Comment on “Significance of the highest occupied Kohn-Sham eigenvalue”

Abstract

With more explanation than usual and without appeal to Janak's theorem, we review the statement and proof of the ionization potential theorems for the exact Kohn-Sham density-functional theory of a many-electron system: ͑1͒ For any average electron number N between the integers ZϪ1 and Z, and thus for N→Z from below, the highest occupied or partly occupied Kohn-Sham orbital energy is minus the ionization energy of the Z-electron system. ͑2͒ For ZϪ1ϽNϽZ, the exact Kohn-Sham effective potential v s (r) tends to zero as ͉r͉→ϱ. We then argue that an objection to these theorems. ͓L. Kleinman, Phys. Rev. B 56, 12 042 ͑1997͔͒ overlooks a crucial step in the proof of theorem ͑2͒: The asymptotic exponential decay of the exact electron density of the Z-electron system is controlled by the exact ionization energy, but the decay of an approximate density is not controlled by the approximate ionization energy. We review relevant evidence from the numerical construction of the exact Kohn-Sham potential. In particular, we point out a model two-electron problem for which the ionization potential theorems are exactly confirmed. Finally, we comment on related issues: the self-interaction correction, the discontinuity of the exact Kohn-Sham potential as N passes through the integer Z, and the generalized sum rule on the exchange-correlation hole. ͓S0163-1829͑98͒04403-8͔

Ionization Potential, Electron Affinity, Electronegativity, Hardness, and Electron Excitation Energy: Molecular Properties from Density Functional Theory Orbital Energies

“…This equation has been interpreted as showing that the highest occupied KS orbital energy of an N-electron system represents the negative of the exact ionization potential within exact KS density functional theory. [8][9][10][11][12] In subsequent work, Kleinman 13,14 argued that this was not correct and that the IP should not be exactly equal to the highest occupied molecular orbital eigenvalue. In a response to the Kleinman work, Perdew and Levy 8 showed that eq 3 holds and that this can be derived without Janak's theorem.…”

Long-range excitations in time-dependent density functional theory

“…the acceptor LUMO orbital energy minus the donor HOMO orbital energy. The latter is equal to minus the ionization energy of the donor, I D , while the former is the KS electron affinity [32,33,35,36], A A,S = A A − A A,XC , not the true electron affinity of the acceptor, A A . The resulting frequency, ω = I D − A A,S , is a severe underestimate to the true CT energy: aside from the usual local/semi-local approximations underestimating the ionization energy, it lacks the xc contribution to the electron affinity, as well as the −1/R tail [25,26,27,28].…”

“…The excited xc electron affinity accounts for relaxation when an electron is added to an N -electron system, forming an (N + 1)-electron excited state. (No correction is needed for ionization out of species 1 [35]: the KS HOMO energy exactly equals minus the ionization potential.) Eqs.…”

“…A crucial role is played by the step structure in the exact ground-state KS potential that develops as a heteroatomic molecule dissociates [32,33,34,35,36]. The step has size equal to the difference in the ionization potentials of the two fragments, so aligns the highest occupied molecular orbitals (HOMOs) of each.…”

First-Principles Photoemission Spectroscopy of DNA and RNA Nucleobases from Koopmans-Compliant Functionals

“…Unfortunately, their accuracy in the calculation of ground state energies is not complemented by a comparable precision in predicting electronic excitation energies and photoemission spectra 18 . These drawbacks are intrinsic to Kohn-Sham (KS) DFT whose single particle energies [except for the highest occupied molecular orbital (HOMO) 19,20 ] cannot even in principle be interpreted as quasiparticle excitation energies 18,21,22 (though arguments exist suggesting that exact KS eigenvalues may provide good approximations to them [23][24][25] ).…”