Vibrationally-resolved X-ray spectra of diatomic systems. I. Time-independent simulations with density functional theory

We performed a systematic first-principles study on vibrationally-resolved X-ray absorption (XAS) and photoelectron (XPS) spectra of a series of diatomic molecules and cations (XAS, N$_2$, N$_2^+$, NO$^+$, CO, CO$^+$; XPS, CO) at the C/N/O K-edges. All computations were done in a time-independent (TI) framework under the harmonic oscillator approximation. To evaluate the performance of different functionals, two common pure (BLYP and BP86) and two hybrid (B3LYP and M06-2X) functionals were used. Excellent agreement between theoretical and experimental spectra was observed in most systems. Two instances, where the peak separations were underestimated, were seen in the O1s XAS spectra of CO and NO$^+$, and we explain this discrepancy to the anharmonic effects. The functional dependence can be evident or negligible, depending on the specific system and spectrum under consideration. In all these examples, the pure functionals exhibit a better or similar spectral accuracy to the hybrid functionals. This was attributed to better accuracy in bond lengths and vibrational frequencies (in both the initial and final states) predicted by pure functionals, as compared with the experiments. Structural and frequency changes induced by the core hole were summarized. We highlight the use of density functional theory with pure functionals for such diatomic calculations for easy execution and generally reliable accuracy.