A three-state effective Hamiltonian for symmetric cationic diarylmethanes.

We analyze the low-energy electronic structure of a series of symmetric cationic diarylmethanes, which are bridge-substituted derivatives of Michler's Hydrol Blue. We use a four-electron, three-orbital complete active space self-consistent field and multi-state multi-reference perturbation theory model to calculate a three-state diabatic effective Hamiltonian for each dye in the series. We exploit an isolobal analogy between the active spaces of the self-consistent field solutions for each dye to represent the electronic structure in a set of analogous diabatic states. The diabatic states can be identified with the bonding structures in classical resonance-theoretic models of cyanine dyes. We identify diabatic states with opposing charge and bond-order localization, analogous to the classical resonance structures, and a third state with charge on the bridge. While the left- and right-charged structures are similar for all dyes, the structure of the bridge-charged diabatic state, and the Hamiltonian matrix elements connected to it, change significantly across the series. The change is correlated with an inversion of the sign of the charge carrier on the bridge, which changes from an electron pair to a hole as the series is traversed.