SternheimerGW: A program for calculating [formula omitted] quasiparticle band structures and spectral functions without unoccupied states

Abstract

The SternheimerGW software uses time-dependent density-functional perturbation theory to evaluate GW quasiparticle band structures and spectral functions for solids. Both the Green’s function G and the screened Coulomb interaction W are obtained by solving linear Sternheimer equations, thus overcoming the need for a summation over unoccupied states. The code targets the calculation of accurate spectral properties by convoluting G and W using a full frequency integration. The linear response approach allows users to evaluate the spectral function at arbitrary electron wavevectors, which is particularly useful for indirect band gap semiconductors and for simulations of angle-resolved photoelectron spectra. The software is parallelized efficiently, integrates with version 6.3 of Quantum Espresso, and is continuously monitored for stability using a test farm. Program summaryProgram Title:SternheimerGWProgram Files doi:http://dx.doi.org/10.17632/7ywzjng9t5.1Licensing provisions: GNU General Public License v3.0Programming language: Fortran 2003Nature of problem: The lack of the exchange–correlation discontinuity in density-functional theory (DFT) leads to a systematic underestimation of the band gap between conduction and valence states. Many-body perturbation theory in the GW approximation provides an effective solution to this problem, as well as other limitations faced by DFT in the description of electronic excitations. However, the GW method comes with its own set of limitations: (i) The perturbation of the system is typically expressed in terms of the unoccupied states, and achieving numerical convergence with respect to these states is often cumbersome. Since the underlying DFT codes rely only on the occupied states, their default behavior is often ill-suited to provide a sufficient amount of empty states. Combined with the large number of parameters that need to be converged, this limits the use of GW codes by non-expert users and automatic scripts. (ii) Currently, GW codes require that a homogeneous k-point mesh is used in the calculation. Hence, features close to the band edges are often only accessible via prohibitively expensive dense k-point meshes or interpolation techniques. (iii) To evaluate the frequency convolution of the Green’s function G and the screened Coulomb interaction W, many current GW calculations rely on approximations such as the plasmon-pole approximation, the analytic continuation, or the contour deformation. The relative merits and accuracy of the various approximations are not fully understood.Solution method: In SternheimerGW, we address (i) by replacing the summation over unoccupied states with a linear response equation. The solution depends on the occupied states only, and it employs linear response algorithms already provided by the Quantum ESPRESSO suite to compute phonons and related properties. As an additional benefit, transforming the problem in a linear response equation removes the restriction to homogeneous k-point meshes (ii), so that the GW self-energy for any arbitrary point can be evaluated. Finally (iii), we provide the possibility to perform a full frequency convolution along the real frequency axis. This feature can serve as a benchmark for approximate integrations using models or analytic continuation.