The use of Laplace transform for analysis and optimization of time-resolved spectroscopic data

Nagaev E.I., Chesalin D.D., Zabelin A.A., Sarimov R.M., Gudkov S.V., Pischalnikov R.Y.

Prokhorov General Physics Institute of the Russian Academy of Sciences, Moscow, 119991 Russia Federal Research Center “Pushchino Scientifc Center for Biological Research of the Russian Academy of Sciences”, Institute of Basic Biological Problems of the Russian Academy of Sciences, 142290 Pushchino, Moscow Region, Russian Federation

High time-resolution spectroscopy is the main experimental method for studying physicochemical processes in organic and inorganic molecular crystals and pigments that absorb in the visible, ultraviolet, and infrared wavelength ranges. In general, to model the optical response proportional to χ3, it is necessary to use semi-classical theories of the interaction of electron radiation with matter. However, for a whole class of research objects (e.g., organic monomeric pigments and crystals) such calculations are complicated and require serious computational resources. As a consequence, a simpler method based on the Laplace transform is often used for preliminary analysis of experimental data, the essence of which is reduced to the representation of measured kinetic curves as a composition of exponential components. We have developed software that allows optimization using differential evolution, an efficient heuristic algorithm for finding a global minimum for an arbitrary type of function [1]. The work of the algorithm, including the Laplace transform, the procedure for solving differential equations, and differential evolution, was tested on data obtained in pumping-probe experiments performed on samples of photosynthetic pigment-protein complexes (photosystem I and the reaction center of photosystem II [2]).


1. Chesalin, D.D.; Kulikov, E.A.; Yaroshevich, I.A.; Maksimov, E.G.; Selishcheva, A.A.; Pishchalnikov, R.Y. Differential evolution reveals the effect of polar and nonpolar solvents on carotenoids: A case study of astaxanthin optical response modeling // Swarm and Evolutionary Computation, 75, 2022, 101210, doi: 10.1016/j.swevo.2022.101210.

2. Pishchalnikov, R.Y.; Zabelin, A.A.; Kompanetz, V.O.; Shkuropatov, A.Y.; Razjivin, A.P.; Chekalin, S.V. Excitation energy structure of the photosysthem II reaction center: Excitons and charge-separated states // Proceedings of International Conference Laser Optics 2020, ICLO 2020. doi: 10.1109/ICLO48556.2020.9285560


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