Spin localisation 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 potentialbifunctional ~vnadt [ρA;ρB](r) ≈ vnadt [ρA;ρB](r). Open shell systems in which thespin is localized on a speci c molecular fragment are particularly prone to incorrectredistribution of charge depending on the used ~vnadt [ρA;ρB](r). In this work, we present asystematic analysis of spin densities obtained with several semi-local approximations to vnadt [ρA;ρB](r) with the aim of delimiting their respective domains of applicability. Weshow that spin distributions obtained using decomposable semi-local ~vnadt [ρA;ρB](r) fallinto two distinct categories: they are either qualitatively incorrect, or reasonably accurateand consistent with trends previously observed for other properties computed usingthe same approximants. In neither case do gradient-dependent corrections, althoughcrucial for improving the corresponding energy bifunctional (Tnads [ρA;ρB]), resolve thede ciencies 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 approximantis likely to fail. Finally, we show that a recently developed non-decomposable approximant~vnadt [ρA;ρB](r) extends the range of applicability of FDET-based methodsto embedded radicals that are inaccessible to semi-local approximants. Moreover,~vnadt [ρA;ρB](r) yields improved spin densities even in cases where decomposablesemi-local approximants already perform reasonably well.