Hidden asymmetry in one-dimensional alignment of chiral molecules

We studied the inversion symmetry of an ensemble of chiral molecules. We clarified that for rigid molecules aligned by dipole transitions, the positions of any two atoms depend on the molecular chirality, owing to the parity-odd second-rank tensors. This type of asymmetry, hidden in the so-called one-dimensional alignment, such as cos2θ, can be understood on the basis of the equivalence of inversion and rotation for any two points in space. Perfect chiral sensitivity is achieved when the transition dipole moment is 45° to an axis perpendicular to both position vectors of the two atoms. The positions of two specific atoms are calculated for a chiral isotopomer and methyloxirane using the spherical harmonic addition theorem. We discuss the absolute configuration and the orientation of chiral molecules.