Relationship Between the Metallicity Index and Other Topological Characteristics of Chemical Bonding

Expressions are derived for the relationship between the metallicity index m with the ratio of the absolute value of the potential electron energy density (V) to the kinetic energy density (G) at the bond critical point (BCP) using the quantum theory of atoms in molecules (QTAIM) and the electron localization function (ELF) value at the BCP. It is found that the ELF maximum (ELFBCP = 1) is achieved at $$\xi _{m}^{\text{BCP}}=-4$$ . It is shown that calculated $$\xi _{m}^{\text{BCP}}$$ values should not exist in a range $$-4<\xi _{m}^{\text{BCP}}<-1$$ . The $$\xi _{m}^{\text{BCP}}$$ values are calculated and analyzed for some simple molecules and crystals.