Theoretical Investigation of Linear Relationships between the Dihedral Torsion Angles and Diosmium Bond Distances in Diosmium Sawhorse Complexes

Strong linear relationships between their Ceq–Os–Os–Ceq dihedral angles and their Os–Os bond distances in diosmium sawhorse complexes Os2(u-O2CR)2(CO)4L2 (L = CO and/or PR3) form two trendlines depending upon the presence or absence of terminal phosphines. These trends appear unrelated to the basicity of the bridging ligand or the number of phosphines. The mathematical derivation of the relationship between the O–Os–Os–O dihedral angle and the Os–Os bond distance shows how the other geometric parameters affect this relationship. Optimized density functional theory (DFT) structures reveal a similar strong linear correlation, where more electron-donating ligands render shorter Os–Os bond distances and larger dihedral angles, but these results form a single trendline. Computational scans of individual parameters show that the Os–Os bond responds strongly to changes in the dihedral angles, but the dihedral angles only respond weakly to changes in the Os–Os bond distance because the Os–Os–O bond angle links and modifies their direct coupling. Solid-state analysis of their structures, including DFT geometry optimizations, shows that phosphines protect the Os–Os bond distance from packing influences along the Os–Os axis, while in complexes without phosphines, packing compresses the Os–Os bond and the weak dihedral responses create the second trendline.