Relationship between the Dipole Strength of Ligand Pre-Edge Transitions and Metal−Ligand Covalency

The electric dipole contributions to the observed pre-edge intensities in ligand K-edge X-ray absorption (XAS) spectra are analyzed in terms of covalent-bonding contributions between the metal and ligand for a prototype system with one hole in the d shell. One- and two-center contributions to the intensity are identified. By direct evaluation of the integrals involved in the intensity expression, the two-center terms are shown to be at least 1 order of magnitude smaller than the one-center terms and can be ignored to a reasonable approximation. The one-center terms reflect the amount of ligand character in the partially occupied metal-based MOs and are proportional to the intrinsic transition moment of a ligand-centered 1s --> np transition. The final intensity does not contain terms proportional to the square of the metal-ligand distance as might have been expected on the basis of the analogy between ligand K-edge and ligand-to-metal charge transfer (LMCT) transitions that both formally lead to transfer of electron density from the ligand to the metal. This is due to the fact that the transition density is completely localized on the ligand in the case of a ligand K-edge transition but is delocalized over the metal and the ligand in the case of a LMCT transition. The effective nuclear charge dependence of the one-center transition moment integral was studied by Hartree-Fock level calculations and was found to be small. Electronic relaxation effects were considered and found to be small from a Hartree-Fock calculation on a cupric chloride model.