rmgpy.thermo.
Wilhoit
(Cp0=None, CpInf=None, a0=0.0, a1=0.0, a2=0.0, a3=0.0, H0=None, S0=None, B=None, Tmin=None, Tmax=None, comment='')¶A heat capacity model based on the Wilhoit equation. The attributes are:
Attribute | Description |
---|---|
a0 | The zeroth-order Wilhoit polynomial coefficient |
a1 | The first-order Wilhoit polynomial coefficient |
a2 | The second-order Wilhoit polynomial coefficient |
a3 | The third-order Wilhoit polynomial coefficient |
H0 | The integration constant for enthalpy (not H at T=0) |
S0 | The integration constant for entropy (not S at T=0) |
E0 | The energy at zero Kelvin (including zero point energy) |
B | The Wilhoit scaled temperature coefficient in K |
Tmin | The minimum temperature in K at which the model is valid, or zero if unknown or undefined |
Tmax | The maximum temperature in K at which the model is valid, or zero if unknown or undefined |
comment | Information about the model (e.g. its source) |
The Wilhoit polynomial is an expression for heat capacity that is guaranteed to give the correct limits at zero and infinite temperature, and gives a very reasonable shape to the heat capacity profile in between:
Above, \(y \equiv T/(T + B)\) is a scaled temperature that ranges from zero to one based on the value of the coefficient \(B\), and \(a_0\), \(a_1\), \(a_2\), and \(a_3\) are the Wilhoit polynomial coefficients.
The enthalpy is given by
where \(f_{ij} = 3 + j\) if \(i = j\), \(f_{ij} = 1\) if \(i > j\), and \(f_{ij} = 0\) if \(i < j\).
The entropy is given by
The low-temperature limit \(C_\mathrm{p}(0)\) is \(3.5R\) for linear molecules and \(4R\) for nonlinear molecules. The high-temperature limit \(C_\mathrm{p}(\infty)\) is taken to be \(\left[ 3 N_\mathrm{atoms} - 1.5 \right] R\) for linear molecules and \(\left[ 3 N_\mathrm{atoms} - (2 + 0.5 N_\mathrm{rotors}) \right] R\) for nonlinear molecules, for a molecule composed of \(N_\mathrm{atoms}\) atoms and \(N_\mathrm{rotors}\) internal rotors.
B
¶The Wilhoit scaled temperature coefficient.
Cp0
¶The heat capacity at zero temperature.
CpInf
¶The heat capacity at infinite temperature.
E0
¶The ground state energy (J/mol) at zero Kelvin, including zero point energy.
For the Wilhoit class, this is calculated as the Enthalpy at 0.001 Kelvin.
H0
¶The integration constant for enthalpy.
NB. this is not equal to the enthlapy at 0 Kelvin, which you can access via E0
S0
¶The integration constant for entropy.
Tmax
¶The maximum temperature at which the model is valid, or None
if not defined.
Tmin
¶The minimum temperature at which the model is valid, or None
if not defined.
a0
¶a0: ‘double’
a1
¶a1: ‘double’
a2
¶a2: ‘double’
a3
¶a3: ‘double’
comment
¶comment: str
copy
(self) → Wilhoit¶Return a copy of the Wilhoit object.
discrepancy
(self, HeatCapacityModel other) → double¶Return some measure of how dissimilar self is from other.
The measure is arbitrary, but hopefully useful for sorting purposes. Discrepancy of 0 means they are identical
fitToData
(self, ndarray Tdata, ndarray Cpdata, double Cp0, double CpInf, double H298, double S298, double B0=500.0)¶Fit a Wilhoit model to the data points provided, allowing the
characteristic temperature B to vary so as to improve the fit. This
procedure requires an optimization, using the fminbound
function
in the scipy.optimize
module. The data consists of a set
of heat capacity points Cpdata in J/mol*K at a given set of
temperatures Tdata in K, along with the enthalpy H298 in kJ/mol and
entropy S298 in J/mol*K at 298 K. The linearity of the molecule,
number of vibrational frequencies, and number of internal rotors
(linear, Nfreq, and Nrotors, respectively) is used to set the
limits at zero and infinite temperature.
