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.