Extended norm-conserving pseudopotentials

Atomic pseudopotentials simplify electronic calculations by eliminating atomic core levels and the potentials that bind them. Outside some core radius, norm-conserving pseudopotentials produce the same scattering properties (radial logarithmic derivatives of wave functions for angular momenta of interest) as full-atomic potentials to zeroth and first order in energy about valence-level eigenvalues. We extend the correctness of the radial logarithmic derivative one order further in energy and present analytic and numerical results showing that this extension improves higher-order energy derivatives as well. We also show how our change improves predictions of excited single-particle eigenvalues in a wide variety of atoms, as well as high-energy scattering properties, with effects visible in a band-structure calculation. Our potentials converge nearly as quickly in reciprocal space as the Vanderbilt (modified Hamann-Schl\"uter-Chiang) potentials from which they are derived, and are easily generated.