A novel class of $σ$/$π$-separating orbital localization functionals

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.