Finding transition structures in extended systems: A strategy based on a combined quantum mechanics–empirical valence bond approach

Abstract

A method for efficient localization and description of stationary points on the potential energy surface of extended systems is presented. It is based on Warshel's empirical valence bond approach, for which we propose a modification, and combines the potential function description of the total system with a quantum mechanical description of the reaction site ͑QM-Pot͒. We describe the implementation of the method in the QMPOT program, which is basically an optimizer for minima and saddle points and has interfaces to existing quantum mechanical ͑e.g., TURBOMOLE, GAUSSIAN94͒ and interatomic potential function codes ͑e.g., GULP, DISCOVER͒. The power of the method is demonstrated for proton transfer reactions in zeolite catalysts, which may have as many as 289 atoms in the unit cell. As a test case the zeolite chabazite is considered in this study. Its limited unit cell size ͑37 atoms͒ makes comparison with the full periodic ab initio limit possible. The inclusion of long-range effects due to the periodic crystal structure by the QM-Pot method proves crucial in obtaining reliable results. The combined quantum mechanics-interatomic potential function calculations yield reaction barriers within 6 kJ/mol and reaction energies within 3.5 kJ/mol of the periodic ab initio limit. The zero-point vibrational energy corrected reaction barriers are between 58 and 97 kJ/mol for the six different proton jump paths. These are density functional results employing the B3LYP functional.

QM/MM: what have we learned, where are we, and where do we go from here?

“…In this subsection, we more specifically address some question about how to treat periodic systems and other solid-state materials such as metals, metal oxides, and surface-adsorbate systems. Excellent discussions [47,56,74,85,96,97,[101][102][103]108,115,133,140,145] are available for many aspects, and we focus here especially on studies of zeolites.…”

Molecular Simulations of Zeolites: Adsorption, Diffusion, and Shape Selectivity

“…Chemical reactions in a zeolite often occur in a small part of the zeolite; it would therefore be much more attractive to use a quantum chemical description of that part of the zeolite that is participating in the chemical reaction, while the remainder of the zeolite is treated using the classical simulation techniques. 41,42 From a simulation point of view, an important question is how to make the transition from the quantum to the classical part. Clearly, the result should not depend on the arbitrary division of the system into a classical part and a quantum part.…”

On the nature of spin- and orbital-resolved Cu+–NO charge transfer in the gas phase and at Cu(I) sites in zeolites

“…In this scheme the selected part of the system, containing adsorbed molecule, cationic centre and its nearest neighborhood, is treated with quantum chemical accuracy (QM) while the rest of the framework is treated with less computationally demanding molecular mechanics (MM) with periodic boundary conditions. Turbomole package was applied at QM level and Gulp code [44] in MM part, both linked via QMPOT interface [45]. In classical part of calculations core-shell model potential [46] was used with the parameterization from papers by Sauer and Sierka [47] for Si, Al, O, and H atoms and Nachtigallová et al [48] for Cu(I) ion.…”