There is still controversy about the structure of the intramolecular charge transfer (ICT) emitting species in pi-electron donor-acceptor systems that show dual fluorescence. Although the twisted ICT model is quite generally accepted, the planar ICT model is not ruled out because firm experimental evidence supports it. Among these it is the fact that some rigidized systems such as bicyclic 4-aminobenzonitrile derivatives exhibit dual fluorescence. We present here an ab initio CASSCF/CASPT2 study of a series of these compounds with the alicyclic chain ranging from 5 to 7 carbon atoms and compare their ICT mechanism with the more flexible 4-aminobenzonitrile (ABN) and 4-(dimethylamino) benzonitrile (DMABN). We present the energetics, geometries, and valence bond structures of the critical points of the potential-energy surfaces of the ground, local excited (LE), and ICT states. Our results show that the photophysical differences of the studied systems may be rationalized by two factors: the position of the ICT and LE potential-energy surfaces at the first stages of the ICT reaction and the relative energies of the excited-state minima. Computational evidence is presented that a twisted ICT structure can be adopted in some molecules such as NXC6 and NXC7 and that the anomalous band of the fluorescence spectra of these systems is emitted from a twisted ICT species.