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Recently ultrafast electron diffraction and microscopy have reached unprecedented temporal resolution, and transient structures with atomic precision have been observed in various reactions. It is anticipated that these extraordinary advances will soon allow direct observation of electronic motions during chemical reactions. We therefore performed a series of theoretical investigations and simulations to investigate the imaging of electronic motions in atoms and molecules by ultrafast electron diffraction. Three prototypical electronic motions were considered for hydrogen atoms. For the case of a breathing mode, the electron density expands and contracts periodically, and we show that the time-resolved scattering intensities reflect such changes of the charge radius. For the case of a wiggling mode, the electron oscillates from one side of the nucleus to the other, and we show that the diffraction images exhibit asymmetric angular distributions. The last case is a hybrid mode that involves both breathing and wiggling motions. Owing to the demonstrated ability of ultrafast electrons to image these motions, we have proposed to image a coherent population transfer in lithium atoms using currently available femtosecond electron pulses. A frequency-swept laser pulse adiabatically drives the valence electron of a lithium atom from the 2s to 2p orbitals, and a time-delayed electron pulse maps such motion. Our simulations show that the diffraction images reflect this motion both in the scattering intensities and the angular distributions.

We investigate theoretically the direct imaging of coherent electronic motion in atoms and molecules using attosecond electron pulses. The theories of time-resolved ultrafast electron diffraction and (e, 2e) momentum spectroscopy as well as the requisite conditions for carrying out time-resolved measurements to obtain timedependent images are discussed. Results of simulations showing images of the motions of coherent superposition states in both the hydrogen atom and the hydrogen molecular ion are shown, thus indicating the capability of ultrafast electron pulses to investigate time-dependent electron dynamics.