Accelerating correlated wave function calculations with hierarchical matrix compression of the two-electron integrals

Area of Science:

• Quantum Chemistry
• Computational Science
• Materials Science

Background:

• Matrix sparsity is key to accelerating quantum chemical calculations.
• Existing methods face challenges in time and space complexity for large systems.

Purpose of the Study:

• To present a novel hierarchical SOS-MP2 algorithm.
• To reduce time and space complexity in quantum chemical calculations using H2 compression.

Main Methods:

• Utilizes hierarchical matrix (H2) compression for the electron repulsion integral (ERI) tensor.
• Employs atomic orbital Laplace transform MP2 calculations.
• Leverages data-sparsity and element-wise sparsity in calculations.

Main Results:

• Achieves theoretical time and space complexity of O(N^2 log N).
• Demonstrates asymptotic time and space complexities better than O(N^2) in numerical tests.
• Successfully applied to linear alkanes and 3D water clusters.

Conclusions:

• The hierarchical SOS-MP2 algorithm offers significant computational advantages.
• H2 compression effectively reduces complexity for quantum chemical calculations.
• This approach paves the way for more efficient large-scale quantum simulations.