Extension of the Launay Quantum Reactive Scattering Code and Direct Computation of Time Delays

Abstract

Scattering computations, particularly within the realm of molecular physics, have seen an increase in study since the development of powerful quantum methods. These dynamical processes can be analyzed via (among other quantities) the duration of the collision process and the lifetime of the intermediate complex. We use the Smith matrix Q = -iℏS^†dS/dE calculated from the scattering matrix S and its derivative with respect to the total energy. Its real part contains the state-to-state time delays, and its eigenvalues give the lifetimes of the metastable states [ Smith Phys. Rev. 1960 , 118 , 349 - 356 ]. We propose an extension of the Launay HYP3D code [ Launay and Le Dourneuf Chem. Phys. Lett. 1989 , 163 , 178 - 188 ] for molecular reactive scattering and give the full details of the mathematical elements needed to compute the Q matrix from the wave function without numerical differentiation of S. The log-derivative of the wave function and its energy derivative are propagated asymptotically with an extended Johnson-Manolopoulos integration [ Manolopoulos J. Chem. Phys. 1986 , 85 , 6425 - 6429 ], from which the Q matrix is calculated. As a first test of our new code, lifetimes of the metastable intermediate ozone complex O₃^* have been calculated for the oxygen exchange reaction ¹⁸O + ¹⁶O¹⁶O → ⁵⁰O₃^* → ¹⁶O¹⁸O + ¹⁶O, related to the mass-independent fractionation problem of stratospheric ozone. These preliminary results reproduce previously published works limited to zero total angular momentum as benchmark.