The energy-differences based exact criterion for testing approximations to the functional for the kinetic energy of non-interacting electrons

Gradient-dependent approximations to the functional of the kinetic energy of non-interacting electrons (T-s[rho]), 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[rho] is known, it is shown that the accuracy of the quantities derivable from a given approximation to T-s[rho]: energy differences and their functional derivatives, does not reflect that of T-s[rho] 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[rho].