FAQ: Why is my energy vs. volume plot jagged

This is a very common questions from people who start to do calculations with plane wave codes. There are two reasons why the energy vs. volume plot looks jagged:

1. Basis set incompleteness. The basis set is discrete and incomplete, and when the volume changes, additional plane waves are added. That causes small discontinuous changes in the energy.
   Solutions:
   
   • use a larger plane wave cutoff:
     This is usually the preferred and cheapest solution.
   • use more k-points :
     This solves the problem, because the criterion for including a plane wave in the basis set is:
     
     $$\vert {\bf G} + {\bf k} \vert < {\bf G}_{\rm cut}.$$
     
     
     That means, at each k-point a different basis set is used, and additional plane waves are added at each k-point at different volumes. In turn, the energy vs. volume curve becomes smoother.
2. However the most probable reason for the jagged E(V) curve is another one: For PREC=High the FFT grids are chosen so that ${\bf H} \vert \phi>$ is exactly evaluated. For PREC=Med the FFT grids are set to 3/4 of the value that is in principle required for an exact evaluation of ${\bf H} \vert \phi>$. This introduces small errors, because when the volume changes the FFT grids do change discontinuously. In other words, at each volume a different FFT-grid is used, causing the energy to jump discontinuously.
   Solutions:
   • Set your FFT grids manually. Choose that one that is used per default for the largest volume
   • use PREC=High. In the new version (starting from VASP.4.4.3) this also increases the plane wave cutoff by 30 %. If this is undesirable, the plane wave cutoff can be fixed manually by specifying ENMAX=... in the INCAR file