ULTRAFAST X-RAY AND ELECTRON-DIFFRACTION - THEORETICAL CONSIDERATIONS

Time-dependent ultrafast diffraction measurements can be directly inve rted to obtain the dynamics of atomic motions, in contrast to ultrafas t spectra which require detailed knowledge of the sample (e.g., potent ial energy surfaces) for their inversion. We consider here how to deri ve time-dependent diffraction (the X-ray and electron diffraction case s being very similar) from nuclear quantum dynamics and vice versa and how this may be used to directly observe the atomic motions in molecu les, in particular how chemical reactions take place. Two simple examp les of dissociative and bound quantum (vibrational and rotational) dyn amics in a gas-phase sample of diatomic molecules, excited by an optic al pump pulse and measured by an electron or X-ray probe pulse, are pr esented. The quantum mechanical basis of the breaking of symmetry due to the linearly polarized optical pump pulse and the superposition and interference between the ground and excited electronic states are dis cussed. We demonstrate how to isolate the short-time excited-state dyn amics from that of the ground state using the symmetry of the electron ic dipole transition. We illustrate that the time-evolving distributio n of interatomic distances can be clearly resolved from the ultrafast diffraction data and thus illustrate that the detailed dynamics of mol ecular vibration and the progress of a photodissociation reaction coul d be watched as they occur. In addition, we show that the duration of ultrafast X-ray and electron pulses can be measured with a time resolu tion of tens of femtoseconds by clocking it against such atomic motion .