pmutt.statmech.vib.QRRHOVib

class pmutt.statmech.vib.QRRHOVib(vib_wavenumbers, Bav=1e-44, v0=100.0, alpha=4, imaginary_substitute=None)

Bases: _ModelBase

Vibrational modes using the Quasi Rigid Rotor Harmonic Oscillator approximation. Equations source from:

Li, Y. P.; Gomes, J.; Sharada, S. M.; Bell, A. T.; Head-Gordon, M. J. Phys. Chem. C 2015, 119 (4), 1840–1850.
Grimme, S. Chem. - A Eur. J. 2012, 18 (32), 9955–9964.

vib_wavenumber

Vibrational wavenumbers (\(\tilde{\nu}\)) in 1/cm

Type:: list of float

Bav

Average molecular moment of inertia as a limiting value of small wavenumbers. Default is 1.e-44 kg m2

Type:: float, optional

v0

Wavenumber to scale vibrations. Default is 100 cm ^-1

Type:: float, optional

alpha

Power to raise ratio of wavenumbers. Default is 4

Type:: int, optional

imaginary_substitute

If this value is set, imaginary frequencies are substituted with this value for calculations. Otherwise, imaginary frequencies are ignored. Default is None

Type:: float, optional

__init__(vib_wavenumbers, Bav=1e-44, v0=100.0, alpha=4, imaginary_substitute=None)

Methods

`__init__`(vib_wavenumbers[, Bav, v0, alpha, ...])
`from_dict`(json_obj)	Recreate an object from the JSON representation.
`get_Cp`(units, **kwargs)	Calculate the heat capacity (constant P)
`get_CpoR`(T)	Calculates the dimensionless heat capacity at constant pressure
`get_Cv`(units, **kwargs)	Calculate the heat capacity (constant V)
`get_CvoR`(T)	Calculates the dimensionless heat capacity at constant volume
`get_F`(units[, T])	Calculate the Helmholtz energy
`get_FoRT`(T)	Calculates the dimensionless Helmholtz energy
`get_G`(units[, T])	Calculate the Gibbs energy
`get_GoRT`(T)	Calculates the dimensionless Gibbs energy
`get_H`(units[, T])	Calculate the enthalpy
`get_HoRT`(T)	Calculates the dimensionless enthalpy
`get_S`(units, **kwargs)	Calculate the entropy
`get_SoR`(T)	Calculates the dimensionless entropy
`get_U`(units[, T])	Calculate the internal energy
`get_UoRT`(T)	Calculates the dimensionless internal energy
`get_ZPE`()	Calculates the zero point energy
`get_q`()	Calculates the partition function
`print_calc_wavenumbers`()	Prints the wavenumbers that will be used in a thermodynamic calculation.
`to_dict`()	Represents object as dictionary with JSON-accepted datatypes

Attributes

vib_wavenumbers

classmethod from_dict(json_obj)

Recreate an object from the JSON representation.

Parameters:: json_obj (dict) – JSON representation
Returns:: QRRHOVib
Return type:: QRRHOVib object

get_Cp(units, **kwargs)

Calculate the heat capacity (constant P)

Parameters:

units (str) – Units as string. See R() for accepted units.
kwargs (keyword arguments) – Parameters needed by get_CpoR

Returns:

Cp – Heat capacity (constant P) in appropriate units

Return type:

float

get_CpoR(T)

Calculates the dimensionless heat capacity at constant pressure

\(\frac{C_{P}^{qRRHO}} {R} = \frac{C_{V}^{qRRHO}} {R}\)

Parameters:: T (float) – Temperature in K
Returns:: CpoR_vib – Vibrational dimensionless heat capacity at constant pressure
Return type:: float

get_Cv(units, **kwargs)

Calculate the heat capacity (constant V)

Parameters:

units (str) – Units as string. See R() for accepted units.
kwargs (keyword arguments) – Parameters needed by get_CvoR

Returns:

Cv – Heat capacity (constant V) in appropriate units

Return type:

float

get_CvoR(T)

Calculates the dimensionless heat capacity at constant volume

\(\frac {C_{v}^{qRRHO}}{R} = \sum_{i}\omega_i\frac{C_{v,i} ^{RRHO}}{R} + \frac{1}{2}(1-\omega_i)\)

\(\frac{C_{v}^{RRHO}}{R} = \sum_{i}\exp \bigg(-\frac{ \Theta_i}{T}\bigg) \bigg(\frac{\Theta_i}{T}\frac{1}{1-\exp(- \frac{\Theta_i}{T})}\bigg)^2\)

Parameters:: T (float) – Temperature in K
Returns:: CvoR_vib – Vibrational dimensionless heat capacity at constant volume
Return type:: float

get_F(units, T=298.15, **kwargs)

Calculate the Helmholtz energy

Parameters:

units (str) – Units as string. See R() for accepted units but omit the ‘/K’ (e.g. J/mol).
T (float, optional) – Temperature in K. Default is 298.15 K
kwargs (keyword arguments) – Parameters needed by get_FoRT

