A theoretical analysis of the reaction between vinyl and acetylene: Quantum chemistry and solution of the master equation

We have studied the reaction between vinyl and acetylene theoretically usin g electronic structure theory (DFT-B3LYP and a G2-like method) to calculate properties of stationary points on the potential, RRKM theory to compute m icrocanonical rate coefficients, and solutions to the time-dependent, multi ple-well master equation to extract information about the thermal rate coef ficient and product distribution as a function of temperature and pressure. For the temperature range, 300 K less than or equal to T less than or equa l to 700 K, both the total rate coefficient k(1)(T,p) and the products are functions of pressure. For 700 K less than or equal to T less than or equal to 900 K, k(1)(T,p) is not always well defined in that the reactants can e xhibit nonexponential decays in time. At sufficiently high pressure, the do minant product of the reaction changes from n-C4H5 to c-C4H5 (a four-number ed ring) to C4H4 + H, where C4H4 is vinyl acetylene, as the temperature is increased from 600 K to 900 K. For T > 900 K, the reaction can be written a s an elementary step, C2H3 + C2H2 --> C4H4 + H (R1), With a rate coefficien t, k(1) = 2.19 x 10(-12)T(0.163) exp(-8312/RT) cm(3)/(molecule.s), independ ent of pressure, even though the intermediate collision complex may suffer numerous collisions. We interpret our results in terms of the eigenvalues a nd eigenvectors of the G matrix, i.e., the relaxation/reaction matrix of th e master equation. For T > 900 K, k(1)(T,p) always corresponds to the large st eigenvalue of G, which in turn corresponds to the zero-pressure-limit ra te coefficient k(0)(T). The situation is more complicated at lower temperat ures. Our predictions are in good agreement with the limited amount of expe rimental information available on the reaction. The quantum chemistry calcu lations indicate that both c-C4H5 and i-C4H5 are more stable than n-C4H5. T he G2-like method gives results for the Delta H-f((0))(0 K) of c-C4H5 and i -C4H5 that are lower that that of n-C4H5 by 9.5 and 11.2 kcal/mol, respecti vely. The DFT-B3LYP results show similar differences of 6.0 and 13.7 kcal/m ol, respectively.