Two-Component GW Calculations: Cubic Scaling Implementation and Comparison of Vertex-Corrected and Partially Self-Consistent GW Variants

We report an all-electron,atomic orbital (AO)-based,two-component(2C) implementation of the GW approximation (GWA)for closed-shell molecules. Our algorithm is based on the space-timeformulation of the GWA and uses analytical continuation (AC) of theself-energy, and pair-atomic density fitting (PADF) to switch betweenAO and auxiliary basis. By calculating the dynamical contributionto the GW self-energy at a quasi-one-component level,our 2C-GW algorithm is only about a factor of 2-3slower than in the scalar relativistic case. Additionally, we presenta 2C implementation of the simplest vertex correction to the self-energy,the statically screened G3W2 correction.Comparison of first ionization potentials (IPs) of a set of 67 moleculeswith heavy elements (a subset of the SOC81 set) calculated with ourimplementation against results from the WEST code reveals mean absolutedeviations (MAD) of around 70 meV for G (0) W (0)@PBE and G (0) W (0)@PBE0. We check the accuracy of ourAC treatment by comparison to full-frequency GW calculations,which shows that in the absence of multisolution cases, the errorsdue to AC are only minor. This implies that the main sources of theobserved deviations between both implementations are the differentsingle-particle bases and the pseudopotential approximation in theWEST code. Finally, we assess the performance of some (partially self-consistent)variants of the GWA for the calculation of first IPs by comparisonto vertical experimental reference values. G (0) W (0)@PBE0 (25% exact exchange) and G (0) W (0)@BHLYP (50% exactexchange) perform best with mean absolute deviations (MAD) of about200 meV. Explicit treatment of spin-orbit effects at the 2Clevel is crucial for systematic agreement with experiment. On theother hand, eigenvalue-only self-consistent GW (evGW) and quasi-particle self-consistent GW (qsGW) significantly overestimate the IPs. Perturbative G3W2 corrections increase the IPs and thereforeimprove the agreement with experiment in cases where G (0) W (0) alone underestimates theIPs. With a MAD of only 140 meV, 2C-G (0) W (0)@PBE0 + G3W2 is in best agreement with the experimental referencevalues.

Automated summary

We present an all-electron, atomic orbital-based, two-component implementation of the GW approximation for closed-shell molecules. Our algorithm accurately predicts the first ionization potentials of molecules with heavy elements and exhibits good performance compared to other codes. It has high practical value due to its computational efficiency and accuracy.