Testing excited-state energy density functional and potential with the ionization potential theorem

TL;DR

This paper evaluates a modified local spin density functional for excited states using the ionization potential theorem, showing it accurately predicts ionization energies when corrected for asymptotic behavior.

Contribution

The study introduces a new excited-state functional based on k-space splitting and corrects its potential for asymptotic accuracy, validated by ionization potential comparisons.

Findings

The corrected potential yields accurate highest occupied orbital energies.

The functional's predicted ionization energies closely match ΔSCF results.

The approach effectively tests excited-state energy density functionals.

Abstract

The modified local spin density functional and the related local potential for excited states is tested by employing the ionization potential theorem. The functional is constructed by splitting $k$-space. Since its functional derivative cannot be obtained easily, the corresponding potential is given by analogy to its ground-state counterpart. Further to calculate the highest occupied orbital energy $\epsilon_{max}$ accurately, the potential is corrected for its asymptotic behavior by employing the van Leeuwen and Baerends correction to it. $\epsilon_{max}$ so obtained is then compared with the $\Delta$SCF ionization energy calculated using the MLSD functional. It is shown that the two match quite accurately.