An ab initio quantum mechanical study of the bis-benzimidazole derivative Hoechst 33342 is presented. Specifically, we report on the molecular geometry, proton affinity, gas-phase basicity, hydration, pKa, and molecular interaction potential map of Hoechst 33342 and the forms obtained by its protonation and deprotonation. Results have been compared with those obtained for Hoechst 33258 to analyze the influence of the chemical structure on the properties of this bis-benzimidazole derivative. Finally, the connection of some theoretical predictions with experimental evidences has been examined.