Prediction of core level binding energies in density functional theory: Rigorous definition of initial and final state contributions and implications on the physical meaning of Kohn-Sham energies

Abstract

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.

Absolute photoionization cross sections of furanic fuels: 2‐ethylfuran, 2‐acetylfuran and furfural

“…In this investigation, absolute values of orbital energies from the B3LYP computations are not used to derive ionization energies, but rather, we employ their difference to yield excitation energies, i.e., term energies for excited electronic states. This approach has been proved to provide reliable results . Based on the study of furan and some of its derivatives by Klapstein et al ., the second band appears as a result of the removal of an electron from the oxygen's lone pair in the furan ring.…”

Adsorption properties of trifluoroacetic acid on anatase (101) and (001) surfaces: a density functional theory study

“…Some reasons are purely technical and some other have a more fundamental origin 58,59. Interestingly, Kohn-Sham orbital energies with respect to a given reference follow the experimental trend, as shown in recent work50,51 and illustrated here with the example of C(1s) for the TFAA molecule above, and this is the origin of the success of many theoretical works. This is usual convention but note the experiments for the gas phase TFAA molecule report C(1s) binding energies of 296.5 and 299.3 for the C atom in the -COO and -CF 3 groups respectively 60.…”

Predicting core level binding energies shifts: Suitability of the projector augmented wave approach as implemented in VASP

“…Other approaches include initial state (IS) approximations, which considers that Kohn–Sham (KS) eigenstate energies in the electronic ground state as approximations to BE —similar to Koopmans theorem in HF, a statement recently discussed unambiguously showing that while Koopmans theorem does not hold for the KS eigenvalues, it properly reflects the trends in ΔBEs . The proper way to define IS BEs from DFT calculations has also been described by some of us . An alternative approach is provided by the model known as Janak–Slater (JS) transition state method, which, in a nutshell, considers half occupation of the CL when estimating BEs rather than a full core‐hole as in the FS approach, see Figure .…”