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The Frozen Density Embedding scheme represents an embedding method in whichenvironmental effects onto a given subsystem are included by representing theother subsystems making up the surroundings quantum mechanically, by means oftheir electron densities. In the present paper, we extend the full 4-componentrelativistic Dirac-Kohn-Sham method, as implemented in the BERTHA code, toinclude environmental and confinement effects with the FDE scheme. Thisimplementation has been enormously facilitated by BERTHA's python API(PyBERTHA), which provides a flexible framework of development by using allPython advantages in terms of code re-usability, portability while facilitatingthe interoperability with other FDE implementations available through the PyADFframework. The computational performance has been evaluated on a series of goldclusters (Au$_n$, with n=2,4,8) embedded into an increasing number of watermolecules (5, 10, 20, 40 and 80 water molecules). We found that the procedurescales approximately linearly both with the size of the frozen surroundingenvironment (in line with the underpinnings of the FDE approach) and with thesize 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_60on their electronic structure. We compare the results from our simulations withmore approximate models employed in the atomic physics literature, in whichconfinement is represented by a radial potential slightly affected by thenature of the central atom. Our results indicate that the specific interactionsdescribed by FDE are able to improve upon the cruder approximations currentlyemployed, and thus provide a basis from which to generate more realistic radialpotentials for confined atoms.

journal of chemical theory and computation

Frozen-Density Embedding for including environmental effects in the  Dirac-Kohn-Sham theory: an implementation based on density fitting and  prototyping techniques