EE-ONIOM-CT Method to Efficiently Account for the Missing Interactions in ONIOM: Energies and Analytic Gradients

Hybrid methods such as ONIOM (QM:QM) are widely used for the study of local processes in large systems. However, the intrinsic need for system partitioning often leads to a less-than-desirable performance for some important chemical processes. This is due to the missing interactions in the chemically important model region (i.e., active site) of the high-level theory. The missing interactions can be categorized into two classes, viz. charge transfer (i.e., charge redistribution) and long-range electrostatic interactions. Our group presented two entirely different methods to treat these deficiencies individually. ONIOM-CT and ONIOM-EE methods have been demonstrated to improve the performance of ONIOM by incorporating charge transfer and missing electrostatic interactions, respectively. In general, the inclusion of the missing interactions separately in two different calculations may not be sufficient to reach a high accuracy. Thus, it is highly desirable to develop a method to correct both deficiencies simultaneously. In this work, we aim to connect the methods ONIOM-CT and ONIOM-EE for a more comprehensive treatment. A "stepwise" model was found to be necessary for a robust performance. This model employs a stepwise procedure by first satisfying the ONIOM-CT condition for charge balance before accounting for the electrostatic interactions from the rest of the system perturbatively. This has the advantage of easy interpretation due to the clear separation of the two effects. We demonstrate the performance of our method using embedding charges determined from a Mulliken population analysis. An efficient analytic gradient expression for this method is derived and implemented by requiring three sets of z-vector self-consistent equations. The performance of our method is assessed against full system calculations in high-level theory for a set of three proton transfer reactions representing different degrees of electrostatic embedding.