10.5 Visualizing and Plotting Orbitals, Densities, and Other Volumetric Data 10.5.6 Noncovalent Interactions (NCI) Plots 10.5.8 Electrostatic Potentials and Electric Fields

10.5.7 Electron Localization Function

(February 4, 2022)

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

\text{ELF}=\Bigg{[}1+\Bigg{(}\frac{\tau_{\sigma}-\frac{(\nabla\rho_{\sigma})^{% 2}}{4\rho_{\sigma}}}{\frac{3}{5}(6\pi^{2})^{2/3}(\rho_{\sigma}^{5/3})}\Bigg{)}% ^{2}\Bigg{]}^{-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 $\text{ELF}(\mathbf{r})$ has values that lie between 0 and 1, with $\text{ELF}=1$ representing perfect localization and $\text{ELF}=1/2$ 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 $\alpha$ -spin ELF is calculated whereas for open-shell systems (spin-unrestricted calculations), both $\alpha$ - and $\beta$ -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 H ${}_{2}$ O 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.

Search Results

10.5.7 Electron Localization Function