def applyInverseLaplaceTransformMethod(kinetics, E0, Elist, densStates, T=None):
"""
Calculate the microcanonical rate coefficient for a reaction using the
inverse Laplace transform method, where `kinetics` is the high pressure
limit rate coefficient, `E0` is the ground-state energy of the transition
state, `Elist` is the array of energies in J/mol at which to evaluate the
microcanonial rate, and `densStates` is the density of states of the
reactant.
"""
k = numpy.zeros_like((Elist))
if isinstance(kinetics, ArrheniusModel) and (T is not None or (kinetics.Ea >= 0 and kinetics.n >= 0)):
A = kinetics.A
n = kinetics.n
Ea = kinetics.Ea
dE = Elist[1] - Elist[0]
# The inverse Laplace transform is not defined for Ea < 0 or n < 0
# In these cases we move the offending portion into the preexponential
# at the temperature of interest
# This is an approximation, but it's not worth a more robust procedure
if Ea < 0:
A *= math.exp(-Ea / constants.R / T)
Ea = 0.0
if n < 0:
A *= T**n
n = 0.0
if n == 0:
# Determine the microcanonical rate directly
s = int(math.floor(Ea / dE))
for r in range(len(Elist)):
if Elist[r] > E0 and densStates[r] != 0:
k[r] = A * densStates[r - s] / densStates[r]
elif n > 0.0:
import scipy.special
# Evaluate the inverse Laplace transform of the T**n piece, which only
# exists for n >= 0
phi = numpy.zeros(len(Elist), numpy.float64)
for i, E in enumerate(Elist):
if E == 0.0:
phi[i] = 0.0
else:
phi[i] = E**(n-1) / (constants.R**n * scipy.special.gamma(n))
# Evaluate the convolution
phi = convolve(phi, densStates, Elist)
# Apply to determine the microcanonical rate
s = int(math.floor(Ea / dE))
for r in range(len(Elist)):
if Elist[r] > E0 and densStates[r] != 0:
k[r] = A * phi[r - s] / densStates[r]
else:
raise ReactionError('Unable to use inverse Laplace transform method for non-Arrhenius kinetics or for n < 0.')
return k
def calculateDensitiesOfStates(self, Elist, E0):
"""
Calculate and return an array containing the density of states for each
isomer and reactant channel in the network. `Elist` represents the
array of energies in J/mol at which to compute each density of states.
The ground-state energies `E0` in J/mol are used to shift each density
of states for each configuration to the same zero of energy. The
returned density of states is in units of mol/J.
"""
Ngrains = len(Elist)
Nisom = len(self.isomers)
Nreac = len(self.reactants)
densStates = numpy.zeros((Nisom+Nreac, Ngrains), numpy.float64)
dE = Elist[1] - Elist[0]
# Densities of states for isomers
for i in range(Nisom):
logging.debug('Calculating density of states for isomer "%s"' % self.isomers[i])
densStates0 = self.isomers[i].states.getDensityOfStates(Elist)
# Shift to common zero of energy
r0 = int(round(E0[i] / dE))
if r0 < 0: r0 = 0
densStates[i,r0:] = densStates0[:-r0+len(densStates0)]
# Densities of states for reactant channels
# (Only if not minimizing the number of density of states calculations)
if not settings.minimizeDensityOfStatesCalculations:
for n in range(Nreac):
r0 = int(round(E0[n+Nisom] / dE))
if self.reactants[n][0].states is not None and self.reactants[n][1].states is not None:
logging.debug('Calculating density of states for reactant channel "%s"' % (' + '.join([str(spec) for spec in self.reactants[n]])))
densStates0 = self.reactants[n][0].states.getDensityOfStates(Elist)
densStates1 = self.reactants[n][1].states.getDensityOfStates(Elist)
densStates0 = states.convolve(densStates0, densStates1, Elist)
# Shift to common zero of energy
densStates[n+Nisom,r0:] = densStates0[:-r0+len(densStates0)]
elif self.reactants[n][0].states is not None:
logging.debug('Calculating density of states for reactant channel "%s"' % (' + '.join([str(spec) for spec in self.reactants[n]])))
densStates0 = self.reactants[n][0].states.getDensityOfStates(Elist)
# Shift to common zero of energy
densStates[n+Nisom,r0:] = densStates0[:-r0+len(densStates0)]
elif self.reactants[n][1].states is not None:
logging.debug('Calculating density of states for reactant channel "%s"' % (' + '.join([str(spec) for spec in self.reactants[n]])))
densStates0 = self.reactants[n][1].states.getDensityOfStates(Elist)
# Shift to common zero of energy
densStates[n+Nisom,r0:] = densStates0[:-r0+len(densStates0)]
else:
logging.debug('NOT calculating density of states for reactant channel "%s"' % (' + '.join([str(spec) for spec in self.reactants[n]])))
logging.debug('')
return densStates
