ADAPTIVE RIEMANNIAN METRIC FOR ALL-ELECTRON CALCULATIONS

We present two techniques that make feasible the application of the ad aptive Riemannian metric technique to all-electron local-density-funct ional calculations. The first overcomes both the real-(r=0) and Fourie r- (G=0) space divergences of the nuclear Coulomb potential by computi ng the electron-ion energy as the smooth periodic electrostatic potent ial due to the electrons measured at the positions of the ions. The se cond overcomes the problem of slow convergence of the extreme metrics which the r=0 Coulomb divergence necessitates by giving an explicit pr escription for a suitable metric for arbitrary ionic configurations. A ll-electron-diamond calculations then serve as a proving ground for th ese ideas and demonstrate the viability of adaptive Riemannian methods for bypassing the pseudopotential approximation in solid-state calcul ations.