  The enantiopurification of racemic mixtures of chiral molecules is important
for a range of applications. Recent work has shown that chiral group-directed
photoisomerization is a promising approach to enantioenrich racemic mixtures of
BINOL, but increased control of the diasteriomeric excess (de) is necessary for
its broad utility. Here we develop a cavity quantum electrodynamics (QED)
generalization of time-dependent density functional theory and demonstrate
computationally that strong light-matter coupling can alter the de of chiral
group-directed photoisomerization of BINOL. The relative orientation of the
cavity mode polarization and the molecules in the cavity dictates the nature of
the cavity interactions, which either enhance the de of the (R)-BINOL
diasteriomer (from 17% to $\approx$ 40%) or invert the favorability to the
(S)-BINOL derivative (to $\approx$ 34% de). The latter outcome is particularly
remarkable because it indicates that the preference in diasteriomer can be
influenced via orientational control, without changing the chirality of the
directing group. We demonstrate that the observed effect stems from
cavity-induced changes to the Kohn-Sham orbitals of the ground state.
