Numerical Simulation of Multistage Bimolecular Photoreactions in Liquids: Algorithms and Software

In this paper we consider the tools for numerical simulation of multistage bimolecular photoreactions assisted by diffusive mobility of reactant molecules in viscous solutions. To describe these processes, the differential encounter theory (DET) is extended to account for the coherent dynamics of certain degrees of freedom (for example, electronic spins of reactants and intermediates). The model involves diffusion of reactants in solution and multistage/multichannel physicochemical processes proceeding both at the level of individual molecules and encounter complexes. Algorithms for numerical solution of model equations are proposed, which are related to evaluation of evolution operators. The algorithm for computing the quantum propagator for the density matrix based on the Trotter splitting is presented. A software package for simulation of multistage photoreactions has been developed using the suggested numerical approaches. The structure of the key software components is presented, examples of the program model construction are presented. A software testing has been carried out, showing good correspondence between the numerical results and exact solutions of the model equations in certain particular cases. As an example, a photoreaction with participation of 9,10-dimethylanthracene and 1,3-dicyanobenzene in acetonitrile solution has been considered, and basic procedures for configuring and simulating multistage bimolecular photoprocesses are shown. An importance of coherent description of the electronic spin evolution at the radical stage is shown.