Relativistic Prolapse-Free Gaussian Basis Set of Quadruple-ζ Quality: (aug-)RPF-4Z. II. The d-Block Elements

Relativistic Effects in Ligand Field Theory (I): Optical Properties of d1 Atoms in Oh' Symmetry

Ligand field theory, which explains the splitting of degenerate nd atomic orbitals due to static electric fields from point-charge ligands, is rederived using Dirac orbitals instead of Schrödinger orbitals, specifically using the nd3/2 and nd5/2 spinors. This formalism is, to some extent, equivalent to incorporating the spin-orbit interaction either in the nd atomic orbitals or in the ligand field orbitals (e.g., the t2g and eg orbitals arising from Oh symmetry). The spin-orbit interaction is of fundamental importance in the description of the magnetic and optical properties of the 4d and 5d transition metal complexes. Algebraic equations for the relativistic energy levels of d1 octahedral complexes as functions of the spin-orbit coupling constant ξnd and the ligand field parameters Dq and Dp are derived. It is demonstrated that these parameters allow a direct link between the ligand field theory and ab initio relativistic calculations, consistent with the emerging ab initio ligand field theory. The spin-orbit coupling constant and ligand field parameters of ReF6 obtained from optical absorption spectra are carefuly in the light of the new theory.

The relativistic effects on the methane activation by gold(I) cations

The reactivity of gold has been investigated for a long time. Here, we performed an in-depth analysis of relativistic effects over the chemical kinetic properties of elementary reactions associated with methane activation by gold(I) cations, CH₄ + Au⁺ ↔ AuCH₂ ⁺ + H₂. The global reaction is modeled as a two-step process, CH₄ + Au⁺ ↔ HAuCH₃ ⁺ ↔ AuCH₂ ⁺ + H₂. Moreover, the barrierless dissociation of the initial adduct between reactants, AuCH₄ ⁺, is discussed as well. Higher-order relativistic treatments are used to provide corrections beyond the commonly considered scalar effects of relativistic effective core potentials (RECPs). Although the scalar relativistic contributions predominate, lowering the forward barrier heights by 48.4 and 36.1 kcal mol^-1, the spin-orbit coupling effect can still provide additional reductions of these forward barrier heights by as much as 9% (1.0 and 2.2 kcal mol^-1). The global reaction proceeds rapidly at low temperatures to the intermediate attained after the first hydrogen transfer, HAuCH₃ ⁺. The relativistic corrections beyond the ones from RECPs are still able to double the rate constant of the CH₄ + Au⁺ → HAuCH₃ ⁺ process at 300 K, while the reverse reaction becomes five times slower. The formation of global products from this intermediate only becomes significant at much higher temperatures (∼1500 K upward). The scalar relativistic contributions decrease the dissociation energy of the initial adduct, AuCH₄ ⁺, into the global products by 105.8 kcal mol^-1, while the spin-orbit effect provides an extra lowering of 1.8 kcal mol^-1.