Vibronic Model for Intercommunication of Localized Spins via Itinerant Electron

In this article, we propose a vibronic pseudo Jahn-Teller model for partially delocalized mixed-valence molecules aimed to describe the magnetic coupling between the localized spins mediated by the delocalized electron. The simplest partially delocalized system that retains the main studied features is assumed to consist of a one-electron mixed-valence dimer, which is connected to the two terminal magnetic ions. The model involves the following key interactions: electron transfer in the spin-delocalized subsystem of a mixed-valence molecule, which is mimicked by a dimeric unit, coupling of the itinerant electrons with the molecular vibrations, and isotropic magnetic exchange between the localized spins and delocalized electron. The proposed model, which can be referred to as the vibronic "toy" model, is intentionally restricted to the named basic interactions and therefore it is aimed to describe only the key features of a wide class of mixed-valence clusters exhibiting partial electronic delocalization without entering the details of their electronic and vibrational structures. The pseudo Jahn-Teller vibronic coupling, which is considered in the framework of the Piepho, Krausz, and Schatz model adapted to the case of partially delocalized mixed-valence molecules, is shown to give rise to specific patterns of the adiabatic potentials and spin-vibronic levels. It is revealed (qualitatively and quantitively) how the vibronic coupling affects the connection of the localized spins via the itinerant electron. In particular, the vibronic coupling acts as a localization factor and significantly influences the conditions for realization of physically different limits of double exchange and indirect exchange. The vibronic coupling in partially delocalized mixed-valence systems is also shown to produce a strong impact on the selection rules for the optical transitions and gives rise to the specific shapes of the intervalence absorption profiles.