First principle simulation approach for attosecond XUV pump – XUV probe spectra for small organic molecules

Tunable sub-fs soft X-Ray (SXR) pulses are now available at the LCLS X-Ray free electron laser (XFEL) at intensities that exceed those of current SXR high harmonic generation (HHG) sources by many orders of magnitude [1]. This overcomes the intensity related limitation of HHG-based attosecond XUV pump-probe experiments to using sub-fs XUV or SXR pulses as either the pump or the probe field. The first realizations of nonlinear X-Ray spectroscopic experiments employing sub-fs SXR pulses for driving and interrogating the attosecond electron-nuclear dynamics in molecules are currently undertaken.

To decipher the measured traces of intricate dynamics, high level theoretical modeling of the final observable would be desirable. However, accurate simulations of the individual steps, i.e., (i) the ionization by the sub-fs SXR pump, (ii) the ensuing coupled electron-nuclear dynamics, and (iii) the interaction with the sub-fs SXR probe are extremely challenging tasks on their own. Their combination limits the computationally tractable system size severely, in particular, if the transient photoionization spectrum is sought after, which requires probe ionization calculations as well.

We present a protocol that balances computational cost and accuracy to allow complete, (i)-(iii), simulations of sub-fs pump-probe spectra in the XUV to SXR photon energy range for small organic molecules. Therein, we describe the bound molecular states with the CASPT2 method and use the static exchange B-spline DFT approach to model the outgoing electrons’ wave functions. The coupled electron-nuclear dynamics after the pump is modeled with the trajectory surface hopping method [2], where an ensemble of trajectories representing the nuclear zero-point energy of the system is launched in each state populated by the pump. To decipher the dynamics from multiple perspectives, we evaluate three different spectroscopic observables, i.e., the transient absorption, valence photoionization, and core photoionization spectra, respectively.

Further, various simplifications to our protocol will be scrutinized, such as neglecting the motion of the nuclei and disregarding continuum states for the probe ionization, i.e., the sudden approximation.

[1] J. Duris et al. Nat. Phot. 14, 30 (2020)

[2] J. Delgado et al. Faraday Discuss. 228, 349 (2021)