A systematic study of the N(1s) core level binding energies (BE's) in a broad series of molecules is presented employing Hartree-Fock (HF) and the B3LYP, PBE0, and LC-BPBE density functional theory (DFT) based methods with a near HF basis set. The results show that all these methods give reasonably accurate BE's with B3LYP being slightly better than HF but with both PBE0 and LCBPBE being poorer than HF. A rigorous and general decomposition of core level binding energy values into initial and final state contributions to the BE's is proposed that can be used within either HF or DFT methods. The results show that Koopmans' theorem does not hold for the Kohn-Sham eigenvalues. Consequently, Kohn-Sham orbital energies of core orbitals do not provide estimates of the initial state contribution to core level BE's; hence, they cannot be used to decompose initial and final state contributions to BE's. However, when the initial state contribution to DFT BE's is properly defined, the decompositions of initial and final state contributions given by DFT, with several different functionals, are very similar to those obtained with HF. Furthermore, it is shown that the differences of Kohn-Sham orbital energies taken with respect to a common reference do follow the trend of the properly calculated initial state contributions. These conclusions are especially important for condensed phase systems where our results validate the use of band structure calculations to determine initial state contributions to BE shifts.

Both initial state effects, to a good approximation the electrostatic potential at the nucleus, and final state effects, due to the response of the electrons to the presence of the core-hole, contribute to core-level binding energies, BE's. For Hartree-Fock, HF, wavefunctions, Koopmans' theorem, KT, which states that the initial state BE = -ε ιs rigorous. However, the KT relationship is commonly used for Kohn-Sham, KS, ε's. We review that the KT relationship with KS ε's fails to give the absolute initial state contribution to the BE. However, we demonstrate that the shifts of initial state BE's from a reference value are accurately obtained from the shifts of the KS ε's. Thus the initial state contributions to BE shifts can be obtained from KT using KS ε's. This result validates a large body of work where KT has been used with KS ε's to define initial state contributions to BE shifts.

Here we explored the performance of Hartree-Fock (HF), Perdew-Burke-Ernzerhof (PBE), and Tao-Perdew-Staroverov-Scuseria (TPSS) functionals in predicting core level 1s binding energies (BEs) and BE shifts (ΔBEs) for a large set of 68 molecules containing a wide variety of functional groups for main group elements B → F and considering up to 185 core levels. A statistical analysis comparing with X-ray photoelectron spectroscopy (XPS) experiments shows that BEs estimations are very accurate, TPSS exhibiting the best performance. Considering ΔBEs, the three methods yield very similar and excellent results, with mean absolute deviations of ∼0.25 eV. When considering relativistic effects, BEs deviations drop approaching experimental values. So, the largest mean percentage deviation is of 0.25% only. Linear trends among experimental and estimated values have been found, gaining offsets with respect to ideality. By adding relativistic effects to offsets, HF and TPSS methods underestimate experimental values by solely 0.11 and 0.05 eV, respectively, well within XPS chemical precision. TPSS is posed as an excellent choice for the characterization, by XPS, of molecules on metal solid substrates, given its suitability in describing metal substrates bonds and atomic and/or molecular orbitals.

Here, we assess the accuracy of various approaches implemented in Vienna ab initio simulation package code to estimate core‐level binding energy shifts (ΔBEs) using a projector augmented wave method to treat core electrons. The performance of the Perdew–Burke–Ernzerhof (PBE) and the Tao–Perdew–Staroverov–Scuseria (TPSS) exchange‐correlation density functionals is examined on a dataset of 68 molecules containing B→F atoms in diverse chemical environments, accounting for 185 different 1s core level binding energy shifts, for which both experimental gas‐phase X‐ray photoemission (XPS) data and accurate all electron ΔBEs are available. Four procedures to calculate core‐level shifts are investigated. Janak–Slater transition state approach yields mean absolute errors of 0.37 (0.21) eV at PBE (TPSS) level, similar to highly accurate all electron ΔSCF approaches using same functionals, and close to XPS experimental accuracy of 0.1 eV. The study supports the use of these procedures to assign ΔBEs of molecular moieties on material surfaces of interest in surface science, nanotechnology, and heterogeneous catalysis. © 2017 Wiley Periodicals, Inc.