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

TL;DR

This paper extends the Energy Decomposition Analysis-Natural Orbitals for Chemical Valence (EDA-NOCV) method to include four-component relativistic effects, enabling accurate analysis of heavy-element chemical bonds with spin-orbit coupling.

Contribution

The authors develop and validate a four-component relativistic EDA-NOCV method, allowing for comprehensive chemical bond analysis involving heavy and superheavy elements.

Findings

Validated the method on simple molecules with negligible relativistic effects.

Applied the method to transition metal-ethylene bonds across group 6, highlighting relativistic effects.

Provided detailed donation and back-donation analysis in heavy-element coordination bonds.

Abstract

Chemical bonding is a ubiquitous concept in chemistry and it provides a common basis for experimental and theoretical chemists to explain and predict the structure, stability and reactivity of chemical species. Among others, the Energy Decomposition Analysis (EDA, also known as the Extended Transition State method) in combination with Natural Orbitals for Chemical Valence (EDA-NOCV) is a very powerful tool for the analysis of the chemical bonds based on a charge and energy decomposition scheme within a common theoretical framework. 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-C$_2$H$_4$, 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 (also in combination with the CD analysis) 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.