Protein Field Effect on the Dark State of 11-<i>cis</i> Retinal in Rhodopsin by Quantum Monte Carlo/Molecular Mechanics

The accurate determination of the geometrical details of the dark state of 11-<i>cis</i> retinal in rhodopsin represents a fundamental step for the rationalization of the protein role in the optical spectral tuning in the vision mechanism. We have calculated geometries of the full retinal protonated Schiff base chromophore in the gas phase and in the protein environment using the correlated variational Monte Carlo method. The bond length alternation of the conjugated carbon chain of the chromophore in the gas phase shows a significant reduction when moving from the β-ionone ring to the nitrogen, whereas, as expected, the protein environment reduces the electronic conjugation. The proposed dark state structure is fully compatible with solid-state NMR data reported by Carravetta et al. [<i>J. Am. Chem. Soc</i>. <b>2004</b>, <i>126</i>, 3948–3953]. TDDFT/B3LYP calculations on such geometries show a blue opsin shift of 0.28 and 0.24 eV induced by the protein for S₁ and S₂ states, consistently with literature spectroscopic data. The effect of the geometrical distortion alone is a red shift of 0.21 and 0.16 eV with respect to the optimized gas phase chromophore. Our results open new perspectives for the study of the properties of chromophores in their biological environment using correlated methods