Naphthalene diimide ligands have the potential to stabilize human telomeric G-quadruplex DNA via noncovalent interactions. Stabilization of G-quadruplex high order structures has become an important strategy to develop novel anticancer therapeutics. In this study four naphthalene diimide based ligands were analyzed in order to elucidate the principal factors determining contributions to G-quadruplex-ligand binding. Three possible modes of binding and their respective Gibbs free energies for two naphthalene diimide based di-N-alkylpyridinium substituted ligands have been determined using a molecular docking technique and compared to experimental results. The structures obtained from the molecular docking calculations, were analyzed using the ab initio based fragment molecular orbital (FMO) method in order to determine the major enthalpic contributions to the binding and types of interactions between the ligand and specific residues of the G-quadruplex. A computational methodology for the efficient and inexpensive ligand optimization as compared to fully ab initio methods based on the estimation of binding affinities of the naphthalene diimide derived ligands to G-quadruplex is proposed.