On the Quantum‐Mechanical and Classical Treatment of Chemical Kinetics

Abstract

AbstractIn a recent quantum‐mechanical formulation of reaction rate theory the concept of a potential‐energy surface was used to derive an exact rate equation of the usual exponential form under the unique assumption of thermal equilibrium of reactants. In the present paper the notion of the “activated complex” is introduced in the sense of a virtual state to derive a mathematically equivalent expression of the same exponential form. This exact expression may be considered in a conditional sense as a generalization of “transition state theory”.The classical limits of the exact quantum scattering theory are investigated for the extreme conditions of very slow (adiabatic) and very fast (non‐adiabatic) motion along the reaction coordinate using the two equivalent forms of the general rate equation, respectively. In this way two classical rate expressions are derived, one of which is identical with the familar Eyring's equation of transition state theory. The quantum corrections and, in particular, the “tunneling corrections” to these equations are defined exactly in a suitable manner and two corresponding simple criteria for determining the conditions of a classical reaction course are introduced.Two‐dimensional quantum corrections for the colinear triatomic reaction H2 + H → H + H2 (D2 + D → D + D2) are calculated exactly using Weston's potential surface for the extreme conditions of both adiabatic and (truly) non‐adiabatic change of the vibration mode. A comparison is made with corresponding approximate formulas for the tunneling corrections. The activated complex hypothesis is shown to be not justified from physical point of view for reactions of the type AH + B → A + HB, where A and B are H, D, T or hypothetical super‐heavy hydrogen isotopes.Finally, a discussion is made on the conditions of validity of the activated complex theory from physical standpoint and on its importance as a method for exact calculations of reaction rates which is shown to be largely independent from its physical justification.