Numerical simulation of coherent optical transitions in electron–donor–acceptor complexes

Ultrafast photochemical processes, involving intramolecular and intermolecular charge transfer in polar solvents, often proceed on subpicosecond timescales comparable with duration of the pump pulse. One of the well-known examples is ultrafast (up to $0.1$ ps) charge recombination (CR) in photoexcited electron donor–acceptor complexes (DACs). In these molecular systems, donor and acceptor compounds of the DAC emit and receive electron, respectively, upon optical excitation of the charge transfer band. Among the most intensively studied DACs are the complexes with hexametylbenzene, pentametylbenzene, isodurene and trimetoxybenzene acting as electron donors, and tetracyanoethylene—as electron acceptor [5].
Kinetics of the back electron transfer in DACs is known to depend on the time of delivery of the noneqilibrium wavepacket to the ground and excited states term crossings region. In its turn, dynamics of the wavepacket motion on the excited state free energy surface (FES) is determined by character of solvent relaxation in vicinity of the donor and acceptor, and may proceed with several relaxation timescales ranging from hundreds of femtoseconds to tens of picoseconds. Influence of complex multimode dynamics of solvent relaxation on ultrafast CR processes can be taken into account properly within the general stochastic model of electron transfer in polar medium [9]. This model considers motion of nonequilibrium wavepackets on the excited state FES of the DAC in terms of several reaction coordinates coupled to the corresponding solvent relaxation modes.
The drawback of the common approach to numerical simulation of photochemical reaction within the general model is a supposition on instantaneous optical pumping of the DAC. Within this approximation, solvent modes and intramolecular vibrational degrees of freedom are treated as “frozen” during the pump [2; 9]. This is not, however, always true, especially in nonequilibrium reactions with participation of the vibrationally excited states of the products. The rate of such reactions can be comparable or even exceed the rate of solvent relaxation, while duration of the laser pulse can exceed the characteristic time of CR.
The aim of this study is the development of numerical algorithms for computer simulation of coherent optical excitation processes in DACs within the Brownian simulation technique [4]. The proposed algorithms are based on propagation of trajectories of quasiparticle on the corresponding FES with generation of random “hops” from the ground to excited state FES as a result of interaction with the laser pulse. Our new approach extends the area of applicability for the numerical method described earlier in [3] with account for spectral properties of the pulse.
In this study we obtained analytic expression for the probability of quantum transition of quasiparticle from the ground to the excited state within a simple two-level/weak-coupling model. This expression can be used for calculation of surface–hop criteria. The proposed algorithm is universal enough to be applicable for different models, involving one or more classical solvent modes, and one or more high-frequency quantum vibrational modes. The main advantages of the approach are, on the one hand, account for the coherent quantum dynamics, and on the other hand—high performance of computations with respect to direct numerical solution of the Schroedinger equation.