## 5 Discussion
It is interesting to compare the spectra simulated with different MC. Using spectra with MC = 10,000 as a reference, we calculated the differences according to \(\eta_{qr}^{MC}=\frac{1}{N}\sum_{n=1}^{N}\left[\sigma_{abs}^{MC}(\omega_{n})_{ q}-\sigma_{abs}^{10000}(\omega_{n})_{r}\right]^{2}\). The results are shown in Figure 3. If MC = 1000, 2000 and 5000, the order of \(\eta_{qr}^{MC}\) is about -5 and we can consider these PSIIRC spectra to be very close to those simulated at MC = 10,000, while MC = 100 and 200 give large differences between spectra. Before the fitting of measured data, we conducted preliminary DE runs with spectra calculated at MC = 10,000 as target functions. To obtain a definitive answer to the question of which value of MC is preferable when calculating the optical response, we ran two datasets with one and two free parameters. Moreover, \(FWHM_{\Omega}\) is a fixed parameter in the first dataset and free in the second one. The results for one free parameter are in Table 14; \(\chi^{2}\) decreases with an increasing number of MCM realizations and reaches -6 orders of magnitude at all five runs at MC = 500. Similar values for \(\chi^{2}\) were obtained for modeling with two free parameters (Table 15). \(FWHM_{\Omega}\) gradually tends from 175 (MC = 100) to 182 (MC = 2000), which is closer to 180. The standard deviation of \(FWHM_{\Omega}\) also decreases rapidly as MC realizations increase. At the same time, it is difficult to say about the unambiguous dependence of the standard deviation of dielectric constant \(\varepsilon\) on MC for both cases. This can be explained by the fact that its standard deviation is initially small, and these meanings of the standard deviations are a consequence of stochastic processes. Therefore, balancing between reasonable computational time and the quality of simulated spectra, we decided to take MC = 500 as optimum to fit the real data. The best results of the fitting of PSIIRC linear spectroscopy data after ten runs of DE are presented in Figure 4. Eleven free parameters of the exciton model were considered for simulation. The overall quality of the fit can be regarded as satisfactory; however, circular and linear dichroism definitely require additional improvement (Figure 4C,D). First of all, it should be stressed that to achieve better fitting, at least another three free parameters must be added to the current set of eleven. These are the frequency, the Huang-Rhys factor and the damping factor, \(\{\omega_{low},S_{low},T_{low}\}\) of the lowest frequency mode used to calculate the spectral density of a pigment [40; 41; 42]. At the moment, there are some technical problems preventing such improvement of our software and considering these three parameters in the fitting, but this is our immediate goal to enhance computational procedures. \(\chi^{2}\) decreased quite fast in the first ten generations, and then there was a slow asymptotic stagnation. Similar behavior of \(\chi^{2}\) was observed in the modeling of monomeric pigments' absorption in solvents [41; 42]. The maximum number of generations was set to 100. This definitely has to be increased up to 300 or 400 [40], but for the first attempt at running the fitting, it was decided to use 100. Interestingly enough, the \(I_{12}\), the coupling between special pair Chls, can be estimated without any optimization simply using physical theories describing the interaction of electronic excited states [45]. Aside from the magnitude of \(I_{12}\), the sign is also important (positive-repulsion, negative-attraction). Calculations for the D1-D2 dimer give the positive sign. On the other hand, \(I_{12}\) was a free parameter in the fitting with initial boundaries \([-200;200]\). As a result, the best convergence was exclusively achieved for the positive values of \(I_{12}\). Thus, we can state that DE optimization is sensitive to the exciton model of PSIIRC.