def fitStatmechPseudo(Tlist, Cvlist, Nvib, Nrot, molecule=None):
"""
Fit `Nvib` harmonic oscillator and `Nrot` hindered internal rotor modes to
the provided dimensionless heat capacities `Cvlist` at temperatures `Tlist`
in K. This method assumes that there are relatively few heat capacity points
provided, so the vibrations must be combined into one real vibration and
two "pseudo-vibrations" and the hindered rotors must be combined into a
single "pseudo-rotor".
"""
# Construct the lower and upper bounds for each variable
bounds = []
# x[0] corresponds to the first harmonic oscillator (real) frequency
bounds.append((hoFreqLowerBound, hoFreqUpperBound))
# x[1] corresponds to the degeneracy of the second harmonic oscillator
bounds.append((1.0, float(Nvib - 2)))
# x[2] corresponds to the second harmonic oscillator pseudo-frequency
bounds.append((hoFreqLowerBound, hoFreqUpperBound))
# x[3] corresponds to the third harmonic oscillator pseudo-frequency
bounds.append((hoFreqLowerBound, hoFreqUpperBound))
# x[4] corresponds to the hindered rotor pseudo-frequency
bounds.append((hrFreqLowerBound, hrFreqUpperBound))
# x[5] corresponds to the hindered rotor pseudo-barrier
bounds.append((hrBarrLowerBound, hrBarrUpperBound))
# Construct the initial guess
x0 = numpy.zeros(6, numpy.float64) # Initial guess
x0[0] = 300.0
x0[1] = float(math.floor((Nvib - 1) / 2.0))
x0[2] = 800.0
x0[3] = 1600.0
x0[4] = 100.0
x0[5] = 300.0
# Execute the optimization
fit = PseudoFit(Tlist, Cvlist, Nvib, Nrot)
fit.initialize(Neq=len(Tlist), Nvars=len(x0), Ncons=0, bounds=bounds, maxIter=maxIter)
x, igo = fit.solve(x0)
# Check that the results of the optimization are valid
if not numpy.isfinite(x).all():
raise StatmechFitError('Returned solution vector is nonsensical: x = {0}.'.format(x))
if igo == 8:
logging.warning('Maximum number of iterations reached when fitting spectral data for {0}.'.format(molecule.toSMILES()))
# Postprocess optimization results
Nvib2 = int(round(x[1]))
Nvib3 = Nvib - Nvib2 - 1
if Nvib2 < 0 or Nvib2 > Nvib-1 or Nvib3 < 0 or Nvib3 > Nvib-1:
raise StatmechFitError('Invalid degeneracies {0} and {1} fitted for pseudo-frequencies.'.format(Nvib2, Nvib3))
vib = [x[0]]
for i in range(Nvib2): vib.append(x[2])
for i in range(Nvib3): vib.append(x[3])
hind = []
for i in range(Nrot):
hind.append((x[4], x[5]))
return vib, hind
def fitStatmechToHeatCapacity(Tlist, Cvlist, Nvib, Nrot, molecule=None):
"""
For a given set of dimensionless heat capacity data `Cvlist` corresponding
to temperature list `Tlist` in K, fit `Nvib` harmonic oscillator and `Nrot`
hindered internal rotor modes. External and other previously-known modes
should have already been removed from `Cvlist` prior to calling this
function. You must provide at least 7 values for `Cvlist`.
This function returns a list containing the fitted vibrational frequencies
in a :class:`HarmonicOscillator` object and the fitted 1D hindered rotors
in :class:`HinderedRotor` objects.
"""
# You must specify at least 7 heat capacity points to use in the fitting;
# you can specify as many as you like above that minimum
if len(Tlist) < 7:
raise StatmechFitError('You must specify at least 7 heat capacity points to fitStatmechToHeatCapacity().')
