Time-, Frequency-, and Wavevector-Resolved X-Ray Diffraction from Single Molecules

TL;DR

This paper develops a quantum electrodynamic framework to analyze time-, frequency-, and wavevector-resolved X-ray diffraction from single molecules, distinguishing between coherent and incoherent scattering contributions and guiding future nano-structure experiments.

Contribution

It introduces a comprehensive theoretical model for off-resonant X-ray scattering from single molecules, including both incoherent and coherent effects, and applies it to a cysteine molecule example.

Findings

Incoherent scattering is more affected by inelastic processes in single-molecule experiments.

The technique can directly measure charge densities under specific conditions.

Simulations demonstrate time- and wavevector-resolved signals from a cysteine molecule.

Abstract

Using a quantum electrodynamic framework, we calculate the off-resonant scattering of a broad-band X-ray pulse from a sample initially prepared in an arbitrary superposition of electronic states. The signal consists of single-particle (incoherent) and two-particle (coherent) contributions that carry different particle form factors that involve different material transitions. Single-molecule experiments involving incoherent scattering are more influenced by inelastic processes compared to bulk measurements. The conditions under which the technique directly measures charge densities (and can be considered as diffraction) as opposed to correlation functions of the charge-density are specified. The results are illustrated with time- and wavevector-resolved signals from a single amino acid molecule (cysteine) following an impulsive excitation by a stimulated X-ray Raman process resonant with the sulfur K-edge. Our theory and simulations can guide future experimental studies on the structures of nano-particles and proteins.