We prove complete controllability for rotational states
of an asymmetric top molecule belonging to degenerate
values of the orientational quantum number M. Based on this
insight, we construct a pulse sequence that energetically
separates population initially distributed over degenerate
M-states, as a precursor for orientational purification.
Introducing the concept of enantio-selective controllability,
we determine the conditions for complete enantiomer-specific
population transfer in chiral molecules and construct pulse
sequences realizing this transfer for population initially
distributed over degenerate M-states. This degeneracy
presently limits enantiomer-selectivity for any initial
state except the rotational ground state. Our work thus
shows how to overcome an important obstacle towards separating,
with electric fields only, left-handed from right-handed
molecules in a racemic mixture.