Plane wave basis
In electronic structure calculations, the wave function is often expanded as a linear combination of plane waves. Plane waves comprise an orthonormal basis set, so that increasing the basis size (using many plane waves with different wavelengths) leads to a monotonic improvement in the reproduction of the wave function. However, it is unsuitable for describing steeply-varying wave functions near the core since disproportionately many plane waves are necessary for expanding steep functions. The (L)APW and pseudopotential methods were developed to circumvent this difficulty.