Structural features and interionic interactions play a crucial role in determining the overall stability of ionic liquids and their physicochemical properties. Therefore, we performed high-level quantum-chemical study of different cation-anion pairs representing the building units of protic ionic liquids based on triethanolammonium cation and anions of sulfuric, nitric, phosphoric, and phosphorus acids to provide essential insight into these phenomena at the molecular level. It was shown that every structure is stabilized through multiple H bonds between the protons in the N-H and O-H groups of the cation and different oxygen atoms of the anion acid. Using atoms in molecules topological parameters and natural bond orbital analysis, we determined the nature and strength of these interactions. Our calculations suggest that the N-H group of the cation has more proton donor-like character than the O-H group that makes the N-H center dot center dot center dot O hydrogen bonds stronger. A close relation between the binding energies of these ion pairs and experimental melting points was established: the smaller the absolute value of the binding energy between ions, the lower is the melting point.