A statistical, ab initio, quantum mechanical study of the photolysis and final state distributions of singlet ketene

Abstract

A new quantum mechanical, statistical, total angular momentum conserving theory designed to describe relative kinetic energy and fragment quantum state distributions in unimolecular dissociation processes is described. The theory is called the statistical adiabatic product distribution method and is based on a variational Rice–Ramsperger–Kassel–Marcus (RRKM) treatment of the break-up process. It requires the definition of a break-up pathway or intrinsic reaction coordinate and the normal mode vibrational frequencies in the coordinate space orthogonal to this coordinate. In the present application to the break up of highly excited singlet ketene, the reaction coordinate and vibrational frequencies are evaluated using ab initio molecular electronic structure codes. The variational aspect of the theory involves locating, independently for every total angular momentum and total energy, the reaction coordinate value which leads to the lowest sum-of-states. In order to make predictions of the product quantum state and relative kinetic energy distributions the variational RRKM treatment is augmented by a J conserving quantum phase space treatment of the dissociation process. This treatment also takes into account the variation of the electronic energy along the reaction coordinate during the final stage of the break-up process. The conserved modes of the molecule are treated adiabatically during the break-up process as the fragment separation increases beyond the position of the critical geometry. The quantum phase space theory treatment enables us to identify the energy associated with rotation and translation at the critical geometry. The rotational motion of the fragments is also treated adiabatically during the break-up process, while the relative translational energy is used to surmount the potential and centrifugal barrier which may still have to be overcome to permit the fragments to separate. The phase space theory used takes proper account of the limitations placed on the dynamics by the necessity for the system to surmount these barriers. Extensive investigations are carried out as to whether the transition state or critical geometry arising in the variational RRKM treatment is best computed by treating the system as a bound molecule or as two separated fragments. For the dissociation of ketene at the high levels of excitation treated in the present work, we conclude that the variational calculation of the critical geometry is best performed by treating the system as a bound molecule and using the ab initio computed normal mode vibrational frequencies in the coordinate space perpendicular to the reaction path.