Tractable spin-pure methods for bond breaking: Local many-electron spin-vector sets and an approximate valence bond model

For a given number of electrons, total spin, and matching spin z-component, we construct a set that spans the many-electron spin subspace associated with these spin values. Each vector in the set is tensorially related to spin-pure vectors of six electrons or less. We show that in the limit of separated atoms coupled to any allowed overall spin, the corresponding spin vector has a simple form relative to the introduced sets. From this, we set up a model that is computationally simple, spin pure, size consistent, and able to properly treat molecules as they dissociate into atoms or fragments.