Scattering Matrix and Chemical Reaction Rates

摘要

The connection between macroscopic bimolecular chemical reaction rate expressions and microscopic collision properties is usually based formally on collision cross sections. An alternative formulation based on spherical waves, or on classical trajectories classified according to the initial angular momentumLof the collision, leads to a direct connection between reaction rates and the scattering matrix, from which the collision cross sections can always be derived. Because of the ease of expressing the scattering matrix for manyhyphen;body collisions, this formulation can be used for threehyphen;body or manyhyphen;body reactions, as well as for twohyphen;body ones. For a gas otherwise in thermodynamic equilibrium, the rate coefficient for a reaction takingn+1 reactant molecules in internal states collectively labeled byitonprime;+1 products in internal statesjiskijlpar;nplus;1rpar;equals;h22pgr;mgr;kT3nsol;2hminus;10infin;ggr;ggr;prime;verbar;Siggr;,jggr;prime;lpar;Erpar;verbar;2explpar;minus;Esol;kTrpar;dE.Here mgr; is the common reduced mass,mgr;nkequals;1nplus;1mkequals;kequals;1nplus;1mk,and ggr; and ggr;prime; are the 3nmdash;1 or 3nprime;mdash;1 orbital quantum numbers of ordinary and generalized angular momentum which, together withE,specify the initial and final relative motion of the particles. The close connection between the scattering matrix and the lifetime matrix makes it possible to bring out effects, such as those characterizing unimolecular reactions, depending on the lifetime of a metastable intermediate.