We analyze two simple model planar molecules: an ionic molecule with $D_3$ symmetry and a covalent molecule with $D_6$ symmetry. Both symmetries allow the existence of chiral molecular orbitals and normal modes that are coupled to each other in a Jahn-Teller manner, invariant under U(1) symmetry with the generator a pseudo-angular momentum. In the ionic molecule, the chiral mode possesses an electric dipole but lacks physical angular momentum, whereas in the covalent molecule, the situation is reversed. In spite of that, we show that in both cases, the chiral modes can be excited by a circularly polarized light and are subsequently able to induce rotational motion of the entire molecule.

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• Phonons
• Molecules
• Second quantization
• Tight-binding model