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 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_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_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_h(self):
# Test h for all units (bar=False)
self.assertAlmostEqual(c.h('J s', bar=False), self.ans.at['test_h', 0])
self.assertAlmostEqual(c.h('kJ s', bar=False), self.ans.at['test_h',
1])
self.assertAlmostEqual(c.h('eV s', bar=False), self.ans.at['test_h',
2])
self.assertAlmostEqual(c.h('Eh s', bar=False), self.ans.at['test_h',
3])
self.assertAlmostEqual(c.h('Ha s', bar=False), self.ans.at['test_h',
4])
# Test h for all units (bar=True)
self.assertAlmostEqual(c.h('J s', bar=True), self.ans.at['test_h', 5])
self.assertAlmostEqual(c.h('kJ s', bar=True), self.ans.at['test_h', 6])
self.assertAlmostEqual(c.h('eV s', bar=True), self.ans.at['test_h', 7])
self.assertAlmostEqual(c.h('Eh s', bar=True), self.ans.at['test_h', 8])
self.assertAlmostEqual(c.h('Ha s', bar=True), self.ans.at['test_h', 9])
# Test h raises an error when an supported unit is passed
with self.assertRaises(KeyError):
c.h('arbitrary unit')
# <a id='section_3'></a>
# # 3. Constants
#
# The [constants module](https://vlachosgroup.github.io/pMuTT/constants.html) has a wide variety of functions for constants and unit conversion.
# <a id='section_3_1'></a>
# ## 3.1. Access common constants in appropriate units
# Below, we access Planck's constant in J s.
# In[1]:
from pmutt import constants as c
h1 = c.h('eV s', bar=True)
print('h = {} eV s'.format(h1))
# <a id='section_3_2'></a>
# ## 3.2. Convert between units
# Below, we convert 12 atm of pressure to psi.
# In[2]:
from pmutt import constants as c
P_atm = 12. # atm
P_psi = c.convert_unit(num=P_atm, initial='atm', final='psi')
print('{} atm = {} psi'.format(P_atm, P_psi))
def test_h(self):
self.assertEqual(c.h('J s', bar=False), 6.626070040e-34)
self.assertEqual(c.h('J s', bar=True), 6.626070040e-34 / (2. * np.pi))
with self.assertRaises(KeyError):
c.h('arbitrary unit')