Issue 39, 2013

The Kohn–Sham gap, the fundamental gap and the optical gap: the physical meaning of occupied and virtual Kohn–Sham orbital energies

Abstract

A number of consequences of the presence of the exchange–correlation hole potential in the Kohn–Sham potential are elucidated. One consequence is that the HOMO–LUMO orbital energy difference in the KS-DFT model (the KS gap) is not “underestimated” or even “wrong”, but that it is physically expected to be an approximation to the excitation energy if electrons and holes are close, and numerically proves to be so rather accurately. It is physically not an approximation to the difference between ionization energy and electron affinity IA (fundamental gap or chemical hardness) and also numerically differs considerably from this quantity. The KS virtual orbitals do not possess the notorious diffuseness of the Hartree–Fock virtual orbitals, they often describe excited states much more closely as simple orbital transitions. The Hartree–Fock model does yield an approximation to IA as the HOMO–LUMO orbital energy difference (in Koopmans' frozen orbital approximation), if the anion is bound, which is often not the case. We stress the spurious nature of HF LUMOs if the orbital energy is positive. One may prefer Hartree–Fock, or mix Hartree–Fock and (approximate) KS operators to obtain a HOMO–LUMO gap as a Koopmans' approximation to IA (in cases where A exists). That is a different one-electron model, which exists in its own right. But it is not an “improvement” of the KS model, it necessarily deteriorates the (approximate) excitation energy property of the KS gap in molecules, and deteriorates the good shape of the KS virtual orbitals.

Graphical abstract: The Kohn–Sham gap, the fundamental gap and the optical gap: the physical meaning of occupied and virtual Kohn–Sham orbital energies

Article information

Article type
Perspective
Submitted
19 Jun 2013
Accepted
13 Aug 2013
First published
14 Aug 2013

Phys. Chem. Chem. Phys., 2013,15, 16408-16425

The Kohn–Sham gap, the fundamental gap and the optical gap: the physical meaning of occupied and virtual Kohn–Sham orbital energies

E. J. Baerends, O. V. Gritsenko and R. van Meer, Phys. Chem. Chem. Phys., 2013, 15, 16408 DOI: 10.1039/C3CP52547C

To request permission to reproduce material from this article, please go to the Copyright Clearance Center request page.

If you are an author contributing to an RSC publication, you do not need to request permission provided correct acknowledgement is given.

If you are the author of this article, you do not need to request permission to reproduce figures and diagrams provided correct acknowledgement is given. If you want to reproduce the whole article in a third-party publication (excluding your thesis/dissertation for which permission is not required) please go to the Copyright Clearance Center request page.

Read more about how to correctly acknowledge RSC content.

Social activity

Spotlight

Advertisements