# In DFT, if I complete a convergence test once, then want to study a different system with the same atoms, do I have to do a new convergence test?

Any time you start a new DFT calculation, it is recommended to do a convergence test. The parameters to include in the tests vary depending on the DFT implementation, i.e. plane-waves, Gaussian basis set, numerical orbitals, etc.

The idea is to choose a property, in general the energy of the system, and then vary a parameter in order to obtain the property that converges to a value (attaining a plateau).

The usual parameters used in convergence tests are mesh cut-off, k-points, energy cut-off, etc.

My question is: if I achieve convergence for a system A formed by atoms X, Y, and Z, do I need to repeat the convergence test for a new system, B, formed by the same atoms or I just could use the same parameters for system A?

• Very interesting question! May 3 '20 at 15:00

As you might expect, the answer is: it depends. It really boils down to how different the two systems are. There are obvious cases where the settings will not transfer between two systems.

The trivial example (at least for plane-wave, periodic DFT) is to consider System A as having the same elements as System B, but the former is a $$10\times10\times10$$ unit cell of the latter. In this case, the number of $$k$$-points required to achieve convergence in System B is going to be much higher than that of System A, and a convergence test in terms of $$k$$-points on System A will not be appropriate for System B.

To get around this, you can check to see what the ideal $$k$$-points per (reciprocal) atom is for System A and then use that same value for System B. In this case, the number of $$k$$-points would be adjusted by the number of atoms in the system. For instance, in Pymatgen's automatic_density() function, you could tweak kppa for one system and then see if that works well for another. Same thing for the $$k$$-point generator from the Mueller group, where KPPRA is one of the key input arguments. So, in this example, the $$k$$-points per number of atoms will likely lead to transferable convergence between systems of different sizes, but the $$k$$-points themselves will likely not.

If you specifically meant both the same types of atoms and the same number of atoms per cell, the above answer still holds. What if one system has a really small lattice constant whereas the other system does not? You'll need more $$k$$-points along the small lattice constant dimension. Most $$k$$-point generation codes will account for this in determining how to distribute the given $$k$$-points.

The Materials Project and Open Quantum Materials Database both rely on the assumption that, generally speaking, the used parameters will be appropriate for many of the materials under investigation. You can see several examples of this evaluation in the 2011 Comput. Mater. Sci paper by Jain and coworkers. Of course, there's no guarantee that a given plane-wave kinetic energy cutoff, $$k$$-point grid, and so on will be applicable to all materials, so it helps to be a bit conservative in your choice.

You should converge each calculation with respect to all the parameters; however, some parameters are relatively transferable between related systems. Let's consider the two main ones in a condensed-phase simulation:

1. Size of basis set

2. Brillouin zone sampling ("k-points") (Only relevant for periodic systems)

The basis set is largely dependent on the external potential (usually meaning the nuclear Coulomb or effective core/pseudopotential). Increasing the size of the basis set means describing shorter-wavelength variations of the wavefunction, and the wavefunction typically has the shortest oscillations near nuclei, where the nuclear potential is strong and changes sharply. However, the nuclear potential is so strong in these regions that the wavefunctions tend to be fairly insensitive to the chemical environment the atoms are in, so this is quite a transferable property between any simulations using the same nuclear potentials. (Note that this isn't quite the case if you also have localised bond-centred basis states, as that obviously depends on the bonding.)

In contrast to basis sets, the quality of k-point sampling you need depends on the nature of the bands in the system, so is very sensitive to changes in chemistry, bonding, defects etc. k-point sampling is generally not transferable between systems, even introducing a single vacancy can change the k-point sampling you need considerably. Since the k-points sample the Brillouin zone, the size of which depends on the real-space simulation cell, the appropriate quantity to consider is the k-point spacing (or, equivalently, k-point sampling density), rather than the number of k-points directly. You need smaller k-point spacing for systems with degenerate states at the Fermi-level (e.g. metals), in order to sample the Fermi surface well. The k-point spacing you need also interacts with any Fermi-level broadening you are using; the greater the Fermi-level broadening, the smoother the Fermi surface and so you can use a larger k-point spacing (i.e. fewer k-points).

For PAW and ultrasoft pseudopotentials there is often an auxiliary grid used to represent the hard "augmentation" charge, and this also should be converged. This is very similar to the basis set size, in that it is a property of the pseudopotential and transfers well to other systems with the same pseudopotentials.

Finally, beware of relying on total energy as your sole property of interest when converging. Different chemical and materials properties can have very different convergence rates. Typically forces and stresses are more sensitive than total energies, and vibrational properties are even more sensitive, as are NMR chemical shifts. When converging with respect to basis set size, k-points etc. you should always focus on the property you're actually interested in or a reasonable proxy.

• A huge problem here is the need time to run all the calculations and also that there are secondary properties that you can not obtain directly from the simulation. For example, if you are interested in the topological analysis of the electronic density (critical points, basins, etc.). But I have to agree that this should be the corrected way.
– Camps
May 13 '20 at 14:21
• You don't need to do a full convergence check for everything each time though, you just have to check that your current parameters are sufficient. In general, basis set quality is fairly transferable and you just need to check that it is alright when you go to a different atomic arrangement or stoichiometry. Brillouin zone sampling is the one which usually needs to be tested very carefully each time. May 15 '20 at 2:28