The Many-Electron Perspective on Local Spins and their Implication for Chemical Bonding

The concept of local spin has become an important tool for analyzing chemical bonding, yet, as a nonobservable quantity, there is no unique definition leading to a multitude of different approaches. In this work, a general framework for evaluating local spin distributions is developed within probability density analysis (PDA), where the many-electron probability density |Ψ|2 is analyzed directly. Within this framework, the influence of spin multiplicity is explicitly accounted for. The method is applied to a range of molecules containing first-row elements and hydrogen. The analysis reveals that covalent bonding is directly reflected in the exchange of opposite-spin electrons, manifesting as redistributions of the local spin weights. Furthermore, local spin distributions tending toward higher local spin states are associated with increased electron delocalization. Clear connections between local spin distributions, molecular geometry, the hybridization model, and molecular orbital theory are established. This real-space definition establishes a theory-independent, real-space framework in which local spins and chemical bonding can be understood directly from the many-electron wave function.