  First-principles Hubbard-corrected approximate density-functional theory
(DFT+U) is a low-cost, potentially high throughput method of simulating
materials, but it has been hampered by empiricism and inconsistent band-gap
correction in transition-metal oxides. DFT+U property prediction of
non-magnetic systems such as d0 and d10 transition-metal oxides is typically
faced with excessively large calculated Hubbard U values, and with difficulty
in obtaining acceptable band-gaps and lattice volumes. Meanwhile, Hund's
exchange coupling J is an important but often neglected component of DFT+U, and
the J parameter has proven challenging to directly calculate by means of linear
response. In this work, we provide a revised formula for computing Hund's J
using established self-consistent field DFT+U codes. For non-magnetic systems,
we introduce a non-approximate technique for calculating U and J simultaneously
in such codes, at no additional cost. Using unmodified Quantum ESPRESSO, we
assess the resulting values using two different DFT+U functionals incorporating
J, namely the widely used DFT+(U-J) and the readily available DFT+U+J. We
assess a test set comprising TiO2, ZrO2, HfO2, Cu2O and ZnO, and apply the
corrections both to metal and oxygen centered pseudoatomic subspaces. Starting
from the PBE functional, we find that DFT+(U-J) is significantly out-performed
in band-gap accuracy by DFT+U+J, the RMS band-gap error of which matches that
of the hybrid functional HSE06. ZnO, a long-standing challenge case for DFT+U,
is addressed by means of Zn 4s instead of Zn 3d correction, in which case the
first-principles DFT+U+J band-gap error is half of that reported for HSE06.
