full optimization

If your DFT code has a stress tensor formalism, you can usually do the full optimization of all degrees of freedom (volume, shape and positions) simultaneously and automatically (see the hands-on document with instructions for your DFT code in the “let’s play” section). You might do this for Fe-Al, starting from the most optimed unit cell you got so far. In order to get a sufficiently precise stress tensor, you need the higher precission settings that were listed at the start of this chapter. This full optimization is not a light calculation, expect 5-6 hours on a laptop. It’s the kind of calculation you might want to run overnight. How much do the volume, b/a and c/a still change? If they do change, it means that the different degrees of freedom (volume, shape and positions) are not fully independent, and cannot be optimized one separated from the other.

If you DFT code does not have a stress tensor formalism, you should go in principle through the entire procedure once again: optimize volume, optimize shape, optimize positions (or in a different order, depending on which one has the largest impact on the total energy). If that results in a cell that is not very different from the one obtained after going the first time through the procedure, then you’re done. If there are still changes, you have to repeat the proces once more. Usually 2-3 such iterations are sufficient to get very close to the actual minimum.

As an optional exercise that takes quite a share of computing time, you can use the stress tensor to determine a better value of the bulk modulus: do a full optimization with a target pressure that is different from zero (say ±10 GPa, ±20 GPa, …). Don’t go beyond volume changes of more than plus or minus 10%. Collect the volumes and energies, and fit an E(V) equation of state through them, just as you did earlier in this chapter for a cell where only the volume was changed. The bulk modulus you will obtain now from this fit, is the true DFT/PBE prediction for the bulk modulus: the curvature near equilibrium of E(V), where E is the total energy for a unit cell at volume V, with all other degrees of freedom fully optimized.