## 1 Introduction
The first attempts at modeling kinetics and the exciton dynamics in photosystem I [27], simulating the spectroscopic characteristics for the light-harvesting complex II from higher plants [28], localization of the triplet states in PSIIRC [19], linear spectroscopy of monomeric photosystem I [17] and a study of red chlorophylls in photosystem I [29] have been made in the last 25 years applying the genetic algorithm. Nevertheless, the differential evolution algorithm (DE) [30; 31] can be considered a more appropriate method for modeling primary photosynthetic processes. Compared with other evolution algorithms, DE deals with the real type variables allowing the fitting parameters to be varied continuously during program run [32; 33]. Recent reviews on applications of DE have shown [32; 34] that, in addition to the classical version of the algorithm, so-called self-adaptive DE modifications [35; 36; 37; 38], designed to improve convergence, are now actively used for many tasks [39]. However, these modifications in the case of PPC optical properties modeling have no significant effect on the convergence rate and the spectra fitting results. To deal with this situation, we have developed software combining the DE algorithm and procedures for the calculation of the spectra of photosynthetic pigments and pigment-protein complexes [40; 41]. Starting with the modeling of linear absorption of monomeric Chl, bacteriochlorophyll and carotenoids in different solvents, the best DE strategy and its optimal settings have been found [41; 42]. The next step was to explore the prospect of using DE to fit the linear spectroscopy of a small PPC, such as PSIIRC. Having a set of artificially simulated spectra as experimental data, we were able to match the DE settings with which the algorithm found the required parameters of the exciton model of PSIIRC [40]. However, it makes no sense to use such a model to fit experimentally measured spectra, since it does not take into account the inhomogeneous broadening of the PSIIRC excited states (Figure 1). Figure 1: Effect of the inhomogeneous broadening on the optical properties of PPC. A dimer of coupling Chls (**A**) with \(\mathrm{Q_{y}}\) transition moments (red arrows) is shown with parameters of the exciton Hamiltonian (5). Calculated absorption spectra of the dimer are presented for different MC values: 10 (**B**), 100 (**C**), 500 (**D**), 5000 (**E**); \(FWHM_{\mathrm{D}}\) = 300 cm\({}^{-1}\). The black line is the resulting dimer absorption, and the red and blue lines are absorptions of the excited states of a dimer. Parameters of the spectral density of the \(\mathrm{Q_{y}}\) transition of Chl was taken from [40]. The crystal structure of PSIRC: positions of Chls and pheobytins and protein subunits. The red circle marks D1–D2 special pair—two Chls where charge separation processes take place. Coupling cofactors of PSIRC creates an exciton manifold of eight states with the characteristic absorption at 77 K (**F**). Thus, the aim of this study is to enhance the previously published PSIIRC exciton model and the quality of linear optical properties modeling [40] by adding the procedure of inhomogeneous broadening by means of MCM. It must be stressed that MCM is a probabilistic method which provides only an approximate solution to a problem. On the other hand, DE is also based on a random generator in order to create new populations of parameters. Therefore, the question arises whether the two probabilistic methods can be used in the same harness, and whether the convergence of DE will be affected by using MCM to simulate the optical response of PPC? Moreover, is it possible to fit measured experimental data with such a combination of methods, while simultaneously obtaining significant parameters for quantum models of primary photosynthetic processes? Thus, our study focuses on answering these two questions.