Ultrafast X-ray Diffraction Theory

Time-resolved X-ray diffraction patterns can be inverted to obtain photoinduced dynamics without resorting to additional and often unknown information (e.g., potential energy surfaces), as required in optical probe experiments. In order to interpret ultrafast X-ray diffraction measurements, we consider several time scales in X-ray experiments involving elastic versus inelastic scattering, quantum interference among electronic states, physical implications of temporaland spatial-averaging, and the coherence of X-ray beams. On the basis of these considerations, it is shown that inelastic scattering can be employed to measure the time dependence of electron correlation and the nonadiabatic effects in curve crossing. As in the snapshot approach, the Born-Oppenheimer approximation and the independent atom model are adopted such that molecular dynamics can be directly probed without explicit reference to electron density. In addition, we show that (i) the inversion for a cylindrically symmetric sample can be simplified by looking along a specific direction and (ii) that by means of molecular “π pulses” the excited state dynamics can be isolated without contamination from the ground electronic state. With certain modifications, the time-dependent analysis presented here can be applied to other experimental methods including electron diffraction and X-ray absorption (chemical shifts, near-edge, and EXAFS).