Adaptive Riemannian metric for all-electron calculations

We present two techniques that make feasible the application of the adaptive Riemannian metric technique to all-electron local-density-functional calculations. The first overcomes both the real- (r=0) and Fourier- (G=0) space divergences of the nuclear Coulomb potential by computing the electron-ion energy as the smooth periodic electrostatic potential due to the electrons measured at the positions of the ions. The second overcomes the problem of slow convergence of the extreme metrics which the r=0 Coulomb divergence necessitates by giving an explicit prescription for a suitable metric for arbitrary ionic configurations. All-electron-diamond calculations then serve as a proving ground for these ideas and demonstrate the viability of adaptive Riemannian methods for bypassing the pseudopotential approximation in solid-state calculations.