## 1 Introduction  
Photosynthesis is a process by which green plants and certain other organisms convert light energy into chemical energy which is then served as an energy source for all forms of life. A common example of the photosynthesis process is the conversion of carbon dioxide (CO\({}_{2}\)) and water (H\({}_{2}\)O) into the carbohydrate and oxygen in the presence of sunlight in plants. This type of photosynthesis is known as oxygenic photosynthesis which occurs in, among others, eukaryotic microorganisms such as algae and in bacteria such as cyanobacteria. There is also another type of photosynthesis, which is known as anoxygenic photosynthesis that does not produce oxygen and is used by other bacteria such as the purple bacteria, the green sulfur and nonsulfur bacteria, as well as by the acidobacteria and the heliobacteria. Significant research efforts have been devoted on using photosynthetic organisms or mechanisms as a source to produce clean, cheap and renewable energy [1]. The photosynthetic process is first initiated by the absorption of sunlight by the light harvesting complexes resulting in the generation of electronically excited state being subsequently transferred to the reaction centre where charge separation occurs. Notably, this transfer of energy is facilitated by the pigment-protein complexes, such as light harvesting complex II, CP26 and CP29 in green plants and algae, as well as model organisms of green sulfur bacteria such as Chlorobium tepidum and Fenna-Matthews-Olson (FMO) complex [2]. The structures of both the light harvesting II and FMO complexes as determined by the X-ray crystallography show that such complexes are built from a network of chromophore molecules, such as bacteriochlorophyll (BChl) _a_[2; 3; 4]. In addition to being important for the plants, the photosynthetic systems are also being used for the production of bioactive compounds, as well as in biomedicine [5; 6; 7]. One such example is the application of the photosynthetic bacteria in the purification of waste water and biomass recovery that has been experimentally demonstrated in [8]. Green sulfur bacteria are photoautotrophic inhabitants of aquatic anoxic environments that possess a unique and complex photosynthetic machinery which permits them to thrive in an oxygen-free, sulfur-rich and often light-limited environment [9; 10]. In photosynthetic green sulfur bacteria, the specialized light-absorbing green pigments called chlorophyll absorbs the light photons that are further transferred through a water-soluble pigment-protein complex known as FMO to the reaction center to drive the charge separation [3]. Owing to the important role played by the FMO complex in the energy transfer in green sulfur bacteria, significant research efforts have been made in the past decade for our better understanding of their optical properties utilizing a wide range of spectroscopic and theoretical approaches, making it an ideal protein model system for studying exciton dynamics and excitation energy transfer in the photosynthetic complexes [3; 4; 11; 12; 13; 14; 15; 16]. In particular, we recall that the FMO protein complex contains seven BChl \(a\) molecules wrapped in a string bag of protein that plays an important role in green sulfur bacteria, connecting the chlorosome antenna to the reaction center where the photosynthesis events occur. Experimentally, the eighth BChl pigment has also been newly resolved in the FMO protein that lies perpendicular to the plane of the other seven BChls [17; 18]. Notably, FMO complex is a homotrimer of three \(\approx 40\) kDa monomer that possesses C3 symmetry whereby three copies of each subunit of seven BChl \(a\) chromophores bind together to the eighth BChl \(a\) pigment [19; 20; 16]. Due to close packing of BChl \(a\) pigments in each monomer subunit, the excited electronic states of FMO complexes are delocalized over multiple pigments.