# Interpreting electron localization function (ELF) results

Studying the interaction of a boron-nitride nanostructure with lead, we calculated the wave function using Gaussian software (single point energy with basis-set mix 6-311G++/lanl2dz and hseh1pbe functional) and did a topological analysis using the Multiwfn software.

The properties analyzed in the topological study were the critical points/basins in the electron density (via QTAIM), the Laplacian of the electron density and the electron localization function (ELF). Images with some of the results are below.

From the QTAIM analysis we got the the lead make a bond with one nitrogen atom at the nanostructure surface. This is due to the interbasin path together with the bond critical point between both atoms.

The electron localization function is shown in Fig. 2. According to its definition1, ELF took values among 0 and 1. The upper limit ELF=1, correspond to perfect localization and ELF=1/2 correspond to electron-gas like probability.

My doubts is: after looking to Fig. 2, if a bond is formed between lead and nitrogen atoms, we shouldn't expect more red regions between both atoms?

Fig. 1. Electron density. Bold deep blue lines: interbasin paths. Brown: (3,-3) nuclear critical point (NCP). Blue: (3,-1) bond critical point (BCP).

Fig. 2. Electron localization function.

Definition of ELF: $$ELF = {\left( {1 + \chi _\sigma ^2} \right)^{ - 1}}$$

$${\chi _\sigma } = {D_\sigma }/D_\sigma ^0$$

$${D_\sigma } = {\tau _\sigma } - \frac{1}{4}\frac{{{{\left( {\nabla {\rho _\sigma }} \right)}^2}}}{{{\rho _\sigma }}}$$

$$D_\sigma ^0 = \frac{3}{5}{\left( {6{\pi ^2}} \right)^{2/3}}\rho _\sigma ^{5/3}$$

$${\tau _\sigma } = \sum\limits_i^\sigma {{{\left| {\nabla {\psi _i}} \right|}^2}}$$

Where: $$\tau _\sigma$$ is the kinetic energy for spin $$\sigma$$, and $$\rho$$ is the electron density.

1. A. D. Becke and K. E. Edgecombe. A simple measure of electron localization in atomic and molecular systems. J. Chem. Phys. 92, 5397 (1990) (DOI: 10.1063/1.458517)
• Could you share your geometric structure? – Jack Nov 11 '20 at 21:05
• @Jack, just the structure (the Gaussian input)? – Camps Nov 11 '20 at 21:44
• Like the POSCAR of VASP. – Jack Nov 12 '20 at 6:57
• @Jack Here is the link – Camps Nov 13 '20 at 21:08
• All your structures cannot be open with VESTA. Can I use what software to open it? I have edited the BN-Pb-p0.poscar file and see an unclosed nanotube of BN, but the Pt atom and all H atoms are missing. – Jack Nov 15 '20 at 9:09