementedError('not working')
V_rcc += self.get_matrix_element_AlbrechtBC(omega, gamma, term='C')
elif self.approximation.lower() == 'albrecht bc':
raise NotImplementedError('not working')
V_rcc += self.get_matrix_element_AlbrechtBC(omega, gamma)
elif self.approximation.lower() == 'albrecht':
raise NotImplementedError('not working')
V_rcc += self.get_matrix_element_AlbrechtA(omega, gamma)
V_rcc += self.get_matrix_element_AlbrechtBC(omega, gamma)
elif self.approximation.lower() == 'albrecht+profeta':
V_rcc += self.get_matrix_element_AlbrechtA(omega, gamma)
V_rcc += self.get_matrix_element_Profeta(omega, gamma)
else:
raise NotImplementedError(
'Approximation {0} not implemented. '.format(
self.approximation) +
'Please use "Profeta", "Albrecht A/B/C/BC", ' +
'or "Albrecht".')
return V_rcc
def get_intensities(self, omega, gamma=0.1):
m2 = ResonantRaman.m2
alpha_rcc = self.get_matrix_element(omega, gamma)
if not self.observation: # XXXX remove
"""Simple sum, maybe too simple"""
return m2(alpha_rcc).sum(axis=1).sum(axis=1)
# XXX enable when appropraiate
# if self.observation['orientation'].lower() != 'random':
# raise NotImplementedError('not yet')
# random orientation of the molecular frame
# Woodward & Long,
# Guthmuller, J. J. Chem. Phys. 2016, 144 (6), 64106
m2 = ResonantRaman.m2
alpha2_r = m2(alpha_rcc[:, 0, 0] + alpha_rcc[:, 1, 1] +
alpha_rcc[:, 2, 2]) / 9.
delta2_r = 3 / 4. * (
m2(alpha_rcc[:, 0, 1] - alpha_rcc[:, 1, 0]) +
m2(alpha_rcc[:, 0, 2] - alpha_rcc[:, 2, 0]) +
m2(alpha_rcc[:, 1, 2] - alpha_rcc[:, 2, 1]))
gamma2_r = (3 / 4. * (m2(alpha_rcc[:, 0, 1] + alpha_rcc[:, 1, 0]) +
m2(alpha_rcc[:, 0, 2] + alpha_rcc[:, 2, 0]) +
m2(alpha_rcc[:, 1, 2] + alpha_rcc[:, 2, 1])) +
(m2(alpha_rcc[:, 0, 0] - alpha_rcc[:, 1, 1]) +
m2(alpha_rcc[:, 0, 0] - alpha_rcc[:, 2, 2]) +
m2(alpha_rcc[:, 1, 1] - alpha_rcc[:, 2, 2])) / 2)
if self.observation['geometry'] == '-Z(XX)Z': # Porto's notation
return (45 * alpha2_r + 5 * delta2_r + 4 * gamma2_r) / 45.
elif self.observation['geometry'] == '-Z(XY)Z': # Porto's notation
return gamma2_r / 15.
elif self.observation['scattered'] == 'Z':
# scattered light in direction of incoming light
return (45 * alpha2_r + 5 * delta2_r + 7 * gamma2_r) / 45.
elif self.observation['scattered'] == 'parallel':
# scattered light perendicular and
# polarization in plane
return 6 * gamma2_r / 45.
elif self.observation['scattered'] == 'perpendicular':
# scattered light perendicular and
# polarization out of plane
return (45 * alpha2_r + 5 * delta2_r + 7 * gamma2_r) / 45.
else:
raise NotImplementedError
def get_cross_sections(self, omega, gamma=0.1):
I_r = self.get_intensities(omega, gamma)
pre = 1. / 16 / np.pi**2 / units.eps0**2 / units.c**4
# frequency of scattered light
omS_r = omega - self.hnu
return pre * omega * omS_r**3 * I_r
def get_spectrum(self, omega, gamma=0.1,
start=200.0, end=4000.0, npts=None, width=4.0,
type='Gaussian', method='standard', direction='central',
intensity_unit='????', normalize=False):
"""Get resonant Raman spectrum.
The method returns wavenumbers in cm^-1 with corresponding
Raman cross section.
Start and end point, and width of the Gaussian/Lorentzian should
be given in cm^-1.