fitToDataForConstantB
(self, ndarray Tdata, ndarray Cpdata, double Cp0, double CpInf, double H298, double S298, double B)¶Fit a Wilhoit model to the data points provided using a specified value of the characteristic temperature B. The data consists of a set of dimensionless heat capacity points Cpdata at a given set of temperatures Tdata in K, along with the dimensionless heat capacity at zero and infinite temperature, the dimensionless enthalpy H298 at 298 K, and the dimensionless entropy S298 at 298 K.
getEnthalpy
(self, double T) → double¶Return the enthalpy in J/mol at the specified temperature T in K.
getEntropy
(self, double T) → double¶Return the entropy in J/mol*K at the specified temperature T in K.
getFreeEnergy
(self, double T) → double¶Return the Gibbs free energy in J/mol at the specified temperature T in K.
getHeatCapacity
(self, double T) → double¶Return the constant-pressure heat capacity in J/mol*K at the specified temperature T in K.
isIdenticalTo
(self, HeatCapacityModel other) → bool¶Returns True
if self and other report very similar thermo values
for heat capacity, enthalpy, entropy, and free energy over a wide
range of temperatures, or False
otherwise.
isSimilarTo
(self, HeatCapacityModel other) → bool¶Returns True
if self and other report similar thermo values
for heat capacity, enthalpy, entropy, and free energy over a wide
range of temperatures, or False
otherwise.
isTemperatureValid
(self, double T) → bool¶Return True
if the temperature T in K is within the valid
temperature range of the thermodynamic data, or False
if not. If
the minimum and maximum temperature are not defined, True
is
returned.
toNASA
(self, double Tmin, double Tmax, double Tint, bool fixedTint=False, bool weighting=True, int continuity=3) → NASA¶Convert the Wilhoit object to a NASA
object. You must specify
the minimum and maximum temperatures of the fit Tmin and Tmax in K,
as well as the intermediate temperature Tint in K to use as the bridge
between the two fitted polynomials. The remaining parameters can be
used to modify the fitting algorithm used:
fixedTint - False
to allow Tint to vary in order to improve the fit, or True
to keep it fixed
weighting - True
to weight the fit by \(T^{-1}\) to emphasize good fit at lower temperatures, or False
to not use weighting
continuity - The number of continuity constraints to enforce at Tint:
- 0: no constraints on continuity of \(C_\mathrm{p}(T)\) at Tint
- 1: constrain \(C_\mathrm{p}(T)\) to be continous at Tint
- 2: constrain \(C_\mathrm{p}(T)\) and \(\frac{d C_\mathrm{p}}{dT}\) to be continuous at Tint
- 3: constrain \(C_\mathrm{p}(T)\), \(\frac{d C_\mathrm{p}}{dT}\), and \(\frac{d^2 C_\mathrm{p}}{dT^2}\) to be continuous at Tint
- 4: constrain \(C_\mathrm{p}(T)\), \(\frac{d C_\mathrm{p}}{dT}\), \(\frac{d^2 C_\mathrm{p}}{dT^2}\), and \(\frac{d^3 C_\mathrm{p}}{dT^3}\) to be continuous at Tint
- 5: constrain \(C_\mathrm{p}(T)\), \(\frac{d C_\mathrm{p}}{dT}\), \(\frac{d^2 C_\mathrm{p}}{dT^2}\), \(\frac{d^3 C_\mathrm{p}}{dT^3}\), and \(\frac{d^4 C_\mathrm{p}}{dT^4}\) to be continuous at Tint
Note that values of continuity of 5 or higher effectively constrain all the coefficients to be equal and should be equivalent to fitting only one polynomial (rather than two).
Returns the fitted NASA
object containing the two fitted
NASAPolynomial
objects.
toThermoData
(self) → ThermoData¶Convert the Wilhoit model to a ThermoData
object.