Highly Efficient Resolution-of-Identity Density Functional Theory Calculations on Central and Graphics Processing Units

We present an efficient method to evaluate Coulomb potential matrices using the resolution of identity approximation and semilocal exchange-correlation potentials on central (CPU) and graphics processing units (GPU). The new GPU-based RI-algorithm shows a high performance and ensures the favorable scaling with increasing basis set size as the conventional CPU-based method. Furthermore, our method is based on the J-engine algorithm [White, Head-Gordon, J. Chem. Phys. 1996, 7, 2620], which allows for further optimizations that also provide a significant improvement of the corresponding CPU-based algorithm. Due to the increased performance for the Coulomb evaluation, the calculation of the exchange-correlation potential of density functional theory on CPUs quickly becomes a bottleneck to the overall computational time. Hence, we also present a GPU-based algorithm to evaluate the exchange-correlation terms, which results in an overall high-performance method for density functional calculations. The algorithms to evaluate the potential and nuclear derivative terms are discussed, and their performance on CPUs and GPUs is demonstrated for illustrative calculations.

Automated summary

An efficient method utilizing GPU for evaluating Coulomb potential matrices and exchange-correlation terms in density functional calculations is proposed, showing high performance and scalability. The approach is based on the J-engine algorithm, allowing for further optimizations and significant improvements over CPU-based methods. Evaluating the exchange-correlation potential on CPUs has become a bottleneck, highlighting the need for GPU-based solutions for improved computational efficiency.