Electron Localization Function

This tutorial explains how to visualize the Electron Localization Function (ELF) with VQkit.

ELF is dimensionless and is conventionally bounded by:

\[0 \le \mathrm{ELF} \le 1\]

VQkit can detect an existing ELF Gaussian cube file and visualize it directly.

Important

The current VQkit ELF workflow is primarily a visualization and analysis workflow.

VQkit expects the final ELF field in:

*.cube

or:

*.cub

For Quantum ESPRESSO, if an ELF cube is not present, VQkit can prepare a pp.x input template using:

plot_num = 8

For VASP or other cases, place the final ELF cube in the working directory before running the analysis.

Open the ELF workflow

From the VQkit main menu choose:

[2] Post-processing

Then choose:

[4] Charge, spin and bonding

Then select:

[3] Electron localization function (ELF)

VQkit searches the current directory for:

*.cube
*.cub

Files containing words such as:

elf
localization

are preferred when several cube files are present.

Existing ELF cube

If exactly one suitable ELF cube is found, VQkit selects it automatically.

If several possible cube files are found, VQkit displays them and asks:

Detected multiple possible ELF cube files:
  [1] ...
  [2] ...
  ...

Select ELF cube [1]:

Choose the final ELF cube corresponding to the calculation you want to analyze.

No ELF cube found

Quantum ESPRESSO

If VQkit detects a Quantum ESPRESSO calculation but no ELF cube, it creates:

VQkit_QE_ELF_pp.in

The generated template is:

&INPUTPP
   prefix = 'CHANGE_ME'
   outdir = 'CHANGE_ME'
   filplot = 'VQkit_QE_ELF'
   plot_num = 8
/
&PLOT
   nfile = 1
   filepp(1) = 'VQkit_QE_ELF'
   weight(1) = 1.0
   iflag = 3
   output_format = 6
   fileout = 'VQkit_QE_ELF.cube'
/

Edit:

prefix
outdir

so that they match your completed Quantum ESPRESSO SCF calculation.

Then run:

pp.x < VQkit_QE_ELF_pp.in > VQkit_QE_ELF_pp.out

After pp.x finishes, the working directory should contain:

VQkit_QE_ELF.cube

Run the VQkit ELF option again.

VASP

If VQkit does not detect a QE calculation and no ELF cube is present, it asks you to place the final ELF cube in the working directory.

The current ELF menu does not generate a VASP ELF cube automatically.

Cube information

When VQkit successfully reads the ELF cube, it reports information such as:

Detected ELF cube
Grid
Atoms
ELF plotting range

The plotting range is fixed to:

0.0 to 1.0

Numerical values outside this range due to small numerical noise are clipped for plotting.

1. XY center slice

Choose:

VQkit takes the central grid point along z and plots the ELF in the xy plane.

Typical outputs:

VQkit_QE_ELF_XY.png
VQkit_QE_ELF_XY.dat

2. XZ center slice

Choose:

VQkit takes the central grid point along y and plots the xz plane.

Typical outputs:

VQkit_QE_ELF_XZ.png
VQkit_QE_ELF_XZ.dat

3. YZ center slice

Choose:

VQkit takes the central grid point along x and plots the yz plane.

Typical outputs:

VQkit_QE_ELF_YZ.png
VQkit_QE_ELF_YZ.dat

4. All center slices

Choose:

or simply press Enter at:

Select plot type [4]:

VQkit generates:

VQkit_QE_ELF_XY.png
VQkit_QE_ELF_XY.dat

VQkit_QE_ELF_XZ.png
VQkit_QE_ELF_XZ.dat

VQkit_QE_ELF_YZ.png
VQkit_QE_ELF_YZ.dat

This is the recommended first inspection.

5. Custom slice position

Choose:

VQkit asks:

Plane [YZ]:

Allowed planes are:

XY
XZ
YZ

Then VQkit asks:

Fractional slice position 0-1 [0.5]:

The value defines the position along the axis perpendicular to the selected plane.

Examples:

25
50
75

Example

To inspect an XZ plane at 40% of the cell along y:

Plane [YZ]: XZ
Fractional slice position 0-1 [0.5]: 0.40

VQkit selects the closest grid index.

Typical output:

VQkit_QE_ELF_XZ_CUSTOM.png
VQkit_QE_ELF_XZ_CUSTOM.dat

ELF data files

Each exported .dat file contains:

axis1_A
axis2_A
ELF

The header also records:

selected plane;
slice index;
physical slice coordinate in Angstrom;
the fact that ELF is dimensionless.

Atomic overlays

VQkit reads atomic positions from the cube file.

Atoms close to the selected slice are overlaid on the ELF contour plot.

They are shown as:

circular markers;
element-symbol labels.

This helps relate localized electronic regions to atoms, bonds, lone pairs, or interstitial regions.

Contour levels

VQkit plots ELF on the fixed interval:

\[0 \le \mathrm{ELF} \le 1\]

and adds contour lines at selected ELF values including approximately:

These contours help identify regions with stronger localization.

