Theory of unimolecular reactions induced by monochromatic infrared radiation

Abstract

A theory of unimolecular reactions induced by coherent, monochromatic infrared radiation (URIMIR) in the absence of collisions is presented. It is shown that the set of first order linear differential equations for the amplitudes of molecular states (Schrödinger equation) can be reduced, under specified conditions, to a much smaller set of first order linear differential equations for the coarse grained populations of levels for polyatomic molecules (master equation). Four limiting situations are identified in which such linear rate equations provide a reasonable approximation. Rate coefficients are obtained as a function of spectroscopic parameters (energy levels and transition moments). Solutions for the master equations are given as a function of time and at steady-state. Simple limiting cases (Strong Field Limit, Weak Field Limit, Reaction Threshold Bottleneck, etc.) are identified and very simple rate expressions are obtained for these cases. A complete statistical mechanical theory of URIMIR is formulated and the computational approaches for the quantitative treatment for any molecule are summarized. Predictions are made concerning the dependence of the unimolecular rate constant and product (state) distributions upon radiation intensity. In particular at high intensities a less than proportional increase of the rate constant with intensity is predicted. The possibility of specific pumping of reaction paths with high energy thresholds is discarded. Comparison with thermal unimolecular reactions shows that collisionless URIMIR are quite different in all respects. Fundamentally these differences are traced to the fact that the underlying molecular distribution functions are different. They are Boltzmann distributions for thermal reactions and ’’microcanonical’’ [without exp (−E/kT)] in URIMIR. Although real distribution functions are still different in general, the underlying distribution functions often dominate the dynamical behavior.