Statistical Thermodynamic Models
StatMech Base Class
The StatMech class stores the classes associated with each mode. Each mode
has methods that specifies how to calculate thermodynamic quantities, such as
partition functions, heat capacities, internal energy, enthalpy, entropy,
Helmholtz energy and Gibbs energy.
The StatMech object can be initialized in two ways:
- by each passing each mode as objects or
- passing each mode as a class and the associated parameters.
The examples below give an equivalent result:
Example of initialization using objects
import numpy as np
from ase.build import molecule
from pmutt.statmech import StatMech, trans, vib, rot, elec
atoms = molecule('H2O')
H2O_trans = trans.FreeTrans(n_degrees=3, atoms=atoms)
H2O_vib = vib.HarmonicVib(vib_wavenumbers=[3825.434, 3710.2642, 1582.432])
H2O_rot = rot.RigidRotor(symmetrynumber=2, atoms=atoms)
H2O_elec = elec.GroundStateElec(potentialenergy=-14.2209, spin=0)
H2O_statmech = StatMech(trans_model=H2O_trans,
vib_model=H2O_vib,
rot_model=H2O_rot,
elec_model=H2O_elec)
Example of initialization using classes and parameters
import numpy as np
from ase.build import molecule
from pmutt.statmech import StatMech, trans, vib, rot, elec
H2O_statmech = StatMech(trans_model=trans.FreeTrans,
n_degrees=3,
vib_model=vib.HarmonicVib,
vib_wavenumbers=[3825.434, 3710.2642, 1582.432],
rot_model=rot.RigidRotor,
symmetrynumber=2,
atoms=molecule('H2O'),
elec_model=elec.GroundStateElec,
potentialenergy=-14.2209,
spin=0)
Presets
If you are using a common model (e.g. the ideal gas model), then you can get
the default parameters from the dictionary, pmutt.statmech.presets.
The same H2O StatMech object can be specified without the need to pass all the
types of modes:
from ase.build import molecule
from pmutt.statmech import StatMech, presets
idealgas_defaults = presets['idealgas']
H2O_new = StatMech(vib_wavenumbers=[3825.434, 3710.2642, 1582.432],
potentialenergy=-14.2209,
atoms=molecule('H2O'),
spin=0,
symmetrynumber=2,
**idealgas_defaults)
Currently supported presets are described below. The first table shows the
attributes already specified, and the second table shows the attributes that
are still required, and the third table shows the required and optional
parameters to calculate a thermodynamic property (where the value in
parentheses is the default value).
Ideal Gas (idealgas)
Useful for modeling ideal gases. Assumes the system has:
- 3 degrees of translational freedom and no interactions with other molecules
- harmonic vibrations
- rigid rotor rotations
- electronic ground state
- nuclear ground state
| Set Attributes |
Default Value |
|---|
| trans_model |
FreeTrans |
| n_degrees |
3 |
| vib_model |
HarmonicVib |
| elec_model |
GroundStateElec |
| rot_model |
RigidRotor |
| Required Attributes |
Description |
|---|
| molecular_weight |
(float) Molecular weight in g/mol |
| vib_wavenumbers |
(list of float) Vibrational wavenumbers in 1/cm |
| potentialenergy |
(float) Electronic potential energy in eV |
| spin |
(float) Electron spin. 0 if all electrons are paired
(e.g. N2), 0.5 if the specie is a radical (e.g. CH3.),
1 if the specie exists as a triplet (e.g. O2). |
| geometry |
(str) Geometry of molecule |
| rot_temperatures |
(list of float) Rotational temperatures in K |
| symmetrynumber |
(int) Symmetry number |
| atoms |
(ase.Atoms object) Optional. If this parameter is
specified, molecular_weight, geometry,
rot_temperatures, and potentialenergy do not
have to be specified. |
| Thermodynamic Quantity |
Expected Parameters |
Optional Parameters |
|---|
| \(q\) |
T |
- ignore_q_elec (False)
- P (1.01325 bar)
|
| \(\frac {C_V} {R}\) |
T |
|
| \(\frac {C_P} {R}\) |
T |
|
| \(\frac {U} {RT}\) |
T |
|
| \(\frac {H} {RT}\) |
T |
|
| \(\frac {S} {R}\) |
T |
P (1.01325 bar) |
| \(\frac {A} {RT}\) |
T |
P (1.01325 bar) |
| \(\frac {G} {RT}\) |
T |
P (1.01325 bar) |
Harmonic Approximation (harmonic)
Typically used to model adsorbates. Assumes the system has:
- harmonic vibrations
- electronic ground state
| Parameter |
Default Value |
|---|
| vib_model |
HarmonicVib |
