Computing the work function

The workfunction is defined as the work needed to move an electron from a surface to a point in vacuum sufficiently far away from this surface. It is a central quantity in surface science, vacuum science, catalysis and other related fields as it characterizes a given surface; illustrating the presence of impurities, adsorbates and possible surface reconstruction. It is typically measured using surface science techniques such as thermionic emission, the Kelvin probe method, etc. It has also served as a important measure in various theoretical models about metallic surfaces. On this page, we describe how the workfunction is computed using outputs from a DFT calculation performed using VASP. We detail best-practices, required INCAR tags and possible pitfalls.

Warning: The workfunction is a property of a surface, not a bulk property. Hence, the content of this page only applies to systems with reduced dimensionality (such as surfaces) i.e. systems where there is expected to be a charge density free region in at least one direction of the cell.

Computing the workfunction

The workfunction, ${\textstyle \Phi}$, is computed using the expression,

$$\Phi = e\phi_{\mathrm{vacuum}} - \mu_{\mathrm{Fermi}}$$

where ${\textstyle \phi_{\mathrm{vacuum}}}$ is the vacuum potential, i.e. the potential sufficiently far away from a surface, such that if an electron were to be placed there, it would not feel the presence of the surface. ${\textstyle \mu_{\mathrm{Fermi}}}$ is the Fermi level of the surface and ${\textstyle e}$ is the charge on the electron (equal to 1 in atomic units). In this section, we describe how ${\textstyle \phi_{\mathrm{vacuum}}}$ and ${\textstyle \mu_{\mathrm{Fermi}}}$ are determined from the LOCPOT and OUTCAR files respectively.

Fermi energy

The Fermi energy is written directly to the OUTCAR file. Simply grep for the following lines in the OUTCAR

grep "Fermi energy" OUTCAR

to get the Fermi energy in eV.

Vacuum potential

To compute the vacuum potential, perform the following steps:

1. Ensure that the chosen structure has a large enough atom-free (i.e. charge density free) and field-free region in the direction of the surface normal. A good rule-of-thumb is to center the atoms in your cell and have anywhere between 8-12Failed to parse (Conversion error. Server ("cli") reported: "[INVALID]"): {\textstyle \r{A}} of vacuum on either side in this direction. ::note:: Not using enough vacuum causes a field within the vacuum region, leading to inaccurate values of the vacuum potential (see point 3).
2. Perform a ground state DFT calculation. We suggest setting PREC=Accurate . If your cell has a net dipole moment (i.e. it is not symmetric along the direction of the surface normal), we suggest switching on the dipole correction by using the following INCAR tags (LDIPOL, IDIPOL, DIPOL). The use of the dipole correction is critical to obtaining a flat field-free region in the potential (c.f. next point). In addition to to these tags, set the LVHAR = T to output only the Hartree and ionic potentials to the LOCPOT file. ::note:: The use of LVHAR instead of LVTOT is because the exchange-correlation potential decays very slowly in vacuum. Using the sum of the Hartree and ionic potentials allows for determining the workfunction with significantly less vacuum requirements (and hence lower computational cost).
3. Compute the vacuum potential. Average the contents of the LOCPOT file along the lattice vectors of the surface (i.e. both directions perpendicular to the surface normal). Find the field free region by determining the region of space where the potential remains constant. This value of the potential is the vacuum potential. ::note:: There exist two vacuum potential regions, one for either direction of the surface normal. Depending on your system, one of the directions may be more relevant than another. ::note:: An alternative way to determine the vacuum potential is to let VASP compute it and write the result to the OUTCAR. Simply add the tag VACPOTAV = T to the INCAR file. After the calculation is completed, grep for the following:

grep upper OUTCAR

which gives the following examplar output:

 vacuum level on the upper side and lower side of the slab         8.049         7.778

Figure XYZ shows a representative example of the vacuum potential referenced to the fermi energy (left hand side of Equation XYZ) plotted against the distance along the surface normal (x-axis) for two system, fcc Pt(111) surface (in blue) and Pt(111) surface with a carbon atom adsorbed on one surface termination (Pt(111)-C*). The vacuum potentials are flat (i.e. constant) on either side (magnified in insets). The workfunction on either side of the slab are annotated in the insets as ${\textstyle \Phi}$; equal for both sides for the slab, but slightly higher for the case of Pt(111)-C*.

Figure Vacuum potential referenced to the Fermi energy plotted against the distance along the surface normal. Insets to the figure show the workfunction for (red) a clean Pt(111) surface (blue) Pt(111) with a carbon atom adsorbed on only one surface termination (atom center ~15 Å on the x-axis)