In this paper, the structures and energetics of 1,3-bis[3-methylimidazolium-yl] pentane ([bis-Mim]2+) dication and bis(mandelato) borate [BMB]− and bis(salicylato) borate [BScB]−anions in isolated forms, ion pairs (IPs) and dicationic ionic liquids (DILs) were studied by Density Functional Theory (DFT) at the M06-2X/6-31G(d,p) level of theory. According to the IUPAC criteria, the hydrogen bonds between anion and cation were characterized and classified in the optimized geometries of the isolated ions, IPs and DILs. Inspection of the optimized structures revealed that the interionic hydrogen binding has important effect on the ions structures. The interaction energies between a dication and anions have been described in terms of NBO charge distribution, the stabilization energy E(2) values, changes of vibrational frequencies and the reduced density gradient (RDG) analysis. Also, the reactivity and interactions between chemical species were interpreted in terms of global electronic properties. Electrostatic potential surfaces (ESP) have been applied for visualizing the charge related properties and characterization of the most energetic sites of isolated ions and ion complexes.