Electron localization function

For example, the shell structure of heavy atoms is obvious when plotting ELF against the radial distance from the nucleus; the ELF for radon has six clear maxima, whereas the electronic density decreases monotonically and the radially weighted density fails to show all shells.

For density functional theory, the approach was generalized by Andreas Savin in 1992,[2] who also have applied the formulation to examining various chemical and materials systems.

[3] In 1994, Bernard Silvi and Andreas Savin developed a method for explaining ELFs using differential topology.

[6] Bader's analysis allows many properties such as multipole moments, energies and forces, to be partitioned in a defensible and consistent manner to individual atoms within molecules.

Both the Bader approach and the ELF approach to partitioning of molecular properties have gained popularity in recent years because the fastest, accurate ab-initio calculations of molecular properties are now mostly made using density functional theory (DFT), which directly calculates the electron density.

Electron localization function of the krypton atom at the Hartree–Fock / cc-pV5Z level of theory. Also shown is the radial density , 4π r 2 ρ ( r ), scaled by a factor of 0.0375.
Image of the ELF of water at level 0.8, generated using PyMOL