Optimizing two-electron repulsion integral calculations with McMurchie-Davidson method on graphic processing unit

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• High-Performance Computing

Background:

• Two-electron repulsion integrals are computationally intensive in quantum chemistry.
• Existing methods, like McMurchie-Davidson (MD), require significant computational resources.
• Optimization for graphics processing units (GPUs) is crucial for accelerating these calculations.

Purpose of the Study:

• To develop and present optimized methods for two-electron repulsion integral calculations on GPUs.
• To enhance the efficiency of the McMurchie-Davidson (MD) method.
• To achieve significant speedups compared to existing CPU-based calculations.

Main Methods:

• Introduction of a novel Boys function evaluation method for GPU computation.
• Combination of series summation, error function, and finite sum formula for performance.
• Derivation of three optimization approaches based on Hermite expansion coefficients and recurrence relations.
• Implementation of a common sub-expression elimination (CSE) method derived from general term formula equalities.

Main Results:

• The new recurrence relation for coefficient evaluation saves 26% float operations and 37% memory operations on average.
• The optimized method achieved up to 3.09 speedups compared to the original MD method on GPU.
• Achieved up to 92.75 speedups compared to GAMESS calculations on a central processing unit (CPU).

Conclusions:

• The presented optimization methods significantly enhance the performance of two-electron repulsion integral calculations on GPUs.
• The novel approaches, including CSE, offer substantial computational advantages for quantum chemistry simulations.
• These GPU-accelerated methods pave the way for more efficient and faster electronic structure calculations.