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In this paper, we present a novel approach to track the origin of the metal complex structure from the topology of the α and β spin densities as an extension of the Linnett-Gillespie model. Usually, the theories that explain the metal-ligand interactions consider the disposition and the relative energies of the empty or occupied set of d orbitals, ignoring the spin contribution explicitly. Our quantum topological approach considers the spatial distribution of the α and β spin valence shells, and the energy interaction between them. We used the properties of the atomic graph, a topological object that summarises the charge concentrations and depletions on the valence shell of an atom in a molecule, and the interacting quantum atoms (IQA) energy partition scheme. Unlike the Linnett-Gillespie model, which is based on electron-electron repulsion, our approach states that the ligands provoke a redistribution of the electron density to maximize the nuclear-electron interactions in each spin valence shell to bypass the concentration of electron-electron interactions, resulting in a polarization pattern which determines the position of the ligands.

Quantum Chemical Topology (QCT) is a well established structural theoretical approach, but the development of its reactivity component is still a challenge. The hypothesis of this work is that the reactivity of an atom within a molecule is a function of its electronic population, its delocalization in the rest of the molecule, and the way it polarizes within an atomic domain. In this paper, we present a topological reactivity predictor for cabonyl additions, κ. It is a measure of the polarization of the electron density with the carbonyl functional group. κ is a model obtained from a QSAR procedure, using quantum-topological atomic descriptors and reported hydration equilibrium constants of carbonyl compounds. To validate the predictive capability of κ, we applied it to organic reactions, including a multicomponent reaction. κ was the only property that predicts the reactivity in each reaction step. The shape of κ can be interpreted as the change between two electrophilic states of a functional group, reactive and non-reactive.