Alkylamine-strapped chromophores based on a dithienylpyrrole core, and in which the Excited State Intramolecular Proton Transfer (ESIPT) process yields a zwitterionic structure rather than a keto tautomer have been reported recently (Suzuki et al., Angew. Chem. Int. Ed., 2014, 53, 8231), and are known to exhibit large Stokes shifts. Using Time-Dependent Density Functional Theory (TD-DFT) we investigate the ESIPT mechanism in this family of chromophores considering various substituents and two solvents (cyclohexane and acetone). In order to model the solvent effects, three polarisation models have been applied: the linear response (LR), the corrected linear-response (cLR), and the combination of these two formalisms (LR + cLR). The selected protocol is shown to be effective for a series of compounds with known experimental behaviors, and is then applied to novel derivatives with various donor and acceptor groups and heteroatoms. We determine the absorption and emission wavelengths as well as the energies of the different states that play a role in the ESIPT process. We show that the introduction of electron-withdrawing and electron-donating groups plays an important role in achieving redshifted emission from the ESIPT state.