## 5 Discussion  
By analyzing and comparing the quantum models of the simple Chl dimer and rather more complex proteins such as PSIIRC, it becomes clear that the required number of MCM realizations depends precisely on the relation between the parameters of the exciton model. The dimer of Chls, used as an example, has \(\Delta\Omega=\Omega_{2}-\Omega_{1}=300\) cm\({}^{-1}\), \(J_{12}=200\) cm\({}^{-1}\); the corresponding eigenvalues \(\epsilon_{\mathrm{a}}\) are 14,800 cm\({}^{-1}\) and 15,300 cm\({}^{-1}\). Such eigenvalues give a gap of 500 cm\({}^{-1}\) which is greater than \(FWHM_{\Omega}=300\) cm\({}^{-1}\). As a result, absorption bands of the dimer are well separated in the spectrum (Figure 1B-E). This means that if we want to achieve a smooth quality spectrum, it is necessary to set a large value for MC. For a simple model such as a dimer, there is no problem with running optimization with thousands of MCM realizations, but for a system of many pigments, especially with sparse absorption bands, this may already be problematic. Potential exciton models of PSIIRC have already been discussed many times [19; 23; 46; 47]. Characteristic features of PSIIRC include small differences between transition energies of cofactors \(\Delta\Omega_{nm}\in(10;100)\) cm\({}^{-1}\), coupling energies \(J_{nm}\in(10;200)\) cm\({}^{-1}\) and \(FWHM_{\Omega}\in(100;200)\) cm\({}^{-1}\). This exciton configuration leads to an optical response in which the exciton states are either close together, or overlap with each other. The resulting spectra look relatively broad and featureless, however, at lower temperatures some peculiarities do emerge (Figure 1F). It is obvious that fitting experimental data with such models is hardly possible without optimization, however, much of the analysis has been carried out by hand. DE seems to be a promising solution to fit experimental data of PPC. Studies of the optical properties of monomeric photosynthetic pigments in different solvents with DE have proved to be quite optimistic [41; 42]. To proceed with PSIIRC modeling considering MCM for inhomogeneous broadening, the effect of MC on the averaged spectra has to be investigated. Generally, with increasing MC, the perfection of simulated data increases; the higher MC value, the better. However, any experimental data have their limits of perfection, which are determined by errors of measurements and other physical effects that are not included in the mathematical description of the model. Therefore, it is clear that, to analyze the experimental data, there must be an optimal value of MC which will speed up MCM and, on the other hand, will provide enough perfection for the simulated spectra to match the quality of the measured ones. The simulation of PSIIRC spectra was carried out for MC equal to 100, 200, 500, 1000, 2000, 5000 and 10,000. To estimate the difference in the optical response, without loss of generality, only absorption spectra were used. The results are shown in Figure 2. Plots A, C, E, G, I, K and M of Figure 2 present an example of the statistical distribution of \(\delta_{n}^{j}\) for Chl\({}_{\mathrm{D1}}\) of the special pair. Histograms for 2000, 5000 and 10,000 MCM realizations demonstrate symmetrical Gaussian profiles, while distributions with smaller MCs have asymmetry and exhibit a clear lack of sampling. The differences between spectra with the same MC stored in the \(\theta_{qr}^{MC}\) matrix are shown in plots B, D, F, H, J, L and N of the same figure. Table A1 contains \(\theta_{qr}^{MC}\) for all MC and also the median and worst differences. One can observe an unambiguous dependence: with an increase in realizations, their median and worst values decrease. For 10,000 realizations, the worst \(\theta_{qr}^{10000}\) does not exceed -6 orders of magnitude, which suggests that this amount of MC will be enough. At the same time, when MC = 5000, although there are predominantly -6 orders of magnitude, this does not give an exact guarantee of the required simulation results.