Analytical Harmonic Vibrational Frequencies for the Green Fluorescent Protein Computed with ONIOM: Chromophore Mode Character and Its Response to Environment

A systematic comparison of different environmental effects on the vibrational modes of the 4-hydroxybenzylidene-2,3-dimethylimidazolinone (HBDI) chromophore using the ONIOM method allows us to model how the molecule's spectroscopic transitions are modified in the Green Fluorescent Protein (GFP). ONIOM(QM:MM) reduces the expense of normal mode calculations when computing the majority of second derivatives only at the MM level. New developments described here for the efficient solution of the CPHF equations, including contributions from electrostatic interactions with environment charges, mean that QM model systems of similar to 100 atoms can be embedded within a much larger MM environment of similar to 5000 atoms. The resulting Vibrational normal modes, their associated frequencies, and dipole derivative vectors have been used to interpret experimental difference spectra (GFP(12)-GFP(A)), chromophore vibrational Stark shifts, and changes in the difference between electronic and vibrational transition dipoles (mode angles) in the protein environment.