Functional derivative of noninteracting kinetic energy density functional

Proofs from different theoretical frameworks, namely, the Hohenbergh--Kohn theorems, the Kohn--Sham scheme, and the first-order density matrix representation, have been presented in this paper to show that the functional derivative of the noninteracting kinetic energy density functional can uniquely be expressed as the negative of the Kohn--Sham effective potential, arbitrary only to an additive orbital-independent constant. Key points leading to the current result as well as confusion about the quantity in the literature are briefly discussed.