Assessing the G0W0Γ0(1) Approach: Beyond G0W0 with Hedin's Full Second-Order Self-Energy Contribution

We present and benchmark a self-energy approach for quasiparticle energy calculations that goes beyond Hedin's GW approximation by adding the full second-order self-energy (FSOS-W) contribution. The FSOS-W diagram involves two screened Coulomb interaction (W) lines, and adding the FSOS-W to the GW selfenergy can be interpreted as first-order vertex correction to GW (GW Gamma((1))). Our FSOS-W implementation is based on the resolution-of-identity technique and exhibits better than O(N-5) scaling with system size for small- to medium-sized molecules. We then present one-shot GW Gamma((1)) (G(0)W(0)Gamma((1))(0)) benchmarks for the GW100 test set and a set of 24 acceptor molecules. For semilocal or hybrid density functional theory starting points, G(0)W(0)Gamma((1))(0) systematically outperforms G(0)W(0) for the first vertical ionization potentials and electron affinities of both test sets. Finally, we demonstrate that a static FSOS-W self-energy significantly underestimates the quasiparticle energies.

Automated summary

A self-energy approach beyond the Hedin's GW approximation is presented and benchmarked, showing superior performance. The addition of the full second-order self-energy (FSOS-W) contribution allows for a first-order vertex correction to GW and exhibits better scaling with system size for small- to medium-sized molecules. In specific cases, this approach outperforms traditional methods in accuracy and results.