An enhanced interest in the phytochrome-based fluorescent proteins is explained by their ability to absorb and emit light in the far-red and infra-red regions particularly suitable for bioimaging. The fluorescent protein IFP1.4 was engineered from the chromophore-binding domain of a bacteriophytochrome in attempts to increase the fluorescence quantum yield. We report the results of simulations of structures in the ground S0 and excited S1 electronic states of IFP1.4 using the methods of quantum chemistry and quantum mechanics/molecular mechanics. We construct different protonation states of the biliverdin (BV) chromophore in the red-absorbing form of the protein by moving protons from the BV pyrrole rings to a suitable acceptor within the system and show that these structures are close in energy but differ by absorption bands. For the first time, we report structures of the minimum energy conical intersection points S1/S0 on the energy surfaces of BV in the protein environment and describe their connection to the local minima in the excited S1 state. These simulations allow us to characterize the deactivation routes in IFP1.4.