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Chemical bonding is a ubiquitous concept in chemistry and it provides acommon basis for experimental and theoretical chemists to explain and predictthe structure, stability and reactivity of chemical species. Among others, theEnergy Decomposition Analysis (EDA, also known as the Extended Transition Statemethod) in combination with Natural Orbitals for Chemical Valence (EDA-NOCV) isa very powerful tool for the analysis of the chemical bonds based on a chargeand energy decomposition scheme within a common theoretical framework. Whilethe approach has been applied in a variety of chemical contexts, the currentimplementations of the EDA-NOCV scheme include relativistic effects only atscalar level, so simply neglecting the spin-orbit coupling effects and de factolimiting its applicability. In this work, we extend the EDA-NOCV method to therelativistic four-component Dirac-Kohn-Sham theory that variationally accountsfor spin-orbit coupling. Its correctness and numerical stability have beendemonstrated in the case of simple molecular systems, where the relativisticeffects play a negligible role, by comparison with the implementation availablein the ADF modelling suite (using the non-relativistic Hamiltonian and thescalar ZORA approximation). As an illustrative example we analyse themetal-ethylene coordination bond in the group 6-element series(CO)$_5$TM-C$_2$H$_4$, with TM =Cr, Mo, W, Sg, where relativistic effects arelikely to play an increasingly important role as one moves down the group. Themethod provides a clear measure (also in combination with the CD analysis) ofthe donation and back-donation components in coordination bonds, even whenrelativistic effects, including spin-orbit coupling, are crucial forunderstanding the chemical bond involving heavy and superheavy atoms.

Chemical bond analysis for the entire periodic table: Energy  Decomposition and Natural Orbitals for Chemical Valence in the Four-Component  Relativistic Framework