Efficient Algorithms for GPU Accelerated Evaluation of the DFT Exchange-Correlation Functional

Area of Science:

• Computational Chemistry
• Materials Science
• Quantum Mechanics

Background:

• Kohn-Sham density functional theory (KS-DFT) is crucial for electronic structure calculations.
• Hardware-aware implementations enhance KS-DFT efficiency for larger systems and machine learning datasets.
• GPU acceleration is key to advancing computational chemistry.

Purpose of the Study:

• To comparatively study four GPU-accelerated algorithms for KS-DFT exchange-correlation (XC) potential evaluation.
• To identify the most efficient algorithms for different molecular system types and sizes.
• To improve computational cost and enable larger-scale simulations.

Main Methods:

• Developed and benchmarked four GPU-accelerated KS-DFT XC potential evaluation algorithms.
• Utilized batched dense linear algebra techniques.
• Tested algorithms on diverse molecular systems including glycine chains, water clusters, and diamond nanoparticles.

Main Results:

• Two batched linear algebra approaches outperformed others across benchmarks.
• Batched XC matrix formation from density matrix is best for large, sparse systems (>1000 basis functions).
• Molecular orbital coefficient-based algorithms excel for smaller, denser systems, despite higher scaling.

Conclusions:

• GPU-accelerated KS-DFT algorithms significantly reduce computational cost (1.4-5.2x speedup).
• Algorithm choice depends on system size and density, impacting performance.
• Future work should focus on mixed-precision and emerging GPU architectures for further gains.