Symmetric Electron Transfer Coordinates are Intrinsic to Bridged Systems: An ab Initio Treatment of the Creutz-Taube Ion.

A long-standing question in electron transfer research concerns the number and identity of collective nuclear motions that drive electron transfer or localisation. It is well established that these nuclear motions are commonly gathered into a so-called electron transfer coordinate. In this theoretical study, we demonstrate that both anti-symmetric and symmetric vibrational motions are intrinsic to bridged systems, and that both are required to explain the characteristic shape of their intervalence charge transfer bands. Using the properties of a two-state Marcus-Hush model, we identify and quantify these two coordinates as linear combinations of normal modes from ab initio calculations. This quantification gives access to the potential coupling, reorganization energy and curvature of the potential energy surfaces involved in electron transfer, independent of any prior assumptions about the system of interest. We showcase these claims with the Creutz-Taube ion, a prototypical Class III mixed valence complex. We find that the symmetric dimension is responsible for the asymmetric band shape, and trace this back to the offset of the ground and excited state potentials in this dimension. The significance of the symmetric dimension originates from geometry dependent coupling, which in turn is a natural consequence of the well-established superexchange mechanism. The conceptual connection between the symmetric and anti-symmetric motions and the superexchange mechanism appears as a general result for bridged systems.