Hartree-Fock calculations with linearly scaling memory usage

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Hartree-Fock calculations are fundamental in quantum chemistry.
• Traditional methods exhibit cubic or higher scaling, limiting system size.
• Efficient algorithms are crucial for simulating larger, more complex systems.

Purpose of the Study:

• To develop and implement algorithms for linear-scaling Hartree-Fock calculations.
• To reduce computational resource requirements (time and memory) proportional to system size.
• To enable large-scale electronic structure calculations on single computing nodes.

Main Methods:

• Implementation of algorithms for direct computation of the Hartree-Fock exchange matrix in sparse form.
• Utilizing sparse matrix techniques to minimize addressing overhead.
• Benchmarking calculations on systems up to 11,650 atoms and 67,204 Gaussian basis functions.

Main Results:

• Demonstrated linear scaling in both time and memory requirements.
• Achieved efficient calculations on a single computer with 32 GB of memory.
• Showcased sparsity of overlap, Fock, and density matrices for various system sizes.
• Reported band gap calculations for linear and 3D systems.

Conclusions:

• The developed algorithms provide a significant advancement for large-scale Hartree-Fock calculations.
• Linear scaling performance allows for unprecedented system sizes on standard hardware.
• The sparse matrix approach offers a practical solution for computational efficiency in quantum chemistry.