The derivation of the total induced current density vector
field,
in the presence of static and uniform magnetic and electric fields,
is illustrated in a more clear and formally correct language together
with a discussion on the charge-current conservation law not presented
before for the spin–orbit coupling contribution. The theory
here exposed turns out to be in fully agreement with the theory of
Special Relativity and it is applicable to open-shell molecules in
the presence of a nonvanishing spin orbit coupling. The discussion
here exposed turns out to be accurately valid for a strictly central
field due to the chosen approximation of the spin–orbit coupling
Hamiltonian, but it is appropriate to deal correctly with molecular
systems. The ab initio calculation of spin current densities has been
implemented at both unrestricted Hartree–Fock and unrestricted
DFT levels of theory. Some maps of spin currents on molecules of interest,
i.e., the CH3radical and the superoctazethrene molecule
are also illustrated.