In biological and life science applications photosynthesis is an important process that involves the absorption and transformation of sunlight into chemical energy. During the photosynthesis process, the light photons are captured by the green chlorophyll pigments in their photosynthetic antennae and further funneled to the reaction center. One of the most
important light harvesting complexes that are highly important in the study of photosynthesis is the membrane-attached Fenna-Matthews-Olson (FMO) complex found in the green sulfur bacteria. In this review, we discuss the mathematical formulations and computational modeling of some of the light harvesting complexes including FMO. The most recent research developments in the photosynthetic light harvesting complexes are thoroughly discussed. The theoretical background related to the spectral density, quantum coherence and density functional theory (DFT) has been elaborated.
Further, details about the transfer and excitation of energy in different sites of the FMO complex along with other vital photosynthetic light harvesting complexes have also been provided. In particular, we will review recent results on spectral density, quantum coherence, quantum entanglement and excitonic energies of different pigments in the light harvesting complexes. We will also discuss the issues pertinent to the highest occupied orbital (HOMO) and lowest unoccupied
orbital (LUMO) energies for all the bacteriochlorophyll utilizing the time-dependent DFT. These results would
be helpful in studying the excitonic dynamics of the light harvesting complexes among different applications. Finally, we conclude this review by providing the current and potential applications in environmental science, energy, health and medicine, where such mathematical and computational studies of the photosynthesis and the light harvesting complexes can be readily integrated.