Exploring the Influence\nof Approximations for Simulating\nValence Excited X‑ray Spectra

First-principles simulations of excited-state X-ray spectra\nare\nbecoming increasingly important to interpret the wealth of electronic\nand geometric information contained within femtosecond X-ray absorption\nspectra recorded at X-ray Free Electron Lasers (X-FELs). However,\nbecause the transition dipole matrix elements must be calculated between\ntwo excited states (i.e., the valence excited state and the final\ncore excited state arising from the initial valence excited state)\nof very different energies, this can be challenging and time-consuming\nto compute. Herein using two molecules, protonated formaldimine and\ncyclobutanone, we assess the ability of <i>n</i>-electron\nvalence-state perturbation theory (NEVPT2), equation-of-motion coupled-cluster\ntheory (EOM-CCSD), linear-response time-dependent density functional\ntheory (LR-TDDFT) and the maximum overlap method (MOM) to describe\nexcited state X-ray spectra. Our study focuses in particular on the\nbehavior of these methods away from the Franck–Condon geometry\nand in the vicinity of important topological features of excited-state\npotential energy surfaces, namely, conical intersections. We demonstrate\nthat the primary feature of excited-state X-ray spectra is associated\nwith the core electron filling the hole created by the initial valence\nexcitation, a process that all of the methods can capture. Higher\nenergy states are generally weaker, but importantly much more sensitive\nto the nature of the reference electronic wave function. As molecular\nstructures evolve away from the Franck–Condon geometry, changes\nin the spectral shape closely follow the underlying valence excitation,\nhighlighting the importance of accurately describing the initial valence\nexcitation to simulate the excited-state X-ray absorption spectra.