Electron density and Fisher information of Dirac-Fock atoms

Numerical calculations on the gradient and Laplacian forms of the position space Fisher information measure are reported using the 1-normalised Dirac-Fock densities (shape function), σ(r), for atoms H-Lr. It is shown that the difference in effective electrostatic potentials, corresponding to the gradient and the Laplacian form of Fishers' information, is completely defined by the shape function (the density per particle) at the nucleus, σ(r=0). The influence of relativistic effects on the Fisher information is recovered for the first time.