Master equations for photochemistry with intense infrared light (IV). A unified treatment of case B and case C including nonlinear effects

Abstract

A unified master equation for unimolecular reactions induced by monochromatic infrared radiation (URIMIR) is presented. Its effective rate coefficient matrix covers both case B (Pauli equation) and case C, properly including the nonlinearity of the latter. Exact quantum mechanical model solutions are compared with results from the approximate unified master equation. The exact analytical solutions of the master equation are presented for the URIMIR of some realistic molecular models. The important new properties of the transition range between case B and case C are quantitatively discussed with respect to time dependent and steady state level populations, time dependent and steady state rate coefficients and their nonlinear intensity dependence, and with respect to the influence of molecular properties. The role of case C for the interpretation of static field effects and its importance for efficient isotope separation are pointed out.

The role of quantum intramolecular dynamics in unimolecular reactions

“…Secondly, the disappearance of the nonlinearity at the highest intensity for CF3I is inconsistent with an explanation by direct multiphoton transitions. Thirdly, pressure broadening with inert gases allows us to remove the spectral line structure (figure 1) and such experiments, indeed, indicate a transition from the nonlinear case C to case B for the reactions considered (Quack 1981;. We can thus consider the quantum nonlinearity for the stepwise multiphoton process to be safely established, although further work, particularly on a more quantitative intensity dependence and time resolution to shorter timescales is desirable (presently limited to greater than 1 ns).…”

“…Making use of the statistical theory of spectra with simple models for the distribution functions, analytical formulae have been derived for optical transition rates in master equations for the multiphoton process (Quack 1978(Quack , 1981(Quack , 1982. Accurate numerical (quantum Monte Carlo) results can be derived for realistic spectra (Quack & Sutcliffe 1985).…”

“…The one-dimensional adiabatic channel potentials can be used both for calculations of reaction (Quack & Troe 1974, 1981 and of bound states (Quack 1981). Recent experimental and theoretical results on bound states indicate a surprisingly good validity of the fundamental approximations involved, if the calculation of channel potentials is carried out accurately (Quack & Suhm 1990).…”