Bending vibrations in the infrared spectra of ammonia adsorbed on Lewis acidic metal oxides, i.e., Al2O3, ZrO2 and TiO2, and zeolite were analyzed with an aid of density functional theory (DFT) calculations. The results by DFT methods reveal the wavenumbers of the vibration modes (nu (4) and nu (2)) of NH4 bonded to Bronsted acid site and the vibration modes (delta (s) and delta (d) ) of NH3 species coordinated to a Lewis acidic metal center (M = Al, Zr or Ti). The wavenumbers calculated based on DFT were reasonably in agreement with the experimentally observed values. The estimation of wavenumbers suggests that the delta (s) vibration of NH3 hydrogen-bonded is invisible on a zeolite, because it is hidden by an intense absorption due to skeletal vibration. On the other hand, multiple bands of asymmetric bending modes (delta (d) and nu (2)) observed on a zeolite were assigned. A quantification method of Bronsted and Lewis acid sites, and hydrogen-bonded NH3 is provided based on the peak assignments. Bending vibration bands in infrared (IR) spectra of ammonia adsorbed on Bronsted and Lewis acid sites, and hydrogen-bonded species were assigned with an aid of density functional theory.