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The breakdown of the Born-Oppenheimer approximation causes rich dynamics of the coupled vibronic states. Conical intersections (CIs) are well-known examples of where such complex processes can be probed spectroscopically. They operate as nonradiative ultrafast decay channels for electronically excited molecules with at least two degrees of freedom.
Spectroscopic detection of such dynamics, however, still poses a great challenge due to: the sub-100 femtosecond timescale of such events and the rapidly changing energy separation between potential energy surfaces. These reasons make pulses in the extreme ultraviolet (XUV) to the short X-ray spectral region perfect candidates to probe nonadiabatic dynamics in the proximity of a CI. The focus of this thesis is a pump-probe soft X-ray stimulated Raman technique, which is sensitive to ultrafast coherences, generated when a wave packet crosses a CI. Different schemes are investigated for the probe using attosecond pulse trains (APTs). In addition, we discuss how Raman selection rules and symmetry considerations affect the spectroscopic signal. We use two model systems, representing molecules of different symmetries, and carry out quantum dynamics simulations to study the difference in the spectra.