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The modified local spin density functional and the related local potentialfor excited states is tested by employing the ionization potential theorem. Thefunctional is constructed by splitting $k$-space. Since its functionalderivative cannot be obtained easily, the corresponding potential is given byanalogy to its ground-state counterpart. Further to calculate the highestoccupied orbital energy $\epsilon_{max}$ accurately, the potential is correctedfor its asymptotic behavior by employing the van Leeuwen and Baerendscorrection to it. $\epsilon_{max}$ so obtained is then compared with the$\Delta$SCF ionization energy calculated using the MLSD functional. It is shownthat the two match quite accurately.

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