Constructing unoccupied states for G$_0$W$_0$ quasiparticle calculations from plane-waves

Standard methods of first-principles calculations of the quasiparticle energies within the G$_0$W$_0$ scheme require summing over large numbers of unoccupied states. The generation of these states within the ab initio pseudopotential plane-wave density functional theory (DFT) quickly becomes a bottleneck of the calculation with increasing system size, especially in low-dimensional systems. In this work, we propose a method for approximating the high-energy continuum and resonant states in low-dimensional systems. The continuum and resonant states above a chosen energy are replaced with symmetrized plane-waves and localized DFT states computed with short-range localized basis functions (such as in the SIESTA code), respectively. The Gram-Schmidt process is used to orthogonalize these constructed high-energy unoccupied states. The method opens a route towards precise G$_0$W$_0$ quasiparticle calculations in large low-dimensional systems using a small number of unoccupied DFT states. This work was supported by NSF Grant No. DMR10-1006184, the U.S. DOE under Contract No. DE-AC02-05CH11231. Computational resources have been provided by NSF through TeraGrid at NICS and DOE at LBNL's NERSC.