Non-orthogonal configuration interaction for molecular excited states: Valence and core excitations and strong correlations

Most electronic structure methods are designed using a single set of orthogonal orbitals. Using multiple sets of orbitals, that are orthogonal within a given configuration, but non-orthogonal from one configuration to another, is an interesting alternative that is the basis of the non-orthogonal configuration interaction (NOCI) approach to electronic structure. NOCI provides great flexibility to compactly incorporate the different physics of different configurations. A very simple example is a molecule in which an ionic configuration (e.g. Li⁺F^-) competes with a covalent configuration (e.g. LiF). Orbital relaxation is very different in the two configurations, and accounts for a large part of what would conventionally be termed dynamic correlation. Far more complicated examples natural arise in mixed valent systems, and systems with low-lying charge-transfer excited states. Core excitations are another natural class of examples. I shall discuss the NOCI method, ways in which it can be made nearly black-box for interesting classes of valence and core excitations, and how to describe remaining dynamic correlation effects using a generalized second order perturbation theory. A variety of molecular examples will be shown for each of these types of NOCI. I hope to convey the message that the NOCI framework can be very useful for both computing and interpreting electronic structure, with bright prospects for further developments in the future.