Optimizing the Multimode Brownian Oscillator Model for the Optical Response of Carotenoids in Solution by Fine Tuning of Differential Evolution

Abstract

During last twenty years, the Differential evolution algorithm (DE) has proved to be one of the powerful methods to solve minimization problems for multidimensional functions. Being a member of the family of evolutionary optimization algorithms, its main principle is based upon the concepts of natural selection and mutation. In this study, we test the potential of DE to find a proper set of parameters for the multimode Brownian oscillator model, which was then used to simulate absorption lineshapes of carotenoid molecules in solution: spheroidene and spheroidenone. This theory assumes that the correlation function of a particular electronic state of the carotenoid is calculated using the semiclassical spectral density function. Considering our previous studies on photosynthetic pigments, we employed several DE strategies to do fitting of the carotenoid experimental spectra. We found that simulated absorption spectra are very sensitive to several parameters that characterize carotenoid vibronic modes, namely, Huang–Rhys factors. Fine tuning of DE crossover parameter (Cr) and the scaling factor (F) provided acceptable convergence of the algorithm. It appears that to get good convergence of DE, a certain spectral range of carotenoid absorption from 400 to 600 nm must be chosen. This fact can be explained by the limitations of the applied theory, which simply does not predict properly the carotenoid absorption at higher frequencies.