  A formulation for the efficient calculation of the electromagnetic retarded
potential generated by time-dependent electron density in the context of
real-time time dependent density functional theory (RT-TDDFT) is presented. The
electron density is considered to be spatially separable, which is suitable for
systems that include several molecules or nano-particles. The formulation is
based on splitting the domain of interest into sub-domains and calculating the
time dependent retarded potentials from each sub-domain separately. The
computations are accelerated by using the fast Fourier transform and
parallelization. We demonstrate this formulation by solving the orbitals
dynamics in systems of two molecules at varied distances. We first show that
for small distances we get exactly the results that are expected from
non-retarded potentials, we then show that for large distances between
sub-domains we observe substantial retardation effects.
