Many Body Current Density from Foldy–Wouthuysen Transformation of the Dirac–Coulomb Hamiltonian

This paper analyzes how special relativity changes the equation for many-body-induced current density starting from Foldy–Wouthuysen diagonalization of Dirac–Coulomb Hamiltonian. differs that obtained with Gordon decomposition due to presence a spin-orbit coupling contribution not considered before many-body molecular systems. diverges on atomic nuclei nature point charges in nonrelativistic approach, demonstrating conventionally used methods are suitable dealing spin effects such as or smaller than α2, α fine structure constant, and fully relativistic approach finite charge should be used. Despite singularity, becomes an important total open-shell systems high-spin multiplicity high number nuclear proximity. On long ranges, this is overcome by Coulomb potential derived electric field which decays very quickly small distances charges. An evaluation has been performed linear response at HF/DFT level theory.