<i>GW</i> -BSE for molecular excited states in REST: State-of-the-art methods, acceleration strategies, and the LAMB approximation

Abstract

We present a comprehensive implementation of the GW-BSE approach for molecular excited states within the Rust-based electronic structure toolkit. Utilizing the resolution-of-identity approximation and contour deformation technique, our implementation achieves both numerical robustness and computational efficiency. The module encompasses a hierarchy of established GW variants, including one-shot G0W0, eigenvalue-self-consistent evGW, and the cost-effective renormalized singles rsGW, followed by full or Tamm–Dancoff approximation BSE calculations. As an original methodological contribution, we introduce the low angular momentum basis approximation for BSE, which systematically truncates the auxiliary basis to reduce computational cost while preserving accuracy. Validation against MolGW confirms meV-level agreement for both quasiparticle and excitation energies. Benchmarking on the GW100 set demonstrates that rsGW achieves a mean absolute error of 376 meV for quasiparticle HOMO energies, substantially improving upon G0W0. To address the computational demands of GW-BSE, we propose and systematically evaluate three acceleration strategies: (i) a GW extrapolation scheme that reduces explicit quasiparticle calculations by an order of magnitude while maintaining chemical accuracy (errors below 43 meV); (ii) a virtual orbital cutoff that delivers a 9× speedup for a 94-atom Au(III) complex with minimal errors (10 meV); and (iii) the LAMB-BSE approximation, which achieves 1.5× acceleration while confirming the essential role of d-type functions, with deviations below 20 meV for both singlets and triplets. All functionalities presented in this study have been made publicly available in the REST open-source repository (https://gitee.com/restgroup), accompanied by detailed documentation and usage examples to facilitate community adoption. Together, these methodological developments establish the GW-BSE implementation in REST as an efficient and reliable tool for excited-state studies and provide practical guidelines for balancing accuracy and efficiency in molecular GW-BSE calculations.