The noninteracting kinetic energy density tau(r) = 1/2 Sigma(i)(occ)\del phi(i)(r)\(2), calculated from the Kohn-Sham orbitals phi(i), has recently been used to model the exchange energy (E-X). The question arises whether it is in principle possible to obtain E-X or, more general, all the properties of a noninteracting ground-state system exclusively in terms of tau(r). We produce evidence to counter this possibility by showing that a one-to-one correspondence between local potentials v(r), which differ by more than a constant, and tau(r) does not exist. Furthermore, we show that E-X cannot be obtained exactly in terms of tau. However, in the slowly varying limit a one-to-one mapping between tau and v can be established. Thus we are able to derive the gradient expansion of the electron density and of E-X in terms of tau. (C) 2000 American Institute of Physics. [S0021-9606(00)31010-8].