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This study introduces a new class of orbital localization functionals that effectively separate $\sigma$- and $\pi$-orbitals, addressing a significant limitation in existing methods that hinder accurate descriptions of chemical bonding and reactivity. By leveraging nucleus-electron physical observables, the proposed functionals enhance the precision of chemical analysis in molecular systems. The authors also outline a general mechanism for creating additional $\sigma/\pi$-separating functionals, expanding the toolkit available for quantum chemists.
A new class of localization functionals can now accurately separate $\sigma$ and $\pi$ orbitals, revolutionizing our understanding of chemical bonding.
Orbital localization methods have a long history in quantum chemistry, as they provide a convenient way to describe individual chemical bonds and local properties. However, only a handful of localization functionals are known up to date, and most localization methods do not separate $\sigma$- and $\pi$-orbitals, which is important to describe chemical bonding patterns and reactivity. In this work, we present a new class of localization functionals, based on nucleus-electron physical observables, that preserve $\sigma$- and $\pi$-orbitals separation in molecular systems. We also present a general mechanism behind $\sigma/\pi$-separating variational localization which can be used for constructing a broader class of $\sigma/\pi$-separating localization functionals from other local physical quantities.