Scalable Molecular GW Calculations: Valence and Core Spectra

We present a scalable implementation of the $GW$ approximation using Gaussian atomic orbitals to study the valence and core ionization spectroscopies of molecules. The implementation of the standard spectral decomposition approach to the screened Coulomb interaction, as well as a contour deformation method are described. We have implemented both of these approaches using the robust variational fitting approximation to the four-center electron repulsion integrals. We have utilized the MINRES solver with the contour deformation approach to reduce the computational scaling by one order of magnitude. A complex heuristic in the quasiparticle equation solver further allows a speed-up of the computation of core and semi-core ionization energies. Benchmark tests using the GW100 and CORE65 datasets and the carbon 1{\it s} binding energy of the well-studied ethyl trifluoroacetate, or ESCA molecule, were performed to validate the accuracy of our implementation. We also demonstrate and discuss the parallel performance and computational scaling of our implementation using a range of water clusters of increasing size.