A Diabatic Three-State Representation of Photoisomerization in the Green Fluorescent Protein Chromophore

We give a quantum chemical description of bridge photoisomerization reaction of green fluorescent protein (GFP) chromophores using a representation over three diabatic states. Bridge photoisomerization leads to non-radiative decay, and competes with fluorescence in these systems. In the protein, this pathway is suppressed, leading to fluorescence. Understanding the electronic structure of the photoisomerization is a prerequisite to understanding how the protein suppresses this pathway and preserves the emitting state of the chromophore. We present a solution to the state-averaged complete active space problem, which is spanned at convergence by three fragment-localized orbitals. We generate the diabatic-state representation by applying a block diagonalization transformation to the Hamiltonian calculated for the anionic chromophore model HBDI with multi-reference, multi-state perturbation theory. The diabatic states that emerge are charge-localized structures with a natural valence-bond interpretation. At planar geometries, the diabatic picture recaptures the charge transfer resonance of the anion. The strong S0-S1 excitation at these geometries is reasonably described within a two-state model, but extension to a three-state model is necessary to describe decay via two possible pathways associated with photoisomerization of the (methine) bridge. Parametric Hamiltonians based on the three-state ansatz can be fit directly to data generated using the underlying active space. We provide an illustrative example of such a parametric Hamiltonian.