Coordinate Scaling of the Kinetic Energy in Pair Density Functional Theory: A Legendre Transform Approach

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. (C) 2009 Wiley Periodicals, Inc. Int J Quantum Chem 109: 1699-1705, 2009