  Quasiparticle energies and fundamental band gaps in particular are critical
properties of molecules and materials. It was rigorously established that the
generalized Kohn-Sham HOMO and LUMO orbital energies are the chemical
potentials of electron removal and addition and thus good approximations to
band edges and fundamental gaps from a density functional approximation (DFA)
with minimal delocalization error. For other quasiparticle energies, their
connection to the generalized Kohn-Sham orbital energies has not been
established but remains highly interesting. We provide the comparison of
experimental quasiparticle energies for many finite systems with calculations
from the GW Green's function and localized orbitals scaling correction (LOSC),
a recently developed correction to semilocal DFAs, which has minimal
delocalization error. Extensive results with over forty systems clearly show
that LOSC orbital energies achieve slightly better accuracy than the GW
calculations with little dependence on the semilocal DFA, supporting the use of
LOSC DFA orbital energies to predict quasiparticle energies. This also leads to
the calculations of excitation energies of the $N$-electron systems from the
ground state DFA calculations of the $\left(N-1\right)$-electron systems.
Results show good performance with accuracy similar to TDDFT and the delta SCF
approach for valence excitations with commonly used DFAs with or without LOSC.
For Rydberg states, good accuracy was obtained only with the use of LOSC DFA.
This work highlights the pathway to quasiparticle and excitation energies from
ground density functional calculations.
