Complexity of Dirac-Fock atom increases with atomic number

Abstract

Using the Dirac-Fock relativistic wave functions in the position space the shape complexity, C^s_LMC, form of the statistical complexity measure due to López-Ruiz, Mancini, and Calbet and the simple two parameter complexity measure, Γ_α,β, proposed by Shiner, Davison and Landsberg for atoms H-Lr are calculated. A comparison with the non-relativistic Hartee-Fock results is carried out to ascertain the influence of the relativistic effects on complexity. Unlike the non-relativistic Hartree-Fock results, which lead to the non-increasing C^s_LMC, the Dirac-Fock calculations lead to both C^s_LMC and Γ_α,β clearly displaying an increasing trend in complexity as the atomic number increases.