Calculation of strong-collision dissociation rate constants from NASA thermodynamic polynomials

A new method for calculating low-pressure strong-collision rate constants of dissociation and recombination reactions was proposed. The method is based on determining the density of states of the internal degrees of freedom of the reactant molecule by applying the inverse Laplace transform to the respective partition function, which, in turn, is calculated from the thermodynamic properties in the form of NASA polynomials. The proposed model is universal in the sense that the required NASA polynomials can be calculated using molecular properties obtained by various methods, both theoretical and experimental or a combination thereof. In the present study, the NASA polynomials were taken from the available databases or calculated from thermodynamic functions, either tabulated or determined by statistical mechanics in the rigid-rotor harmonic-oscillator approximation, with a simple anharmonicity correction introduced when necessary. In addition, a model for calculating the rotational factor is developed and tested. It is based on determination of the centrifugal barrier as a function of the dissociating bond length at a given rotational energy through calculating the principal moments of inertia of the molecule at each step of elongation of the bond. The proposed approach is exemplified for the dissociation of the H₂O, HO₂, and H₂O₂ molecules and the corresponding reverse reactions. A comparison with the available experimental data made it possible to estimate the weak-collision efficiency. At high temperatures, for all the reactions studied, the weak collision efficiency appears to be quite reasonable, whereas, at low temperatures, the situation is unsatisfactory, except perhaps for H₂O dissociation. Given that the energy threshold E₀ of dissociation reactions is typically well known, the calculated and measured dissociation rate constants are represented and handled in terms of the preexponential factor A(T) in the expression k(T) = A(T)exp(−E₀/RT). A new formula for fitting A(T) was proposed: log A(T) = a + b(1000/T) + c(1000/T)^p, which turned out to be a good approximation for the preexponential factors of not only the rate constants but also the equilibrium constants.