The Spin-Pair Compositions as Local Indicators of the Nature of the Bonding

The spin-pair compositions at a given point of the position space are defined as the following ratios:  that of the parallel spin-pair concentration to the antiparallel spin-pair concentration Danti(r), to the total spin-pair concentration Dtot(r), and to the single spin-pair concentration Ds(r). The spin-pair concentrations are calculated by the integration of the pair functions παα(r1,r2), παβ(r1,r2), πβα(r1,r2), and πββ(r1,r2) over an arbitrary volume V(r) around the reference point r. Because the numbers of spin pairs are not proportional to the sampling volume, the dependence of the D(r) functions upon the sample size V(r) has been studied. It is shown that all D(r) functions depend on the population N(r) of the sample. For N((r) ≤ 10-3, all D(r) functions behave as N2/3(r); therefore, size-independent spin-pair composition functions are defined as cπ(r) = N2/3(r)D(r). Approximate expressions of the cπ(r) functions are proposed, which enable the recovery of the electron localization function of B...