The effects of couplings to symmetric and antisymmetric modes and minor asymmetry on the spectral properties of mixed-valence and related charge-transfer systems

The most common methods used to describe the energy levels of charge-transfer systems (including mixed-valence systems) are the linear response approach of Rice and co-workers and the essentially equivalent PKS model described initially by Piepho, Krausz, and Schatz, While these methods were quite successful, in their original form they omitted the effects of overall symmetric vibrations. As a consequence. in particular they were not capable of adequately describing the electronic band width in the strong-coupling limit: Hush and later Ondrechen et al. demonstrated that symmetric modes are essential in this case, and modern versions of these models now include them. Here, we explore the relationship between symmetric and antisymmetric modes, concentrating on how this is modified by the presence of weak (e,g., environmentally or substitutionally induced) asymmetry, For the symmetric case, we show that when the electronic Hamiltonian operators are transformed from their usual localized diabatic representation into a delocalized diabatic representation, the effects of the symmetric and antisymmetric modes are interchanged. The primary effect of weak asymmetry is to mix the properties of the various modes, and possible consequences of this for the spectroscopy of bacterial photosynthetic reaction centre and substituted Creutz-Taube cations are discussed. We also consider the problem from an adiabatic Born-Oppenheimer perspective and examine the regions in which this approach is appropriate.