Choosing Supercell Dimensions and Wavefunction Cutoff in Practice

The accuracy of isolated system calculations depends a lot on the correct choice of both the supercell dimensions and the plane wave cutoff value for given set of pseudopotentials. This may be accomplished by choosing some relevant parameter of the system under consideration (e.g. total energy or the energy difference between important configurations) and looking on how does it depend on the box size and the cutoff value.

Figure 7: Potential energy profile along reaction pathway with 25 Ry cutoff 7(a), and 45 Ry cutoff 7(b) with different box size. The noise in vacuum areas results in the artifact observed for large box with small cutoff. Functional: BLYP, pseudopotentials: Vanderbilt.

[R $_{\mathrm {cut}}$ = 25 Ry, Symm. = 1]

[R $_{\mathrm {cut}}$ = 45 Ry, Symm. = 1]

Since this is a two-dimensional optimization in the CPMD program parameter space you should perform the benchmark in a systematic way. One approach, that applies to isolated systems, is to start with the recommended 3 Å  spacing between the outermost atoms and the boundary of the box (when using the default setting of POISSON SOLVER HOCKNEY and run the tests for different cutoff values. These would be e.g. 20, 25, 30, and 35 Ry for Vanderbilt pseudopotentials and 60, 70, 80, and 90 Ry for Troullier-Martins. A good choice is the minimum value at which the control parameter of the system does not change any further. Then by decreasing box dimensions (in 1 Å  steps) in each direction try to minimize it by running the benchmarks for different cutoff values and observing the control parameter. Simulating lots of empty space does not teach us a lot but impacts the CPU time significantly. At the same time one has to take into account that the molecule may change shape or fluctuate around. If the system has no initial rotation or translation, the molecule should stay in place, but due to numerical errors, this is not always the case. Check out the keyword SUBTRACT for one method to cope with it.

Another issue is that large vacuum areas tend to produce ``noise'', particularly with gradient corrected functionals (see Figure 7). In principle this can be reduced by increasing the wavefunction cutoff, but the value required to completely remove the noise may be ridiculously large. Alternatively you can increase the gradient correction cutoff (GC-CUTOFF), but that in itself can be the source of noise. The situation may also change with different functionals. In the case of planar molecules using orthorhombic symmetry (SYMMETRY 8) with small box height would save additional empty space and CPU time, but then one has to take care, that the molecule does not rotate significantly.