Bathochromic Shift in Green Fluorescent Protein: A Puzzle for QM/MM Approaches

We present an extensive investigation of the vertical excitations of the anionic and neutral forms of wild-type green fluorescent protein using time-dependent density functional theory (TDDFT), multiconfigurational perturbation theory (CASPT2), and quantum Monte Carlo (QMC) methods within a quantum mechanics/molecular mechanics (QM/MM) scheme. The protein models are constructed via room-temperature QM/MM molecular dynamics simulations based on DFT and are representative of an average configuration of the chromophore-protein complex. We thoroughly verify the reliability of our structures through simulations with an extended QM region, different nonpolarizable force fields, as well as partial reoptimization with the CASPT2 approach. When computing the excitations, we find that wave function as well as density functional theory methods with long-range corrected functionals agree in the gas phase with the extrapolation of solution experiments but fail in reproducing the bathochromic shift in the protein, which should be particularly significant in the neutral case. In particular, while all methods correctly predict a shift in the absorption between the anionic and neutral forms of the protein, the location of the theoretical absorption maxima is significantly blue-shifted and too close to the gas-phase values. These results point to either an intrinsic limitation of nonpolarizable force-field embedding in the computation of the excitations or to the need to explore alternative protonation states of amino acids in the close vicinity of the chomophore.