NONLOCAL FUNCTIONAL DERIVATIVE OF KINETIC-ENERGY FOR THE SELF-CONSISTENT THOMAS-FERMI ATOM

It is well known in the Thomas-Fermi (TF) theory that the functional d erivative delta T/delta n(r), with T the kinetic energy and n(r) the g round-state electron density, is proportional to n(2/3)(r). But the di fferential equation satisfied by the TF self-consistent density for at oms is shown here to express n(1/3)(r) as a linear combination of del( 2)n/n and (del n/n)(2). Hence a nonlocal form for delta T/delta n (r) follows, solely in terms of these two variables.