Scattering off molecules far from equilibrium

Abstract

Pump-probe gas phase X-ray scattering experiments, enabled by the development of Xray Free Electron Lasers, have advanced to reveal scattering patterns of molecules far from their equilibrium geometry. For polyatomic molecular systems, large amplitude vibrational motions are associated with anharmonicity and shifts of interatomic distances (known as the 'shrinkage effect' in linear molecules), making analytical solutions using traditional harmonic approximations inapplicable. More generally, the interatomic distances in a polyatomic molecule are not independent and the traditional equations commonly used to interpret the data may give unphysical results. Here we introduce a novel method based on molecular dynamic trajectories and illustrate it on two examples of hot, vibrating molecules at thermal equilibrium. When excited at 200 nm, 1,3cyclohexadiene (CHD) relaxes on a sub-picosecond time scale back to the reactant molecule, the dominant pathway, and to various forms of 1,3,5-hexatriene (HT). With internal energies of about 6 eV, the energy thermalizes quickly, leading to structure distributions that deviate significantly from their vibrationless equilibrium. The experimental and theoretical results are in excellent agreement and reveal that a significant contribution to the scattering signal arises from transition state structures near the inversion barrier of CHD. In HT, the analysis clarifies that previous inconsistent structural parameters determined from electron diffraction were artifacts resulting from the use of inapplicable analytical equations.

Advances in ultrafast gas-phase x-ray scattering

“…Shortly afterward, analysis of the time-dependent scattering signals of NMM following photoexcitation revealed coherent vibrations that dephase on a picosecond time scale 7 . Recently, similar experiments also revealed multiple competing pathways in the UV-induced photodissociation of trimethylamine 42 and an array of insights into the initial electronic redistribution 14 , structural dynamics 45 , and product species formed 43 A c c e p t e d M a n u s c r i p t result, rather than the overall accuracy. As the calculation of structures in highly excited electronic states of polyatomic molecules is unreliable, theoretical results cannot be used as absolute benchmarks.…”

Observation of the molecular response to light upon photoexcitation

“…The current experiment is aided by the fact that CHD is a comparatively small organic molecule, consisting of light elements, and that the change in electronic structure is large while structural changes are small. However, given the upcoming improvements in XFEL repetition rate, time resolution, and mean photon energy 34 and the ongoing development of robust methods for data analysis 13,35,36 , which may come to include sophisticated…”

Determination of excited state molecular structures from time-resolved gas-phase X-ray scattering

“…First, it inherently overcomes the problem of correlation among different structural parameters of the molecule since the scattering patterns used to compare with experiments are directly computed from 3D structures instead of a subset of independently adjustable structural parameters. 37 Second, the method utilizes a large number of trial structures that are sufficiently comprehensive and dense to include a structure that is close to the 'right' one, while reducing the space of all possible atom arrangements by restricting their positions to those that conform with fundamental chemistry concepts. This prevents the analysis from converging to a structure that is physically or chemically impossible.…”

“…This prevents the analysis from converging to a structure that is physically or chemically impossible. 37 Third, the analysis does not need to restrain the molecular symmetry or manually dene independent structural parameters, making it applicable to relatively large polyatomic molecular systems.…”

“…We note that a list of determined structural parameters does not necessarily correspond to a physically possible structure because there may be correlations between structural parameters. 37 One could examine this effect by characterizing the similarity between the representative structures in the pool and the list of experimentally determined best-tting structural parameters, as explained in detail in Section 3.…”