Application of the Hartree-Fock-Slater Method in Photoelectron Spectroscopy

Baerends, Evert Jan; Snijders, J.G.; Lange, C.A. de; Jonkers, G.

doi:10.1007/978-1-4899-2142-0_22

Cited by 7 publications

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“…In all cases where the ionization is out of symmetry-equivalent lone pairs or out of symmetry-equivalent atomic (core) shells, the symmetrized calculations exhibit a bad error with standard (semi-)local functionals. 61,[69][70][71] "Delocalization error" has been associated 25 with the convex behavior of the LDFA1 energy curve for fractional electron numbers, compared to the "exact" linear energy behavior of the energy of a mixture (ensemble) of (N − 1)-and N-electron systems; see Fig. 2.…”

Section: Local Approximation Error Of Ionization Energy and Affinity ...mentioning

confidence: 99%

Density functional approximations for orbital energies and total energies of molecules and solids

Baerends

2018

The Journal of Chemical Physics

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The relation of Kohn-Sham (KS) orbital energies to ionization energies and electron affinities is different in molecules and solids. In molecules, the local density approximation (LDA) and generalized gradient approximations (GGA) approximate the exact ionization energy (I) and affinity (A) rather well with self-consistently calculated (total energy based) I and A, respectively. The highest occupied molecular orbital (HOMO) energy and lowest unoccupied molecular orbital (LUMO) energy, however, differ significantly (by typically 4-6 eV) from these quantities, ϵ(mol)>-I(mol)≈-I(mol), ϵ(mol)<-A(mol)≈-A(mol). In solids, these relations are very different, due to two effects. The (almost) infinite extent of a solid makes the difference of orbital energies and (L)DFA calculated ionization energy and affinity disappear: in the solid state limit, ϵ(solid)=-I(solid) and ϵ(solid)=-A(solid). Slater's relation ∂E/∂n = ϵ for local density functional approximations (LDFAs) [and Hartree-Fock (HF) and hybrids] is useful to prove these relations. The equality of LDFA orbital energies and LDFA calculated -I and -A in solids does not mean that they are good approximations to the exact quantities. The LDFA total energies of the ions with a delocalized charge are too low, hence I(solid) < I and A(solid) > A, due to the local-approximation error, also denoted delocalization error, of LDFAs in extended systems. These errors combine to make the LDFA orbital energy band gap considerably smaller than the exact fundamental gap, ϵ(solid)-ϵ(solid)=I(solid)-A(solid)

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