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

10.5.6 Electron Localization Function

Formulated by Becke and Edgecombe,Becke:1990 the electron localization function (ELF),

ELF=[1+(τσ-(ρσ)24ρσ35(6π2)2/3(ρσ5/3))2]-1 (10.18)

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.Fuentealba:2007 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.Kohout:1996

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

Example 10.14  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
make_cube_files true

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

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