Electron localization in molecules and solids: The meaning of ELF

The orbital underpinnings of the electron localization function (ELF), devised by Becke and Edgecombe, are explored in terms of an interpretation of the dominant term in this expression, rho(-5/3)Sigma(i)\del psi(i)\(2). High Sigma(i)\del psi(i)\(2) implies large electronic kinetic energy and electron delocalization. It is shown how this arises in practice through the population of noded wave functions. Such an approach provides an attractive way with which to view electron localization in systems that obey the Hund localization condition, hypervalent and electron-deficient molecules, and metals and insulators. ELF is shown to provide a description of the term "electron localization" that is highly self-consistent when interpreted in terms of nodes and also consistent with many of the present uses of the term.