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

X Blanc (1) , Eric Cancès (2) , Mi-Song Dupuy (1)

1 LJLL - Laboratoire Jacques-Louis Lions
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique

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 PAW (projector augmented-wave) method circumvents this issue by replacing the original eigen-value problem by a new one with the same eigenvalues but smoother eigenvectors. Here a slightly different method, called VPAW (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.

Domaines: Analyse numérique [math.NA]

X Blanc, Eric Cancès, Mi-Song Dupuy. Variational projector augmented-wave method: theoretical analysis and preliminary numerical results. 2017. ⟨hal-01637724⟩