In the context of quantum mechanics and computational materials science, plane wave basis sets are typically not re-optimized for each material individually.
Plane wave basis sets are a commonly used basis set in electronic structure calculations, where they form a part of the numerical representation of the electronic wavefunctions in a solid or molecule. These basis sets consist of plane waves with different wave vectors, and the completeness of the set allows for accurate representation of the electronic structure.
When performing electronic structure calculations, such as density functional theory (DFT) calculations, a set of plane waves is chosen based on a predetermined energy cutoff. This energy cutoff determines the maximum kinetic energy of the electrons that can be described accurately within the chosen basis set. The basis set is typically chosen to be sufficiently large to obtain converged results within a reasonable computational effort.
The choice of the energy cutoff is often based on empirical guidelines and is not typically optimized for each individual material. However, different materials may require different energy cutoffs to achieve accurate results, especially when dealing with materials that have significantly different electronic properties, such as metals versus insulators.
It is worth noting that while the plane wave basis set is not re-optimized for each material, other aspects of the calculation, such as exchange-correlation functionals in DFT, may be selected or optimized specifically for a given material or class of materials. Additionally, more advanced techniques, such as hybrid functionals or many-body perturbation theory, may require additional considerations beyond the choice of the basis set.