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

$\frac{C_v^{qRRHO}}{R}=\sum _i{\omega }_i\frac{C_{v,i}^{RRHO}}{R}+\frac{1}{2}(1-{\omega }_i)$

$\frac{C_v^{RRHO}}{R}=\sum _i\exp (-\frac{{\mathrm{\Theta }}_i}{T})(\frac{{\mathrm{\Theta }}_i}{T}\frac{1}{1-\exp (-\frac{{\mathrm{\Theta }}_i}{T})}{)}^2$

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

$\frac{S^{qRRHO}}{R}=\sum _i{\omega }_i\frac{S_i^H}{R}+(1-{\omega }_i)\frac{S_i^{RRHO}}{R}$

$\frac{S_i^{RRHO}}{R}=\frac{1}{2}+\log ([\frac{8{\pi }^3{\mu }_i^{\prime }{k}_{B}T}{h^2}{]}^{\frac{1}{2}})$

$\frac{S_i^H}{R}=(\frac{{\mathrm{\Theta }}_i}{T})\frac{1}{\exp (\frac{{\mathrm{\Theta }}_i}{T})-1}-\log (1-\exp (\frac{-{\mathrm{\Theta }}_i}{T}))$

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

$\frac{U^{qRRHO}}{RT}=\sum _i{\omega }_i\frac{U^{RRHO}}{RT}+\frac{1}{2}(1-{\omega }_i)$

$\frac{U_i^{RRHO}}{RT}=\frac{{\mathrm{\Theta }}_i}{T}(\frac{1}{2}+\frac{\exp (-\frac{{\mathrm{\Theta }}_i}{T})}{1-\exp (-\frac{{\mathrm{\Theta }}_i}{T})})$

Parameters:

T (float) – Temperature in K

Returns:

UoRT_vib – Vibrational dimensionless internal energy

Return type:

float

get_ZPE()

Calculates the zero point energy

$ZPE=\frac{1}{2}{k}_b\sum _i{\omega }_i{\mathrm{\Theta }}_{V,i}$

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