DENSITY-FUNCTIONAL STUDY OF CLUSTER-MODELS OF ZEOLITES .1. STRUCTURE AND ACIDITY OF HYDROXYL-GROUPS IN DISILOXANE ANALOGS

In this work we calculate the structures and acidities of a series of clusters that mimic terminal and bridging hydroxyl groups in zeolites and molecular sieves using the local density functional (LDF) program DMol. The clusters include silanol, H3Si-OH, and its anion, the simplest model of terminal hydroxyl groups at zeolite surfaces and defect sites. We also consider disiloxane, H3Si-O-SiH3, and a series of structural analogs of disiloxane, H3T-O(H)-TH3 (T = tetrahedrally coordinated atom) in which Si is substituted by Al, B, P, Ga, or Ge. The accuracy of these LDF calculations is determined in part by the size of the numerical basis set and quadrature grid. We find that the structures of the clusters are insensitive to increases in quadrature grid size beyond almost-equal-to 3000 points/atom. However, the optimized values of the internal coordinates, particularly the T-O-T bond angle, are much more sensitive to basis set size. The largest basis set used in these calculations (DNP+) shows convergence in key internal coordinates to almost-equal-to 0.1-degrees-5.0-degrees for T-O(H)-T bond angles and better than 0.01 angstrom for T-O bond lengths. We also gauge the accuracy of the LDF results against extended basis set Hartree-Fock MP2 results (MP2/DZ+2d) and experimental data. Agreement between the LDF and MP2/DZ+2d values is generally good, with some notable exceptions. For example, while most of the bond angles are well represented by the LDF, the T-O-T bond angles are systematically 5-degrees-11-degrees smaller than the MP2/DZ+2d results. In addition, we find that the differences between the LDF and MP2/DZ+2dT-O bond lengths correlate with bond strength. Thus, very good agreement between the methods is observed for the stronger Si-O and P-O bonds (<0.005 angstrom), while LDF predicts a significantly shorter (by >0.03 angstrom) length for the weaker B-O bond. Bond lengths involving hydrogen are almost-equal-to 0.02 angstrom too large with the smaller basis sets, although the O-H bond lengths markedly improve with the DNP+ basis set. The theoretical trend in acidity of the hydroxyls, as determined by the proton affinity, agrees with the experimental trend for isomorphously substituted ZSM-5 zeolites and our MP2/DZ+2d results.