Ultrafast Imaging of photochemical dynamics via x-ray scattering: connecting theory and experiments

Although photochemical reactivity has been extensively studied, a clear picture of the underlying dynamics is largely missing predominantly because of the extremely short reaction times involved in these processes. The rapid development of X-ray free electron laser (XFEL) facilities in the last decade has fostered the emergence of new types of experiments that target photochemical dynamics. One of these new prominent techniques is non-resonant Ultrafast X-ray Scattering (UXS). In a pump-probe fashion, it enables the direct observation of structural dynamics on a femtosecond timescale. Due to the extreme brightness of the XFEL, these experiments can be performed even in gas phase. Because of the unconstrained molecular motion and lack of intermolecular interference, gas-phase UXS is a meeting ground for experimental and theoretical studies of the quantum nature of photochemical dynamics. As promising as they are, gas-phase UXS experiments are still in their early days. A lot of fundamental aspects remain unexplored, and rigorous theoretical and computational frameworks are not established. This thesis aims to bridge existing gaps between theory and experiments, presenting an account of recent advances in data analysis and interpretation. The work gives an outline of the theory of time-dependent molecular quantum mechanics following photoexcitation, as well as X-ray-matter interaction. Practical aspects of the post-experimental analysis are presented. These include separation of the observed signal into isotropic and anisotropic scattering components, which allows internal and rotational molecular degrees of freedom to be dealt with independently in the analysis. The process of extracting useful information about the dynamics of the molecule as the reaction unfolds requires careful consideration of how to optimally represent the experimental signal and what inversion schemes are feasible given the limitations of the experiment. The data interpretation often relies on input from computational modelling. This thesis also describes a computational scheme for calculating generalised (elastic, inelastic, total and coherent mixed) isotropic X-ray scattering cross-sections directly from the ab initio wave function of the molecule. This methodological apparatus is applied in the analysis of a number of experiments, and the findings are presented. It is shown that X-ray scattering is in principle sensitive even to small rearrangements of the electrons upon absorption of light. The ability to detect the initially excited electronic state by means of transition dipole moment alignment is demonstrated in the case of the excitation of N-methylmorpholene (NMM) by a 200 nm linearly polarised laser. The subsequent dynamics, more specifically the fast coherent vibrations, are extracted from the experiment creating a “molecular movie” with high spatial resolution via high-throughput conformational sampling guided by computational modelling. Separately, the rate of dissociation of trimethylamine (TMA) after excitation is obtained from the loss of scattering interference between the fragments over the course of the reaction

Excited Electronic States in Total Isotropic Scattering from Molecules

Ultrafast x-ray scattering experiments are routinely analyzed in terms of the isotropic scattering component. Here we present an analytical method for calculating total isotropic scattering directly from ab initio two-electron densities of ground and excited electronic states. The method is generalized to compute isotropic elastic, inelastic, and coherent mixed scattering. The computational results focus on the potential for differentiating between electronic states and on the composition of the total scattering in terms of elastic and inelastic scattering. By studying the umbrella motion in the first excited state of ammonia, we show that the associated electron density redistribution leaves a comparably constant fingerprint in the total signal that is similar in magnitude to the contribution from the changes in molecular geometry

Ultrafast X-ray scattering offers a structural view of excited-state charge transfer

Intramolecular charge transfer and the associated changes in molecular structure in N,N'-dimethylpiperazine are tracked using femtosecond gas-phase X-ray scattering. The molecules are optically excited to the 3p state at 200 nm. Following rapid relaxation to the 3s state, distinct charge-localized and charge-delocalized species related by charge transfer are observed. The experiment determines the molecular structure of the two species, with the redistribution of electron density accounted for by a scattering correction factor. The initially dominant charge-localized state has a weakened carbon-carbon bond and reorients one methyl group compared with the ground state. Subsequent charge transfer to the charge-delocalized state elongates the carbon-carbon bond further, creating an extended 1.634 Å bond, and also reorients the second methyl group. At the same time, the bond lengths between the nitrogen and the ring-carbon atoms contract from an average of 1.505 to 1.465 Å. The experiment determines the overall charge transfer time constant for approaching the equilibrium between charge-localized and charge-delocalized species to 3.0 ps