UC San Diego

X-ray diffraction has been widely used as a fundamental tool to probe the structure of molecules and their symmetry. Conventional diffraction techniques rely on plane-wave X-rays, which obey Friedel’s law – a principle stating that diffraction patterns exhibit centrosymmetric intensity distributions, regardless of the intrinsic symmetry of the molecule. This thesis introduced the possibility of using twisted X-rays carrying orbital angular momentum (OAM) to break this fundamental constraint. Through analytical derivations and numerical simulations, it shows that twisted X-ray diffraction has enhanced sensitivity to the symmetry of M-fold symmetric molecules and can clearly differentiate these molecules, which is otherwise impossible for traditional X-ray diffraction. Twisted X-rays, characterized by a helical phase front, possess an additional quantum number l associated with their orbital angular momentum. Unlike circularly polarized X-rays, which only carry spin angular momentum (SAM), twisted X-rays exhibit OAM, enabling them to interact with electrons in unique ways. When such beams are used in diffraction experiments, they introduce phase-dependent modulations that can break Friedel’s law, leading to asymmetries in the diffraction pattern that directly reflect the intrinsic symmetry of the target molecule. This property provides an alternative route to probing molecular chirality, which is crucial in fields ranging from structural biology to materials science. In this thesis, I will first review the theoretical background of standard X-ray diffraction and the fundamental properties of twisted X-rays. I will then present how the scattered amplitude of twisted X-ray is derived by incorporating Bessel functions. Additionally, I will describe the computational methods used for diffraction pattern simulations and present our simulated results. In chapter 2 of this thesis, I focus on advancing the understanding of ultrafast X-ray diffraction for probing quantum coherence, particularly in time-resolve twisted X-ray diffraction experiments which is an extend of chapter 1. Quantum coherence governs the outcome and efficiency of photochemical reactions and ultrafast molecular dynamics. Recent advances in ultrafast gas-phase X-ray scattering and electron diffraction have enabled the direct observation of femtosecond nuclear motions driven by vibrational coherence. These techniques provide an essential insight into molecular behavior on ultrafast timescales, capturing the interplay between electronic and nuclear dynamics. However, probing attosecond electron dynamics and coupled electron-nuclear interactions remains a great challenge. This chapter explores emerging methodologies aimed at resolving attosecond charge migration and vibronic coupling at conical intersections, which are key process that define reaction pathways in complex molecular systems. Ultrafast diffraction, enhanced by structured beams carrying orbital angular momentum, provide new possibilities for selectively probing coherence contributions.