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

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• The GW approximation is crucial for calculating quasiparticle energies and excitation spectra within many-body perturbation theory.
• High computational costs and scaling issues limit the application of GW methods to large molecular systems.

Purpose of the Study:

• To develop a computationally efficient and scalable GW algorithm for large molecular systems.
• To extend the block tensor decomposition (BTD) algorithm for low-rank tensor compression to GW calculations.

Main Methods:

• Integration of the block tensor decomposition (BTD) algorithm with an imaginary-time GW formalism.
• Implementation of a real-space screening strategy for polarizability calculations.
• Optimization of algorithm parameters using the JADE algorithm on the S66 dataset.

Main Results:

• Achieved a formally O(N^3) scaling GW algorithm with observed O(N^2) scaling in test systems.
• Demonstrated O(N^2) scaling for the BTD-based random phase approximation.
• Enabled eigenvalue-self-consistent GW calculations for systems exceeding 3000 basis functions.

Conclusions:

• The block tensor decomposition (BTD) algorithm offers an efficient and scalable approach for large-scale GW calculations.
• This method significantly enhances the feasibility of electronic structure calculations for complex molecular systems.