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We visualize the Kohn-Sham kinetic energy density (KED), and the ingredients-- the electron density, its gradient and Laplacian -- used to constructorbital-free models of it, for the AE6 test set of molecules. These arecompared to related quantities used in metaGGA's, to characterize two importantlimits -- the gradient expansion and the localized-electron limit typified bythe covalent bond. We find the second-order gradient expansion of the KED to bea surprisingly successful predictor of the exact KED, particularly at lowdensities where this approximation fails for exchange. This contradicts theconjointness conjecture that the optimal enhancement factors for orbital-freekinetic and exchange energy functionals are identical. In addition we findsignificant problems with a recent metaGGA-level orbital-free KED, especiallyfor regions of strong electron localization. We define an orbital-freedescription of electron localization and a revised metaGGA that improves uponatomization energies significantly.

Visualization and analysis of the Kohn-Sham kinetic energy density and its orbital-free description in molecules