Theoretical Study of the Isotope Effect in Optical Rotation

In this work, the isotope effect in optical rotation (OR) is examined by exploring structure-property relationships for H → D substitutions in chiral molecules. While electronic effects serve as the dominant source of optical activity, there is a non-negligible contribution from nuclear vibrations, which changes with isotopic substitution. We employ a test set of 50 small organic molecules: three-membered rings with varying heteroatoms (PCl, PH, S, NCl, NH, O, and NBr) and functional groups (Me, F), and simulations were run at the B3LYP/aug-cc-pVDZ level of theory. The objectives of this work are to determine locations of isotopic substitution that result in significant changes in the vibrational correction to the OR and to evaluate which vibrational modes and electronic response are the major contributors to the isotope effect. Molecules with more polarizable heteroatoms in the ring (e.g., S and P) have the largest change in the vibrational correction compared to the unsubstituted parent molecules. In many cases, isotopic substitution made to the hydrogens on the opposite side of the ring from the functional group provides the largest change in the OR. H/D wagging modes and C vibrations (for D-C centers) are the largest contributors to the isotope effect. This is explained with a molecular orbital decomposition analysis of the OR. The relevant vibrational modes affect the orbital transitions that are already significant at the equilibrium geometry. However, this effect is only large when polarizable heteroatoms are involved because the electron density surrounding them is diffuse enough to feel the subtle effect of change in mass due to isotopic substitution on the relevant vibrational modes.