In a recent paper by Faber et . al., Mean Absolute Error and DFT (B3LYP) error (relative to the experiments) for 9 properties of QM9 dataset molecules has been reported. \begin{equation} \begin{array}{l|ccccccccc} {} & {\mu} & {\alpha} & {\varepsilon_{\text {HOMO }}}& {\varepsilon_{\text {LUMO }}} & {\Delta \varepsilon} & {\left\langle\mathrm{R}^{2}\right\rangle} & {\text { ZPVE }} & { U_{0}} & {C_{v}} \\ \hline & {\text { Debye }} & {\text { Bohr }^{3}} & {\text { eV }} & {\text { eV }} &{\text { eV }} & {\text { Bohr }^{2}} & {\text { eV }} & {\text { eV }} &{\text {cal/molK}}\\ \hline {\mathrm{MAD}} & {1.17} & {6.29}& {0.439} & {1.05} & {1.07} & {203} & {0.717} & {8.19} & {3.21} \\ {\mathrm{DFT}} & {0.10} & {0.4}& {2.0} & {2.6} & {1.2} &{-} & {0.0097} & {0.10} & {0.34} \\ \hline\end{array} \end{equation}
I was wondering why the DFT results for frontier orbital energies have such high errors in comparison with atomization energy $U_0$. For instance, the error reported for $\varepsilon_{\text {HOMO }}$ is $2.0$ while the breadth of values is $0.439$. Now compare this with the error $0.1$ for $U_0$ with breadth of values for the dataset reported as $8.19$, which is much more diverse.
A study on different DFT methods has been conducted by Zhang and Musgrave, which discusses inaccurate computation of frontier orbital energies. Some works have proposed the use ML methods to predict these values with very low errors. Since DFT is Ab initio, would suggesting to use ML methods even make sense?
Edits:
In the first paper (by Faber et al.) we read
Frontier molecular orbital energies (HOMO, LUMO and HOMO-LUMO gap) can not be measured directly. However, for the exact (yet unknown) exchange-correlation potential, HOMO and LUMO eigenvalues correspond to the negative of the vertical ionization potential (IP) and electron affinity (EA), respectively.
Based on this, I was wondering if DFT is the main approach to compute frontier orbital energies or this paper is just trying to find it using DFT in order to include the errors for DFT method.