Ms. Stave et Jb. Nicholas, DENSITY-FUNCTIONAL STUDY OF CLUSTER-MODELS OF ZEOLITES .1. STRUCTURE AND ACIDITY OF HYDROXYL-GROUPS IN DISILOXANE ANALOGS, Journal of physical chemistry, 97(38), 1993, pp. 9630-9641
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 simple
st model of terminal hydroxyl groups at zeolite surfaces and defect si
tes. We also consider disiloxane, H3Si-O-SiH3, and a series of structu
ral 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 nu
merical basis set and quadrature grid. We find that the structures of
the clusters are insensitive to increases in quadrature grid size beyo
nd 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 a
lmost-equal-to 0.1-degrees-5.0-degrees for T-O(H)-T bond angles and be
tter than 0.01 angstrom for T-O bond lengths. We also gauge the accura
cy of the LDF results against extended basis set Hartree-Fock MP2 resu
lts (MP2/DZ+2d) and experimental data. Agreement between the LDF and M
P2/DZ+2d values is generally good, with some notable exceptions. For e
xample, 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 str
ength. Thus, very good agreement between the methods is observed for t
he 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 b
ond. 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 aci
dity of the hydroxyls, as determined by the proton affinity, agrees wi
th the experimental trend for isomorphously substituted ZSM-5 zeolites
and our MP2/DZ+2d results.