Unveiling Molecular Symmetry Through Twisted X-Ray Diffraction

The centrosymmetric constraint of Friedel's law in standard x-ray diffraction limits its ability to reveal complex molecular symmetry. In contrast, twisted x-ray diffraction with vortex beams, which carry orbital angular momentum, breaks Friedel's law yielding diffraction patterns that reflect the intrinsic symmetry of molecules. Through analytical derivations and numerical simulations, we demonstrate the enhanced sensitivity of twisted x-ray diffraction to the symmetry of M-fold symmetric molecules. Our results show that, while traditional standard x-ray diffraction struggles to distinguish between structurally similar molecules with different symmetries, twisted x-ray diffraction patterns can clearly differentiate these molecules. Additionally, we show that increasing the orbital angular momentum enhances the diffraction resolution and reveals finer symmetry-specific features of the molecules. This positions twisted x-ray diffraction as a promising tool for molecular imaging, capable of revealing intricate structures with complex symmetry.