Huzinaga projection embedding for efficient and accurate energies of systems with localized spin-densities

We demonstrate the accuracy and efficiency of the restricted open-shell and unrestricted formulation of the absolutely localized Huzinaga projection operator embedding method. Restricted open-shell and unrestricted Huzinaga projection embedding in the full system basis is formally exact to restricted open-shell and unrestricted Kohn-Sham density functional theory, respectively. By utilizing the absolutely localized basis, we significantly improve the efficiency of the method while maintaining high accuracy. Furthermore, the absolutely localized basis allows for high accuracy open-shell wave function methods to be embedded into a closed-shell density functional theory environment. The open-shell embedding method is shown to calculate electronic energies of a variety of systems to within 1 kcal/mol accuracy of the full system wave function result. For certain highly localized reactions, such as spin transition energies on transition metals, we find that very few atoms are necessary to include in the wave function region in order to achieve the desired accuracy. This extension further broadens the applicability of our absolutely localized Huzinaga level-shift projection operator method to include open-shell species. Here, we apply our method to several representative examples, such as spin splitting energies, catalysis on transition metals, and radical reactions.