Electron-Spin Structure and Metal-Ligand Bonding in Open-Shell Systems from Relativistic EPR and NMR: A Case Study of...

Electron and nuclear magnetic resonance spectroscopies are indispensable and powerful methods for investigating the molecular and electronic structures of open-shell systems. We demonstrate that the NMR and EPR parameters are extremely sensitive quantitative probes for the electronic spin density around heavy-metal atoms and the metal-ligand bonding. Using relativistic density-functional theory, we have analyzed the relation between the spin density and the EPR and NMR parameters in paramagnetic iridium(II/IV) complexes with a PNP pincer ligand. As the magnetic-response parameters for compounds containing 5d transition metal(s) are heavily affected by spin-orbit coupling, relativistic effects must be included in the calculations. We have used a recent implementation of the fully relativistic Dirac-Kohn-Sham (DKS) method employing the hybrid PBE0 functional and an implicit solvent model to calculate EPR parameters and hyperfine NMR shifts. The modulation of the metal-ligand bond by the trans substituent (-Cl or ≡N) and the electronic spin structure around the central metal atom and ligands are shown to be reflected in the "long-range" through-bond Fermi-contact (FC) contributions to the ligand ¹³C and ¹H hyperfine couplings. Interestingly, the hyperfine coupling constant of the ligand atom L ( A_L) bonded directly to the iridium center changes its sign because of the dominating role of the paramagnetic spin-orbit (PSO) term. Furthermore, the electronic g-shift and the PSO contribution to the ligand A_L are shown to invert their signs when nitrogen is substituted for chlorine, reflecting the different formal metal oxidation states and the change in metal-ligand bond character. A full understanding of the substituent effects is provided by using chemical bond concepts in combination with a molecular-orbital (MO) theory analysis of the second-order perturbation theory expression for the EPR parameters. Our findings are easily transferable to other systems containing d-block elements and beyond. Relativistic DFT calculations of magnetic-resonance parameters are expected to frequently assist in future experimental observations and the characterization of hitherto unknown unstable or exotic species.