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

AbstractThe Energy Decomposition Analysis in combination with Natural Orbitals for Chemical Valence (EDA-NOCV) 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)5TM-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.Keywords: Relativistic effetcschemical bondEnergy decomposition Analysis AcknowledgmentsL. B. and P. B. acknowledge Università degli Studi di Perugia and MUR, CNR for support within the project Vitality. L. B. and L. S. thank all the attendances at the REHE conference held in September 2022 in Assisi (Italy) for stimulating discussions which inspired this work.Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 Note that the number of NOCV pairs is equal to the number (N) of occupied spin orbitals, which is 20 in the case of the water dimer. For closed-shell systems, the α and β spin orbitals provide exactly the same contribution, which is implicitly accounted for in the ADF implementation by doubling the eigenvalue and by denoting the NOCV pairs from 1 to the number of spatial orbitals (N/2), avoiding any reference to spin. In BERTHA these degenerate contributions appear naturally as Kramers pairs, which for simplicity are summed up for direct comparison with the ADF results.Additional informationFundingThis work received financial support from ICSC-Centro Nazionale di Ricerca in High Performance Computing, founded by European Union-Next-Generation-UE-PNRR, Missione 4 Componente 2 Investimento 1.4. CUP: B93C22000620006. Research at SCITEC-CNR has been funded by the European Union – NextGenerationEU under the Italian Ministry of University and Research (MUR) National Innovation Ecosystem grant ECS00000041 – VITALITY.