| elec_model |
GroundStateElec |
| Required Parameters |
Description |
|---|
| vib_wavenumbers |
(list of float) Vibrational wavenumbers in 1/cm |
| potentialenergy |
(float) Electronic potential energy in eV |
| spin |
(float) Electron spin |
| atoms |
(ase.Atoms object) Optional. If this parameter
is specified, potentialenergy does not have
to be specified. |
| Thermodynamic Quantity |
Expected Parameters |
Optional Parameters |
|---|
| \(q\) |
T |
ignore_q_elec (True) |
| \(\frac {C_V} {R}\) |
T |
|
| \(\frac {C_P} {R}\) |
T |
|
| \(\frac {U} {RT}\) |
T |
|
| \(\frac {H} {RT}\) |
T |
|
| \(\frac {S} {R}\) |
T |
|
| \(\frac {A} {RT}\) |
T |
|
| \(\frac {G} {RT}\) |
T |
|
Electronic (electronic)
Typically used to model systems where the electronic modes dominate and changes
due to temperature are not important. Assumes the system has:
| Parameter |
Default Value |
|---|
| elec_model |
GroundStateElec |
| Required Parameters |
Description |
|---|
| potentialenergy |
(float) Electronic potential energy in eV |
| spin |
(float) Electron spin |
| atoms |
(ase.Atoms object) Optional. If this
parameter is specified,
potentialenergy does not have to be
specified |
| Thermodynamic Quantity |
Expected Parameters |
Optional Parameters |
|---|
| \(q\) |
T |
ignore_q_elec (True) |
| \(\frac {C_V} {R}\) |
|
|
| \(\frac {C_P} {R}\) |
|
|
| \(\frac {U} {RT}\) |
T |
|
| \(\frac {H} {RT}\) |
T |
|
| \(\frac {S} {R}\) |
|
|
| \(\frac {A} {RT}\) |
T |
|
| \(\frac {G} {RT}\) |
T |
|
Placeholder (placeholder)
Typically used to model species that have no contribution. The partition
function is set to 1 and all other thermodynamic quantities evaluate to 0.
| Parameter |
Default Value |
|---|
| trans_model |
EmptyMode |
| vib_model |
EmptyMode |
| rot_model |
EmptyMode |
| elec_model |
EmptyMode |
| nucl_model |
EmptyMode |
| Required Parameters |
Description |
|---|
| N/A |
|
| Thermodynamic Quantity |
Expected Parameters |
Optional Parameters |
|---|
| \(q\) |
|
|
| \(\frac {C_V} {R}\) |
|
|
| \(\frac {C_P} {R}\) |
|
|
| \(\frac {U} {RT}\) |
|
|
| \(\frac {H} {RT}\) |
|
|
| \(\frac {S} {R}\) |
|
|
| \(\frac {A} {RT}\) |
|
|
| \(\frac {G} {RT}\) |
|
|
Constant (constant)
Arbitrarily specify a constant for each quantity. This is primarily used for
testing so be careful as you can disobey some fundamental thermodynamic
quantities. For example,
\(G = H - TS\)
may not be obeyed.
| Parameter |
Default Value |
|---|
| elec_model |
ConstantMode |
| Required Parameters |
Description |
|---|
| q |
(float) Optional. Partition function. Default is 1 |
| Cv |
(float) Optional. Heat capacity at constant volume
in eV/K. Default is 0 |
| Cp |
(float) Optional. Heat capacity at constant pressure
in eV/K. Default is 0 |
| U |
(float) Optional. Internal energy in eV. Default is 0 |
| H |
(float) Optional. Enthalpy in eV. Default is 0 |
| S |
(float) Optional. Entropy in eV/K. Default is 0 |
| F |
(float) Optional. Helmholtz energy in eV. Default is 0 |
| G |
(float) Optional. Gibbs energy in eV. Default is 0 |
| Thermodynamic Quantity |
Expected Parameters |
Optional Parameters |
|---|
| \(q\) |
|
|
| \(\frac {C_V} {R}\) |
|
|
| \(\frac {C_P} {R}\) |
|
|
| \(\frac {U} {RT}\) |
|
|
| \(\frac {H} {RT}\) |
|
|
| \(\frac {S} {R}\) |
|
|
| \(\frac {A} {RT}\) |
|
|
| \(\frac {G} {RT}\) |
|
|
The pmutt.statmech.presets dictionary is flexible where you can create a
new entry if you will use a model often.
Vibrational Models
vib.HarmonicVib |
|
vib.QRRHOVib |
|
vib.EinsteinVib |
|
vib.DebyeVib |
|
Electronic Models
elec.GroundStateElec |
|
lsr.LSR |
|
Nuclear Models
Typically these are unimportant for chemical reactions, but the module is
present in case nuclear modes become important in the future.
Creating New StatMech Models
New models should inherit from pmutt._ModelBase. This class already has the
dimensional methods (e.g. get_Cv, get_U, get_S), and some routine
methods (e.g. get_FoRT, get_GoRT, from_dict, to_dict)
implemented.
For full accessibility, the following methods should be implemented:
get_qget_CvoRget_CpoRget_UoRTget_HoRTget_SoR