Hybrid methods such as ONIOM are widely used for the study of local processes in large systems. However, the intrinsic need for system partition leads to less-than-desirable performance for some chemical processes. This is due to the missing interactions in the chemically important model region (i.e., active site) at the high-level theory. The missing interactions can be categorized into two classes, viz. charge transfer (i.e., charge reorganization between regions) and long-range electrostatic interactions. Our group has 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.<br/>In general, the separation of missing interactions into two individual categories may not be sufficient to reach high accuracy. Thus, it is highly desirable to develop a method to correct both deficiencies simultaneously. We have developed new methods aimed at connecting the methods ONIOM-CT and ONIOM-EE for a more comprehensive treatment. We will demonstrate our method using embedding charges determined from a Mulliken population analysis. The analytic gradient expressions for this method have been derived and implemented. They require solving three sets of z-vector self-consistent equations, one for the full system at the low-level, and one each for the model system at low-level and high-level. Nevertheless, our implementation is efficient, and is assessed against full system calculations at high-level theory for sample problems involving proton transfer and other reactive processes.<br/>Finally, an active site model such as ONIOM may have limitations for more challenging problems involving larger molecules. We present extensions of the method for multiple active sites as well as a generalization of our treatment to fragmentation-based models such as MIM (Molecules-in-Molecules).

New models incorporating electrostatic embedding and charge redistribution in ONIOM and MIM: Energies and analytic gradients

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