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 ∼100 atoms can be embedded within a much larger MM environment of ∼5000 atoms. The resulting vibrational normal modes, their associated frequencies, and dipole derivative vectors have been used to interpret experimental difference spectra (GFPI2-GFPA), chromophore vibrational Stark shifts, and changes in the difference between electronic and vibrational transition dipoles (mode angles) in the protein environment.
Hyperfine coupling tensors of the water molecule coordinated to the Prohance contrast agent in liquid water were calculated within and beyond the point dipole approximation along an ab initio molecular dynamics trajectory. We observe the non-equivalence at short time scales on structural as well as magnetodynamical properties of inner sphere water protons due to hydrogen bonds formation with the solvent. In addition, the influence of ultrafast internal motions on the anisotropic, dipolar, contribution to hyperfine couplings was probed thanks to a decomposition of its fluctuations in terms of a small set of meaningful collective variables.
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