Scattering off molecules far from equilibrium

Pump-probe gas phase X-ray scattering experiments, enabled by the development of X-ray free electron lasers, have advanced to reveal scattering patterns of molecules far from their equilibrium geometry. While dynamic displacements reflecting the motion of wavepackets can probe deeply into the reaction dynamics, in many systems, the thermal excitation embedded in the molecules upon optical excitation and energy randomization can create systems that encompass structures far from the ground state geometry. For polyatomic molecular systems, large amplitude vibrational motions are associated with anharmonicity and shifts of interatomic distances, 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, 1,3-cyclohexadiene (CHD) relaxes on a subpicosecond 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, our analysis clarifies that previous inconsistent structural parameters determined by electron diffraction were artifacts that might have resulted from the use of inapplicable analytical equations.