## 1 Introduction
The previous research in this field is mainly focused on developing and testing new computational and experimental methods for a better understanding of the delocalization of excited states over multiple pigments and the unfolding of the relationship between atomic structure and absorbance along with the fluorescence spectra [19; 20]. Owing to the rotational symmetric of the monomer subunit of FMO trimer around the symmetry axis, there are two types of FMO complex structures widely analyzed in the literature. The first structure comprises of only a single monomer of protein complex given by the pdb code 3 EOJ [17; 18]. Another structure available in the protein data bank is the 3 ENI which exists as a dimer of the protein complex with each monomer having eight BChl pigments [21]. The difference between these structures lies in the fact that the former is taken from the species Prosthecochloris aestuarii with the resolution of 1.3 A and the latter is from the species Chlorobium tepidum with the resolution of 2.3 A. The structure of FMO complex including the entire protein taken from protein data bank (3 ENI) is shown in Figure 1a and the corresponding model without protein is shown in Figure 1b. There are also some other structures of the FMO protein taken from the Chlorobium tepidum [22]. Many experimental and computational studies have been reported on the structure of chlorophyll utilizing the density functional theory (DFT) and nuclear magnetic resonance (NMR) techniques (including solid-state and liquid-state NMR) for understanding its role in the photosynthesis process [24; 25; 26; 27; 28; 29]. Calculation of the electronic g-tensors of the semiquinone active sites of photosynthetic reaction centers in a variety of protein environments using DFT has also been reported in [30]. Furthermore, calculation of the nuclear quadrupole parameters has been performed on the chlorophyll _a_[31], but no such a systematic computational study for the BChl has been reported till now. Hence, the calculation of these parameters on the BChl of FMO protein is an important subject to study. We also note that the quantum coherence studies of the FMO complex have been reported in a number of works to elucidate the quantum mechanical time-dependent phenomenon associated with the process of photosynthesis [32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42]. Moreover, the mutation of the FMO light harvesting complex can cause changes in the observed phenomenon of quantum coherence. In some of the studies, the effect of the mutation has also been studied by conducting the site-specific mutagenation for the FMO complex and accordingly its absorption spectra and circular dichroism has been reported and analyzed [43; 44; 45]. It is well-known that apart from the absorption of light from the sun, the light harvesting complexes are also responsible for maintaining the energetic state and chemical state of the complexes available in the photosynthetic reaction center. The parts of the light harvesting complex systems that control the reaction center's chemical and energetic state are known as the quenchers such as carotenoids. Although such quenchers are not available in the FMO protein, it has been experimentally found that the cysteine residues located near the low-energy BChls are responsible for regulating the effective energy transfer in aerobic conditions in the reaction center of green sulfur bacteria [46; 47]. A complete elucidation and better understanding of the associated phenomena would significantly assist in the design of bio-inspired light harvesting antennas along with the redesign of the natural photosynthetic systems [47]. The infrared spectra of the chlorophylls \(a\), \(d\) and \(f\) have been calculated using modern density functional (CAM-B3 LYP) and high-level symmetric adapted coupled cluster configuration interaction (SAC-CI) in [48]. The effect of magnesium ligation on the geometry and spin density distribution of the cation free radicals have also been quantified in the models of chlorophyll and BChl using DFT in [49].