Returns:

F – Hemholtz energy in appropriate units

Return type:

float

get_FoRT(T)

Calculates the dimensionless Helmholtz energy

\(\frac{A^{qRRHO}}{RT} = \frac{U^{qRRHO}}{RT}- \frac{S^{qRRHO}}{R}\)

Parameters:: T (float) – Temperature in K
Returns:: FoRT_vib – Vibrational dimensionless Helmholtz energy
Return type:: float

get_G(units, T=298.15, **kwargs)

Calculate the Gibbs energy

Parameters:

units (str) – Units as string. See R() for accepted units but omit the ‘/K’ (e.g. J/mol).
T (float, optional) – Temperature in K. Default is 298.15 K
kwargs (keyword arguments) – Parameters needed by get_GoRT

Returns:

G – Gibbs energy in appropriate units

Return type:

float

get_GoRT(T)

Calculates the dimensionless Gibbs energy

\(\frac{G^{qRRHO}}{RT} = \frac{H^{qRRHO}}{RT}- \frac{S^{qRRHO}}{R}\)

Parameters:: T (float) – Temperature in K
Returns:: GoRT_vib – Vibrational dimensionless Gibbs energy
Return type:: float

get_H(units, T=298.15, **kwargs)

Calculate the enthalpy

Parameters:

units (str) – Units as string. See R() for accepted units but omit the ‘/K’ (e.g. J/mol).
T (float, optional) – Temperature in K. Default is 298.15 K
kwargs (keyword arguments) – Parameters needed by get_HoRT

Returns:

H – Enthalpy in appropriate units

Return type:

float

get_HoRT(T)

Calculates the dimensionless enthalpy

\(\frac{H^{qRRHO}} {RT} = \frac{U^{qRRHO}} {RT}\)

Parameters:: T (float) – Temperature in K
Returns:: HoRT_vib – Vibrational dimensionless enthalpy
Return type:: float

get_S(units, **kwargs)

Calculate the entropy

Parameters:

units (str) – Units as string. See R() for accepted units.
kwargs (keyword arguments) – Parameters needed by get_SoR

Returns:

S – Entropy in appropriate units

Return type:

float

get_SoR(T)

Calculates the dimensionless entropy

\(\frac{S^{qRRHO}}{R}=\sum_i\omega_i\frac{S_i^{H}}{R}+(1- \omega_i)\frac{S_i^{RRHO}}{R}\)

\(\frac {S^{RRHO}_i}{R} = \frac{1}{2} + \log \bigg(\bigg[ \frac{8\pi^3\mu'_ik_BT}{h^2}\bigg]^{\frac{1}{2}}\bigg)\)

\(\frac {S^{H}_i}{R}=\bigg(\frac{\Theta_i}{T}\bigg)\frac{1} {\exp(\frac{\Theta_i}{T})-1}-\log\bigg(1-\exp(\frac{-\Theta_i} {T})\bigg)\)

Parameters:: T (float) – Temperature in K
Returns:: SoR_vib – Vibrational dimensionless entropy
Return type:: float

get_U(units, T=298.15, **kwargs)

Calculate the internal energy

Parameters:

units (str) – Units as string. See R() for accepted units but omit the ‘/K’ (e.g. J/mol).
T (float, optional) – Temperature in K. Default is 298.15 K
kwargs (keyword arguments) – Parameters needed by get_UoRT

Returns:

U – Internal energy in appropriate units

Return type:

float

get_UoRT(T)

Calculates the dimensionless internal energy

\(\frac {U^{qRRHO}}{RT} = \sum_{i}\omega_i\frac{U^{RRHO}}{RT} + \frac{1}{2}(1-\omega_i)\)

\(\frac {U^{RRHO}_{i}}{RT} = \frac{\Theta_i}{T} \bigg( \frac{1}{2} + \frac{\exp(-\frac{\Theta_i}{T})}{1-\exp(-\frac{ \Theta_i}{T})}\bigg)\)

Parameters:: T (float) – Temperature in K
Returns:: UoRT_vib – Vibrational dimensionless internal energy
Return type:: float

get_ZPE()

Calculates the zero point energy

\(ZPE=\frac{1}{2}k_b\sum_i \omega_i\Theta_{V,i}\)

Returns:: zpe – Zero point energy in eV
Return type:: float

get_q()

Calculates the partition function

Returns:: q_vib – Vibrational partition function
Return type:: float

print_calc_wavenumbers(): Prints the wavenumbers that will be used in a thermodynamic calculation. If self.imaginary_substitute is a float, then imaginary frequencies are replaced with that value. Otherwise, imaginary frequencies are ignored.

to_dict()

Represents object as dictionary with JSON-accepted datatypes

Returns:: obj_dict
Return type:: dict

property vib_wavenumbers