Variational Theory of Chemical Reaction Rates Applied to Three-Body Recombinations

A ``variational'' theory, which gives a least upper bound to the rate of a chemical reaction, is presented. The reaction is represented by the motion of a point in phase space across a trial surface dividing the ``initial'' and ``final'' chemical states. The trial surface is well defined in regions of phase space where interactions causing reaction are negligible, but is subject to arbitrary variations otherwise. It is shown that a least upper bound to the reaction rate can be obtained by calculating the rate at which representative points cross the ``trial'' surface and then minimizing this rate with respect to allowed variations of the surface. Explicit calculations of the recombination rate of attracting atoms in the presence of repulsive third bodies are made for a simple trial surface having one adjustable parameter. At low temperatures, the experimental rate constants are quite close to the theoretical bounds; at high temperatures, the experimental data fall away from the bounds in a manner which can be understood in terms of various approximations contained in the theory. Promising methods of improving the agreement between theory and experiment are discussed.