Energy Window Augmented Plane Waves Approach to Density Functional Theory

Abstract

In this work we present a new method for basis set generation for electronic structure calculations of crystalline solids. This procedure is aimed at applications to Density Functional Theory (DFT). In this construction, Energy Window Augmented Plane Waves (EWAPW), we take advantage of the fact that most DFT calculations use a convergence loop in order to obtain the self consistent eigenstates of the final (converged) Kohn Sham (KS) Hamiltonian. Here we propose that, for the basis used at each step of the self consistency iteration, we use the previous eigenstate basis, in the interstitial region, and augment it, inside each Muffin Tin (MT) sphere, with the solution to the spherically averaged KS Hamiltonian for the linearization energy of the energy window which contains the energy of that previous eigenstate. Indeed, to reduce the number of times the spherically averaged KS potential needs to be solved inside the MT spheres it is advantageous break up the spectrum into non-overlapping intervals, windows, and solve the spherically averaged KS Hamiltonian inside the MT region only once per window per angular momentum channel (at the linearization energy relevant to that window, usually near the middle of the window). For practical applications it is reasonable to have on the order of five to fifty windows. At each step of the iteration of the solution of the KS equations the EWAPW basis is that of near eigenstates of the KS Hamiltonian for that iteration. Overall the basis size is the comparable with the Augmented Plane Waves (APW) basis set but the number of radial wavefunctions is comparable or greater to Linearized Augmented Plane Waves + Local Orbitals + Higher Derivative Local Orbitals + High Energy Local Orbitals (LAPW+LO+HDLO+HELO) basis set.