Even Faster Exact Exchange for Solids via Tensor Hypercontraction.

Area of Science:

• Computational Chemistry
• Materials Science
• Quantum Mechanics

Background:

• Hybrid density functional theory (DFT) is computationally expensive for large periodic systems due to the cost of exact exchange calculations.
• Developing efficient methods is crucial for applying accurate quantum mechanical simulations to larger and more complex materials.

Purpose of the Study:

• To reduce the computational scaling of periodic hybrid DFT calculations.
• To enable accurate electronic structure calculations for larger systems by lowering computational cost and memory requirements.

Main Methods:

• Application of the tensor hypercontraction (THC) approximation, also known as interpolative separable density fitting, to periodic hybrid DFT.
• Utilizing the Gaussian plane wave approach with Gaussian-type orbitals.
• Development of an algorithm to fit only occupied orbital products via THC (THC-oo-K) for further computational savings.

Main Results:

• The proposed THC method lowers the computational scaling with respect to the number of basis functions and k-points.
• The THC-oo-K algorithm exhibits linear scaling with k-points and cubic scaling with unit cell size, with no explicit dependence on basis set size.
• Significant speedups and reduced memory usage were observed, particularly for larger k-point meshes.
• Adequate accuracy was achieved for self-consistent calculations, as demonstrated by hybrid DFT calculations on a benzene crystal.

Conclusions:

• Tensor hypercontraction (THC) provides an efficient and accurate approach for periodic hybrid DFT calculations.
• The THC-oo-K algorithm effectively reduces computational cost and memory, making larger systems tractable.
• This method holds promise for advancing computational materials science and condensed matter physics research.