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10.5 Visualizing and Plotting Orbitals, Densities, and Other Volumetric Data

10.5.7 Electron Localization Function

(February 4, 2022)

Formulated by Becke and Edgecombe,70 the electron localization function (ELF),

ELF=[1+(τσ-(ρσ)24ρσ35(6π2)2/3(ρσ5/3))2]-1 (10.22)

is a measure of electron localization. It is derived from the Hartree-Fock conditional pair probability and can reveal information about bonding and shell structure.337 The function ELF(𝐫) has values that lie between 0 and 1, with ELF=1 representing perfect localization and ELF=1/2 representing electron-gas-like pair probability. To generate ELF plots with Q-Chem, set the PLOT_ELF $rem variable to TRUE. For closed-shell systems, only the α-spin ELF is calculated whereas for open-shell systems (spin-unrestricted calculations), both α- and β-spin ELFs are computed.580

The following example illustrates the calculation of the ELF for a water molecule.

Example 10.17  A job that evaluates the ELF for H2O on a 50 x 50 x 50 grid. The output is in a cube file called elf_alpha.0.cube.

   0 1
   O    -4.5320698567   0.2524215916      0.0130780103
   H    -3.5641829319   0.2173288989     -0.0173259969
   H    -4.8109190521  -0.4489616171     -0.5945943692

   JOBTYPE           opt
   METHOD            b3lyp
   BASIS             6-31g*
   PLOT_ELF          true

50 -7 7
50 -4 4
50 -4 4
0 1 0 0

View output

Please refer also to elf_methane.in the $QC/samples directory, which uses the newer $plots format.