Coordinate scaling of the kinetic energy in pair density functional theory: A Legendre transform approach

Abstract We show that the kinetic energy functional in pair density functional theory is homogeneous of degree 2 with respect to coordinate scaling. Although this result was already derived by Levy and Ziesche using the constrained search method (Levy and Ziesche, J Chem Phys 2001, 115, 9110 ), we derive our result using the Legendre transform formulation (Ayers et al., J Chem Phys 2006, 124, 054101 ). The advantage of this approach is that in the Legendre transform functional, the N ‐representability problem is solved by the functional. By contrast, in the Levy–Ziesche approach, the computationally impracticable N ‐representability constraints have to be imposed separately. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009