Advancements in Low-Scaling GW Calculations Improve Precision for Complex Systems
Recent advancements in computational methods for electronic structure calculations have been reported in a paper titled "Solving multi-pole challenges in the GW100 benchmark enables precise low-scaling GW calculations" by Mia Schambeck, Dorothea Golze, and Jan Wilhelm. The authors address the limitations of conventional $GW$ algorithms, which exhibit a computational complexity that scales as $O(N^4)$ with the system size $N$. This complexity restricts the application of $GW$ methods to larger and more complex systems.
The study highlights the development of low-scaling $GW$ algorithms, which are actively being refined to improve efficiency. Benchmark tests conducted at the single-shot $G_0W_0$ level demonstrate that these new algorithms achieve high numerical precision for quasiparticle energies, with mean absolute deviations of less than 10 meV when compared to standard implementations using the widely recognized GW100 test set.
However, the authors note that achieving high precision for five specific molecules—O3, BeO, MgO, BN, and CuCN—remains a challenge, with deviations reaching several hundred meV at the $G_0W_0$ level. This issue arises from a spurious transfer of spectral weight in the calculations, leading to multi-pole features that low-scaling algorithms struggle to accurately describe.
To overcome these challenges, the authors propose incorporating eigenvalue self-consistency in the Green's function, referred to as $ ext{ev}GW_0$. This approach successfully separates the satellite and quasiparticle peaks, resulting in quasiparticle energies that closely align with reference calculations. The mean absolute error for the five challenging molecules is reduced to just 12 meV, indicating that low-scaling $GW$ methods with self-consistency are well-suited for computing frontier quasiparticle energies.
These findings could significantly enhance the ability to perform accurate electronic structure calculations in larger systems, potentially impacting various fields such as materials science and molecular chemistry. The full paper can be accessed at arXiv:2405.20473.