## 1 Introduction
This study reported that there is a formation of the radical orbitals without significant changes in the  
Figure 1: (Color online) (**a**) the FMO trimer structure from C. tepidum (PDB ID: 3 ENI) demonstrating the packing of BChls (colored in blue) inside the protein backbone (colored yellow), and (**b**) the spatial arrangement of BChls taken out from the protein pocket. The eight BChls of the same monomer are colored in green while the BChl 8’ of the nearest-neighboring monomer is colored in purple. (This figure is reproduced from [23] under the terms of the creative commons attribution 4.0 International License ([[http://creativecommons.org/licenses/by/4.0/](http://creativecommons.org/licenses/by/4.0/)]([http://creativecommons.org/licenses/by/4.0/](http://creativecommons.org/licenses/by/4.0/))), Copyright © 2020, Springer Nature)  
hyperfine coupling of the systems. It has also been noted that the energy transfer phenomenon in the FMO complex is well described by solving the hierarchical equations of motion for such systems [50; 51; 52; 53; 54]. The potential energy surface for the BChl pigments taken from the FMO complex has also been computed using a combination of molecular dynamics and quantum mechanics simulations [55]. A more detailed description of such computational methods and their advancements in this field of research has been elaborated in [56]. The excitonic energy transfer for the biological systems related to the photosynthesis phenomenon, i.e., the biological chromophore and light harvesting complexes, can be evaluated using the path integral dynamics as highlighted in [57; 58; 59]. Furthermore, the normal mode analysis of the spectral density has been studied using the time-dependent DFT in [60] for computing the spectral densities due to coupling between light harvesting pigments and their corresponding protein. This method is a combination of the charge density coupling and the transition charge density electrostatic potential with the normal modes of the protein pigment that is studied via correlation in the site energies of the complex, as well as the scheme of its returning from the coherence state to the original state. Several advances have been reported on the computational study of the FMO complex, using molecular dynamics simulation as well as the DFT to study its spectral density, excitation energy and optical spectra [61; 62; 63; 64; 65; 66]. The comparative study for the excited energy distribution and spectral density of the two different kinds of light harvesting complexes, i.e., PE545 photosynthetic complex and FMO complex, has been done utilizing molecular dynamics simulation along with the quantum mechanical calculations incorporating the environment of the complexes in [67; 68]. These studies are also supporting the existence of quantum coherence which is a subject of continuing debate [69; 70; 71; 72; 73; 74; 75; 76]. The study of pump-probe polarization phenomena of the photosynthetic light harvesting complexes has also been reported in the previous works for several kinds of coherences and the long-time vibronic coherences have been observed in the FMO [77; 78; 79]. The electron-nuclear interaction in the BChl systems of the FMO complex has also been described in a molecular dynamics-based study of [80], which also signifies the influence of electronic relaxation caused by the environmental changes. Significant efforts have been devoted for studying the light harvesting complex II and the FMO complex for quantifying the correlation between the energies of different pigments existing in the FMO protein [81; 82]. The pathways for the energy transfer between different pigments of the FMO complex have also been previously studied by using a combination of the quantum mechanical and molecular dynamics simulations. By knowing the direction of energy transfer between different pigments of FMO, one could easily find out their excitation which ultimately depends on the position of these pigments [23; 44; 83].