The formalism of the spin-partitioned total position spread (SP-TPS) tensor is applied to model systems treated at ab initio level. They are hydrogen linear chains having different geometries and showing qualitatively different behaviors. Indeed, the SP-TPS behavior depends in a crucial way on the entanglement properties of the chain wave function. It is shown that the SP-TPS tensor gives a measure of the spin delocalization in the chain. This is very low in the case of isolated fixed-length dimers and maximal for chains of equally spaced atoms. The present formalism could be used to describe, for instance, the spin fluctuation associated with spintronic devices.