How chiral vibrations drive molecular rotation

TL;DR

The paper addresses how chiral vibrational modes coupled to degenerate electronic orbitals can mediate angular-momentum transfer from circularly polarized light to a rotating molecule. It develops two planar toy models, a $D_3$ ionic molecule and a $D_6$ covalent molecule, each hosting degenerate chiral modes and Jahn–Teller couplings that preserve a pseudo angular momentum $J$, while analyzing the light–matter interactions within a $U(1)$-invariant framework. The authors show that circular polarization can selectively excite these chiral modes and transfer angular momentum to the whole molecule, either directly through a dipole-carrying mode in the ionic case or via virtual particle–hole processes in the covalent case, with rotation persisting after the light pulse. This work clarifies the role of pseudo angular momentum in Jahn–Teller systems and proposes experimental schemes for light-driven molecular rotation that could shed light on chiral phonon dynamics in bulk materials. The findings suggest broad implications for angular-momentum transfer mechanisms in both molecular and extended systems.

Abstract

We analyze two simple model planar molecules: an ionic molecule with D3 symmetry and a covalent molecule with D6 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 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.

Figures (6)

• Figure 1: Toy planar molecule with $D_3$ symmetry. The bonds represent springs with spring constants $K$, the blue bonds, and $\gamma K$, the red ones.
• Figure 2: Sketch of the normal modes of the molecule in Fig. \ref{['NF3']} in the limit $\gamma\gg 1$.
• Figure 3: Time evolution of the angular velocity $\dot{\phi}(t) = p_\phi(t) / I$, and its time-average $\langle \dot{\phi}(t)\rangle$, obtained by integrating the Lanczos chain defined in (\ref{['Lanczos chain']}). The undamped oscillations over time result from the exchange of angular momentum between the molecule and the electron in the singly occupied $E$-type molecular orbital during the unitary evolution. The chosen parameters correspond to those of AlF$_{3}$, with $\omega_0 = \nu_4 \simeq 240~\text{cm}^{-1}$Pak-JCP1997, a moment of inertia $I \simeq 36$ in units of $\hbar ^{2} / \omega_{0}$. The Jahn-Teller coupling $g$ obtained through (\ref{['HJT triangle']}) is $1.8\,\omega_0$.
• Figure 4: Time evolution of $\dot{\phi}(t)$ induced by a circularly polarized electric field pulse in resonance with the chiral mode 1 of Fig. \ref{['FigureToy1']}. For times longer than the pulse duration, i.e., $t \gtrsim 100\,\text{ps}$, $\dot{\phi}(t)$ becomes constant. The frequency and moment of inertia are the same as in Fig. \ref{['FigureToy1']}. We take $\tau=33~\text{ps}$, the electric field maximum amplitude $E_0=800~\text{kV}/\text{cm}$, and estimate $d_*=0.1~e\text{\AA}$.
• Figure 5: Toy planar molecule with $D_6$ symmetry.