Topological population analysis and pairing/unpairing electron distribution evolution: Atomic B3 cluster bending mode, a case study.

Local and non-local topological treatment of electronic distributions are applied to a simple out of equilibrium case of an electron-deficient three-atom cluster, B3. The bending movement is described in detail through the onset and disappearance of critical points defining two kinds of molecular structures, characterizing a transition state (TS) and predicting two stable equilibrium geometries. All points in this rich evolution and the structural change in the out of equilibrium conformations has been featured and distinguished by the behavior of the population magnitudes and of the paired and unpaired electron densities within the non-local and local points of view of the topological formalism. The unpaired or electron hole density appears as relevant in both versions, the non-local or integrated one, in which it is sometimes called free-valence and also for its complementary counterpart, the local one, to describe and to quantify the interatomic interactions. The stability of the cluster B is characterized in terms of a topologically defined ring structure and the highest total two- and three-center populations, thus showing the role of the geometry, the covalence, and the complex patterns. Consideration of the electron correlation effects constitutes the basement of the results gathered, thus displaying their influence in the formation and breaking of boron bonding interactions.