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We find that the multi-valued character of the G factor as a function of the reduced gradient (s) still exists after accounting for pseudopotential artifacts and the kinetic energy global upper bound. We also find that the VT84F functional indeed exhibits stable convergence and more reasonable results for self-consistent bulk properties compared to other generalized gradient approximation (GGA) kinetic energy density functionals (KEDFs) that we tested earlier. However, VT84F generally yields overestimated equilibrium volumes, which may result from its inability (as with all GGAs) to reproduce the G-s multi-valued character. The analogous failure to predict the multi-valued character of G as a function of the reduced density (d) is also likely to be responsible for the inaccuracy of our vWGTF functionals reported earlier. Our multi-valuedness analysis therefore does not impugn any particular GGA KEDF. Instead, it merely confirms the importance of pointwise analysis for improving KEDFs, by emphasizing the need to resolve the multi-valuedness of G with respect to various density

physical review. b, condensed matter and materials physics

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