Exploring the Influence of Approximations for Simulating Valence Excited X-ray Spectra

First principles simulations of excited state X-ray spectra are becoming increasingly important to interpret the wealth of electronic and geometric information contained within femtosecond X-ray absorption spectra recorded at X-ray Free Electron Lasers (X-FELs). However, because the transition dipole matrix elements must be calculated between two excited states (i.e. the valence excited state and the final core-excited state arising from the initial valence excited state) of very different energies, this can be challenging and time-consuming to compute. Herein using two molecules, protonated formaldimine and cyclobutanone, we assess the ability of n-electron valence state perturbation theory (NEVPT2), equation-of-motion coupled cluster theory (EOM-CCSD), linear-response time-dependent density functional theory (LR-TDDFT) and the maximum overlap method (MOM) to describe excited state X-ray spectra. Our study focuses in particular on the behaviour of these methods away from the Franck-Condon geometry and in the vicinity of important topological features of excited-state potential energy surfaces, namely conical intersections. We demonstrate that the primary feature of excited state X-ray spectra is associated with the core electron filling the hole created by the initial valence excitation, a process that all the methods can capture. Higher-energy states are generally weaker and more sensitive to the nature of the reference electronic wavefunction. As molecular structures evolve away from the Franck-Condon geometry, changes in the spectral shape closely follow the underlying valence excitation, highlighting the importance of accurately describing the initial valence excitation to simulate the excited state X-ray absorption spectra.