Partial Sigma Covalent Bonding in Transition Metals

This work establishes partial σ-covalent bonding as a general electronic phenomenon extending from main-group biradicals to d⁸-d⁸ transition-metal systems (Co(I), Rh(I), Ir(I)). Using dispersion-corrected DFT (B3LYP-D3/def2-TZVP for transition metals and 6-31+G(d) for other elements) in combination with Wiberg bond index and frontier molecular orbital analyses, we show that partial σ-bonding is strongly governed by ligand field and orbital symmetry. While shorter metal-metal distances correlate with larger bond orders, singlet-triplet energetic differences arise from competition between ligand-field splitting and exchange energy and spin-orbit coupling. Compared to isolated metal-metal ion dimers at the same distance, both ligand types in the study modify not only the orbital characters but also the frontier orbital energy levels. Strong field C-donor ligands significantly widen the HOMO-LUMO gap while changing orbital ordering so that the HOMO has d_z ²-d_z ² antibonding character and the LUMO has a bonding p_z-p_z orbital. Consequently, it leads to triplet-dominant metal-metal bonding, (WBO_Triplet = 0.4; d_M-M = 2.9 Å). In contrast, N-donor lantern organic frameworks (LOFs) narrow the HOMO-LUMO gap while alternating orbital ordering so that the HOMO becomes the ligand-based bonding π-orbital and the LUMO corresponds to a d_z ²-d_z ² antibonding orbital, thereby enabling substantial σ-bonding in both spin states (WBO_Triplet = 0.3 with d_M-M = 3.1 Å; and WBO_Singlet = 0.7 with d_M-M = 2.7 Å). More importantly, N-donor LOF environments significantly reduce the HOMO-LUMO gap up to 2.00 eV relative to comparable conventional systems, suggests a viable strategy for band gap engineering at the single-unit-cell level, without requiring infinite stacking.