11.5 Visualizing and Plotting Orbitals, Densities, and Other Volumetric Data 11.5.6 Electrostatic Potentials 11.6 Spin and Charge Densities at the Nuclei

11.5.7 ELF Plots

Formulated by Becke and Edgecombe⁷⁴, 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}

(11.18)

is a measure of electron localization. It is derived from the Hartree-Fock conditional pair probability and can reveal information about bonding and shell structure²⁷⁹. ELF values lie between 0 and 1, with an ELF=1 representing perfect localization,and an 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, the $\alpha$ spin ELF is calculated. For open-shell systems, the $\alpha$ , $\beta$ and spin-adapted ELFs are calculated⁴⁸⁵.

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

Example 11.14 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

(Please refer also to elf_methane.in the $QC/samples directory. This uses the newer $plots format).

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11.5.7 ELF Plots