High DFT error for HOMO-LUMO calculation In a paper by Zhang and Musgrave it is stated that

Unfortunately, although molecular orbital (MO) theory is of immense utility, commonly used DFT functionals that can economically calculate the electronic structure of molecules may not predict orbital energies accurately.

I was wondering while DFT is an ab initio method to calculate molecular properties, why it not performing well for computing frontier molecular orbital energies.
 A: Density functional theory really is a total energy method, and total energies as functionals of the electron densities are often relatively well predicted; even better is the prediction of total energy differences (i.e. reaction energies) due to somewhat fortuitous error cancellation.
Orbital or spectral properties are here based on interpreting the Kohn-Sham eigenvalues as quasiparticle (or "orbital") energies, while the Kohn-Sham equations are only an auxiliary construct to approximate the non-interacting (electronic) kinetic energy. In other words: Kohn-Sham orbital energies do not - strictly speaking - have any physical meaning in terms of observable spectral properties. However, the (not necessarily well understood) resemblance of the Kohn-Sham spectrum and actual single-/quasiparticle spectra, and the lower computational cost compared to other ab initio methods makes it tempting to interpret the Kohn-Sham spectrum as an actual electronic spectrum. Another well-known example of the failure of "over-interpreting" the Kohn-Sham spectrum this way is the significant underestimation of band gaps. To properly compute electronic spectra starting from DFT, one has to incorporate quasiparticle corrections, e.g. in the form of the so-called GW approach (which is computationally significantly more expensive than DFT).
