Dynamics Study of the Reaction Ar + HCN f Ar + H + CN S. P. J. Rodrigues and A. J. C. Varandas* Departamento de Quı ´mica, UniVersidade de Coimbra, P-3049 Coimbra, Portugal ReceiVed: March 11, 1998; In Final Form: May 18, 1998 A dynamics study of the reaction Ar + HCN f Ar + H + CN for a wide range of initial vibrational and translational energies is reported. All calculations have been carried out with the quasiclassical trajectory method and a realistic potential energy surface for ArHCN. An attempt is made to reproduce the thermal rate coefficient for the reaction. Agreement with experiment is found to be good, and the limitations of the approach are stressed. A brief analysis of rotational effects, energy transfer, and unimolecular dissociation of highly excited HCN* molecules is also presented. 1. Introduction Unimolecular dissociation and the reverse recombination process are an important class of elementary reactions involved in combustion chemistry. According to the Lindemann ap- proach and its subsequent refinements, namely, the extensively tested and widely accepted 1 Rice-Ramsperger-Kassel-Marcus (RRKM) scheme, such reactions become pressure-dependent in the so-called low-pressure limit (LPL), which is attained when the collisional excitation and deexcitation processes are domi- nant. At high temperatures reached in the flames, these processes govern the kinetics and the LPL rate constants become very important to rationalize such reactions. Furthermore, if Ar is assumed to be a representative example of a closed-shell third body, then the title reaction is of major importance for studying the propellant combustion reactions and, more gener- ally, the combustion of nitrogen-containing materials at high temperatures. 2 Although these reactions have not been con- sidered in the classical article of Miller and Bowman 3 on modeling the combustion chemistry of nitrogen compounds (they considered only temperatures up to 2500 K), for high temperatures the HCN removal by dissociation is expected to be competitive with oxidation by atomic oxygen. Although widely used to rationalize mechanisms and evaluate rates, the RRKM framework is not yet predictive. The most severe and essential difficulty of RRKM theory is the need to specify a collision efficiency, or mean collisional energy transfer, quantities that cannot be obtained independentely. With this drawback, the RRKM rate constants must be calculated by using “typical” values for such quantities, often obtained from related systems for which the rate was fitted to experimental results. Of course, this may occasionally lead to the use of unrealistic values for the mean collisional energy. The goal of the present work is to study theoretically the dynamics of the title reaction. The model is dynamical, and the thermal rate coefficient is calculated avoiding the usual energy transfer-based master equation formulation. The fol- lowing fundamental assumptions are made: (a) the reaction occurs only on the ground potential energy surface of ArHCN, (b) the model potential energy surface describes accurately the reactive paths, (c) the classical trajectory method is adequate for studying the title reaction, (d) below the classical dissociation limit the HCN molecules are in thermal equilibrium, and (e) the density of states F(E) can be described by a classical continuous function which can be approximated by using the harmonic approximation. We have found these assumptions acceptable, with (d) and (e) being the most problematic, as will be discussed later. An extra assumption concerns the definition of the HCN internal energy: (f) the internal energy of HCN is taken to be only vibrational. Thus, the angular momentum component perpendicular to the molecular axis is assumed to be vanishingly small, which implies that the trajectories begin with no rotational energy. Nevertheless, since this molecule is linear, a vibrational angular momentum l will appear. 4 This fact has been taken into account in the classical trajectory calculations by making a microcanonical sampling of the internal energy that has been distributed through the four normal modes of vibration: the degenerate bending modes and the two stretching ones. The plan of the paper is as follows. In section 2 we describe the potential energy surface used for ArHCN. Section 3 presents the method used for the dynamics calculations. The technical details used for running the quasiclassical trajectories and the definition of the reactive channels are then examined. Section 4 is devoted to the theoretical framework utilized to calculate the thermal rate constant from the quasiclassical trajectories and to the analysis of the results. Rotational effects are also discussed in this section, where some remarks are made about the energy transfer in the title system. Similarly, the unimo- lecular dissociation of the HCN* complexes is briefly analyzed. Section 5 gathers the major conclusions. 2. Potential Energy Surface for ArHCN To our knowledge, the only ab initio potentials available for the ArHCN van der Waals molecule are those of Clary et al., 5 who have used the coupled electron-pair approximation (CEPA- 1), and Tao et al., 6 who have employed the Moller-Plesset (MP4) method. Both potentials have been fitted to analytical functions but the validity of these is restricted to the atom- rigid triatom Ar-HCN configurational regions. Other potentials have been reported 7-10 although the only six-dimensional (6D) is that of Bowman and co-workers. 9,10 This potential has been modeled by using Lennard-Jones pair potentials, which are known to be unrealistic in the inner repulsive wall. As this topographical feature can affect the dynamics, 11,12 the construc- tion of a more realistic potential energy surface for ArHCN has been undertaken in the present work. 6266 J. Phys. Chem. A 1998, 102, 6266-6273 S1089-5639(98)01466-2 CCC: $15.00 © 1998 American Chemical Society Published on Web 07/10/1998 Downloaded by PORTUGAL CONSORTIA MASTER on June 29, 2009 Published on July 10, 1998 on http://pubs.acs.org | doi: 10.1021/jp981466v