What Density Functional Theory could do for Quantum Information

Ann Elisabet Wills

Ágnes Nagy

According to the density functional theory, the density contains sufficient information to compute the value of any observable. It is shown that the Fisher information density also includes this knowledge. The Fisher information density functional theory is constructed. The variational principle is extended to the energy as a functional of the Fisher information density. Hohenberg-Kohn-like theorems are shown to be valid.

Ángel Rubio

Viraht Sahni, Xiao‐Yin Pan

Hugo J. Bohórquez

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.

Ágnes Nagy

The Euler equation of the density functional theory is derived from the principle of minimum Fisher information. Both time-independent and time-dependent cases are analyzed. It is shown that Fisher information is a measure of the quality of the approximate density.