Density functional crystal vs. cluster models as applied to zeolites

In order to compare solid and cluster models of zeolites, we have studied the substitution Si⁴⁺→Al³⁺+H⁺ on the T₁ site of mordenite in the dilute limit using a self-consistent, full potential, local density functional (LDF) approach. Clusters size ranged from 9 to 105 atoms. Two crystal models with different Al concentrations were used. The first contained one substitution site per primitive cell of 72 atoms, the other one per conventional cell, containing 144 atoms. The unrelaxed substitution energies as computed with cluster and crystal models correspond well if the cluster results are extrapolated to infinite radius. Size effects are much smaller in crystal models. In addition, a structure relaxation (with fixed unit cell) was carried out for pure-silica offretite, a zeolite with 54 atoms per unit cell, and pure-silica mordenite, with 144 atoms per unit cell, starting from the low aluminum content X-ray crystallographic structure. In the offretite and mordenite optimizations full use was made of the D3h¹–P6m2 and the nonsymmorphic D2h¹⁷–Cmcm space group symmetry, respectively.