Electron localization function (ELF) shows the localization degree of electrons at different locations in threedimensional space. Localization of electrons describes the extent to which its motion is trapped in a particular spatial range. According to Becke's theory, ELF can be expressed by the function, where χ_{σ}(r) is dimensionless localization index. ELF, which facilitates calculation and analysis, is an important approach to studying electronic structure characteristics in quantum chemistry. Therefore, ELF is employed in chemical research such as atomic shell structure, aromaticity, hydrogenation bonds, metal bonds, etc.
Figure 1. Electron localization function analysis (Parise, A.; et al. 2018)
Application of Electron Localization Function Prediction
 ELF can clearly and quantitatively describe chemical bonds and has been widely used to study atoms, molecules, and solid systems.
 ELF can be used to investigate the atomic shell structures, chemical bonds, the position of lone pair electrons, the breaking, and the generation of chemical bonds in the reaction process.
 ELF studies the degree of electronic localization in the external field of different positions and can be used to analyze the dynamic changes of chemical bonds in pattern scattering.
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 HartreeFock theory can be used to calculate ELF
HartreeFock is commonly used to calculate the electronelectron interaction energy. The core idea of this theory is the average field approximation, which applies to the overall effect of an electron by other electrons that an equivalent field can represent. Unlike DFT, the HartreeFock method only considers the exchange of energy between electrons and electrons. At Alfa Chemistry, we use the HartreeFock approach to complete the ELF calculation via accurate nonlocal exchange and hybrid functionals.
 Based on ELF, we can provide topological analysis, dynamic changes analysis of chemical bonds and electron dynamics:
1. We utilize some important methods in topological analysis, such as critical points, to analyze the threedimensional realspace in ELF.
2. Our teams can make an animation of the ELF isosurface to show the changes in the electronic structure.
3. Our ELF can also be applied to perform electronic structure calculations and quantum mechanicsmolecular dynamics simulations.
 Electron localization function is critical for the development of novel algorithms and we have a great wealth of experience in this service
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Alfa Chemistry can offer you but not limited to the following
 Hydrogen bonds and halogen bonds calculation
We apply ELF to observe whether there are bonds between atoms and perform an ELF analysis to demonstrate some weak interactions between molecules, including hydrogen bonds as well as halogen bonds. The strength of the interaction can be determined by color in the ELF isosurface, and the ELF value between the two bonding atoms is different can be used to conduct the calculation.
 Molecular orbital analysis
ELF is an effective tool to analyze the degree of electronic localization, such as analyzing the electron shell arrangement. Therefore, we use this method to distinguish the nuclear state and the valence state. Moreover, ELF can display the covalent bond and the unshared electron pair to help in analyzing the molecular orbital.
 Chemical reaction mechanism calculation
ELF function can be used not only to discuss the static characteristics of molecules but also to study the process of chemical reactions. Our teams use it to observe the appearance, disappearance, range and shape of the bond region and lone pair electrons in the reaction path. In the chemical reaction process, the ELF values can be treated as a continuous and differentiable scalar field in 3D space. The maxima of ELF (critical points) are named attractors and are located on atoms, bonds, and lone pairs following chemical intuition. We analyze the reaction's progress and calculate the related mechanism by monitoring the changes of ELF structural stability domains associated with a sequence of elementary chemical steps.
 Excited state structure determination
The excited state refers to the state in which electrons are excited to a higher energy level but not yet ionized after atoms or molecules absorb a certain amount of energy. Our experts utilize the ELF approach to characterize the distribution characteristics of electrons and we determine the excited state structure by observing whether the electron is in the larger radius of the atom.
Alfa Chemistry provides fast, specialized, highquality electron localization function prediction services at competitive prices for global customers. Personalized and customized service of electron localization function prediction satisfies innovative scientific study demands. Our clients have direct access to our staff and prompt feedback to their inquiries. If you are interested in our services, please contact us for more details.
Reference
 Parise, A.; et al. Quantum chemical topology of the electron localization function in the field of attosecond electron dynamics. J. Phys. Chem. Lett. 2018, 9(4), 844850.