Brønsted acidity in zeolites measured by deprotonation energy.

Acid forms of zeolites have been used in industry for several decades but scaling the strength of their acid centers is still an unresolved and intensely debated issue. In this paper, the Brønsted acidity strength in aluminosilicates measured by their deprotonation energy (DPE) was investigated for FAU, CHA, IFR, MOR, FER, MFI, and TON zeolites by means of periodic and cluster calculations at the density functional theory (DFT) level. The main drawback of the periodic DFT is that it does not provide reliable absolute values due to spurious errors associated with the background charge introduced in anion energy calculations. To alleviate this problem, we employed a novel approach to cluster generation to obtain accurate values of DPE. The cluster models up to 150 T atoms for the most stable Brønsted acid sites were constructed on spheres of increasing diameter as an extension of Harrison's approach to calculating Madelung constants. The averaging of DPE for clusters generated this way provides a robust estimate of DPE for investigated zeolites despite slow convergence with the cluster size. The accuracy of the cluster approach was further improved by a scaled electrostatic embedding scheme proposed in this work. The electrostatic embedding model yields the most reliable values with the average deprotonation energy of about 1245 ± 9 kJ·mol for investigated acidic zeolites. The cluster calculations strongly indicate a correlation between the deprotonation energy and the zeolite framework density. The DPE results obtained with our electrostatic embedding model are highly consistent with the previously reported QM/MM and periodic calculations.