def get_SoR(self, Ts, P=1., verbose=False):
"""Calculate the dimensionless entropy.
Parameters:
Ts : float or (N,) `numpy.ndarray`_
Temperature(s) in K
P : float, optional
Pressure in atm. Default is 1 atm.
verbose : bool
Whether a table breaking down each contribution should be printed
Returns:
SoR : float or (N,) `numpy.ndarray`_
Dimensionless entropy (S/R) at the specified temperature and pressure
"""
try:
iter(Ts)
except TypeError:
SoR = self.model.get_entropy(
Ts,
pressure=P * c.convert_unit(from_='atm', to='Pa'),
verbose=verbose) / c.R('eV/K')
else:
SoR = np.zeros_like(Ts)
for i, T in enumerate(Ts):
SoR[i] = self.model.get_entropy(
T,
pressure=P * c.convert_unit(from_='atm', to='Pa'),
verbose=verbose) / c.R('eV/K')
return SoR
def get_GoRT(self, Ts, P=1., verbose=False):
"""Returns the dimensionless Gibbs energy at a given temperature
Parameters:
Ts : float or (N,) `numpy.ndarray`_
Temperature(s) in K
P : float, optional
Pressure in bar. Default is 1 atm.
verbose : bool
Whether a table breaking down each contribution should be printed
Returns:
GoRT : float or (N,) `numpy.ndarray`_
Dimensionless heat capacity (G/RT) at the specified temperature
"""
try:
iter(Ts)
except TypeError:
GoRT = self.model.get_gibbs_energy(
Ts, pressure=P*c.convert_unit(from_='bar', to='Pa'), verbose=verbose) / \
(c.kb('eV/K') * Ts)
else:
GoRT = np.zeros_like(Ts)
for i, T in enumerate(Ts):
GoRT[i] = self.model.get_gibbs_energy(
T, pressure=P*c.convert_unit(from_='bar', to='Pa'), verbose=verbose) / \
(c.kb('eV/K') * T)
return GoRT
def __init__(self,
A_st=None,
atoms=None,
symmetrynumber=None,
inertia=None,
geometry=None,
vib_energies=None,
potentialenergy=None,
**kwargs):
super().__init__(atoms=atoms,
symmetrynumber=symmetrynumber,
geometry=geometry,
vib_energies=vib_energies,
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 = vib_energies
self.theta = np.array(vib_energies) / c.kb('eV/K')
self.zpe = sum(np.array(vib_energies)/2.) *\
c.convert_unit(from_='eV', to='kcal')*c.Na
if np.sum(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(from_='A2', to='m2') *\
c.convert_unit(from_='amu', to='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(from_='g',
to='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_GoRT(self, Ts, P=1., verbose=False):
"""Calculate the dimensionless Gibbs energy.
Parameters:
Ts : float or list
Temperature(s) in K
P : float
Pressure in atm. Default is 1 atm
verbose : bool
Whether a table breaking down each contribution should be printed
Returns:
GoRT: float or (N,) `numpy.ndarray`_
Dimensionless heat capacity (G/RT) at the specified temperature
"""
press = P * c.convert_unit(from_='atm', to='Pa')
try:
iter(Ts)
except TypeError:
GoRT = self.model.get_helmholtz_energy(Ts, verbose=verbose) / \
(c.kb('eV/K') * Ts)
else:
GoRT = np.zeros_like(Ts)
for i, T in enumerate(Ts):
GoRT[i] = self.model.get_helmholtz_energy(T, verbose=verbose) / \
(c.kb('eV/K') * T)
return GoRT
def get_Vm(self, T=c.T0('K'), P=c.P0('bar'), gas_phase=True):
"""Calculates the molar volume of a van der Waals gas
Parameters
----------
T : float, optional
Temperature in K. Default is standard temperature
P : float, optional
Pressure in bar. Default is standard pressure
gas_phase : bool, optional
Relevant if system is in vapor-liquid equilibrium. If True,
return the larger volume (gas phase). If False, returns the
smaller volume (liquid phase).
