What are the advantages and disadvantages in using special quasirandom structures (SQS) vs virtual-crystal approximation (VCA) to simulate electronic properties of disordered alloys?
You do not need to named all advantages and all disadvantages. Instead you can answer even if you know one advantage or one disadvantage of either package.
For VCA, as the construction is as simple as averaging the potentials of atomic species, the main advantage is computational. This is in the sense that it is very simple to change the compositional ratio of a solid solution by just changing how you average the potentials, instead of having to work with supercells (as you would have to do with SQS or other approaches even for simple ratios).
However, simply by doing this, you can imagine that the new potential will not be physical and neither the calculations associated to it. To give some examples, properties which depend on the local environment won't be correctly reproduced (e.g., the band gap in GaAlAsN and GaPN and GaAsN).
Then, how is it that VCA has been shown to be successful for same cases? Well, it happens that for some materials, the contributions of some atomic species are very similar to each other. Thus, averaging their potentials doesn't change the general properties (so much). Having said this, the real limitation of VCA is that it depends on how similar the parent atomic species are to each other.
For special quasirandom structures, the main advantage is that treating the atoms explictly allows the cell shape and ionic positions to be relaxed, capturing local atomic distortions which play a relatively large role in the electronic structure, energy and other properties. In principle, the VCA and other mean field approaches to disorder capture the same physical information as the unrelaxed SQS, and the ability to relax the SQS enables the calculated properties to be more physically realistic than the mean field approaches.
The additional degrees of freedom in the supercell are also related to a potential disadvantage of using SQS to predict the properties of disordered materials. SQS can often be mechanically unstable and the true energy that would be observed experimentally is often between the unrelaxed (higher energy) and relaxed (lower energy) states. When relaxing SQS, care must be taken to be sure that the symmetry of the ordered structure is preserved, otherwise the results will not be meaningful. An example can be seen in Figure 3 of Skripnyak et al., which shows that for bcc Ti-V, unrelaxed SQS predicts the same mixing energies as the Coherent Potential Approximation (CPA), another mean field method, while the relaxed SQS predicts much lower mixing energies and the experimentally measured mixing energies are in between the unrelaxed and relaxed states.
