QM:QM electronic embedding using Mulliken atomic charges: energies and analytic gradients in an ONIOM framework

An accurate first-principles treatment of chemical reactions for large systems remains a significant challenge facing electronic structure theory. Hybrid models, such as quantum mechanics:molecular mechanics (QM:MM) and quantum mechanics:quantum mechanics (QM:QM) schemes, provide a promising avenue for such studies. For many chemistries, including important reactions in materials science, molecular mechanics or semiempirical methods may not be appropriate, or parameters may not be available (e.g., surface chemistry of compound semiconductors such as indium phosphide or catalytic chemistry of transition metal oxides). In such cases, QM:QM schemes are of particular interest. In this work, a QM:QM electronic embedding model within the ONIOM (our own N-layer integrated molecular orbital molecular mechanics) extrapolation framework is presented. To define the embedding potential, we choose the real-system low-level Mulliken atomic charges. This results in a set of well-defined and unique embedding charges. However, the parametric dependence of the charges on molecular geometry complicates the energy gradient that is necessary for the efficient exploration of potential energy surfaces. We derive an efficient form for the forces where a single set of self-consistent field response equations is solved. Initial tests of the method and key algorithmic issues are discussed.