10.5 Visualizing and Plotting Volumetric Quantities 10.5.6 Noncovalent Interactions (NCI) Plots 10.5.8 Electrostatic Potentials

10.5.7 Electron Localization Function

(April 13, 2024)

Formulated by Becke and Edgecombe, ⁷⁷ Becke A. D., Edgecombe K. E.
J. Chem. Phys.
(1990), 92, pp. 5397. Link 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. 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. ⁶³⁵ 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 10.19 A job that evaluates the ELF for H ${}_{2}$ O on a $50\times 50\times 50$ 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
   geom_opt_driver optimize
$end

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

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

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10.5.7 Electron Localization Function