"""
self.type = type.lower()
assert self.type in ['gaussian', 'lorentzian']
if not npts:
npts = int((end - start) / width * 10 + 1)
frequencies = self.get_frequencies(method, direction).real
intensities = self.get_cross_sections(omega, gamma)
prefactor = 1
if type == 'lorentzian':
intensities = intensities * width * np.pi / 2.
if normalize:
prefactor = 2. / width / np.pi
else:
sigma = width / 2. / np.sqrt(2. * np.log(2.))
if normalize:
prefactor = 1. / sigma / np.sqrt(2 * np.pi)
# Make array with spectrum data
spectrum = np.empty(npts)
energies = np.linspace(start, end, npts)
for i, energy in enumerate(energies):
energies[i] = energy
if type == 'lorentzian':
spectrum[i] = (intensities * 0.5 * width / np.pi /
((frequencies - energy)**2 +
0.25 * width**2)).sum()
else:
spectrum[i] = (intensities *
np.exp(-(frequencies - energy)**2 /
2. / sigma**2)).sum()
return [energies, prefactor * spectrum]
def write_spectrum(self, omega, gamma,
out='resonant-raman-spectra.dat',
start=200, end=4000,
npts=None, width=10,
type='Gaussian', method='standard',
direction='central'):
"""Write out spectrum to file.
First column is the wavenumber in cm^-1, the second column the
absolute infrared intensities, and
the third column the absorbance scaled so that data runs
from 1 to 0. Start and end
point, and width of the Gaussian/Lorentzian should be given
in cm^-1."""
energies, spectrum = self.get_spectrum(omega, gamma,
start, end, npts, width,
type, method, direction)
# Write out spectrum in file. First column is absolute intensities.
outdata = np.empty([len(energies), 3])
outdata.T[0] = energies
outdata.T[1] = spectrum
fd = open(out, 'w')
fd.write('# Resonant Raman spectrum\n')
fd.write('# omega={0:g} eV, gamma={1:g} eV\n'.format(omega, gamma))
fd.write('# %s folded, width=%g cm^-1\n' % (type.title(), width))
fd.write('# [cm^-1] [a.u.]\n')
for row in outdata:
fd.write('%.3f %15.5g\n' %
(row[0], row[1]))
fd.close()
def summary(self, omega, gamma=0.1,
method='standard', direction='central',
log=sys.stdout):
"""Print summary for given omega [eV]"""
hnu = self.get_energies(method, direction)
s = 0.01 * units._e / units._c / units._hplanck
intensities = self.get_intensities(omega, gamma)
if isinstance(log, basestring):
log = paropen(log, 'a')
parprint('-------------------------------------', file=log)
parprint(' excitation at ' + str(omega) + ' eV', file=log)
parprint(' gamma ' + str(gamma) + ' eV', file=log)
parprint(' approximation:', self.approximation, file=log)
parprint(' observation:', self.observation, '\n', file=log)
parprint(' Mode Frequency Intensity', file=log)
parprint(' # meV cm^-1 [e^4A^4/eV^2]', file=log)
parprint('-------------------------------------', file=log)
for n, e in enumerate(hnu):
if e.imag != 0:
c = 'i'
e = e.imag
else:
c = ' '
e = e.real
parprint('%3d %6.1f%s %7.1f%s %9.3g' %
(n, 1000 * e, c, s * e, c, intensities[n]),
file=log)
parprint('-------------------------------------', file=log)
parprint('Zero-point energy: %.3f eV' % self.get_zero_point_energy(),
file=log)
def __del__(self):
self.timer.write(self.txt)
# FCOverlap
fco = FranckCondonOverlap()
# check factorial
assert (fco.factorial(8) == factorial(8))
# the second test is useful according to the implementation
assert (fco.factorial(5) == factorial(5))
# check T=0 and n=0 equality
S = np.array([1, 2.1, 34])
m = 5
assert (((fco.directT0(m, S) - fco.direct(0, m, S)) / fco.directT0(m, S) <
1e-15).all())
# check symmetry
S = 2
n = 3
assert (fco.direct(n, m, S) == fco.direct(m, n, S))
# ---------------------------
# specials
S = 1.5
for m in [2, 7]:
equal(
fco.direct0mm1(m, S)**2,
fco.direct(1, m, S) * fco.direct(m, 0, S), 1.e-17)
equal(
fco.direct0mm2(m, S)**2,
fco.direct(2, m, S) * fco.direct(m, 0, S), 1.e-17)
sys.stderr.write('WARNING: %s\n' % msg)
# FCOverlap
fco = FranckCondonOverlap()
# check factorial
assert(fco.factorial(8) == factorial(8))
# the second test is useful according to the implementation
assert(fco.factorial(5) == factorial(5))
# check T=0 and n=0 equality
S = np.array([1, 2.1, 34])
m = 5
assert(((fco.directT0(m, S) - fco.direct(0, m, S)) / fco.directT0(m, S) <
1e-15).all())
# check symmetry
S = 2
n = 3
assert(fco.direct(n, m, S) == fco.direct(m, n, S))
# ---------------------------
# specials
S = 1.5
for m in [2, 7]:
equal(fco.direct0mm1(m, S)**2,
fco.direct(1, m, S) * fco.direct(m, 0, S), 1.e-17)
equal(fco.direct0mm2(m, S)**2,
fco.direct(2, m, S) * fco.direct(m, 0, S), 1.e-17)