Validation of Koopmans' theorem for density functional theory binding energies

Abstract

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.

Structural, energetic and electronic properties of (100) surfaces for alkaline earth metal oxides as calculated with hybrid density functional theory

“…The exchange-correlation functional is given in parentheses for theoretical results. ionisation potentials for core electrons [81,80,78], however it does produce reasonably accurate ionisation potentials for valence electrons [76,77], as analysed here, as well as accurately reproducing the relative shift in binding energies for core electrons in different chemical environments [78]. Calculating the first ionisation potential, which involves taking an electron from the valence band maximum (VBM) to the vacuum, is thus I VBM = − eV bg − ϵ VBM .…”

“…The validity of Koopmans' theory for Kohn-Sham eigenvalues has been debated previously [75][76][77][78][79][80][81]: the method results in significant errors in absolute Table 2 Structural properties obtained from previous theoretical and experimental work for the (100) surfaces of the alkaline earth metal oxides CaO, SrO and BaO, along with surface energies (γ surf ). Method acronyms are as stated in the text, and the -SIC appenditure on to LDA stands for "self-interaction correction", as applied in these specific calculations.…”

Spectral change of simulated X-ray photoelectron spectroscopy from graphene to fullerene

“…It has been known that the initial and final state effects have an influence on the XPS spectra [25][26][27]. However, we simulated the XPS spectra using only the initial state effect by applying the scaling factor to the spectra in this work because of the simplicity of this method with good correlation between actual and calculated results [21,22].…”

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

“…One of the commonly used ways of determining the FO or initial state contributions to BE's and ∆BE's is to use Koopmans' theorem, KT. 33 For HF wavefunctions and for closed shell systems, the result of Eq. (2) reduces to…”

“…To provide evidence that initial and final state contributions to core level BE's can be obtained in both HF and KS formalisms, appropriate calculations have been carried out for a series of nitrogen containing molecules which extends our recent work on the validity of KT 33 and also is related to a recent study exploring the N(1s) BE's of N-doped graphene models. 43 The present set includes 17 molecules for which experimental values in the gas phase are known; see Ref.…”