Search and Characterization of Transition State Structures in Crystalline Systems Using Valence Coordinates

Several tools that allow molecules, polymers, slabs, and crystals to be optimized in valence coordinates as well as a suitable saddle point optimization technique to search for transition state structures for this kind of system have been implemented in the ab initio periodic CRYSTAL code. The adoption of these localized coordinate systems largely facilitates the study of chemical processes in periodic systems with atomic connectivity, as occurs in catalytic reactions on zeolites, clathrates, or oxidic surfaces. As a paradigmatic case, the new features have been illustrated to study the proton jump between oxygen atoms of the Brønsted site in the H-chabazite zeolite. The electronic and Gibbs free energy profiles of the most representative proton jump channels have been computed at the B3LYP level, both for a dry H-chabazite as well as in the presence of one H2O molecule acting as a proton transfer helper. Because of the accuracy allowed by the optimization technique, all stationary points located have been characterized as minima or saddle points by computing the harmonic frequencies and checking, for the latter, that the corresponding transition eigenvectors were in agreement with the selected reaction path. The remarkable agreement between the results with both theoretical and experimental literature data gives credit to the accuracy and robustness of the present implementations in the CRYSTAL code.