A measure of electron localizability

A functional of the same‐spin electron pair density is proposed as a measure of electron localizability. This functional yields the average number of same‐spin electron pairs in a region Ω enclosing a fixed charge. The functional equals zero if the fixed charge in Ω originates from one electron only, with all other same‐spin electrons outside the region Ω. Then, the correlation of the electronic motion in Ω and thus the localizability of an electron is high. If the motion of the same‐spin electrons becomes less correlated, more electrons participate in the fixed charge contained in Ω, the average number of same‐spin electron pairs (the functional) increases. In the Hartree–Fock approximation the Taylor expansion of the proposed localizability functional can be related to the electron localization function of Becke and Edgecombe without using an arbitrary reference to the uniform electron gas.