Differential evolution reveals the effect of polar and nonpolar solvents on carotenoids: A case study of astaxanthin optical response modeling

Abstract

• Unique software that simulates optical response of biological pigments was developed • Differential evolution is used for finding the best model to fit experimental data • Multimode Brownian oscillator models were created to simulate carotenoid absorption • The optimal settings of Differential evolution allowing fast convergence were found • Differential evolution allowed distinguishing models for polar and nonpolar solvents The task to simulate realistic absorption spectra of electronic transitions in pigment molecules takes the form of the art of optimization, particularly if one must choose between the quality of the results obtained and the calculation time necessary to get such quality. The semiclassical theory of optical response provides us with a good opportunity to escape a so-called sum-over-state procedure of considering the innumerable number of vibronic states of a pigment by applying a correlation function approach. This approach, known as the multimode Brownian oscillator model (MBOM), involves replacing an infinite set of vibronic states, which interacts with an electronic transition, with a finite set of effective vibronic modes. Thus, the parameters of effective vibronic modes and an electronic transition can be found only by fitting experimental data. This situation gives rise to the following problem: as the number of free parameters increases, it becomes more difficult to find a single solution. To overcome this obstacle, differential evolution (DE), a method of global optimization, which is based on the idea of natural selection, seems to be the right choice. To test the efficiency of DE in solving quantum mechanical problems, we simulated absorption spectra of astaxanthin (AST) in 18 different organic solvents by using the MBOM. To do so, we developed software that implements both the DE algorithm and linear absorption modeling procedures. We have shown that simulating practically identical AST spectra, DE allows determining the effect of polar and nonpolar solvents on several parameters of MBOM of AST with high accuracy.