A generalized method for the estimation of the intensity of electron-phonon interaction in photosynthetic pigments using the evolutionary optimization algorithm

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Resumo

Modeling of the optical response of photosynthetic pigments is an essential part of the study of fundamental physical processes of interaction of multi-atomic molecules with an external electromagnetic field. The use of semiclassical quantum theories in this case is more preferable than the use of ab initio methods for calculating the ground and excited states of a molecule, since semiclassical theories allow us to use characteristic functions, such as spectral density, to calculate absorption spectra rather than to take into account the full set of electron and atom configurations. The main disadvantage of this approach is the necessity of constant comparison of the calculated and experimental spectra and, as a consequence, the need to justify the uniqueness of the obtained parameters of the system under study and to evaluate their statistical significance. One of the possible options to significantly improve the quality of the optical response calculation is the use of a heuristic evolutionary optimization algorithm that minimizes the difference between the measured and theoretical spectra by determining the most appropriate set of model parameters. Using the spectra of photosynthetic pigments measured in different solvents as an example, we have shown that the modeling optimization not only allows us to obtain a good agreement between the calculated and experimental data, but also to unambiguously determine such parameters of the theory as the electron-phonon interaction coefficients for the electronic excited states of chlorophyll, lutein and β-carotene.

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Sobre autores

V. Kurkov

Prokhorov General Physics Institute of the Russian Academy of Sciences; Moscow Institute of Physics and Technology (National Research University)

Email: rpishchal@kapella.gpi.ru
Rússia, Moscow; Dolgoprudny

D. Chesalin

Prokhorov General Physics Institute of the Russian Academy of Sciences

Email: rpishchal@kapella.gpi.ru
Rússia, Moscow

A. Razjivin

Lomonosov Moscow State University

Email: rpishchal@kapella.gpi.ru

Belozersky Research Institute of Physico-Chemical Biology

Rússia, Moscow

U. Shkirina

Prokhorov General Physics Institute of the Russian Academy of Sciences; Lomonosov Moscow State University

Email: rpishchal@kapella.gpi.ru

Department of Mechanics and Mathematics

Rússia, Moscow; Moscow

R. Pishchalnikov

Prokhorov General Physics Institute of the Russian Academy of Sciences

Autor responsável pela correspondência
Email: rpishchal@kapella.gpi.ru
Rússia, Moscow

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2. Fig. 1. Chemical structure and absorption spectra of the studied photosynthetic pigments measured at room temperature: a – lutein (1) and β-carotene (2) in THF and b – Chl a in diethyl ether (1), pyridine (2) and THF (3).

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3. Fig. 2. The generalized spectral density function before the start of spectrum modeling (a) and after (b). Initially, vibronic frequencies are uniformly distributed in the range from 500 to 3020 cm−1, the attenuation coefficient is the same for each mode and is fixed, the Huang–Rhys factors are free parameters (this fact is reflected by the same intensities for each mode). After the end of optimization, the values ​​of the Huang–Rhys factors are determined and correspond to the theoretical spectrum, which maximally coincides with the experimental one.

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4. Fig. 3. The result of modeling the absorption spectra of lutein (a) and β-carotene (b) in THF. The intermediate results of calculations for the first seven generations of the DE algorithm are indicated by thin lines. The dynamics of the minimized residual function of the experimental and theoretical spectra depending on the number of calls of the function for calculating the spectra for lutein and β-carotene is shown in Fig. 3b and d.

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5. Fig. 4. Result of modeling the absorption spectra of Chl a in diethyl ether (a), pyridine (c) and THF (d). Thin lines indicate intermediate results of calculations for the first seven generations of DE operation. The dynamics of the minimized residual function of the experimental and theoretical spectra depending on the number of calls of the function for calculating the spectra of Chl a in each solvent is shown in Fig. 4b, d and e, respectively.

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6. Fig. 5. Spectral densities for lutein (a) and β-carotene (b) in THF obtained after 10 runs of the optimization algorithm. In all cases, the residual value did not exceed 10−4. Arrows indicate the frequency range in which the greatest differences are observed.

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7. Fig. 6. Spectral densities for Chl a in diethyl ether (a), pyridine (b) and THF (c) obtained after 10 runs of the optimization algorithm. In all cases, the residual value did not exceed 10−4. Arrows indicate the frequency range in which the greatest differences are observed.

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