A general procedure for classical variational rate calculations for three-body exchange reactions

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A general procedure for the variational minimization of the classical flux across a dividing surface for any three-dimensional reaction of the type A+BC→AB+C has been developed. The dividing surface is expresed in terms of a linear combination of internal coordinates (LCIC) that span the entire hyperspace of the potential surface. This LCIC-variational method has been applied to the H+H2 and H+I2 reactions. For the H+H2 exchange, it is found that even a truncated LCIC expansion for the dividing surface yields minimum variational rate coefficients that are never more that 26% in excess of the classical trajectory (CT) results. With the DS defined in terms of a full LCIC expansion, the computed variational rates are found to converge to the corresponding CT values. The H+I2 reaction is found to be a more demanding test due to the presence of a potential well in the entrance valley combined with a barrier that is relatively independent of approach angle. For this system, a full LCIC-variational calculation yields a minimum rate coefficient that is a factor of 2.26 greater than the CT value. For the H+H2 system, the computed variational activation energy is in exact agreement with the trajectory result, but the frequency factor obtained variationally is 11.6% in excess of the CT value. It is shown that the computation of the variational rate at five temperatures requires only 4% of the computer time required for corresponding trajectory calculations. When the LCIC-variational procedure is combined with a CPST calculation, it is shown that exact classical rate coefficients, activation energies, and frequency factors may be computed with greater statistical accuracy and with very large reduction in computer time. In the case of the H+H2 exchange, the combined LCIC–CPST method is found to give rate coefficients at five temperatures in agreement with trajectory calculations with a factor of 18.4 overall reduction in computer time and a decrease of a factor of 4 in the statistical error.