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Synopsis
In order to calculated reversed reaction coefficients using the assumption of detailed balance, one needs the difference in Gibbs free energy (GFE) between reactants and products (Grassi et al. 2014, section 3.6). In principle, one can also use the difference in Gibbs free energy of formation (GFEoF) because the additional contribution of individual atoms cancels out because the atoms on both sides of the reaction are the same. Using GFEoF has the advantage of being calculated by different databases, e.g. Third Millennium Ideal Gas and Condensed Phase Thermochemical Database for Combustion with Updates from Active Thermochemical Tables (nasa-polynomials), NIST-JANAF Thermochemical Tables. However, there are inconsistencies between databases (same species having different GFEoF values), experimental values of quantities at room temperature have large error bars, and the details of the calculations/experiments are unclear as these have been performed in the '50-'70. In order to have more grasp on the consistency, we advise to use GFE instead of GFEoF.
Using Gibbs free energy
Information
Calculation of reversed reactions happens by the functions
krome_subs.revKc_with_GFE() krome_subs.gibbs_free_energy()
The latter contains the GFE in function of temperature for all species in the network of which GFE data is available. All GFE data files are located in data. These file originate from a new local collection developed by J. Boulangier. This Google Drive also contains:
- information on how these values are calculated
- what literature values are used
- all references of all used sources
The used python script is also available on a git repository and is designed to read in Gaussian output files, csv-files containing quantum data of the species, csv-files of partition functions, and thermochemical database tables.
Method
In order to calculate the GFE of a species in function of temperature, one needs the total partition function and the electronic potential energy. The total partition function (excluding the translation part) can often be found in literature, if not, this can be calculated from internal energy levels (rotational, vibrational, electronic). Note that this latter will most likely be less precise due to approximations as rigid rotator, harmonic oscillator,... The electronic potential energy can often be found in literature from density functional calculations, if not, this has to be done yourself. Reference files (.ref) mentioned below can be found in the Google Drive.
Used equation to calculate
\(\text{GFE} = N U_0 - N k_B T_{gas} * \ln(Z_1) + N k_B T_{gas} \ln(N)\) where \(N\) is the number of particles (in large limit) often 1 mole (Avogadro's number), \(U_0\) is the electronic potential energy, \(T_{gas}\) the gas temperature, \(k_B\) is the Boltzmann constant, and \(Z_1\) is the total partition function for \(1\) particle. See Appendix of Boulangier et al. 2018 (in prep.) or a course in thermodynamics for more info.
Partition function
Use literature determined values if available (see partition_function.ref details and references). Note, that the translation contribution still needs to be calculated. If not found, Boulangier et al. (2018) calculated the partition function themselves via individual partition function contributions (translation, rotation, vibration, electronic). This latter needs the quantum mechanical information of energy levels (rotation, vibration, electronic). This information is most often available in literature/databases (see quantum_data.ref for details and references). If no quantum mechanical data is available, we computed this ourselves using density functional theory (see density_functional_theory.ref for details and references).
Electronic potential energy
Use literature determined values (see quantum_data.ref for details and references). If no data is available, Boulangier et al. (2018) computed this themselves using density functional theory (see density_functional_theory.ref for details and references).
Using Gibbs free energy of formation
Information
Calculation of reversed reactions happens by the functions
krome_subs.revKc() krome_subs.revHS()
The latter contain the GFEoF values of all species in the network of which data is available. This data mainly comes from nasa-polynomials and can be found in thermo30.dat. Support for data from NIST is also available in thermoNIST.dat. We discourage to mix both databases as we have found inconsistencies between them which can lead to incorrect results. No thorough check for all species has been done, so we advice the user to be cautious check GFEoF values themselves. Support for using NIST-JANAF tables has been included in past but removed again to avoid being used because we do not trust the calculations of the database to due lack of documentation, and different values of GFEoF than given by the nasa-polynomials.
J. Boulangier has also calculated GFEoF values of species via its definition (given on the bottom of Gaussian's wiki), and using NIST-JANAF tables for necessary atomic data but found values that were inconsistent with either database.
Updated