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 tw o-center molecules with one and two electrons in the limit of a space of la rge dimensions. For one electron, the phase diagram in the internuclear dis tance-nuclear charge (R-Z) plane has two different stable phases. One corre sponds 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 elec trons 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 unequa l, the phase diagram shows only two stable phases, covalent and ionic. This phase diagram is characterized by a tricritical point, where the first-ord er transition line meets with the second-order transition line. The role of the inter-electron Coulombic repulsion in giving rise to different electro nic structures and the distinction between a continuous deformation of one structure into another versus a discontinuous, so-called first-order, trans ition, where two isomers can coexist, are emphasized. The connection to the spectroscopic notion of intersecting potential energy curves is discussed.