Chemical bond analysis for the entire periodic table: energy decomposition and natural orbitals for chemical valence in the four-component relativistic framework

The Energy Decomposition Analysis in combination with Natural Orbitals for Chemical Valence (EDANOCV) is a very powerful tool for the analysis of the chemical bonds. While the approach has been applied in a variety of chemical contexts, the current implementations of the EDA-NOCV scheme include relativistic effects only at scalar level, so simply neglecting the spin-orbit coupling effects and de facto limiting its applicability. In this work, we extend the EDA-NOCV method to the relativistic four-component Dirac-Kohn-Sham theory that variationally accounts for spin-orbit coupling. Its correctness and numerical stability have been demonstrated in the case of simple molecular systems, where the relativistic effects play a negligible role, by comparison with the implementation available in the ADF modelling suite (using the non-relativistic Hamiltonian and the scalar ZORA approximation). As an illustrative example we analyse the metal-ethylene coordination bond in the group 6-element series (CO)(5)TM-C2H4, with TM = Cr, Mo, W, Sg, where relativistic effects are likely to play an increasingly important role as one moves down the group. The method provides a clear measure of the donation and back-donation components in coordination bonds, even when relativistic effects, including spin-orbit coupling, are crucial for understanding the chemical bond involving heavy and superheavy atoms.