ONIOM-based QM:QM electronic embedding method using Löwdin atomic charges: Energies and analytic gradients

In this work, we report a new quantum mechanical:quantum mechanical (QM:QM) method which provides explicit electronic polarization of the high-level region by using the Löwdin atomic charges from the low-level region. This provides an embedding potential which naturally evolves with changes in nuclear geometry. However, this coupling of the high-level and low-level regions introduces complications in the energy gradient evaluation. Following previous work, we derive and implement efficient gradients where a single set of self-consistent field response equations is solved. We provide results for the calculation of deprotonation energies of a hydroxylated spherosiloxane cluster ( Si 8 O 12 H 7 OH ) and the dissociation energy of a water molecule from a [ ZnIm 3 ( H 2 O ) ] 2 + complex. We find that the Löwdin charge embedding model provides results which are not only an improvement over mechanical embedding (no electronic embedding) but which are also resistant to large overpolarization effects which occur more often with Mulliken charge embedding. Finally, a scaled-Löwdin charge embedding method is also presented which provides a method for fine tuning the extent of electronic polarization.