A diabatic three-state representation of photoisomerization in the green fluorescent protein chromophore

We give a quantum chemical description of the photoisomerization reaction of green fluorescent protein (GFP) chromophores using a representation over three diabatic states. Photoisomerization leads to nonradiative decay, and competes with fluorescence in these systems. In the protein, this pathway is suppressed, leading to fluorescence. Understanding the electronic states relevant to photoisomerization is a prerequisite to understanding how the protein suppresses it, 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 block diagonalization transformation of the Hamiltonian calculated for the anionic chromophore model HBDI with multireference, multistate perturbation theory. The diabatic states are charge localized and admit a natural valence-bond interpretation. At planar geometries, the diabatic picture of the optical excitation reduces to the canonical two-state charge-transfer resonance of the anion. 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.