Delocalized relativistic effects: Unraveling cooperative and anticooperative mechanisms

The term "relativistic effects" originates from the history of quantum mechanics and refers to the discrepancies between values calculated by models that consider relativity and those that do not. We introduce a methodology that opens up the possibility of analyzing the mechanisms by which relativistic effects combine in molecular structures containing multiple heavy elements. Through an n-body decomposition of relativistic effects, the individual contributions of each heavy element are revealed, along with collective contributions that can be either cooperative or anticooperative. Illustrations are given of the effects of spin-orbit coupling on total energy, electron density, and the intricate mechanisms by which these effects are transferred through space to the molecular electrostatic potential or the strength of intermolecular interactions. Near a heavy atom, such properties can be significantly more affected by the spin-orbit coupling effects produced by other distant heavy atoms, not bonded to the atom of interest or to each other. For molecular properties, it is shown that the influence of collective components (two-body, three-body, etc.) account for about one-tenth of the total effect of spin-orbit coupling.