Four-electron, three-orbital model for the low-energy electronic structure of cationic diarylmethanes: notes on a...

We examine a four-electron, three-orbital complete active space self-consistent field (SA-CASSCF) and multistate multireference perturbation theory (MS-MRPT2) model of the electronic structure associated with the two lowest-lying electronic excitations of a series of cationic diarylmethanes related to Michler's Hydrol Blue. These dyes are of interest because of the sensitivity of their excited-state dynamics to environmental influence in biological and other condensed phases. We show that the model corresponds to an easily understandable physical approximation where the dye electronic structure is mapped onto the π-electron system of an allyl anion. We show that reported trends in solution-state absorbance bands and transition dipole moments associated with the first two electronic excitations can be described within reasonable accuracy by the model. We also show, for Michler's Hydrol Blue, that the four-electron, three-orbital model provides a more balanced description of the electronic difference densities associated with electronic excitation calculated with the full π-electron space than can be achieved with active space models intermediate between these limits. The valence excitation energies predicted by the model are not sensitive to the underlying basis set, so that considerable computational savings may be possible by using split-valence basis sets with a limited number of polarization functions. We conclude that the model meets the criteria for a "Pauling Point": a point where the cancellation of large errors leads to physically balanced model, and where further elaboration degrades, rather than improves, the quality of description. We advocate that this Pauling Point be exploited in condensed-phase dynamical models where the computational overhead associated with the electronic structure must kept to a minimum (for example, nonadiabatic dynamics simulations coupled to QM/MM environmental models).