(360c) Combining Multilevel Methods with Modern Sampling Schemes

One of the main aims of catalysis is to develop detailed models of catalytic processes at the atomic level. Together with experimental scattering and spectroscopic techniques, computational methods have been used in the last decade to accurately model the structures of active sites, the diffusion processes to and from the active sites, and the mechanisms of the catalytic reactions. Despite the increasing computational resources and improved algorithms available, molecular modeling and simulation of large, complex systems at the atomic level remains a challenge. One solution is to use multilevel methods, such as QM/MM methods, that combine quantum mechanics (QM) and molecular mechanics (MM), since their efficiency potentially allows one to perform accurate calculations for large reactive systems over long time scales.

Most systems studied with the QM/MM approach consist of a small localized reactive region treated at a high level of theory (the QM region) submerged in an extended system treated at a low level of theory (the MM region). One goal of these studies is to calculate energy differences between the reactants, products, and transition states so that reaction rates and equilibrium constants can be determined, for example by using the harmonic approximation of transition state theory. However, for processes in solution, diffusion and adsorption in porous media, and reactions on nanoparticles, the active region is not necessarily localized, and it is necessary to average over the positions of the atoms or molecules to properly take environmental effects into account.

Monte Carlo (MC) and molecular dynamics (MD) methods are the state-of-the-art techniques to determine thermodynamic and kinetic properties of such extended systems. In MC or MD simulations of a system such as a hydrocarbon molecule diffusing to an active site within a zeolite, a given atom or molecule may move in or out of the active region and should, therefore, be treated at a high level of theory when it is in the reactive region (for accuracy) and at a lower level of theory otherwise (for efficiency). Thus, the level of theory used to describe such an atom or molecule in the system changes during the simulation. A change in the level of theory used to describe the interaction of an atom with the surrounding atoms usually results in a discontinuity in the potential energy and forces on each atom in the system.

To reduce these discontinuities, which can result in numerical instabilities and/or sampling from a wrong ensemble, Kerdcharoen and coworkers developed the ?hot spot?¹ method. The hot spot method was developed for QM/MM MD simulations. A buffer zone around the reactive high-level zone is defined, and forces on atoms in the buffer zone are smoothed. Since atoms that change subsystems also induce forces on all other atoms in the system, the hot spot method does not fully remove all discontinuities in the forces. In addition, smoothing of forces on atoms in the buffer zone removes the conservation of linear momentum and total energy in the MD simulation. Furthermore, since there is no energy definition corresponding to the smoothed forces, the hot spot method cannot be used for MC or free energy simulations. Nevertheless, the hot spot method has been applied successfully in a number of cases to determine the structure and dynamics of ions in solution.^2,3

To define a continuous potential energy corresponding to smoothed forces, Kerdcharoen et al.⁴ developed the ONIOM-XS method as an improved version of the hot spot method. While this technique removes all discontinuities in the energy and forces if one atom or molecule is in the buffer zone surrounding the reactive high level region, this method often increases the discontinuities in the potential energy and forces if two or more atoms or molecules are in the buffer zone. To overcome these problems, in the present work, two novel techniques were developed and will be presented. These methods are dynamically partitioned multilayer (DPML) algorithms, and they fully remove all discontinuities in the energy and forces. Applications of these methods for studying the adsorption properties of alkenes in acidic zeolites with different aluminum contents will also be discussed.

[1] T. Kerdcharoen, K. R. Liedl, B. M. Rode, Chem. Phys. 211, 313 (1996).

[2] B. M. Rode, T. S. Hofer, B. R. Randolf, C. F. Schwenk, D. Xenides, V. Vchirawongkwin, Theor. Chem. Acc. 115, 77 (2006).

[3] T. S. Hofer, A. B. Pribil, B. R. Randolf, B. M. Rode, J. Am. Chem. Soc. 127, 14231 (2005).

[4] T. Kerdcharoen, K. Morokuma, Chem. Phys. Lett. 355, 257 (2002).