Modeling proton transfer in zeolites: Convergence behavior of embedded and constrained cluster calculations

We have studied the convergence properties of embedded and constrained cluster models of proton transfer in zeolites. We applied density functional theory to describe clusters and ONIOM to perform the embedding. We focused on converging the reaction energy and barrier of the O(1) to 0(4) jump in H-Y zeolite as well as vibrational and structural aspects of this jump. We found that using successively larger clusters in vacuo gives convergence of this reaction energy to 14 +/- 2 W mol(-1) and the barrier to 135 +/- 5 kJ mol(-1) at a cluster size of 5 angstrom, which contains 11 tetrahedral (Si or Al) atoms. We embedded quantum clusters of various sizes in larger clusters with total radii in the range 7-20 angstrom, using the universal force field as the lower level of theory in ONIOM. We found convergence to the same values as the constrained clusters, without the use of reactive force fields or periodic boundary conditions in the embedding procedure. For the reaction energy, embedded cluster calculations required smaller clusters than in vacuo calculations, reaching converged reaction energies for quantum systems containing at least 8 tetrahedral atoms. In addition, optimizations on embedded clusters required many fewer cycles, and hence much less CPU time, than did optimizations on comparable constrained clusters.