Breakdown of the ionization potential theorem of density functional theory in mesoscopic systems

The ionization potential (IP)-theorem of Kohn-Sham (KS) density functional theory (DFT) states that the energy of the highest occupied molecular orbital (HOMO) epsilon(HOMO) equals the negative of the first IP, thus ascribing a physical meaning to one of the eigenvalues of the KS Hamiltonian. We scrutinize the fact that the validity of the IP-theorem relies critically on the electron density n(r), far from the system, to be determined by HOMO only, behaving as n(r)& SIM;r & RARR;& INFIN;e-2-2 epsilon HOMOr. While this behavior always holds for finite systems, it does not hold for mesoscopic ones, such as quasi-two-dimensional (Q2D) electron gas or Q2D crystals. We show that this leads to the violation of the IP-theorem for the latter class of systems. This finding has a strong bearing on the role of the KS valence band with respect to the work-function problem in the mesoscopic case. Based on our results, we introduce a concept of the IP band structure as an observable alternative to its unphysical KS counterpart. A practical method of the determination of the IP band structure in terms of DFT quantities is provided.

Automated summary

The ionization potential (IP) theorem in Kohn-Sham density functional theory explains the relationship between HOMO energy and the first IP, but it may not hold for mesoscopic systems. Research shows that this could lead to issues with the KS valence band in addressing the work-function problem.