As an index of acid strength, ammonia adsorption energies (E ads ) were calculated with density functional theory on cluster models of Brønsted acid sites belonging to FAU, BEA, MFI, FER, MWW, and MOR structures, which were selected because of the availability of experimental data and industrial importance.The calculated E ads were reasonably consistent with experimental results from the ammonia IRMS-TPD (infrared mass spectroscopy-temperature-programmed desorption) method. The calculated value was slightly (10-20 kJ mol -1 ) lower than the observed value, and its change with varying structure was approximately in agreement with the experiments. A thorough study was carried out to find the geometric parameters of the zeolite clusters (in the H and NH 4 forms) relevant to E ads and to discuss parameters controlling the acidic property. Hydrogen bonding interactions between ammonium cations and neighboring zeolitic oxygens were found to affect E ads observed in small cavities. When NH 4 + was stabilized in relatively open spaces (large cavities), acid strength was controlled by the local geometry of the Brønsted acid site, indicating a contribution of strain around Si(OH)Al to acid strength. In these cases, a shorter Al-O distance (a) gave a higher E ads . This is consistent with the explanation that Lewis acidic Al withdraws the electron charge of the SiOH contributing to Brønsted acid strength. A relationship was found between a and the distance (b) and planar angle (ω) between two triangles consisting of three oxygens each, which surrounded the Si(OH)Al unit, and finally, a relationship was found in which a smaller b and ω brought a higher E ads . The strain (compression) on atoms surrounding the Si(OH)Al unit is reflected in the extent of b and ω, and this contributes to vary Brønsted acid strength.

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