Quasiparticle and fully self-consistent GW methods: an unbiased analysis using Gaussian orbitals

TL;DR

This work benchmarks G0W0, qpGW-I, qpGW-II, and scGW within a uniform finite-temperature Matsubara framework using Gaussian orbitals to remove basis-related biases. It finds that solids show similar band gaps across self-consistency schemes, whereas molecules favor fully self-consistent GW for accurate ionization potentials, with plasmon satellites recovered by scGW. The analysis highlights the critical role of implementation details, convergence thresholds, and grid quality in GW benchmarks, resolving prior discrepancies in the literature. The results offer practical guidance: use scGW for robust accuracy and spectral features, while qpGW variants can be advantageous only under tight memory or convergence constraints.

Abstract

We present a comparison of various approximations to self-consistency in the GW method, including the one-shot G0W0 method, different quasiparticle self-consistency schemes, and the fully self-consistent GW (scGW) approach. To ensure an unbiased and equitable comparison, we have implemented all the schemes with the same underlying Matsubara formalism, while employing Gaussian orbitals to describe the system. Aiming to assess and compare different GW schemes, we analyze band gaps in semiconductors and insulators, as well as ionization potentials in molecules. Our findings reveal that for solids, the different self-consistency schemes perform very similarly. However, for molecules, full self-consistency outperforms all other approximations, i.e., the one-shot and quasiparticle self-consistency GW schemes. Our work highlights the importance of implementation details when comparing different GW methods. By employing state-of-the-art fully self-consistent, finite temperature GW calculations, we have successfully addressed discrepancies in the existing literature regarding its performance. Our results also indicate that when stringent thresholds are imposed, the scGW method consistently yields accurate results.

Figures (5)

• Figure 1: Schematic representation of different self-consistency schemes in the $GW$ approximation. The central object in sc$GW$ is the correlated Green's function $G$, whereas in qp$GW$, it is the effective mean-field Hamiltonian.
• Figure 2: Band gap errors, with respect to experiment, for selected semiconductors and insulators, as predicted by full and quasiparticle self-consistent $GW$ methods. PBE and $G_0W_0$-PBE results are also included for reference.
• Figure 3: Variation in BN and SiC band gaps with respect to Brillouin-zone sampling. The linear fit is performed using $N_k^{1/3} = 4$ and $6$ grids. The results from $N_k^{1/3} = 8$ show excellent agreement with this fit, demonstrating the reliability of the extrapolation procedure.
• Figure 4: Convergence trends for band gaps (eV) and total energy per unit cell ($E_h$) for qp$GW$-I, qp$GW$-II and sc$GW$, all calculated for $4\times 4 \times 4$$k$-mesh sampling in the BZ. We consider SiC and BN as typical examples of easy convergence, while ZnS proves to be a challenging system for qp$GW$-I.
• Figure 5: Spectral function for the $\Gamma_1$ and $\Gamma_{25}$ bands in diamond, calculated using $G_0W_0$-PBE, sc$GW$ and qp$GW$-II. The results use a $6\times 6\times 6$$k$-mesh, and Padé analytical continuation for $G_0W_0$ and sc$GW$. The $y$-axis is magnified to emphasize the satellites.