Returns
-------
Vm : float
Volume in m3
"""
P_SI = P * c.convert_unit(from_='bar', to='Pa')
Vm = np.roots([
P_SI, -(P_SI * self.b + c.R('J/mol/K') * T), self.a,
-self.a * self.b
])
real_Vm = np.real([Vm_i for Vm_i in Vm if np.isreal(Vm_i)])
if gas_phase:
return np.max(real_Vm)
else:
return np.min(real_Vm)
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(from_='g', to='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 test_convert_unit(self):
self.assertEqual(c.convert_unit(num=0., from_='C', to='K'), 273.15)
self.assertEqual(c.convert_unit(from_='m', to='cm'), 100.)
with self.assertRaises(ValueError):
c.convert_unit(from_='cm', to='J')
with self.assertRaises(ValueError):
c.convert_unit(from_='arbitrary unit', to='J')
with self.assertRaises(ValueError):
c.convert_unit(from_='cm', to='arbitrary unit')
def get_Pc(self):
"""Calculates the critical pressure
Returns
-------
Pc : float
Critical pressure in bar
"""
return self.a / 27. / self.b**2 * c.convert_unit(from_='Pa', to='bar')
def get_rot_temperatures_from_atoms(atoms, geometry=None):
"""Calculate the rotational temperatures from ase.Atoms object
Parameters
----------
atoms : ase.Atoms object
Atoms object
geometry : str, optional
Geometry of molecule. If not specified, it will be guessed from
Atoms object.
Returns
-------
rot_temperatures : list of float
Rotational temperatures
"""
if geometry is None:
geometry = get_geometry_from_atoms(atoms)
rot_temperatures = []
for moment in atoms.get_moments_of_inertia():
if np.isclose(0., moment):
continue
moment_SI = moment*c.convert_unit(from_='amu', to='kg') \
*c.convert_unit(from_='A2', to='m2')
rot_temperatures.append(c.inertia_to_temp(moment_SI))
if geometry == 'monatomic':
# Expecting all modes to be 0
assert np.isclose(np.sum(rot_temperatures), 0.)
return [0.]
elif geometry == 'linear':
# Expecting one mode to be 0 and the other modes to be identical
if not np.isclose(rot_temperatures[0], rot_temperatures[1]):
warn('Expected rot_temperatures for linear specie, {}, to be '
'similar. Values found were:{}'.format(
atoms, rot_temperatures))
return [max(rot_temperatures)]
elif geometry == 'nonlinear':
# Expecting 3 modes. May or may not be equal
return rot_temperatures
else:
raise ValueError('Geometry, {}, not supported.'.format(geometry))
def get_SoR(self, temperature, pressure=1.0, verbose=False):
"""Calculate the dimensionless entropy.
Parameters:
temperature (float): Temperature(s) in K
pressure (float, optional): Pressure in atm. Default is 1 atm.
verbose (bool): Print a table breaking down each contribution
"""
if self.specie_type == 'ideal gas':
entropy = self.model.get_entropy(
temperature,
pressure=pressure * c.convert_unit(from_='atm', to='Pa'),
verbose=verbose)
else:
entropy = self.model.get_entropy(temperature, verbose=verbose)
return entropy / c.R('eV/K')
def get_V(self, T, P):
"""Calculates the molar volume of an ideal gas at T and P
:math:`V_m=\\frac{RT}{P}`
Parameters
----------
T : float
Temperature in K
P : float
Pressure in bar
Returns
-------
V : float
Molar volume in m3
"""
return T * c.R('J/mol/K') / (P * c.convert_unit(from_='bar', to='Pa'))
def get_GoRT(self, temperature, pressure=1.0, verbose=False):
"""Calculate the dimensionless Gibbs energy.
