Mechanisms of Ligand Hyperfine Coupling in Transition-Metal Complexes: σ and π Transmission Pathways

Theoretical interpretation
of hyperfine interactions was pioneered
in the 1950s–1960s by the seminal works of McConnell, Karplus,
and others for organic radicals and by Watson and Freeman for transition-metal
(TM) complexes. In this work, we investigate a series of octahedral
Ru(III) complexes with aromatic ligands to understand the mechanism
of transmission of the spin density from the d-orbital of the metal
to the s-orbitals of the ligand atoms. Spin densities and spin populations
underlying ligand hyperfine couplings are analyzed in terms of π-conjugative
or σ-hyperconjugative delocalization vs spin polarization based
on symmetry considerations and restricted open-shell vs unrestricted
wave function analysis. The transmission of spin density is shown
to be most efficient in the case of symmetry-allowed π-conjugative
delocalization, but when the π-conjugation is partially or fully
symmetry-forbidden, it can be surpassed by σ-hyperconjugative
delocalization. Despite a lower spin population of the ligand in σ-hyperconjugative
transmission, the hyperfine couplings can be larger because of the
direct involvement of the ligand s-orbitals in this delocalization
pathway. We demonstrate a quantitative correlation between the hyperfine
couplings of aromatic ligand atoms and the characteristics of the
metal–ligand bond modulated by the trans substituent,
a hyperfine trans effect.