Floating Orbitals Reconsidered: The Difference an Imaginary Part Can Make

Floating orbitals for valence electrons have made cameo appearances at several stages in the history of quantum chemistry. Most often, they were considered as potentially useful basis functions and, more recently, also as muses for the development of subatomistic force fields. To facilitate computation, these orbitals are generally taken to be real spherical Gaussians. However, the computational advantages carry over to complex Gaussians. Here, we explore the potential utility of an imaginary part. Analytical equations for two mobile electrons show that an imaginary part shifts the balance between contributions to the exchange energy that favor parallel versus antiparallel electron spins. However, an imaginary part also carries a large kinetic energy penalty. The imaginary part is therefore negligible for two valence electrons, except in the case of strong core-valence exchange interactions. This consideration allows a self-consistent model for the nd² triplet ground states of transition metal ions versus the ns² singlet ground states of main group ions.