Effect of the size of the quantum region in a hybrid embedded-cluster scheme for zeolite systems

Recently we presented an improved scheme for constructing the border region within the covEPE hybrid quantum mechanics/molecular mechanics (QM/MM) embedded cluster approach for zeolites and covalent oxides in the framework of the elastic polarizable environment method. In the present study we explored how size and shape of the embedded QM cluster affect the results for structural features, energies, and characteristic vibrational frequencies of two model systems, adsorption complexes of H₂O and Rh₆ in faujasite frameworks that contain Brønsted acid sites. Comparison of calculated characteristics of different QM cluster models suggests that the local structure and vibrational frequencies of acid sites in adsorbate-free zeolite are well reproduced with all embedded QM clusters, which contain from 5T to 14T atoms. A proper description of systems with an H₂O adsorbate requires larger QM clusters, with at least 8T atoms, whereas vibrational frequencies of OH groups participating in hydrogen bonds demand even larger quantum clusters, preferably with 12T or 14T atoms. The structure of the metal particle in adsorbed rhodium species is well reproduced with all QM clusters scrutinized, from 12T atoms. Larger QM models, with 18T or 24T atoms, are recommended when one aims at a high accuracy of Rh-O and Rh-H distances and characteristic energies.