Spin localization in intermolecular complexes: A challenge for semi-local approximants for the embedding potential

Regardless of how the electron correlation is treated, all methods based on frozen-density embedding theory rely on approximations to the non-additive kinetic potential bi-functional ṽtnad[ρA,ρB](r)≈vtnad[ρA,ρB](r). Open shell systems, in which the spin is localized on a specific molecular fragment, are particularly prone to incorrect redistribution of charge depending on the used ṽtnad[ρA,ρB]. In this work, we present a systematic analysis of spin densities obtained with several semi-local approximations to vtnad[ρA,ρB], with the aim of delimiting their respective domains of applicability. We show that spin distributions obtained using decomposable semi-local ṽtnad[ρA,ρB] fall into two distinct categories: they are either qualitatively incorrect or reasonably accurate and consistent with trends previously observed for other properties computed using the same approximants. In neither case do gradient-dependent corrections, although crucial for improving the corresponding energy bi-functional (Tsnad[ρA,ρB]), resolve the deficiencies observed for spin densities. We propose a simple criterion based on orbital energies that allows one to identify a priori the situations in which a given approximant is likely to fail. Finally, we show that a recently developed non-decomposable approximant ṽtnad(NDCS)[ρA,ρB] extends the range of applicability of FDET-based methods to embedded radicals that are inaccessible to semi-local approximants. Moreover, ṽtnad(NDCS)[ρA,ρB] yields improved spin densities even in cases where decomposable semi-local approximants already perform reasonably well.