Fundamental Limits on Spatial Resolution in Ultrafast X-ray Diffraction

Abstract

X-ray Free-Electron Lasers have made it possible to record time-sequences of diffraction images to determine changes in molecular geometry during ultrafast photochemical processes. Using state-of-the-art simulations in three molecules (deuterium, ethylene, and 1,3-cyclohexadiene), we demonstrate that the nature of the nuclear wavepacket initially prepared by the pump laser, and its subsequent dispersion as it propagates along the reaction path, limits the spatial resolution attainable in a structural dynamics experiment. The delocalization of the wavepacket leads to a pronounced damping of the diffraction signal at large values of the momentum transfer vector q, an observation supported by a simple analytical model. This suggests that high-q measurements, beyond 10-15 Å −1 , provide scant experimental payback, and that it may be advantageous to prioritize the signal-to-noise ratio and the time-resolution of the experiment as determined by parameters such as the repetition-rate, the photon flux, and the pulse durations. We expect these considerations to influence future experimental designs, including source development and detection schemes.

Ab Initio Fragment Method for Calculating Molecular X-ray Diffraction

“…Based on our own interest in dynamics and ultrafast imaging, we have in recent years developed methods to calculate elastic, 33 inelastic, 34 and total 35 x-ray scattering directly from ab initio electronic structure calculations. We have further considered the e↵ect of electronic, 33,36 vibrational and rotational [37][38][39] states on the scattering, have extensively investigated the intersection of quantum dynamics and scattering, [40][41][42][43] and have been involved in interpreting new experiments 6,7,9,10,14,17,44,45 performed at the LCLS at Stanford in California. 46 Our starting point is the ab initio x-ray di↵raction (AIXRD) method 33 which allows calculation of the molecular scattering (di↵raction) factors directly from electronic structure calculations such as Hartree-Fock (HF), density functional theory (DFT), or various multiconfigurational methods such as complete active-space self-consistent field (CASSCF).…”

Excited Electronic States in Total Isotropic Scattering from Molecules

“…r , and where we have labeled the Fourier integrals over r r r 1 and r r r 2 as J i j (q q q) and J * kr (q q q), respectively, J i j (q q q) = dr r r 1 g i (r r r 1 )g j (r r r 1 )e ιq q q·r r r 1 (20) and J * kr (q q q) = dr r r 2 g k (r r r 2 )g r (r r r 2 )e −iq q q·r r r 2 .…”

Scattering off molecules far from equilibrium

“…This resulted in numerous exciting findings, such as photo-induced ring-opening reactions 12 , 13 , 14 , coherent nuclear vibrations 15 , 16 , and photodissociation reactions 17,18 . While in many systems the nuclear dynamics starts out as a well-defined wavepacket with a structure distribution that resembles a classical system, the large amount of energy in play during the reaction typically relaxes into a hot bath as the molecule returns to a thermal state 13,19 . A complete description of the time resolved scattering patterns therefore requires not only a simulation of the transient dynamic structure, but also a model of the scattering patterns of molecules in thermally hot vibrational conditions.…”