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

10.5.6 Electron Localization Function

(June 30, 2021)

Formulated by Becke and Edgecombe, 68 Becke A. D., Edgecombe K. E.
J. Chem. Phys.
(1990), 92, pp. 5397.
Link
the electron localization function (ELF),

ELF=[1+(τσ-(ρσ)24ρσ35(6π2)2/3(ρσ5/3))2]-1 (10.17)

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. 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. 562 Kohout M., Savin A.
Int. J. Quantum Chem.
(1996), 60, pp. 875.
Link

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

Example 10.15  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.

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

$rem
   JOBTYPE           opt
   METHOD            b3lyp
   BASIS             6-31g*
   PLOT_ELF          true
   MAKE_CUBE_FILES   true
$end

$plots
water
50 -7 7
50 -4 4
50 -4 4
0 1 0 0
0
$end

View output

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