QUANTUM ESPRESSO Tutorial: How to calculate work functions

This is my first post about Quantum ESPRESSO. In this tutorial I'm going to show you how to calculate work function of a material using Quantum ESPRESSO. The calculation is pretty easy, you need only to calculate scf, As an example, let's calculate the work function of Ti3C2 MXene monolayer.

For this calculation, here is scf my input file:

 After scf calculation, you need to calculate the electrostatic potential using pp.x:

After this calculation, we would get MXene_OH_Bridge.pot file which contains its electrostatic potential. Usually, we need to average its electrostatic potential through a plane. In this case, I calculated the average electrostatic potential in xy plane using average.x, here is the input file:

After that you will get an avg.dat file which contains three columns:

The first column is the spatial vector which is represented in bohr units, column 2 represents the averaged quantity, and column 3 represents the macroscopic average of the quantity, in this case, the electrostatic potential. It should be noted that in this output file, the energy is represented in Rydberg unit. Here is the result:

The work function can be calculated as follows:

$$\phi = E_{vac} - E_F $$

where \(\phi\) is the work function, \(E_{vac}\) is the vacuum level, and \(E_F\) is the Fermi level of the material which is obtained from the scf calculation.