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

Abstract

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 non-radiative 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 multi-reference, multi-state 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.

A three-state effective Hamiltonian for symmetric cationic diarylmethanes

“…The fact that SA3-CAS(4,3) solutions with the same structure can be found for these distinct molecules suggests that the solutions are stable, and that they are a general feature of dyes from this class. 45,47,48 Benchmark studies 49,50 have shown that the excitation energies of anionic GFP chromophore models calculated with multireference perturbation theory and SA-CASSCF models are not sensitive to basis set or active space size within a range of 0.2 eV, which is within quoted reliability limits 43,51,52 of such models. The systems studied here should be easier to deal with than this, because they are all cations.…”

“…This time scale separation is a natural consequence of the chemical structure of the dyes. The occurrence of similar self-consistent field solutions for these dyes 33 and others 45,48 is equally a consequence of the common chemical structure.…”

“…48,56,59 We are not aware of previous work where it has been used in conjunction with an isolobal analogy in a comparative survey of the electronic structure of families of similar molecules (although this does seem to us to be an obvious application).…”

“…The isoconfigurational analogy allows us to index the many-electron Hilbert spaces of all our dyes in a common, chemically meaningful, scheme. The isolobal and isoconfigurational analogies shown also map the structure of these dyes onto that of the GFP chromophore, 48 allyl anions, 61 and 1,3-dipoles. 62 The isolobal and isoconfigurational analogies are chemically meaningful only so far as the orbitals localize in a similar sense for each dye.…”

Analytical Derivative Coupling for Multistate CASPT2 Theory

“…The reference CASSCF wave functions were optimized using three-state averaging with the (4e,3o) active space, which provides a reliable description of twisting of the bridge bond. 69,79 The structures and the energy diagram for these geometries are shown in Figure 5. The twisted geometries optimized on the first excited state were found to be lower in energy than the Franck-Condon point by 0.38 and 0.14 eV for the I-and P-twisted minima, respectively.…”