Partial Sigma Covalent Bonding in Transition Metals

ABSTRACT This work establishes partial σ‐covalent bonding as a general electronic phenomenon extending from main‐group biradicals to d 8 –d 8 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.