Correlation of vibrational frequencies with absorption maxima in polyenes, rhodopsin, bacteriorhodopsin, and retinal analogues

The factors that influence the C=C and C=N stretching frequencies in protonated Schiff bases, visual pigments, and bacteriorhodopsin (bR) are considered. For the C=C frequency (ν_C=C) we show that its well-known correlation with absorption maxima (λ_max) cannot be accounted for in terms of π-electron bond orders. Rather, polarizability contributions to diagonal force constants must be taken into account. The lack of any correlation of the C=N frequency (ν_C=N) with absorption maxima is shown to arise from complications due to mixing with the C=N-H bending vibration. Variations in this mode due to different hydrogen-bonding patterns mask any correlation between λ_max and ν_C=N that might otherwise be expected. Independent evidence supporting this conclusion may be derived from the relative magnitude of the deuterium isotope effects in different proteins. Comparing rhodopsin and bacteriorhodopsin, we argue that protein-chromophore interactions in the respective binding sites lead to enhanced π-electron delocalization in different parts of the chromophore. The consequences of this difference for the interpretation of Raman intensities and frequencies are discussed. Finally, we point out that, for highly delocalized π systems such as the primary photoproducts of rhodopsin and bacteriorhodopsin, additional factors may come into play as determinants of ν_C=N. In particular, enhanced coupling with the adjacent single bond may completely reverse the effects expected on the basis of π-electron considerations.