# Permissible amount of forces on ions in a relaxed structure

An equilibrium structure would be at a local minimum but that doesn't happen with all relaxation calculations. Relaxed structures tend to have some resultant forces on ions. What amount of these forces can be accepted? Is 0.05 eV/$$\unicode{xC5}$$ acceptable?

• It's a political choice but using very low values cause the consumption of lots of resources with no measurable gain in results. I mostly stick with 0.01 eV/A. – Bereau Aug 16 at 19:14
• Yeah for vibrational calculations mostly much lower values could be used, but you need to take into account higher time and resources consumption in this case. – Bereau Aug 16 at 22:34
• I think it's difficult to answer this question as-is because it depends on what property is being computed. If only the total energy is important, the maximum forces that are acceptable are larger than what would be required for vibrational calculations for materials with soft vibrational modes. There's also the accuracy/time tradeoff mentioned above. Without being more specific, it's hard to give an answer other than "it depends". – Brandon Aug 18 at 20:25
• The numerical value also isn't enough to specify what is being measured: maximum force? maximum force component? rms force? If the maximum force / maximum force component is small, you might still be an appreciable distance from the minimum if you have a lot of atoms. – Susi Lehtola Aug 18 at 20:43
• This completely depends on what you're looking to model and the type of material you're modeling. Rule-of-thumb is generally no greater than 0.05 eV/Å, but even that can often be too large, particularly (but not exclusively) in the case of highly flexible materials or molecular crystals. I like 0.03 eV/Å, but that's for a very specific class of materials I study (MOFs). For other materials, that may not be sufficient. There is unfortunately no proper answer to this question. You simply have to test it and see. – Andrew Rosen Aug 19 at 1:21

This completely depends on what you're looking to model and the type of material you're modeling. A standard rule-of-thumb is generally no greater than 0.05 eV/Å for the maximum net force on any atom, but even this can often be too large, particularly (but not exclusively) in the case of highly flexible materials or molecular crystals. Personally, I like 0.03 eV/Å, but that's again based on experience for a very specific class of materials I study (MOFs). For other materials, that very well may not be sufficient. It will also depend heavily on the property of interest, with energies being less sensitive than vibrational modes as one example. There is unfortunately no proper answer to this question. You simply have to test it and see.

As others have mentioned, there is no 'rule of thumb', but I do phonon calculations (PHONOPY and DFPT) and did some checking a long time ago to converge the phonon energies. I found ~ 0.001 eV/A to be more than low enough for all cases that I checked. Note that, while relaxation to high precision is expensive, once it gets close to the minimum, the positions usually converge more quickly. Note that in some instances, the energy cutoff (for plane wave codes that I use) might have to be sufficiently high to remove noise in the forces if you want such a low value.

• +1. Welcome to the site and thanks for your contribution! We hope to see much more of you in the future!!! – Nike Dattani Aug 27 at 15:50
• Thanks for the answer @Ty. Which code do you use for DFPT, and do you study bulk crystalline systems? – Hitanshu Sachania Aug 27 at 16:41
• @HitanshuSachania I use ABINIT for DFPT. It is VERY powerful but is honestly a little hard to get the hang of at first, at least for DFPT. I study bulk crystals, mainly correlated electron materials (which is ironically somewhere DFT is expected to not be valid ... ). If you are interested in learning DFPT, I do recommend ABINIT as there are numerous, very good tutorials and all the input variables are explained very well on the site docs.abinit.org/tutorial – Ty Sterling Aug 27 at 18:23
• @HitanshuSachania I understand your problem. The way to get phonon energies and eigenvectors at q /= 0 with VASP is via PHONOPY or some other package. The VASP implementation of DFPT only performs calculations at Gamma (IBRION = 7 of 8). The way to get energies away from the zone center is to use supercells. You can do this with VASP DFPT and the BZ folding will give you the energies at the commensurate q points. Or you use PHONOPY and use finite differences. See the PHONOPY website (phonopy.github.io/phonopy) particularly the examples (one uses DFPT). – Ty Sterling Aug 27 at 19:33
• @TySterling, that's where I'm confused. I understand that we write the partition function using phonon energies and get thermal properties from there. There are two ways to get these frequencies: the frozen phonon method and DFPT. Let's say I create a supercell using \texttt{phonopy}, but that still requires me to do only one DFPT calculation, whereas with the frozen phonon method, I might end up with very many displaced supercells based on the symmetry of the system under study (SQS for example). Doesn't that make DFPT faster and better than the frozen phonon method? – Hitanshu Sachania Aug 27 at 20:35