Algorithms for the computer simulation of ultrafast photoinduced intermolecular charge transfer in liquids


Brownian simulation, recrossing algorithms, encounter theory, intermolecular charge transfer, photochemical reactions


Efficient approaches to the numerical solution of equations describing the kinetics of two-stage photochemical reactions in a viscous polar solvent are proposed. The mathematical model is based on the extended integral encounter theory and takes into account diffusive mobility of reactants in solution, nonequilibrium of solvent and intramolecular degrees of freedom, and remote electron transfer in solvent-separated donor-acceptor pairs. In the framework of the Brownian simulation technique, a number of numerical algorithms for calculating unreactive stochastic trajectories of particles on free energy surfaces corresponding to different electronic states of reactants and products are suggested, some computational schemes for the detection of reaction events and the generation of electronic hops are developed, and algorithms for calculating the time-dependent reaction fluxes between the electronic states and integral kernels of the kinetic equations are implemented. The results of test simulations demonstrating the validity of the numerical solutions and reproducing well-known features of electron transfer reactions in polar solvents are discussed.


  1. Allen M.P., Tildesley D.J. Computer simulation of liquids. New York: Oxford University Press, 1991.
  2. Van Kampen N.G. Stochastic processes in physics and chemistry. Amsterdam: Elsevier Science, 2007.
  3. Landau D.P., Binder K. A guide to Monte Carlo simulations in statistical physics. Cambridge: Cambridge University Press, 2009.
  4. Zharikov A.A., Burshtein A.I. Nonlocal ionization in encounter theory // J. Chem. Phys. 1990. 93, N 8. 5573–5579.
  5. Feskov S.V., Ivanov A.I., Burshtein A.I. Integral encounter theory of strong electron transfer // J. Chem. Phys. 2005. 122. doi 10.1063/1.1871935.
  6. Rosspeintner A., Lang B., Vauthey E. Ultrafast photochemistry in liquids // Annu. Rev. Phys. Chem. 2013. 64. 247–271.
  7. Kumpulainen T., Lang B., Rosspeintner A., Vauthey E. Ultrafast elementary photochemical processes of organic molecules in liquid solution // Chem. Rev. 2017. 117, N 16. 10826–10939.
  8. Zusman L.D. Outer-sphere electron transfer in polar solvents // Chem. Phys. 1980. 49, N 2. 295–304.
  9. Feskov S.V., Mikhailova V.A., Ivanov A.I. Non-equilibrium effects in ultrafast photoinduced charge transfer kinetics // J. Photochem. Photobiol. C. 2016. 29. 48–72.
  10. Sung J., Lee S. Relations among the modern theories of diffusion-influenced reactions. II. Reduced distribution function theory versus modified integral encounter theory // J. Chem. Phys. 2000. 112, N 5. 2128–2138.
  11. Ivanov K.L., Lukzen N.N., Doktorov A.B., Burshtein A.I. Integral encounter theories of multistage reactions. I. Kinetic equations // J. Chem. Phys. 2001. 114, N 4. 1754–1762.
  12. Ivanov K.L., Lukzen N.N., Morozov V.A., Doktorov A.B. Integral encounter theories of multistage reactions. IV. Account of internal quantum states of reactants // J. Chem. Phys. 2002. 117, N 20. 9413–9422.
  13. Burshtein A.I. Non-Markovian theories of transfer reactions in luminescence and chemiluminescence and photo- and electrochemistry // Adv. Chem. Phys. 2004. 129. 105–418. 38 вычислительные методы и программирование. 2020. Т. 21
  14. Gladkikh V., Burshtein A.I., Feskov S.V., et al. Hot recombination of photogenerated ion pairs // J. Chem. Phys. 2005. 123. doi 10.1063/1.2140279.
  15. Feskov S.V., Rogozina M.V., Ivanov A.I., et al. Magnetic field effect on ion pair dynamics upon bimolecular photoinduced electron transfer in solution // J. Chem. Phys. 2019. 150, N 2. doi 10.1063/1.5064802.
  16. Jortner J., Bixon M. Intramolecular vibrational excitations accompanying solvent-controlled electron transfer reactions // J. Chem. Phys. 1988. 88, N 1. 167–170.
  17. Feskov S.V., Ivanov A.I. Solvent-assisted multistage nonequilibrium electron transfer in rigid supramolecular systems: diabatic free energy surfaces and algorithms for numerical simulations // J. Chem. Phys. 2018. 148, N 10. doi 10.1063/1.5016438.
  18. Феськов С.В. Метод броуновского моделирования в задачах расчета динамики электронного переноса // Вычислительные методы и программирование. 2009. 10. 202–210.
  19. Феськов С.В. К обоснованию рекроссинг-алгоритмов численного моделирования многоканальных электронных переходов в вырожденные состояния акцептора // Вычислительные методы и программирование. 2017. 18. 284–292.
  20. Nazarov A.E., Fedunov R.G., Ivanov A.I. Principals of simulation of ultrafast charge transfer in solution within the multichannel stochastic point-transition model // Comp. Phys. Comm. 2017. 210. 172–180.
  21. Stock G., Thoss M. Classical description of nonadiabatic quantum dynamics // Adv. Chem. Phys. 2005. 131. 243–375.
  22. Feskov S.V. The time-dependent j-flux method for stochastic simulations of multistage bimolecular photoinduced electron transfer within the extended integral encounter theory // AIP Conf. Proc. 2018. 2040. doi 10.1063/1.5079051.
  23. Marcus R.A., Sutin N. Electron transfers in chemistry and biology // Biochim. Biophys. Acta. 1985. 811, N 3. 265–322.
  24. Burshtein A.I. Unified theory of photochemical charge separation // Adv. Chem. Phys. 2000. 114. 419–587.
  25. Carslaw H.S., Jaeger J.C. Conduction of heat in solids. Oxford: Oxford University Press, 1986.
  26. Krissinel’ E.B., Agmon N. Spherical symmetric diffusion problem // J. Comput. Chem. 1996. 17, N 9. 1085–1098.
  27. Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P. Numerical recipes: the art of scientific computing. Cambridge: Cambridge University Press, 2007.
  28. Gladkikh V., Burshtein A.I., Angulo G., et al. Kinetics and yields of electron transfer in the inverted region // J. Phys. Chem. A. 2004. 108, N 32. 6667–6678.
  29. Feskov S.V., Burshtein A.I. Double-channel photoionization followed by geminate charge recombination/separation // J. Phys. Chem. A. 2009. 113, N 48. 13528–13540.
How to Cite
Feskov, S., & Khokhlova, S. (2020). Algorithms for the computer simulation of ultrafast photoinduced intermolecular charge transfer in liquids. Numerical Methods and Programming, 21(63), 27-40.
Section 1. Numerical methods and applications

Most read articles by the same author(s)