Modulated structures with a harmonic occupational modulation are not suitable for force field methods (including molecular dynamics) or density functional theory (DFT) calculations because fully occupied sites are required. Instead of assuming a random distribution with some constraints, which is a common approach, the harmonic occupational modulation function from a refinement in superspace can be replaced by a block wave function resulting in a model, that represents the hypothetical completely ordered structure with fully occupied sites. If the modulation wave vector corresponds to a commensurate modulation, the corresponding model in physical space can be used for DFT calculations, otherwise a commensurate approximation is needed. As an example, the present approach is applied to the modulated structure of mullite to determine the ideal Al/Si ordering for different compositions and supercell sizes. For the analyzed composition, the calculations yield consistently the same Al/Si ordering pattern. The results are also in qualitative agreement with the refinement of the not fully ordered structure, i.e. the volumes of tetrahedra with Al/Si disorder follow the trend of the Al/Si ordering pattern from the DFT calculations. The example shows that the approach allows to determine structural parameters, that are very difficult or even impossible to access experimentally.
I remember some cases in the field of organic metals (for instance, Tetrathiafulvalene-Tetracyanoquinodimethane, TTF-TCNQ) where the incommensuration is between the electronic density (or Charge Density Wave) and the positions of the ions (molecules in this case). Can your method be applied to there cases also ?
If I am right, your example has two modulation wave vectors. It depends on these modulation wave vectors if a commensurate approximation of appropriate size is available or not. With improving computing power, larger and larger systems can be investigated in the future and the size limitation will become less relevant.