Photoexciting molecules introduces complex relaxation dynamics which can be studied by time-resolved photoelectron spectroscopy. Hereby, broadband laser sources are used to achieve the desired time resolution. However, if the bandwidth of the laser pulses is broader than the energy spacing between the involved states two problems occur: (i) Exciting the molecule into one specific initial state is not possible. (ii) Simple parallel or sequential decay models are not applicable due to the complex coupling of the different states, and more complex models are underdetermined. Theoretical calculations, in contrast, are not limited by these problems as they can arbitrarily define an initial population and are able to track the transient behavior directly. However, the retrieved dynamics require experimental verification to achieve reliability.
In this study we present a combined approach of time-resolved photoelectron spectroscopy and surface-hopping simulations to investigate the dynamics of electronically excited acetone molecules [1]. The nearly degenerated n3p Rydberg states are ideal to benchmark this approach because (i) the three n3p Rydberg states are energetically well separated to other states, (ii) the kinetic energy of photoelectrons which are created by ionization into the ionic Rydberg ground state show no energy dependence of the vibrational state (because the involved energy curves are parallel) and (iii) the n3p_y state has an avoided crossing with a ππ* valence state which differentiates the n3p_y from n3p_x and n3p_z, introducing more variety in the problem.
The influence of the excitation energy on the relaxation times and ultimately on the coupling between the different involved states can be studied by fitting decay associated spectra to the measured spectrograms. However, the decay associated spectra only show one effective time constant per involved state. To get insight into the intrinsic dynamics surface hopping simulations with the SHARC [2] program package in combination with a linear vibronic coupling model were performed. The reliability of the simulations can be confirmed by computing the effective time constants from the coupling strength between the states and comparing them to the experimental values. The good agreement allows interpretation of the computational results: (i) The coupling from an energetically higher to a lower state is stronger than vice versa because of the larger accessible phase space in the lower state. (ii) The n3p_y state couples strongly to the ππ* valence state because of the avoided crossing. (iii) The coupling between n3p_x and n3p_z to the ππ* state is much weaker than to the n3p_y. Population of these states use the n3p_y as a doorway state in order to relax to the ground state. (iv) Increasing the excitation energy also increases the coupling strength. The good agreement of experiment and simulations provide a detailed understanding into the complex dynamics of the nearly degenerated n3p Rydberg states, which would not be possible by one method alone.

[1] Heim P., et al., JPCL, 2020, 11.4, 1443-1449
[2] Mai S., et. al., WIREs Comput. Mol. Sci., 2018, 8.6, e1370.