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 …