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

Kohn-Sham density functional theory (KS-DFT) has become a cornerstone for studying the electronic structure of molecules and materials. Improving algorithmic efficiency through hardware-aware implementations enables application to larger systems and more efficient generation of larger training data sets for machine-learning. In this work, we present a comparative study of four GPU-accelerated algorithms for evaluating the KS-DFT exchange-correlation (XC) potential with an atom-centered Gaussian basis. Two approaches, both leveraging batched dense linear algebra, are found to outperform the others across a suite of molecular benchmarks. We show that batched formation of the XC matrix from the density matrix yields the best performance for large (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>></mml:mo><mml:mi>O</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>3</mml:mn></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math> basis functions), sparse systems such as glycine chains and water clusters. In contrast, for smaller and denser systems such as diamond nanoparticles, especially if employing large basis sets, algorithms that use the underlying molecular orbital coefficients offer superior performance, despite their higher formal scaling. Our implementations deliver speedups of 1.4-5.2× for XC potential evaluation relative to leading GPU-accelerated KS-DFT codes, significantly lowering the computational cost and enabling the routine use of larger integration grids. Finally, we outline directions for continued performance improvements in light of emerging GPU architectures with emphasis on utilizing mixed-precision capabilities.