Implementation of McMurchie-Davidson Algorithm for Gaussian AO Integrals Suited for SIMD Processors.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Scientific Computing

Background:

• Efficient evaluation of Gaussian integrals is crucial for quantum chemistry calculations.
• Existing methods may not fully leverage modern hardware architectures like SIMD.

Purpose of the Study:

• To implement the McMurchie-Davidson (MD) evaluation scheme for 1- and 2-particle Gaussian atomic orbital (AO) integrals.
• To optimize the implementation for processors with Single Instruction Multiple Data (SIMD) instruction sets.

Main Methods:

• Variable-sized batches of shellsets of integrals are evaluated.
• Optimization focuses on floating-point instruction throughput, not just operation count.
• Utilizes standard C++ and the upcoming std::simd library feature.

Main Results:

• Achieves up to 50% of theoretical hardware peak FP64 performance on common SIMD platforms (AVX2, AVX512, NEON).
• Provides speedups of up to 30x over state-of-the-art methods (Libint's Obara-Saika-type schemes).
• Demonstrates high performance for both primitive and contracted integrals.

Conclusions:

• The new implementation offers a significant performance improvement for Gaussian integral evaluation on SIMD hardware.
• The use of standard C++ ensures portability and maintainability of the code.
• The implementation is available as part of the open-source LibintX library.