def test_get_A(self):
# Testing partition function method
exp_sm_q = self.H2O_TS_sm.get_q(T=c.T0('K'), include_ZPE=False) \
/ self.H2_sm.get_q(T=c.T0('K'), include_ZPE=False) \
/ self.O2_sm.get_q(T=c.T0('K'), include_ZPE=False)**0.5
exp_sm_A = c.kb('J/K') * c.T0('K') / c.h('J s') * exp_sm_q
exp_sm_q_rev = self.H2O_TS_sm.get_q(T=c.T0('K'), include_ZPE=False) \
/ self.H2O_sm.get_q(T=c.T0('K'), include_ZPE=False)
exp_sm_A_rev = c.kb('J/K') * c.T0('K') / c.h('J s') * exp_sm_q_rev
np.testing.assert_almost_equal(self.rxn_sm.get_A(T=c.T0('K')),
exp_sm_A,
decimal=0)
np.testing.assert_almost_equal(self.rxn_sm.get_A(T=c.T0('K'),
rev=True),
exp_sm_A_rev,
decimal=0)
# Testing entropy method
exp_sm_SoR = self.H2O_TS_sm.get_SoR(T=c.T0('K')) \
- self.H2_sm.get_SoR(T=c.T0('K')) \
- self.O2_sm.get_SoR(T=c.T0('K'))*0.5
exp_sm_A = c.kb('J/K') * c.T0('K') / c.h('J s') * np.exp(exp_sm_SoR)
exp_sm_SoR_rev = self.H2O_TS_sm.get_SoR(T=c.T0('K')) \
- self.H2O_sm.get_SoR(T=c.T0('K'))
exp_sm_A_rev = c.kb('J/K')*c.T0('K')/c.h('J s') \
* np.exp(exp_sm_SoR_rev)
np.testing.assert_almost_equal(self.rxn_sm.get_A(T=c.T0('K'),
use_q=False),
exp_sm_A,
decimal=0)
np.testing.assert_almost_equal(self.rxn_sm.get_A(T=c.T0('K'),
rev=True,
use_q=False),
exp_sm_A_rev,
decimal=0)
def __init__(self,
A_st=None,
atoms=None,
symmetrynumber=None,
inertia=None,
geometry=None,
vib_wavenumbers=None,
potentialenergy=None,
**kwargs):
super().__init__(atoms=atoms,
symmetrynumber=symmetrynumber,
geometry=geometry,
vib_wavenumbers=vib_wavenumbers,
potentialenergy=potentialenergy,
**kwargs)
self.A_st = A_st
self.atoms = atoms
self.geometry = geometry
self.symmetrynumber = symmetrynumber
self.inertia = inertia
self.etotal = potentialenergy
self.vib_energies = c.wavenumber_to_energy(np.array(vib_wavenumbers))
self.theta = np.array(self.vib_energies) / c.kb('eV/K')
self.zpe = sum(np.array(self.vib_energies)/2.) *\
c.convert_unit(initial='eV', final='kcal')*c.Na
if np.sum(self.vib_energies) != 0:
self.q_vib = np.product(
np.divide(1, (1 - np.exp(-self.theta / c.T0('K')))))
if self.phase == 'G':
if self.inertia is not None:
self.I3 = self.inertia
else:
self.I3 = atoms.get_moments_of_inertia() *\
c.convert_unit(initial='A2', final='m2') *\
c.convert_unit(initial='amu', final='kg')
self.T_I = c.h('J s')**2 / (8 * np.pi**2 * c.kb('J/K'))
if self.phase == 'G':
Irot = np.max(self.I3)
if self.geometry == 'nonlinear':
self.q_rot = np.sqrt(np.pi*Irot)/self.symmetrynumber *\
(c.T0('K')/self.T_I)**(3./2.)
else:
self.q_rot = (c.T0('K') * Irot /
self.symmetrynumber) / self.T_I
else:
self.q_rot = 0.
if self.A_st is not None:
self.MW = mw(self.elements) * c.convert_unit(initial='g',
final='kg') / c.Na
self.q_trans2D = self.A_st * (2 * np.pi * self.MW * c.kb('J/K') *
c.T0('K')) / c.h('J s')**2
def test_kb(self):
# Test kb for all units
self.assertAlmostEqual(c.kb('J/K'), self.ans.at['test_kb', 0])
self.assertAlmostEqual(c.kb('kJ/K'), self.ans.at['test_kb', 1])
self.assertAlmostEqual(c.kb('eV/K'), self.ans.at['test_kb', 2])
self.assertAlmostEqual(c.kb('cal/K'), self.ans.at['test_kb', 3])
self.assertAlmostEqual(c.kb('kcal/K'), self.ans.at['test_kb', 4])
self.assertAlmostEqual(c.kb('Eh/K'), self.ans.at['test_kb', 5])
self.assertAlmostEqual(c.kb('Ha/K'), self.ans.at['test_kb', 6])
# Test kb raises an error when an unsupported unit is passed
with self.assertRaises(KeyError):
c.kb('arbitrary unit')
def get_q(self, T, ignore_q_elec=True):
"""Calculates the partition function
:math:`q^{elec}=1 + \\omega_i \\exp\\bigg(-\\frac{E}{RT}\\bigg)`
Parameters
----------
T : float
Temperature in K
ignore_q_elec : bool, optional
Ignore contribution of electronic mode to partition function
. Often necessary since DFT's value for potentialenergy is
very negative causing q_elec to go to infinity. Default is True
Returns
-------
q_elec : float
Electronic partition function
"""
if ignore_q_elec:
return 1.
