Recrossing-algorithms for numerical simulations of bimolecular photochemical reactions in the framework of the extended integral encounter theory

Integral encounter theory (IET) is the universal tool for description of bimolecular chemical reactions assisted by diffusive mobility of the reacting particles in liquids [3; 4]. The kernels of IET integral equations allow to take into consideration the influence exerted by different chemical processes in multistage reaction on each other. The memory effects modelled by the IET equations are the result of evolution of the reacting pairs over the interparticle distances. When applied to processes of fluorescence quenching of photoexcited fluorophore molecules by electron transfer to the quencher molecules, the standard formulation of IET suppose the rate constants of thermal electron transfer to be known for the reactants separated by any given distance $r$ [4]. Some stages of photochemical reaction can however proceed in non-equilibrium conditions over the nuclear degrees of freedom of solvent and the reacting particles, so that notion of the thermal rate constant become uncertain.
New approaches proposed in [7; 8] allowed to extend the IET to nonthermal electron transfer reactions by means of expansion of the configuration space and introduction of the auxiliary reaction coordinate $q$ relevant to solvent polarization. Such extension made it possible to refuse the concept of the pair rate constant $W(r)$ and to utilize the more general concept of the intrinsic rate of electronic transitions at the term crossing point $K(r,q)$.
Within the extended integral encounter theory (EIET) the multistage bimolecular reaction is described by a set of integro-differential equations for the populations kinetics of electronic and vibrational states of the system. From computational point of view, the main difficulty of EIET simulation can be attributed to calculation of the integral kernels. Evolution of these kernels in time is governed by a set of parabolic differential equations coupled to each other through a number of delta-type source/sink terms. These diffusive equations determine pair correlation functions for reactants in the space of solvent polarization modes and inter-particle distances between the reacting particles. It should be noted that dimensionality of this space is directly determined by number of solvent relaxation modes.
In this paper new effective methods for numerical solving of the EIET equations are proposed. These methods are based on the recrossing algorithms of the Brownian simulation technique [1]. These algorithms have already shown their high performance in models with several solvent relaxation modes, in chemical reactions with participation of many electronic and vibrational degrees of freedom, as well as in simulations of the transient absorption dynamics in non-equilibrium photochemical systems. Future potential of the proposed algorithms is also tied up with possibilities to utilize them in computational systems with hybrid (CPU+GPU) architecture.