Projector augmented-wave method: an analysis in a one-dimensional setting

Abstract

In this article, a numerical analysis of the projector augmented-wave (PAW) method is presented, restricted to the case of dimension one with Dirac potentials modeling the nuclei in a periodic setting. The PAW method is widely used in electronic ab initio calculations, in conjunction with pseudopotentials. It consists in replacing the original electronic Hamiltonian H by a pseudo-Hamiltonian H P AW via the PAW transformation acting in balls around each nuclei. Formally, the new eigenvalue problem has the same eigenvalues as H and smoother eigenfunctions. In practice, the pseudo-Hamiltonian H P AW has to be truncated, introducing an error that is rarely analyzed. In this paper, error estimates on the lowest PAW eigenvalue are proved for the one-dimensional periodic Schrödinger operator with double Dirac potentials.

Two-dimensional biphenylene: a promising anchoring material for lithium-sulfur batteries

“…The first-principles spin-polarized calculations are performed using the Vienna ab-initio Simulation Package (VASP) 25 . The projector augmented wave method is adopted to describe the ion–electron interactions 25 , which is treated by the generalized gradient approximation with the Perdew-Burke-Ernzerhof formalism 26 . The van der Waals interactions are implemented considering the scheme of Grimme (DFT-D3) with zero damping correction 27 .…”

Exploring the Superior Anchoring Performance of the Two-Dimensional Nanosheets B2C4P2 and B3C2P3 for Lithium–Sulfur Batteries

“…All the density functional theory (DFT) calculations are performed using the Vienna Ab initio Simulation Package. , The plane-wave cutoff energy is set to 500 eV combined with an exchange–correlation functional of the generalized gradient approximation (Perdew–Burke–Ernzerhof flavor). The change in total energy and maximum atomic force converged to 10– 6 and 0.01 eV Å –1 , respectively.…”