if len(Tlist) != len(Cvlist):
raise StatmechFitError('The number of heat capacity points ({0:d}) does not match the number of temperatures provided ({1:d}).'.format(len(Cvlist), len(Tlist)))
# The number of optimization variables available is constrained to be less
# than the number of heat capacity points
# This is also capped to a (somewhat arbitrarily chosen) maximum of 16
maxVariables = len(Tlist) - 1
if maxVariables > 16: maxVariables = 16
# The type of variables fitted depends on the values of Nvib and Nrot and
# the number of heat capacity points provided
# For low values of Nvib and Nrot, we can fit the individual
# parameters directly
# For high values of Nvib and/or Nrot we are limited by the number of
# temperatures we are fitting at, and so we can only fit
# pseudo-oscillators and/or pseudo-rotors
vib = []; hind = []
if Nvib <= 0 and Nrot <= 0:
pass
elif Nvib + 2 * Nrot <= maxVariables:
vib, hind = fitStatmechDirect(Tlist, Cvlist, Nvib, Nrot, molecule)
elif Nvib + 2 <= maxVariables:
vib, hind = fitStatmechPseudoRotors(Tlist, Cvlist, Nvib, Nrot, molecule)
else:
vib, hind = fitStatmechPseudo(Tlist, Cvlist, Nvib, Nrot, molecule)
modes = []
if Nvib > 0:
vib.sort()
ho = HarmonicOscillator(frequencies=(vib[:],"cm^-1"))
modes.append(ho)
for i in range(Nrot):
freq = hind[i][0]
barr = hind[i][1]
inertia = (barr*constants.c*100.0*constants.h) / (8 * math.pi * math.pi * (freq*constants.c*100.0)**2)
barrier = barr*constants.c*100.0*constants.h*constants.Na
hr = HinderedRotor(inertia=(inertia*constants.Na*1e23,"amu*angstrom^2"), barrier=(barrier/1000.,"kJ/mol"), symmetry=1, semiclassical=False, quantum=False)
modes.append(hr)
# Return the fitted modes
return modes
def fit_statmech_direct(Tlist, Cvlist, n_vib, n_rot, molecule=None):
"""
Fit `n_vib` harmonic oscillator and `n_rot` hindered internal rotor modes to
the provided dimensionless heat capacities `Cvlist` at temperatures `Tlist`
in K. This method assumes that there are enough heat capacity points
provided that the vibrational frequencies and hindered rotation frequency-
barrier pairs can be fit directly.
"""
# Construct the lower and upper bounds for each variable
bounds = []
# Bounds for harmonic oscillator frequencies
for i in range(n_vib):
bounds.append((ho_freq_lower_bound, ho_freq_upper_bound))
# Bounds for hindered rotor frequencies and barrier heights
for i in range(n_rot):
bounds.append((hr_freq_lower_bound, hr_freq_upper_bound))
bounds.append((hr_barr_lower_bound, hr_barr_upper_bound))
# Construct the initial guess
# Initial guesses within each mode type must be distinct or else the
# optimization will fail
x0 = np.zeros(n_vib + 2 * n_rot, np.float64)
# Initial guess for harmonic oscillator frequencies
if n_vib > 0:
x0[0] = 200.0
x0[1:n_vib] = np.linspace(800.0, 1600.0, n_vib - 1)
# Initial guess for hindered rotor frequencies and barrier heights
if n_rot > 0:
x0[n_vib] = 100.0
x0[n_vib + 1] = 100.0
for i in range(1, n_rot):
x0[n_vib + 2 * i] = x0[n_vib + 2 * i - 2] + 20.0
x0[n_vib + 2 * i + 1] = x0[n_vib + 2 * i - 1] + 100.0
# Execute the optimization
fit = DirectFit(Tlist, Cvlist, n_vib, n_rot)
fit.initialize(Neq=len(Tlist), Nvars=len(x0), Ncons=0, bounds=bounds, maxIter=max_iter)
x, igo = fit.solve(x0)
# Check that the results of the optimization are valid
if not np.isfinite(x).all():
raise StatmechFitError('Returned solution vector is nonsensical: x = {0}.'.format(x))
if igo == 8:
logging.warning('Maximum number of iterations reached when fitting spectral data for '
'{0}.'.format(molecule.to_smiles()))
elif igo > 8:
logging.warning('A solver error occured when fitting spectral data for {0}.'.format(molecule.to_smiles()))
logging.debug('Fitting remaining heat capacity to {0} vibrations and {1} rotations'.format(n_vib, n_rot))
logging.debug('The residuals for heat capacity values is {}'.format(fit.evaluate(x)[0]))
# Postprocess optimization results
vib = list(x[0:n_vib])
hind = []
for i in range(n_rot):
hind.append((x[n_vib + 2 * i], x[n_vib + 2 * i + 1]))
return vib, hind
def fitStatmechDirect(Tlist, Cvlist, Nvib, Nrot, molecule=None):
"""
Fit `Nvib` harmonic oscillator and `Nrot` hindered internal rotor modes to
the provided dimensionless heat capacities `Cvlist` at temperatures `Tlist`
in K. This method assumes that there are enough heat capacity points
provided that the vibrational frequencies and hindered rotation frequency-
barrier pairs can be fit directly.