Interpreting ELF

ELF close to 1

Values approaching:

\[\mathrm{ELF} \rightarrow 1\]

indicate strong electron localization.

Such regions can be associated with features such as:

localized bonding electrons;
lone-pair-like regions;
strongly localized electron pairs.

ELF around 0.5

Values near:

\[\mathrm{ELF} \approx 0.5\]

are commonly interpreted as electron-gas-like behavior.

ELF close to 0

Very low ELF values indicate regions with weak localization according to the ELF measure.

Example: bonding analysis

Assume your working directory contains:

VQkit_QE_ELF.cube

Step 1 — Start VQkit

Start VQkit in the directory containing the cube.

Step 2 — Open post-processing

Choose:

Step 3 — Open charge, spin and bonding

Choose:

Step 4 — Open ELF

Choose:

VQkit detects:

VQkit_QE_ELF.cube

Step 5 — Generate all central planes

At:

Select plot type [4]:

press Enter.

VQkit generates the XY, XZ and YZ ELF maps.

Step 6 — Inspect the bonding plane

Open the three PNG files and identify which plane intersects the bond or region of interest.

If none of the center slices intersects it correctly, choose the custom slice option.

Step 7 — Generate a custom plane

For example:

Plane [YZ]: XZ
Fractional slice position 0-1 [0.5]: 0.43

Adjust the fractional position until the relevant atoms are visible on the selected plane.

Example: Quantum ESPRESSO workflow

Assume you have completed a QE SCF calculation but have not generated ELF.

Step 1 — Run VQkit ELF

Navigate to:

Post-processing
Charge, spin and bonding
Electron localization function

Because no cube is present, VQkit creates:

VQkit_QE_ELF_pp.in

Step 2 — Edit the pp.x template

Set:

prefix = 'your_prefix'
outdir = 'your_outdir'

Step 3 — Run pp.x

Run:

pp.x < VQkit_QE_ELF_pp.in > VQkit_QE_ELF_pp.out

Step 4 — Check the cube

Confirm that:

VQkit_QE_ELF.cube

has been generated.

Step 5 — Run VQkit ELF again

VQkit now detects the cube and opens the slice-selection menu.

3D visualization

VQkit generates two-dimensional ELF slices.

For three-dimensional ELF isosurfaces, open the original ELF cube in a visualization package such as:

VESTA;
VMD;
XCrySDen.

The input cube is retained unchanged by VQkit.

Common problems

No ELF cube detected

Check that:

the file extension is .cube or .cub;
the file is in the current VQkit working directory;
you are running VQkit from the correct calculation folder.

QE template created instead of plot

This means no ELF cube was found.

Edit:

VQkit_QE_ELF_pp.in

then run pp.x to generate the cube.

Wrong cube selected

If several cube files are present, make sure you select the actual ELF field rather than a charge-density or CDD cube.

Custom slice misses the bond

Change the fractional slice position until the selected plane intersects the atoms or bonding region of interest.

Matplotlib unavailable

ELF slice plotting requires Matplotlib.

If plotting fails because Matplotlib is unavailable, reinstall VQkit with its plotting dependencies.

Scientific cautions

ELF is not charge density

ELF should not be interpreted as the absolute electron density.

It is a localization descriptor.

Coordinate-plane dependence

A two-dimensional slice may miss important three-dimensional features.

Inspect more than one plane or use a 3D visualization for complex bonding environments.

Comparison between systems

When comparing ELF maps across structures, use comparable computational settings, pseudopotentials, exchange-correlation treatment, and numerical accuracy.

Interpretation

High ELF does not by itself uniquely identify a particular chemical bond type.

ELF should be interpreted together with structural information and, where appropriate, complementary electronic-structure analyses such as:

charge-density difference;
Bader charge;
DOS/PDOS;
bonding analysis.

Electron Localization Function

Important

Open the ELF workflow

Existing ELF cube

No ELF cube found

Quantum ESPRESSO

VASP

Cube information

Plot menu

1. XY center slice

2. XZ center slice

3. YZ center slice

4. All center slices

5. Custom slice position

Example

ELF data files

Atomic overlays

Contour levels

Interpreting ELF

ELF close to 1

ELF around 0.5

ELF close to 0

Example: bonding analysis

Step 1 — Start VQkit

Step 2 — Open post-processing

Step 3 — Open charge, spin and bonding

Step 4 — Open ELF

Step 5 — Generate all central planes

Step 6 — Inspect the bonding plane

Step 7 — Generate a custom plane

Example: Quantum ESPRESSO workflow

Step 1 — Run VQkit ELF

Step 2 — Edit the pp.x template

Step 3 — Run pp.x

Step 4 — Check the cube

Step 5 — Run VQkit ELF again

3D visualization

Common problems

No ELF cube detected

QE template created instead of plot

Wrong cube selected

Custom slice misses the bond

Matplotlib unavailable

Scientific cautions

ELF is not charge density

Coordinate-plane dependence

Comparison between systems

Interpretation