Coherent two-dimensional electronic-x-ray spectroscopy

Ultrafast pump-probe time resolved x-ray spectroscopy carries information on the valence-core dynamics of molecular systems. Here, a coherent two-dimensional nonlinear electronic-x-ray spectroscopy (2DEX) application is proposed in order to reveal the frequency-frequency correlations for the valence and the core transition excitations. 2DEX is in the class of extreme-cross peak correlation spectroscopy and is experimentally straightforward to measure as an adaptation of the conventional optical pump-x-ray probe technique by creating a phase-locked pulse pair of the ultrafast laser for the valence excitation. Theoretical evaluation of the coherences and populations for several applications of ultrafast valence-core spectroscopy experiments is shown. Using a response function approach, 2DEX, four wave signals are calculated and evaluated with respect to frequency separation in the electronic and x-ray ranges as well as the line shape characteristics. It is shown that stationary and oscillatory contributions to the rephasing, non-rephasing, and absorptive signals can be resolved depending on pulse shaping and phase cycling, phase matching, x-ray spectrometer, and material response parameters. Calculations are shown for examples that include the valence-core coherences for a vibrational monomer and for Frenkel and charge transfer electronic exciton states, which in the x-ray absorption near-edge structure spectral region has the potential to resolve the population and coherence contributions in the atomic localized basis.