Electron localization function
In quantum chemistry, the electron localization function (ELF) is a measure of the likelihood of finding an electron in the neighborhood space of a reference electron located at a given point and with the same spin. Physically, this measures the extent of spatial localization of the reference electron and provides a method for the mapping of electron pair probability in multielectronic systems.
ELF's usefulness stems from the observation that it allows electron localization to be analyzed in a chemically intuitive way. For example, the
The ELF was originally defined by Becke and Edgecombe in 1990.[1] They first argued that a measure of the electron localization is provided by
where ρ is the electron
The ratio,
is a
ELF = 1 corresponding to perfect localization and ELF = ½ corresponding to the electron gas.
The original derivation was based on
The approach of electron localization, in the form of atoms in molecules (AIM), was pioneered by Richard Bader.[5] Bader's analysis partitions the charge density in a molecule to "atoms" according to zero-flux surfaces (surfaces across which no electron flow is taking place).[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. This electron density is then analyzed using the Bader charge analysis of Electron Localization Functions. One of the most popular functionals in DFT was first proposed by Becke, who also originated Electron Localization Functions.
References
- ^ doi:10.1063/1.458517.
- .
- ISSN 0570-0833.
- S2CID 4362878.
- ISBN 978-0-19-855865-1.
- S2CID 120944734.
External links
- Frank R. Wagner (ed.) Electron localizability: chemical bonding analysis in direct and momentum space. Max-Planck-Institut für Chemische Physik fester Stoffe, 2002. (accessed 2008-09-02).