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

Abstract

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 σhyperconjugative 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 ef fect.

Paramagnetic Effects in NMR Spectroscopy of Transition-Metal Complexes: Principles and Chemical Concepts

“…In prototypical Ru­(III) compounds with pyridine ligands, concepts of σ-donation and π-backdonation have been used to describe the bond between the ruthenium and nitrogen atoms (Figure ). Note that the spin delocalization is quenched in this arrangement because of the unfavorable symmetry of the SOMO . The first σ-channel represents a classical donation of the lone pair of electrons of the nitrogen atom to M. This is slightly more efficient in the α-space (Hund’s rule), thus leaving an overabundance of β density in the σ-space of pyridine.…”

“…The spin delocalization can be defined as the distribution of α-spin density over the atoms with nonzero atomic coefficients in singly occupied molecular orbital(s), SOMO(s), calculated at the spin-restricted level . This can be clearly seen in the example of the N -methylen-4-methyl-pyridinium radical (NMP) depicted in Figure a.…”

“…We start our discussion of concepts with the FC mechanism arising from the propagation of spin density from the paramagnetic center M toward the spectator atom L via chemical bonds . This includes spin delocalization based on electron conjugation (π-space) and hyperconjugation (σ-space) interactions and is further complemented by neighbor-atom or resonance spin polarization steps manifesting Hund’s rule of maximum multiplicity and Pauli’s exclusion principle …”

“…The situation is different for systems with different symmetries of the SOMO relative to the pyridine π-space and the absence of its conjugation. This applies to the NMP with a CH 2 group rotated by 90° in the transition state shown in Figure a.…”

“…Visualization of the hyperconjugation delocalization of the α-spin density in σ-space and the total atomic spin populations of (a) the transition state of NMP and (b) Cu­(acac) 2 calculated at the spin-restricted DFT level (left), with the polarization shown at the spin-unrestricted approach (right). Note the β-spin polarization of the outer shell of the Cu atom. , Adapted with permission from refs and . Copyright 2021 and 2024 American Chemical Society.…”