Comment on “Scaling properties of information-theoretic quantities in density functional reactivity theory” by C. Rong, T. Lu, P. W. Ayers, P. K. Chattaraj and S. Liu, Phys. Chem. Chem. Phys., 2015, 17, 4977–4988

Abstract

The scaling properties of density functionals are key for fundamentally understanding density functional theory. Accordingly, the dependence of density functionals on the number of particles is of paramount relevance. The numerical exploration by Rong et al. addressed N-scaling for a set of quantum information quantities; they found linear relationships between each one of them and the electronic population for atoms, molecules, and atoms in molecules. The main motivation for their computational work was that the theoretical scaling of these quantities is unknown; however, these scaling properties can be analytically determined. Here I reveal the derivation of the N-scaling rules for the quantities studied by Rong et al. by following the procedure introduced in Comput. Theor. Chem., 2015, 1053, 38. In addition, a new atomic scaling rule explains the linear relationship between atomic populations and atomic values of the same quantum information quantities.