"""
# Construct the lower and upper bounds for each variable
bounds = []
# Bounds for harmonic oscillator frequencies
for i in range(Nvib):
bounds.append((hoFreqLowerBound, hoFreqUpperBound))
# Bounds for hindered rotor frequencies and barrier heights
for i in range(Nrot):
bounds.append((hrFreqLowerBound, hrFreqUpperBound))
bounds.append((hrBarrLowerBound, hrBarrUpperBound))
# Construct the initial guess
# Initial guesses within each mode type must be distinct or else the
# optimization will fail
x0 = numpy.zeros(Nvib + 2*Nrot, numpy.float64)
# Initial guess for harmonic oscillator frequencies
if Nvib > 0:
x0[0] = 200.0
x0[1:Nvib] = numpy.linspace(800.0, 1600.0, Nvib-1)
# Initial guess for hindered rotor frequencies and barrier heights
if Nrot > 0:
x0[Nvib] = 100.0
x0[Nvib+1] = 100.0
for i in range(1, Nrot):
x0[Nvib+2*i] = x0[Nvib+2*i-2] + 20.0
x0[Nvib+2*i+1] = x0[Nvib+2*i-1] + 100.0
# Execute the optimization
fit = DirectFit(Tlist, Cvlist, Nvib, Nrot)
fit.initialize(Neq=len(Tlist), Nvars=len(x0), Ncons=0, bounds=bounds, maxIter=maxIter)
x, igo = fit.solve(x0)
# Check that the results of the optimization are valid
if not numpy.isfinite(x).all():
raise StatmechFitError('Returned solution vector is nonsensical: x = {0}.'.format(x))
if igo == 8:
logging.warning('Maximum number of iterations reached when fitting spectral data for {0}.'.format(molecule.toSMILES()))
# Postprocess optimization results
vib = list(x[0:Nvib])
hind = []
for i in range(Nrot):
hind.append((x[Nvib+2*i], x[Nvib+2*i+1]))
return vib, hind
def fit_statmech_pseudo(Tlist, Cvlist, n_vib, n_rot, molecule=None):
"""
Fit `n_vib` harmonic oscillator and `n_rot` hindered internal rotor modes to
the provided dimensionless heat capacities `Cvlist` at temperatures `Tlist`
in K. This method assumes that there are relatively few heat capacity points
provided, so the vibrations must be combined into one real vibration and
two "pseudo-vibrations" and the hindered rotors must be combined into a
single "pseudo-rotor".
"""
# Construct the lower and upper bounds for each variable
bounds = []
# x[0] corresponds to the first harmonic oscillator (real) frequency
bounds.append((ho_freq_lower_bound, ho_freq_upper_bound))
# x[1] corresponds to the degeneracy of the second harmonic oscillator
bounds.append((1.0, float(n_vib - 2)))
# x[2] corresponds to the second harmonic oscillator pseudo-frequency
bounds.append((ho_freq_lower_bound, ho_freq_upper_bound))
# x[3] corresponds to the third harmonic oscillator pseudo-frequency
bounds.append((ho_freq_lower_bound, ho_freq_upper_bound))
# x[4] corresponds to the hindered rotor pseudo-frequency
bounds.append((hr_freq_lower_bound, hr_freq_upper_bound))
# x[5] corresponds to the hindered rotor pseudo-barrier
bounds.append((hr_barr_lower_bound, hr_barr_upper_bound))
# Construct the initial guess
x0 = np.zeros(6, np.float64) # Initial guess
x0[0] = 300.0
x0[1] = float(math.floor((n_vib - 1) / 2.0))
x0[2] = 800.0
x0[3] = 1600.0
x0[4] = 100.0
x0[5] = 300.0
# Execute the optimization
fit = PseudoFit(Tlist, Cvlist, n_vib, n_rot)
fit.initialize(Neq=len(Tlist),
Nvars=len(x0),
Ncons=0,
bounds=bounds,
maxIter=max_iter)
x, igo = fit.solve(x0)
# Check that the results of the optimization are valid
if not np.isfinite(x).all():
raise StatmechFitError(
'Returned solution vector is nonsensical: x = {0}.'.format(x))
if igo == 8:
logging.warning(
'Maximum number of iterations reached when fitting spectral data for '
'{0}.'.format(molecule.to_smiles()))
if igo > 8:
logging.warning(
'A solver error occured when fitting spectral data for {0}.'.
format(molecule.to_smiles()))
logging.debug(
'Fitting remaining heat capacity to {0} vibrations and {1} rotations'.
format(n_vib, n_rot))
logging.debug('The residuals for heat capacity values is {}'.format(
fit.evaluate(x)[0]))
# Postprocess optimization results
n_vib2 = int(round(x[1]))
n_vib_3 = n_vib - n_vib2 - 1
if n_vib2 < 0 or n_vib2 > n_vib - 1 or n_vib_3 < 0 or n_vib_3 > n_vib - 1:
raise StatmechFitError('Invalid degeneracies {0} and {1} fitted for '
'pseudo-frequencies.'.format(n_vib2, n_vib_3))
vib = [x[0]]
for i in range(n_vib2):
vib.append(x[2])
for i in range(n_vib_3):
vib.append(x[3])
hind = []
for i in range(n_rot):
hind.append((x[4], x[5]))
return vib, hind