Analysis of separable nonlocal pseudopotentials.

Abstract

Separable nonlocal pseudopotentials are an important tool in the application of iterative diagonalization methods such as Car-Parrinello molecular dynamics and conjugate gradients. However, if the potentials are not carefully constructed, they can produce spurious states in the eigenvalue spectrum of the nonlocal Hamiltonian. These solutions are called ghost states if they lie below the reference energy of the pseudopotential, and can ruin a calculation if gone undetected. We present an efficient method for ghost-checking separable nonlocal pseudopotentials with an arbitrary number of projector functions. For the single-projector case, we derive the ghost theorems of Gonze et al. Ghost theorems are also derived for the double-projector problem. We present numerical results for single- and double-projector potentials. Because the entire spectrum of the nonlocal Hamiltonian can be efficiently calculated, spurious states above the reference energy may also be detected. The separability of the single-projector potential leads to a mathematical similarity to the bound-state Cooper pair problem.