X-ray diffraction from chiral molecules with twisted beams

Abstract

Structured x-rays carrying an orbital angular momentum break spatial inversion symmetry and have been proposed as a means to probe chirality. We theoretically investigate twisted non-resonant x-ray diffraction from chiral molecules and demonstrate that no dichroic signal can arise from randomly oriented molecules, irrespective of the beam spatial profile. However, a dichroic response is found to emerge if the molecule is oriented. Our results establish the beam and sample conditions for which a measurable dichroic scattering signal survives axial and focal averaging.

Figures (4)

• Figure 1: a) Scattering geometry for twisted x-ray diffraction from an axially oriented molecular ensemble. Inset: CHBrClF molecule (C–F along $+z$). b) Intensity (top) and phase profiles (bottom) in the $z=0$ plane for OAM beams with $\omega_\text{in}=9.25$ keV, $m = +4$, $\Lambda=+1$ and cone angles $\theta_k = 0.1\degree$ (left) and $\theta_k = 30 \degree$(right). Atomic positions shown (C: black; H: white; Br: maroon; Cl: green; F: blue) for a single oriented molecule with carbon at the beam center. Only the phase of $A_y$ is shown. These two cases sample regimes with markedly different paraxial-approximation accuracy for the twisted field–matter interaction.
• Figure 2: a) Scattering yields for a single molecule at the beam center ($\sigma_b = 0.001$ a.u.) after axial averaging: linearly polarized plane wave (PW), Debye-scattering analog for axial averaging (Analytical), and OAM Bessel beam (Bessel) with $\theta_k = 30\degree$, $m= 4$, and $\Lambda = 1$. b) Dissymmetry factor $\delta$ (percentage difference in yield) between enantiomers. c) $\delta$ vs distance from beam center, revealing focal averaging effects. $\phi_s = 90\degree$ for all cases.
• Figure 3: Dissymmetry factor $\delta$ vs Bessel beam parameters. a) $\theta_k$ dependence for fixed $m = 4$. b) $m$-dependence for $\theta_k=0.1\degree$. c) $m$-dependence for $\theta_k = 30\degree$. In all cases, $\Lambda = 1$, $\phi_s = 90\degree$.
• Figure 4: a) Scattering yields for ensembles of 500 and 1000 molecules. “Coh sum”: $|\sum_i F_i|^2$, “Incoh sum”: $\sum_i |F_i|^2$. b) Differential yield between enantiomers for the 500-molecule ensemble. The other parameters are identical to Fig. \ref{['fig:single_molecule']}.