Relationship between electron spin resonance g-values and covalent bonding in tetragonal copper(II) compounds

Abstract

The relationship between the e.s.r. g-values and MO expansion coefficients in tetragonal copper(II) compounds is discussed. Detailed expressions for g_‖ and g⊥ are derived and all relevant integrals are evaluated, by use of Hartree–Fock wave functions, for typical systems. The g-values of square coplanar CuCl₄^2– are calculated from MO coefficients found by semi-empirical calculations, in good agreement with experimental values. The relative importance of the various terms is discussed and the validity of approximations made in previous work is assessed. In particular, we stress the importance of matrix elements involving charge transfer states and the need to take proper account of ligand–ligand and metal–ligand overlap integrals. We conclude that the expressions normally used in the estimation of bonding parameters from e.s.r. data are seriously incomplete, and many of the usual approximations are difficult to justify. The application of e.s.r. to the study of the binding of axial ligands is discussed. Although terms involving axial ligands make very little direct contribution to the g-values, it should be possible to detect the influence of these ligands on the equatorial metal–ligand distance by measuring g_‖, even in the absence of reliable optical data on the d–d excited states. This is demonstrated by correlating e.s.r. data with a theoretical measure of the tetragonality for some tetra-ammine complexes of copper(II). It is not possible to use the anisotropy of the g-tensor in order to assess the relative extent of in-plane and out-of-plane π-bonding. However, the complete expressions derived for g_‖ and g⊥ help to rationalise some features of the e.s.r. spectra of tetragonal copper(II) systems.