An In-Depth Study on the Relativistic Thomas–Fermi Model: Improvements and Numerical Simulations

The relativistic Thomas–Fermi model is revisited in the framework of von Weizsacker's kinetic energy functional. This model, already studied by other authors, is optimized by weighting the von Weizsacker functional with a numerical parameter and introducing a retardation term in the potential energy functional to improve its predictivity when applied to systems with a complex electronic structure. These corrections avoid overestimating the total kinetic energy and underestimating the stabilizing effect of the Coulomb potential, respectively. The model is applied to neutral and ionized atoms with increasing atomic numbers to test the qualitative and quantitative predictivity goodness of the relativistic effects. Due to the simplicity of solving the relativistic equation by numerical methods, the proposed model could be an alternative or a supportive tool to other computational methods for studying the physicochemical properties of compounds containing heavy atoms.