Corresponding orbitals in periodic frozen-density embedding: The case of alkaline-earth subnitrides, Ae 2N, by the example of Ba2N

The metallic metal-rich phase Ba2N, a representative example for the Ae2N alkaline-earth subnitrides, is examined using theoretical methods to investigate its electronic structure and chemical bonding, with a special focus on the "excess" electron found within these structures, alluding to an electride character. To quantify the latter phenomenon, the "corresponding orbital" formalism, introduced by Neese to the molecular quantum chemists about two decades ago [F. Neese, J. Phys. Chem. Solids 65, 781 (2004)], is adapted to the recently developed periodic frozen-density approach [M. Pauls et al., J. Phys. Chem. A 127, 6541 (2023)]. While the existence of Ba2N goes back to both constructive Ba-6s-N-2sp orbital interference (covalency) and significant ionic bonding, we identify that the "excess" electron engaged in a singlet ground state of the presumably non-paramagnetic phase contributes to intra-layer Ba-Ba bonding while destabilizing the inter-layer Ba-Ba bonding by occupying antibonding σ-type orbitals.