def get_UoRT(self, T):
"""Calculates the dimensionless internal energy
:math:`\\frac {U^{qRRHO}}{RT} = \\sum_{i}\\omega_i\\frac{U^{RRHO}}{RT}
+ \\frac{1}{2}(1-\\omega_i)`
:math:`\\frac {U^{RRHO}_{i}}{RT} = \\frac{\\Theta_i}{T} \\bigg(
\\frac{1}{2} + \\frac{\\exp(-\\frac{\\Theta_i}{T})}{1-\\exp(-\\frac{
\\Theta_i}{T})}\\bigg)`
Parameters
----------
T : float
Temperature in K
Returns
-------
UoRT_vib : float
Vibrational dimensionless internal energy
"""
UoRT_QRRHO = []
valid_wavenumbers = _get_valid_vib_wavenumbers(
wavenumbers=self.vib_wavenumbers,
substitute=self.imaginary_substitute)
vib_temperatures = c.wavenumber_to_temp(valid_wavenumbers)
scaled_wavenumbers = self._get_scaled_wavenumber(valid_wavenumbers)
for theta_i, w_i in zip(vib_temperatures, scaled_wavenumbers):
UoRT_RRHO = self._get_UoRT_RRHO(T=T, vib_temperature=theta_i)
UoRT_QRRHO.append(w_i * UoRT_RRHO + (1. - w_i) * 0.5)
return np.sum(UoRT_QRRHO)
def get_CvoR(self, T):
"""Calculates the dimensionless heat capacity at constant volume
:math:`\\frac {C_{v}^{qRRHO}}{R} = \\sum_{i}\\omega_i\\frac{C_{v,i}
^{RRHO}}{R} + \\frac{1}{2}(1-\\omega_i)`
:math:`\\frac{C_{v}^{RRHO}}{R} = \\sum_{i}\\exp \\bigg(-\\frac{
\\Theta_i}{T}\\bigg) \\bigg(\\frac{\\Theta_i}{T}\\frac{1}{1-\\exp(-
\\frac{\\Theta_i}{T})}\\bigg)^2`
Parameters
----------
T : float
Temperature in K
Returns
-------
CvoR_vib : float
Vibrational dimensionless heat capacity at constant volume
"""
CvoR = []
valid_wavenumbers = _get_valid_vib_wavenumbers(
wavenumbers=self.vib_wavenumbers,
substitute=self.imaginary_substitute)
vib_temperatures = c.wavenumber_to_temp(valid_wavenumbers)
vib_dimless = vib_temperatures / T
scaled_wavenumbers = self._get_scaled_wavenumber(valid_wavenumbers)
for vib_dimless_i, w_i in zip(vib_dimless, scaled_wavenumbers):
CvoR_RRHO = np.exp(-vib_dimless_i) \
* (vib_dimless_i/(1. - np.exp(-vib_dimless_i)))**2
CvoR.append(w_i * CvoR_RRHO + 0.5 * (1. - w_i))
return np.sum(CvoR)
def get_ZPE(self):
"""Calculates the zero point energy
:math:`ZPE=\\frac{1}{2}k_b\\sum_i \\Theta_{V,i}`
Returns
-------
zpe : float
Zero point energy in eV
"""
valid_wavenumbers = _get_valid_vib_wavenumbers(
wavenumbers=self.vib_wavenumbers,
substitute=self.imaginary_substitute)
vib_temperatures = c.wavenumber_to_temp(valid_wavenumbers)
return 0.5 * c.kb('eV/K') * np.sum(vib_temperatures)
def get_ZPE(self):
"""Calculates the zero point energy
:math:`ZPE=\\frac{1}{2}k_b\\sum_i \\omega_i\\Theta_{V,i}`
Returns
-------
zpe : float
Zero point energy in eV
"""
zpe = []
valid_wavenumbers = _get_valid_vib_wavenumbers(
wavenumbers=self.vib_wavenumbers,
substitute=self.imaginary_substitute)
vib_temperatures = c.wavenumber_to_temp(valid_wavenumbers)
scaled_wavenumbers = self._get_scaled_wavenumber(valid_wavenumbers)
for theta_i, w_i in zip(vib_temperatures, scaled_wavenumbers):
zpe = 0.5 * c.kb('eV/K') * theta_i * w_i
return np.sum(zpe)
def _get_vib_dimless(wavenumbers, T, substitute=None):
"""Calculates dimensionless temperatures for the wavenumbers and
temperature specified
Parameters
----------
wavenumbers : (N,) np.ndarray
Wavenumbers in 1/cm
T : float
Temperature in K
substitute : float, optional
Value to use to replace imaginary frequencies. If not specified,
imaginary frequencies are ignored. Default is None
Returns
-------
vib_dimless : (N,) np.ndarray
Vibrational temperatures normalized by T
"""
valid_wavenumbers = _get_valid_vib_wavenumbers(wavenumbers=wavenumbers,
substitute=substitute)
vib_dimless = c.wavenumber_to_temp(valid_wavenumbers) / T
return vib_dimless
def get_SoR(self, T):
"""Calculates the dimensionless entropy
:math:`\\frac{S^{qRRHO}}{R}=\\sum_i\\omega_i\\frac{S_i^{H}}{R}+(1-
\\omega_i)\\frac{S_i^{RRHO}}{R}`
:math:`\\frac {S^{RRHO}_i}{R} = \\frac{1}{2} + \\log \\bigg(\\bigg[
\\frac{8\\pi^3\\mu'_ik_BT}{h^2}\\bigg]^{\\frac{1}{2}}\\bigg)`
:math:`\\frac {S^{H}_i}{R}=\\bigg(\\frac{\\Theta_i}{T}\\bigg)\\frac{1}
{\\exp(\\frac{\\Theta_i}{T})-1}-\\log\\bigg(1-\\exp(\\frac{-\\Theta_i}
{T})\\bigg)`
Parameters
----------
T : float
Temperature in K
Returns
-------
SoR_vib : float
Vibrational dimensionless entropy
"""
SoR_QRRHO = []
valid_wavenumbers = _get_valid_vib_wavenumbers(
wavenumbers=self.vib_wavenumbers,
substitute=self.imaginary_substitute)
vib_temperatures = c.wavenumber_to_temp(valid_wavenumbers)
scaled_inertia = self._get_scaled_inertia(valid_wavenumbers)
scaled_wavenumbers = self._get_scaled_wavenumber(valid_wavenumbers)
for theta_i, mu_i, w_i in zip(vib_temperatures, scaled_inertia,
scaled_wavenumbers):
SoR_H = self._get_SoR_H(T=T, vib_temperature=theta_i)
SoR_RRHO = self._get_SoR_RRHO(T=T, vib_inertia=mu_i)
SoR_QRRHO.append(w_i * SoR_H + (1. - w_i) * SoR_RRHO)
return np.sum(SoR_QRRHO)
def test_wavenumber_to_temp(self):
self.assertAlmostEqual(c.wavenumber_to_temp(1.), 1.4387773538277204)