Only a low percentage of the radiation from our Sun is captured by photosynthesis, but this conversion of solar to chemical energy sustains all life on Earth. Photosynthesis could be present in any exoplanetary system fulfilling the main three ingredients for this metabolic route: light, water, and carbon dioxide. To deepen into this idea, the ExoPhot project aims to study the relation between photosynthetic systems and exoplanet conditions around different types of stars by focusing on two aspects: (i) Assessing the photosynthetic fitness of a variety of photopigments (either found on Earth or theoretical) as a function of stellar spectral type, star-exoplanet separation, and planet atmosphere basic parameters, and (ii) delineating a range of stellar, exoplanet, and atmospheric parameters for which photosynthetic activity might be feasible. In order to address these goals, we make use of a new metric, the absorption rate γ, for the evaluation of the exoplanet photosynthetic activity that, based on state-of-the-art planet atmosphere and stellar photosphere spectroscopic models, quantifies the overlap between those models with the absorption spectra of photosynthetic pigments, both terrestrial and theoretical. We provide with a set of results for a combination of photosystems and exoplanetary environments revealing the importance of our metric when compared to previous photosynthesis indicators.