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Gradient-dependent approximations to the functional of the kinetic energy of non-interacting electrons (T_s[Ï]), which reflect various properties of the exact functional, are considered. For specially constructed pairs of electron densities, for which the analytic expression for the differences of T_s[Ï] is known, it is shown that the accuracy of the quantities derivable from a given approximation to T_s[Ï]: energy differences and their functional derivatives, does not reflect that of T_s[Ï] itself. The comparisons between the exact values of the kinetic energy in such cases are proposed as an independent condition/criterion for appraisal of approximations to T_s[Ï].

The energy-differences based exact criterion for testing approximations to the functional of the kinetic energy of non-interacting electrons Y.A. Bernard, M. Dulak, J.W. Kaminski and T.A. Wesolowski Journal of Physics A: Mathematical and Theoretical, 41 (5) (2008), p55302 DOI:10.1088/1751-8113/41/5/055302 \| unige:35 \| Abstract \| Article PDF
Gradient-dependent approximations to the functional of the kinetic energy of non-interacting electrons (T_s[Ï]), which reflect various properties of the exact functional, are considered. For specially constructed pairs of electron densities, for which the analytic expression for the differences of T_s[Ï] is known, it is shown that the accuracy of the quantities derivable from a given approximation to T_s[Ï]: energy differences and their functional derivatives, does not reflect that of T_s[Ï] itself. The comparisons between the exact values of the kinetic energy in such cases are proposed as an independent condition/criterion for appraisal of approximations to T_s[Ï].

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