Modern powerful X-ray sources allow investigation of chemical reactions in real time. The project presents new theory and software code for the purpose.
Recent advances in ultrafast X-ray pulse experiments permit the observation of dynamical changes in atoms and molecules in real time, meaning the femtosecondtimescale (1 fs = 10-15 s). The analysis of these experiments, however, require an elaborate theoretical framework as well as advanced numerical simulations. The project contributes with both theory and new software code to further development of ultrafast X-ray pulse experiment interpretation.
Modern X-Ray Free-Electron Lasers (XFELs) provide extremely intense hard X-ray radiation which makes it possible to conduct experiments with dilute samples of molecules in liquid or gas phase where the intensity of the scattering signal is not enhanced by constructive interference (as in diffraction of X-rays by crystals). Furthermore, the radiation is pulsed and durations of less than 100 fs are currently available, allowing an investigation of structural changes and chemical reactions in real time, since nuclear motion in molecules typically occurs on a timescale of tenths or hundreds of femtoseconds.
In these scattering experiments a target, referred to as the material system, interacts with two subsequent pulses of electromagnetic radiation. The pulses are called the pump and the probe pulse, respectively. The pump pulse excites the material system and thereby induces dynamics such as chemical reactions or relaxation processes. The probe pulse is scattered by the non-stationary material onto a detector. By variation of the pump-probe delay, i.e. the time the probe pulse lags behind the pump pulse, the scattering signal is measured at different points in time. The resulting series of snapshots contains time-resolved information about the dynamics invoked by the pump pulse.
Extracting the desired information from the experimental data is a non-trivial task. In the project, the quantum electro-dynamical description of timeresolved non-resonant X-ray scattering by atoms and molecules in non-stationary states is reviewed. Then, a unified and coherent rederivation is presented. Different contributions to the scattering signal are identified with particular attention to inelastic scattering and to scattering related to electronic coherences. A general analytic solution to one-electron scattering matrix elements of the hydrogen atom is derived. These solutions allow a computationally efficient and mathematically exact evaluation of the X-ray scattering signal of the atom in any non-stationary state.
The analytic solutions are applied to an electronic wave packet of the hydrogen atom. Previously published results that involved numerical integration are reproduced. It is shown that the time-dependence of the scattering signal stems solely from the contributions related to the electronic coherence, whereas the elastic and inelastic signals are independent of time. The effect of the pulse duration on the X-ray scattering signal is revised and explained differently than in the published work. It is shown that the existence of an optimum pulse duration at which the scattering signal displays the strongest time-dependence is entirely due to a restriction on the range of photon energies that are accepted by the detector.
Further, the scattering signal of the hydrogen molecule subsequent to UV excitation from its X1Σg+ groundstate to its B1Σu+ excited state is simulated. This is the first full simulation of two-dimensional timeresolved X-ray scattering patterns of a molecule. All contributions to the scattering signal are evaluated. The separability of the contribution related to the electronic coherence from the total scattering signal is discussed.
Contour plots of the coherence (c) and total (t) time-resolved X-ray scattering patterns dS=d in the qx-qy plane at ve pump-probe delays T.