J . Phys. Chem. 1988, 92, 4784-4787
4784
Nonadiabatic Unimolecular Reactions. 2. Isotope Effects on the Kinetic Energy Release F. Remade,+ D. Dehareng, and J. C. Lorquet* DZpartement de Chimie, UniversitZ de LiPge. Sart- Tilman, B-4000 Liege 1, Belgium (Received: July 30, 1987) This paper investigates the isotope effect that occurs when XOCO’ ions dissociate into XOC’ + 0 on a microsecond time scale (X = H or D). The reaction mechanism involves an electronic spin-forbidden predissociationbetween a stable singlet state and a repulsive triplet. Application of the statistical equations developed in the previous paper shows that, at a given energy, the predissociation rate constant is consistently smaller for DOCO’ than for HOCO+. Therefore, the internal energy necessary to bring about dissociation of the hydrogenated compound with a given rate constant is always lower than that of the deuteriated compound by a quantity AE* which is found to be equal to ca. 0.050 eV when k = lo6 s-l and to ca 0.020 eV for k = lo3 s-’. As a result, the excess energy which is released as kinetic energy carried by the fragments is substantially greater for the deuteriated than for the hydrogenated compound. This accounts for experiments which indicate that, in the microsecond time scale, DOCO’ gives rise to a dished metastable peak whereas the corresponding signal for HOCO’ is simply Gaussian.
I. Introduction Reactions that involve a transition between two electronic states are called nonadiabatic. With respect to adiabatic reactions, they present an additional complexity that has hindered the use of simple theories such as the transition-state method. In the previous paper,l statistical equations have been derived, which we wish to test in forthcoming contributions. In the present one, we present a study of the dissociation of the XOCO+ ion (X = H or D) for which a surprising isotope effect has been observed.* 11. Rate Constants The rate constant of a nonadiabatic process occurring in a polyatomic molecule cannot be estimated by crude methods deriving from a quasi-diatomic model. This results from the fact that, in a classical description, the nuclear trajectory can cross the region of nonadiabatic interaction many times during the ~ ~ ~a singlet-triplet surface crossing, lifetime of the m ~ l e c u l e . For the case that will be considered here, the region of nonadiabatic interaction is the (n - 1)-dimensional surface which represents the locus of intersection Vl(q) - V2(q) = 0. This locus is usually referred to as the “hopping seam”.3 The statistical treatment is enormously simplified when the seam can be represented by a hyperplane perpendicular to the reaction coordinate This requires first that the diabatic potential energy surfaces V,
