Geometry optimization with QM/MM, ONIOM, and other combined methods. I. Microiterations and constraints

TLDR

Hybrid QM/MM and ONIOM methods combine multiple theory levels and have proven effective for large systems, enabling geometry optimizations that exploit a QM region within a larger MM environment. The authors employ microiterations that fully optimize the MM region at each QM optimization step, using Cartesian coordinates that keep QM internal coordinates fixed while allowing rigid‑body translation and rotation of the QM region, and they adjust the QM step size to maintain the system within the same local energy valley. The microiteration approach is essential for constrained MM atoms and enhances unconstrained optimization efficiency, as demonstrated on bacteriorhodopsin and other systems.

Abstract

Hybrid energy methods such as QM/MM and ONIOM, that combine different levels of theory into one calculation, have been very successful in describing large systems. Geometry optimization methods can take advantage of the partitioning of these calculations into a region treated at a quantum mechanical (QM) level of theory and the larger, remaining region treated by an inexpensive method such as molecular mechanics (MM). A series of microiterations can be employed to fully optimize the MM region for each optimization step in the QM region. Cartesian coordinates are used for the MM region and are chosen so that the internal coordinates of the QM region remain constant during the microiterations. The coordinates of the MM region are augmented to permit rigid body translation and rotation of the QM region. This is essential if any atoms in the MM region are constrained, but it also improves the efficiency of unconstrained optimizations. Because of the microiterations, special care is needed for the optimization step in the QM region so that the system remains in the same local valley during the course of the optimization. The optimization methodology with microiterations, constraints, and step-size control are illustrated by calculations on bacteriorhodopsin and other systems.