Electronic isomerism: Symmetry breaking and electronic phase diagrams for diatomic molecules at the large-dimension limit

We present symmetry-breaking and electronic-structure phase diagrams for two-center molecules with one and two electrons in the limit of a space of large dimensions. For one electron, the phase diagram in the internuclear distance - nuclear charge (R-Z) plane has two different stable phases. One corresponds to the electron equidistant from the two nuclei; the other where the electron is localized on one of the nuclei. The phase diagram for two electrons with two equally charged centers shows three different stable phases corresponding to different electronic-structure configurations. This phase diagram is characterized by a bicritical point. When the charges are unequal, the phase diagram shows only two stable phases, covalent and ionic. This phase diagram is characterized by a tricritical point, where the first-order transition line meets with the second-order transition line. The role of the interelectron Coulombic repulsion in giving rise to different electronic structures and the distinction between a continuous deformation of one structure into another versus a discontinuous, so-called first-order, transition, where two isomers can coexist, are emphasized. The connection to the spectroscopic notion of intersecting potential energy curves is discussed.