The absorption band shapes of a solvent tunable donor-acceptor dye have been theoretically investigated by using Kubo's generating function approach, with minimum energy geometries and normal coordinates computed at the DFT level of theory. The adopted computational procedure allows us to include in the computation of Franck-Condon factors the whole set of normal modes, without any limitation on excitation quanta, allowing for an almost quantitative reproduction of the absorption band shape when the equilibrium geometries of the ground and the excited states are well predicted by electronic computations. Noteworthy, the functionals that yield more accurate band shapes also provide good prediction of the moment variations upon excitation; because the latter quantities are rarely available, theoretical simulation of band shapes could be a powerful tool for choosing the most appropriate computational method for predictive purposes.