  Three-wave mixing spectroscopy of chiral molecules, which exist in
left-handed and right-handed conformations, allows for enantio-selective
population transfer despite random orientation of the molecules. This is based
on constructive interference of the three-photon pathways for one enantiomer
and destructive one for the other. We prove here that three mutually orthogonal
polarization directions are required to this end. Two different dynamical
regimes exist to realize enantio-selective population transfer, and we show
that they correspond to different phase conditions in the three-wave mixing. We
find the excitation scheme used in current rotational three-wave mixing
experiments of chiral molecules with $C_1$ symmetry to be close to optimal and
discuss prospects for ro-vibrational three-wave mixing experiments of axially
chiral molecules. Our comprehensive study allows us to clarify earlier
misconceptions in the literature.
