Formal O(N3) scaling GW calculations by block tensor decomposition for large molecule systems

TL;DR

This paper introduces a block tensor decomposition method that reduces the computational scaling of GW calculations to approximately O(N^2), enabling large molecular system simulations with improved efficiency.

Contribution

The authors extend the block tensor decomposition algorithm to achieve a formally O(N^3) scaling GW method, optimized for large molecular systems.

Findings

Achieved approximately O(N^2) scaling in test systems.

Enabled GW calculations for systems with over 3000 basis functions.

Demonstrated efficient and scalable large-scale GW computations.

Abstract

Within the framework of many-body perturbation theory based on Green's functions, the $GW$ approximation has emerged as a pivotal method for computing quasiparticle energies and excitation spectra. However, its high computational cost and steep scaling present significant challenges for applications to large molecular systems. In this work, we extend the block tensor decomposition (BTD) algorithm, recently developed in our previous work [J. Chem. Phys. 163, 174109 (2025)] for low-rank tensor compression, to enable a formally $O(N^3)$-scaling $GW$ algorithm. By integrating BTD with an imaginary-time $GW$ formalism and introducing a real space screening strategy for the polarizability, we achieve an observed scaling of approximately $O(N^2)$ in test systems. Key parameters of the algorithm are optimized on the S66 dataset using the JADE algorithm, ensuring a balanced compromise between accuracy and efficiency. Our BTD-based random phase approximation also exhibits $O(N^2)$ scaling, and eigenvalue-self-consistent $GW$ calculations become feasible for systems with over 3000 basis functions. This work establishes BTD as an efficient and scalable approach for large-scale $GW$ calculations in molecular systems.