  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.
