  We present an investigation into the transferability of pseudopotentials
(PPs) with a nonlinear core correction (NLCC) using the Goedecker, Teter, and
Hutter (GTH) protocol across a range of pure GGA, meta-GGA and hybrid
functionals, and their impact on thermochemical and non-thermochemical
properties. The GTH-NLCC PP for the PBE density functional demonstrates
remarkable transferability to the PBE0 and $\omega$B97X-V exchange-correlation
functionals, and relative to no NLCC, improves agreement significantly for
thermochemical benchmarks compared to all-electron calculations. On the other
hand, the B97M-rV meta-GGA functional performs poorly with the PBE-derived
GTH-NLCC PP, which is mitigated by reoptimizing the NLCC parameters for this
specific functional. The findings reveal that atomization energies exhibit the
greatest improvements from use of the NLCC, which thus provides an important
correction needed for covalent interactions relevant to applications involving
chemical reactivity. Finally we test the NLCC-GTH PPs when combined with
medium-size TZV2P molecularly optimized (MOLOPT) basis sets which are typically
utilized in condensed phase simulations, and show that they lead to
consistently good results when compared to all-electron calculations for
atomization energies, ionization potentials, barrier heights, and non-covalent
interactions, but lead to somewhat larger errors for electron affinities.
