Spin Energy Contributions of the Kinetic Energy Density in the Stabilization of the Metal-Ligand Interactions.

The kinetic energy (KE) density plays an essential role in the stabilization mechanism of covalent, polar covalent, and ionic bondings; however, its role in metal-ligand bindings remains unclear. In a recent work, the energetic contributions of the spin densities α and β were studied to explain the geometrical characteristics of a series of metal-ligand complexes. Notably, the KE density was found to modulate/stabilize the spin components of the intra-atomic nucleus-electron interactions within the metal in the complex. Here, we investigate the topographic properties of the spin components of the KE density for a family of high-spin hexa-aquo complexes ([M(H 2 O) 6 ] 2+ ) to shed light on the stabilization of the metal-ligand interaction. We compute the Lagrangian, G ( r ), and Hamiltonian, K ( r ), KE densities and analyze the evolution of its spin components in the formation of two metal-ligand coordination complexes. We study K α/β ( r ) along the metal-oxygen (M-O) internuclear axis as a function of the metal. Our results indicate that K ( r ) is a more distance-sensitive quantity compared to G ( r ) as it displays topographic features at larger M-O distances. Furthermore, K ( r ) allows one to identify the predominant interaction mechanism in the complexes.