else:
if self.D0 is not None:
Epsilon = self.D0 / c.kb('eV/K') / T
else:
Epsilon = self.get_UoRT(T=T)
return self._degeneracy * (1 + np.exp(-Epsilon))
def get_SoR(self, T, P=c.P0('bar')):
"""Calculates the dimensionless entropy
:math:`\\frac{S^{trans}}{R}=1+\\frac{n_{degrees}}{2}+\\log\\bigg(\\big(
\\frac{2\\pi mk_bT}{h^2})^\\frac{n_{degrees}}{2}\\frac{RT}{PN_a}\\bigg)`
Parameters
----------
T : float
Temperature in K
P : float, optional
Pressure (bar) or pressure-like quantity.
Default is atmospheric pressure
Returns
-------
SoR_trans : float
Translational dimensionless entropy
"""
V = self.get_V(T=T, P=P)
unit_mass = self.molecular_weight *\
c.convert_unit(initial='g', final='kg')/c.Na
return 1. + float(self.n_degrees)/2. \
+ np.log((2.*np.pi*unit_mass*c.kb('J/K')*T/c.h('J s')**2)
** (float(self.n_degrees)/2.)*V/c.Na)
def get_A(self,
sden_operation='min',
include_entropy=True,
T=c.T0('K'),
units='molec/cm2',
**kwargs):
"""Calculates the preexponential factor in the Cantera format
Parameters
----------
sden_operation : str, optional
Site density operation to use. Default is 'min'
include_entropy : bool, optional
If True, includes the entropy of activation. Default is True
T : float, optional
Temperature in K. Default is 298.15 K
units : str or :class:`~pmutt.omkm.units.Units`, optional
Units for A. If `Units` class specified, determines the units for A.
Default is 'molec/cm2'
kwargs : keyword arguments
Parameters required to calculate pre-exponential factor
"""
if self.transition_state is None or not include_entropy:
A = c.kb('J/K') / c.h('J s')
else:
A = super().get_A(T=T, **kwargs) / T
# Uses site with highest site density
site_dens = []
for reactant, stoich in zip(self.reactants, self.reactants_stoich):
# Skip species without a catalyst site
try:
site_den = reactant.phase.site_density
except AttributeError:
continue
site_dens.extend([site_den] * int(stoich))
# Apply the operation to the site densities
if len(site_dens) == 0:
err_msg = ('At least one species requires a catalytic site with '
'site density to calculate A.')
raise ValueError(err_msg)
eff_site_den = _apply_numpy_operation(quantity=site_dens,
operation=sden_operation,
verbose=False)
# Convert site density to appropriate unit
if isinstance(units, Units):
quantity_unit = units.quantity
area_unit = '{}2'.format(units.length)
else:
quantity_unit, area_unit = units.split('/')
eff_site_den = eff_site_den\
*c.convert_unit(initial='mol', final=quantity_unit)\
/c.convert_unit(initial='cm2', final=area_unit)
n_surf = self._get_n_surf()
A = A / eff_site_den**(n_surf - 1)
return A
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
"""
return 0.5 * c.kb('eV/K') * np.sum(self._valid_vib_temperatures)
def get_ZPE(self):
"""Calculates the zero point energy
:math:`u^0_E=u+\\frac{3}{2}\\Theta_E k_B`
Returns
-------
zpe : float
Zero point energy in eV
"""
return self.interaction_energy \
+ 1.5*self.einstein_temperature*c.kb('eV/K')
def get_UoRT(self, T):
"""Calculates the imensionless internal energy
:math:`\\frac{U^{elec}}{RT}=\\frac{E}{RT}`
Parameters
----------
T : float
Temperature in K
Returns
-------
UoRT_elec : float
Electronic dimensionless internal energy
"""
return (self.potentialenergy) / c.kb('eV/K') / T
def _get_SoR_RRHO(self, T, vib_inertia):
"""Calculates the dimensionless RRHO contribution to entropy
Parameters
----------
T : float
Temperature in K
vib_inertia : float
Vibrational inertia in kg m2
