  Accurate exchange-correlation (XC) potentials for 3-dimensional systems --
via solution of the \emph{inverse} density functional theory (DFT) problem --
are now available to test the quality of DFT approximations. Herein, the
\emph{exact} XC potential for six molecules -- hydrogen molecule at three
different bond-lengths, lithium hydride, water, and ortho-benzyne -- are
computed using accurate ground-state densities from full configuration
interaction (CI) calculations. These potentials are then compared to model XC
potentials obtained from DFT calculations with commonly used non-local (B3LYP,
HSE06, SCAN0, and M08-HX) and local/semi-local (SCAN, PBE, PW92) XC
functionals. While relative errors in the ground-state densities from these
models are order $\mathcal{O}(10^{-3}-10^{-2})$, much larger errors in the
model XC potentials are found, $\mathcal{O}(10^{-1}-10^0)$, in both the $L_2$
norm of the potential as well as its gradients. These errors are exacerbated in
strongly correlated situations, such as the stretched $\text{H}_2$ molecule.
Among the model XC functionals under consideration, SCAN0 offers the best
quantitative and qualitative agreement with the exact XC potential, underlining
the significance of satisfying the exact conditions as well as the
incorporation of non-local effects in the construction of XC functionals.
Overall, this work indicates that tests against the exact XC potential will
provide a promising new direction for building more accurate XC functionals for
DFT.