Parameters:
temperature (float): Temperature(s) in K
pressure (float, optional): Pressure in atm. Default is 1 atm.
verbose (bool): Print a table breaking down each contribution
"""
if self.specie_type == 'ideal gas':
G = self.model.get_gibbs_energy(
temperature,
pressure=pressure * c.convert_unit(from_='bar', to='Pa'),
verbose=verbose)
else:
G = self.model.get_helmholtz_energy(temperature, verbose=verbose)
return G / (c.kb('eV/K') * temperature)
def from_critical(cls, Tc, Pc):
"""Creates the van der Waals object from critical temperature and
pressure
Parameters
----------
Tc : float
Critical temperature in K
Pc : float
Critical pressure in bar
Returns
-------
vanDerWaalsEOS : vanDerWaalsEOS object
"""
Pc_SI = Pc * c.convert_unit(from_='bar', to='Pa')
a = 27. / 64. * (c.R('J/mol/K') * Tc)**2 / Pc_SI
b = c.R('J/mol/K') * Tc / 8. / Pc_SI
return cls(a=a, b=b)
def get_P(self, T=c.T0('K'), V=c.V0('m3'), n=1.):
"""Calculates the pressure of a van der Waals gas
Parameters
----------
T : float, optional
Temperature in K. Default is standard temperature
V : float, optional
Volume in m3. Default is standard volume
n : float, optional
Number of moles (in mol). Default is 1 mol
Returns
-------
P : float
Pressure in bar
"""
Vm = V / n
return (c.R('J/mol/K')*T/(Vm - self.b) - self.a*(1./Vm)**2) \
*c.convert_unit(from_='Pa', to='bar')
def get_T(self, V=c.V0('m3'), P=c.P0('bar'), n=1.):
"""Calculates the volume of a van der Waals gas
Parameters
----------
V : float, optional
Volume in m3. Default is standard volume
P : float, optional
Pressure in bar. Default is standard pressure
n : float, optional
Number of moles (in mol). Default is 1 mol
Returns
-------
T : float
Temperature in K
"""
Vm = V / n
return (P*c.convert_unit(from_='bar', to='Pa') + self.a/Vm**2) \
*(Vm - self.b)/c.R('J/mol/K')
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(from_='g', to='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.)
# Gas phase heat capacity data (in J/mol/K) for CH3OH from NIST
# https://webbook.nist.gov/cgi/cbook.cgi?ID=C67561&Units=SI&Mask=1#Thermo-Gas
Ts = np.array([50, 100, 150, 200, 273.15, 298.15, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1750, 2000, 2250, 2500, 2750, 3000])
Cp = np.array([34.00, 36.95, 38.64, 39.71, 42.59, 44.06, 44.17, 51.63, 59.7, 67.19, 73.86, 79.76, 84.95, 89.54, 93.57, 97.12, 100.24, 102.98, 105.4, 110.2, 113.8, 116.5, 118.6, 120, 121])
CpoR = Cp/c.R('J/mol/K')
#Enthalpy of Formation for CH3OH (in kJ/mol) from NIST
T_ref = c.T0('K')
H_ref = -205.
HoRT_ref = H_ref/c.R('kJ/mol/K')/T_ref
#Standard molar entropy (in J/mol/K) from Wikipedia, https://en.wikipedia.org/wiki/Methanol_(data_page)
S_ref = 239.9
SoR_ref = S_ref/c.R('J/mol/K')
#Units to plot the figure
Cp_units = 'J/mol/K'
H_units = 'kJ/mol'
S_units = 'J/mol/K'
G_units = 'kJ/mol'
#Input the experimental data and fitting to a NASA polynomial
CH3OH_nasa = Nasa(name ='CH3OH', Ts=Ts, CpoR=CpoR, T_ref=T_ref, HoRT_ref=HoRT_ref, SoR_ref=SoR_ref)
#Compare the Nasa polynomial to the input data
fig, axes = CH3OH_nasa.plot_empirical(Cp_units=Cp_units, H_units=H_units, S_units=S_units, G_units=G_units)
axes[0].plot(Ts, Cp, 'ko')
axes[1].plot(T_ref, H_ref, 'ko')
axes[2].plot(T_ref, S_ref, 'ko')
axes[3].plot(T_ref, H_ref - T_ref * S_ref * c.convert_unit(from_='J', to='kJ'), 'ko')
plt.show()
