  The Frozen Density Embedding scheme represents an embedding method in which
environmental effects onto a given subsystem are included by representing the
other subsystems making up the surroundings quantum mechanically, by means of
their electron densities. In the present paper, we extend the full 4-component
relativistic Dirac-Kohn-Sham method, as implemented in the BERTHA code, to
include environmental and confinement effects with the FDE scheme. This
implementation has been enormously facilitated by BERTHA's python API
(PyBERTHA), which provides a flexible framework of development by using all
Python advantages in terms of code re-usability, portability while facilitating
the interoperability with other FDE implementations available through the PyADF
framework. The computational performance has been evaluated on a series of gold
clusters (Au$_n$, with n=2,4,8) embedded into an increasing number of water
molecules (5, 10, 20, 40 and 80 water molecules). We found that the procedure
scales approximately linearly both with the size of the frozen surrounding
environment (in line with the underpinnings of the FDE approach) and with the
size of the active system (in line with the use of density fitting). Finally,
we applied the code to a series of Heavy (Rn) and Super-Heavy elements (Cn, Fl,
Og) embedded in a C_60 cage to explore the confinement effect induced by C_60
on their electronic structure. We compare the results from our simulations with
more approximate models employed in the atomic physics literature, in which
confinement is represented by a radial potential slightly affected by the
nature of the central atom. Our results indicate that the specific interactions
described by FDE are able to improve upon the cruder approximations currently
employed, and thus provide a basis from which to generate more realistic radial
potentials for confined atoms.
