Field-Induced Diastereomers for Chiral Separation

A novel approach for the state-specific enantiomeric enrichment and the spatial separation of enantiomers is presented. Our scheme utilizes techniques from strong-field laser physics—specifically an optical centrifuge in conjunction with a static electric field—to create a chiral field with defined handedness. Molecular enantiomers experience unique rotational excitation dynamics, and this can be exploited to spatially separate the enantiomers using electrostatic deflection. Notably, the rotational-state-specific enantiomeric enhancement and its handedness are fully controllable. To explain these effects, the conceptual framework of field-induced diastereomers of a chiral molecule is introduced and computationally demonstrated through robust quantum-mechanical simulations on the prototypical chiral molecule propylene oxide (${\mathrm{C}}_3{\mathrm{H}}_6\mathrm{O}$), for which ensembles with an enantiomeric excess of up to 30% were obtained.

Figure 1

Field-induced diastereomers of a chiral molecule interacting with a chiral electric field, i.e., a rotating optical field in conjunction with a static electric field along the rotation axis of the optical field.

Figure 2

Minimal model of the enantiomer-differentiating transitions in a chiral molecule. A system of three-rotational states originating from the ground state is coupled to the static electric field and optical centrifuge, for instance, by the molecular electric dipole moment ${\mu }_y$ and the polarizability parameters $\mathrm{\Delta }\alpha$ and ${\alpha }_{xz}$ or, alternatively, by ${\mu }_x$, $\mathrm{\Delta }\alpha$, and ${\alpha }_{yz}$; see Eqs. (1)–(3). Here, $\mathrm{\Delta }\alpha (t)=\mathrm{\Delta }\alpha e^{2i\beta t^2}$ and ${\alpha }_{ab}(t)={\alpha }_{ab}{e}^{2i\beta t^2}$, $a,b=x$, $y$, $z$.

Figure 3

Temporal evolution of the rotational-state populations for the lowest-energy excited state pair for $J=2$ and $J=8$ for the $R$ (blue) and $S$ (red) enantiomers of propylene oxide, for a dc field of $10\mathrm{kV}/\mathrm{cm}$. The enantiomeric excess $ee$ of the rotational-state populations is shown beneath each population plot. $ee$ is plotted only for times when the population of either of the enantiomers in the final state is greater than 1% of the initial population in $|0_{00},0⟩$ at $t=0$. The gray shaded regions indicate corresponding populations greater than 10%.

Figure 4

(a) Deflection profiles and enantiomeric excess $ee$ as a function of the vertical transverse beam position $y$, calculated for two release times from the optical centrifuge $t_f=20$ and 100 ps, for the $R$ (blue) and $S$ (red) enantiomer of propylene oxide, for an initial rotational temperature of $T_i=0\mathrm{K}$. $y=0$ corresponds to the center of the undeflected molecular beam, and the deflector’s field strength increases in the negative $y$ direction, down to $y\approx -3\mathrm{mm}$ [36]. (b) Enantiomeric excess $ee$ as a function of the deflection coordinate $y$, computed at release times $t_f=20$ and 44 ps for finite initial rotational temperatures of $T_i=0.2$ and 1 K, respectively. $ee$ is plotted only for deflection positions $y$ at which the ratio between the column density for either of the enantiomers, and the total column density at $y=0\mathrm{mm}$ is greater than 1%. Shaded areas show ratios greater than 10%.