Variational projector augmented-wave method: theoretical analysis and preliminary numerical results

In Kohn–Sham electronic structure computations, wave functions have singularities at nuclear positions. Because of these singularities, plane-wave expansions give a poor approximation of the eigenfunctions. In conjunction with the use of pseudo-potentials, the projector augmented-wave (PAW) method circumvents this issue by replacing the original eigenvalue problem by a new one with the same eigenvalues but smoother eigenvectors. Here a slightly different method, called variational PAW, is proposed and analyzed. This new method allows for a better convergence with respect to the number of plane-waves. Some numerical tests on an idealized case corroborate this efficiency. This work has been recently announced in Blanc et al. (C R Math 355(6), 665–670, 2017. https://doi.org/10.1016/j.crma.2017.05.004).