# Spin Energy Contributions of the Kinetic Energy Density in the Stabilization of the Metal–Ligand Interactions

## TL;DR

This paper explores how kinetic energy density affects the stability of metal-ligand bonds, focusing on spin components in hexa-aquo complexes.

## Contribution

The study introduces a novel analysis of spin components of kinetic energy density in metal-ligand stabilization mechanisms.

## Key findings

- K(r) is more distance-sensitive than G(r), showing features at larger metal–oxygen distances.
- K(r) helps identify the predominant interaction mechanism in metal–ligand complexes.
- Spin components of KE density modulate nucleus–electron interactions in metal complexes.

## Abstract

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(H2O)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 Kα/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.