Multilink F∗ Method for Combined Quantum Mechanical and Molecular Mechanical Calculations of Complex Systems

Combined quantum mechanical and molecular mechanical (QM/MM) studies on catalysis in metal-organic frameworks (MOFs) are relatively undeveloped in contrast to the wide use of QM/MM for enzyme catalysis. One reason is that the currently available methods for treating QM-MM boundaries are not fully compatible with the combination of features in MOFs, namely, their high connectivity, their polar bonds (e.g., metal-oxygen bonds), and their potential boundary atoms with high partial atomic charges. The treatment of polar bonds can be improved by using tuned link atoms, but both the widely used H link atom method and the F∗ link atom method provide limited options in placing the QM-MM boundary in MOFs and other covalently bonded solids, which seriously reduces the efficiency of QM/MM calculations. Here, we propose a generalized version of the F∗ link atom method with greater flexibility for the placement of the QM-MM boundary in MOFs and with a practical scheme for tuning. The new method, called the multilink F∗ method, allows a large part of an inorganic node of a MOF to be partitioned into the MM subsystem to increase the efficiency. Our validation calculations on dimerization of ethylene to 1-butene by a nickel catalyst supported on a MOF show that the overall performance of QM/MM calculations with the multilink F∗ method is excellent for energies, geometries, and partial atomic charges.