I demonstrate that a modification of the resonance color theory (in its form advocated by Brooker (Rev. Mod. Phys. 1942, 14, 275) and by Platt (J. Chem. Phys. 1956, 25, 80)) provides an accurate framework for rationalizing the ab initio excitation energies of the protonation states of the green fluorescent protein (GFP) chromophore (an asymmetric oxonol dye). I suggest that the original model space used in the resonance theory (specifically, a pair of Lewis structures) is formally inconsistent with a core aspect of the theory (specifically, a relationship between excitation energies and group-specific basicities (Brooker basicities) of the terminal rings). I argue that a more appropriate model space would consist of a complete active space ansatz based on group-localized orbitals. I then show that there is a solution to the state-averaged complete active space self consistent field (SA-CASSCF) problem with exactly this form. This family of SA-CASSCF solutions provides an objectively rigorous foundation for the resonance color theory. The solutions can be expressed in a localized set of active space orbitals, which display the same transferability pattern implied by the Brooker basicity scale. Using Platt’s model Hamiltonian formulation of the resonance theory, I show that the accuracy of the set of excitation energies calculated with these solutions can be accurately reproduced using only two parameters per dye in the set. One of these parameters is the isoenergetic energy of the dye—the harmonic mean of the excitation energies of its symmetric parent dyes. The other parameter is a local basicity index (Brooker basicity), which is specific to each terminal ring and independent of the ring to which it is conjugated in a given dye. I proceed to show that the Brooker basicities, defined by differences between many-electron states, are also basicities in the usual (one-electron) sense and, finally, that Platt’s construction of the color theory is an approximation to a ab initio effective Hamiltonian obtained by a minimum-norm block diagonalization procedure. What emerges is a powerful, simple, and accurate conceptual framework for thinking generally about color in monomethine dyes, and specifically about color tuning in the chromophore of green fluorescent proteins.
© 2010 American Chemical Society.