Returns
-------
SoR_RHHO : float
Dimensionless entropy of Rigid Rotor Harmonic Oscillator
"""
return 0.5 + np.log(
(8. * np.pi**3 * vib_inertia * c.kb('J/K') * T / c.h('J s')**2)**
0.5)
def get_UoRT(self, T):
"""Calculates the dimensionless internal energy
:math:`\\frac{U^{vib}}{RT}=\\frac{u^0_E}{k_BT}+3\\frac{\\Theta_E}{T}
\\bigg(\\frac{\\exp(-\\frac{\\Theta_E}{T})}{1-\\exp(-\\frac{\\Theta_E}
{T})}\\bigg)`
Parameters
----------
T : float
Temperature in K
Returns
-------
UoRT_vib : float
Vibrational dimensionless internal energy
"""
theta_E = self.einstein_temperature
return self.get_ZPE()/c.kb('eV/K')/T \
+ 3.*theta_E/T*np.exp(-theta_E/T)/(1. - np.exp(-theta_E/T))
def get_q(self, T):
"""Calculates the partition function
:math:`q^{vib}=\\exp\\bigg({\\frac{-u}{k_BT}}\\bigg)\\bigg(\\frac{
\\exp(-\\frac{\\Theta_E}{2T})}{1-\\exp(\\frac{-\\Theta_E}{T})}\\bigg)`
Parameters
----------
T : float
Temperature in K
Returns
-------
q_vib : float
Vibrational partition function
"""
u = self.interaction_energy
theta_E = self.einstein_temperature
return np.exp(-u/c.kb('eV/K')/T) \
* (np.exp(-theta_E/2./T)/(1. - np.exp(-theta_E/T)))
def get_UoRT(self, T):
"""Calculates dimensionless internal energy
:math:`\\frac{U^{vib}}{RT} = \\frac{u_D^o}{RT} + 3F\\bigg(\\frac{
\\Theta_D}{T}\\bigg)`
:math:`F\\bigg(\\frac{\\Theta_D}{T}\\bigg) = 3\\bigg(\\frac{T}{
\\Theta_D}\\bigg)^3 \\int_0^{\\frac{\\Theta_D}{T}} \\frac{x^3 e^x}
{e^x-1} dx`
Parameters
----------
T : float
Temperature in K
Returns
-------
UoRT : float
Dimensionless internal energy
"""
return self.get_ZPE()/c.kb('eV/K')/T \
+ 3.*self._get_intermediate_fn(T=T, fn=self._F_integrand)
def get_q(self, T):
"""Calculate the partition function
:math:`q^{vib} = \\exp\\bigg(-\\frac{u}{3k_B T} - \\frac{3}{8}
\\frac{\\Theta_D}{T} - G\\big(\\frac{\\Theta_D}{T}\\big)\\bigg)`
:math:`G\\bigg(\\frac{\\Theta_D}{T}\\bigg) = 3\\bigg(\\frac{T}{
\\Theta_D}\\bigg)^3\\int_0^{\\frac{\\Theta_D}{T}}x^2 \\ln
\\bigg(1-e^{-x}\\bigg)dx`
Parameters
----------
T : float
Temperature in K
Returns
-------
q : float
Partition function
"""
G = self._get_intermediate_fn(T=T, fn=self._G_integrand)
return np.exp(-self.interaction_energy/3./c.kb('eV/K')/T \
-3./8.*self.debye_temperature/T - G)
def get_q(self, T, P=c.P0('bar')):
"""Calculates the partition function
:math:`q_{trans} = \\bigg(\\frac{2\\pi \\sum_{i}^{atoms}m_ikT}{h^2}
\\bigg)^\\frac {n_{degrees}} {2}V`
Parameters
----------
T : float
Temperature in K
P : float, optional
Pressure (bar) or pressure-like quantity.
Default is atmospheric pressure
Returns
-------
q_trans : float
Translational partition function
"""
V = self.get_V(T=T, P=P)
unit_mass = self.molecular_weight *\
c.convert_unit(initial='g', final='kg')/c.Na
return V*(2*np.pi*c.kb('J/K')*T*unit_mass/c.h('J s')**2) \
** (float(self.n_degrees)/2.)
def test_kb(self):
self.assertEqual(c.kb('J/K'), 1.38064852e-23)
with self.assertRaises(KeyError):
c.kb('arbitrary unit')
def test_get_HoRT(self):
exp_HoRT = (self.u + 9./8.*self.theta_D*c.kb('eV/K')) \
/c.kb('eV/K')/self.T \
+ 3.*self.F
self.assertAlmostEqual(self.vib_Ag.get_HoRT(T=self.T), exp_HoRT, 4)
def test_get_ZPE(self):
self.assertAlmostEqual(self.vib_Ag.get_ZPE(),
self.u + 9. / 8. * self.theta_D * c.kb('eV/K'))
def test_get_q(self):
exp_q = np.exp(-self.u/3./c.kb('eV/K')/self.T \
-3./8.*self.theta_D/self.T \
-self.G)
self.assertAlmostEqual(self.vib_Ag.get_q(T=self.T), exp_q)
