First-, second- and third-order correlation function in time-resolved X-ray diffraction experiments

In the past decade, sustained progress has been made in the field of time-resolved X-ray diffraction and photocrystallography. Laser systems have been developed rapidly, and the combination of pulsed laser sources with pulsed X-ray sources, particularly by using synchrotron X-ray radiation and X-rays generated by plasma sources, has made the application of pump-probe schemes routine. So far, however, most studies have been focused on two questions: (i) the refinement of structural changes during the course of a reaction, and (ii) possible relations between transient structural changes and the intermediates found by optical spectroscopy. In this work, a kinetic description for different time laws in time-resolved X-ray diffraction experiments is derived in the framework of time-dependent correlation functions. The derived time laws were applied to time-resolved studies on a [2+2] photodimerization and a reversible reaction undergoing structural reorganization.