Over the last decade, Density Functional Theory (DFT) has become one of the major tools in modern quantum chemistry. It has been included in time-dependent methods (Car-Parrinello) as well as in QM/MM hybrid techniques. The development of Time-Dependent Density-Functional Theory (TDDFT) as a rigorous formalism within DFT has been a major step, opening the possibility to calculate exited states of simple molecules and large systems with an accurate precision at low computational cost. TDDFT results usually surpass those of time dependent Hartree-Fock or Configuration Interaction with Single excitation (CIS) and are more comparable in quality to those obtained with ab initio methods. A TDDFT investigation of Charge Transfer Excited States is presented, treating the phenomenon of dual fluorescence of compounds of the same family as 4-(N,N dimethylamino)benzonitrile molecules. A classification of the studied molecules in four classes is proposed based on the Twisting Intramolecular Charge Transfer model. This classification based on the form of the calculated potential energy surfaces of the ground and excited states allows to understand the different fluorescent behaviour of these molecules. Influence of various functionals and future developments are discussed.