Ultrafast X-ray diffraction theory

Time-resolved X-ray diffraction patterns can be inverted to obtain photoind uced dynamics without resorting to additional and often unknown information (e.g., potential energy surfaces), as required in optical probe experiment s. In order to interpret ultrafast X-ray diffraction measurements, we consi der several time scales in X-ray experiments involving elastic versus inela stic scattering, quantum interference among electronic states, physical imp lications of temporal- and spatial-averaging. and the coherence of X-ray be ams. On the basis of these considerations, it is shown that inelastic scatt ering can be employed to measure the time dependence of electron correlatio n and the nonadiabatic effects in curve crossing. As in the snapshot approa ch, the Born-Oppenheimer approximation and the independent atom model are a dopted 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 "pi pulses" the exci ted state dynamics can be isolated without contamination from the ground el ectronic state. With certain modifications, the time-dependent analysis pre sented here can be applied to other experimental methods including electron diffraction and X-ray absorption (chemical shifts, near-edge, and EXAFS).