A new method is presented for describing vibrational effects in x-ray absorption spectroscopy (XAS) and resonant inelastic x-ray scattering (RIXS) using a combination of the classical Franck-Condon (FC) approximation and classical trajectories run on the core-excited state. The formulation of RIXS is an extension of the semiclassical Kramers-Heisenberg (SCKH) formalism of Ref. {Ljungberg_2010} to the resonant case, retaining approximately the same computational cost. To overcome difficulties with connecting the absorption and emission processes in RIXS the classical FC approximation is used for the absorption, which is seen to work well provided that a zero-point-energy correction is included. In the case of core-excited states with dissociative character the method is capable of closely reproducing the main features for one-dimensional test systems, compared to the quantum mechanical formulation. Due to the good accuracy combined with the relatively low computational cost, the method has large potential of being used for complex systems with many degrees of freedom, such as liquids and surface adsorbates.
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