Chemical bonding descriptors based on electron density inhomogeneity measure: a comparison with ELI-D

The electron localizability indicator (ELI-D) is suitable to describe certain aspects of the bonding situation of molecules and solids. ELI-D is based on integrals of electron pair density over very small regions. Recently proposed functional C-p, derived from the electron population in regions of fixed amount of electron density inhomogeneity, is based on the same approach as ELI-D, that is, x-restricted space partitioning. The electron density inhomogeneity is given by the distance of electron density values to the averaged density within chosen region. Thus, in contrast to ELI-D, C-p is a single-electron property. The distance measure depends on a parameter that can be optimized in such way that C-p mimics the topology of the ELI-D distribution for atoms. Such an optimization was performed for the atoms Li to Xe. The optimal parameter p = 0.6 yields the functional C-0.6 that was exemplary applied to a few chosen molecules. In case of molecules the topology of the inner shell and lone-pair regions as given by C-0.6 is comparable with that of the ELI-D representation. However, in the bonding region between the atoms the topology of C-0.6 is dominated by the low density gradient close to the bond critical point. This may result in rather different topologies when comparing C-0.6 and ELI-D.