The results of theoretical studies on structures and energetics are presented for the proton-bound complexes Ar-n-N2H+ (n = 1-12). Complexes are formed due to the consecutive filling of shells. The largest studied cation possesses. the slightly deformed icosahedral geometry. For shells formed outside the Ar-N2H+ core, increasing binding energies are observed during the coordination of consecutive Ar atoms. Such an anomalous behavior is also observed for consecutive values of enthalpy and entropy of ligand binding, Mulliken atomic charges, and Ar-H+ stretching vibrations. The analysis of physical components resulting from interaction energy decomposition allows the observed phenomenon to be rationalized.