Low-Rank Approximations Accelerated Plane-Wave Hybrid Functional Calculations with k-Point Sampling

Area of Science:

• Computational Chemistry
• Materials Science
• Quantum Mechanics

Background:

• Hybrid functional calculations are crucial for accurate electronic structure but computationally expensive.
• Existing low-rank approximation methods (ACE, ISDF) reduce cost in real space but lack k-point sampling for periodic systems.
• Plane-wave basis sets are standard for periodic systems, necessitating reciprocal space methods.

Purpose of the Study:

• To develop a novel algorithm for efficient hybrid functional calculations in periodic systems.
• To enable the application of low-rank approximations in reciprocal space with k-point sampling.
• To reduce the computational complexity and memory footprint of these calculations.

Main Methods:

• Combined the adaptively compressed exchange (ACE) operator and interpolative separable density fitting (ISDF) algorithms.
• Developed an improved reciprocal space ACE operator and integrated k-point Fourier convolution.
• Implemented the new ACE-ISDF algorithm for periodic systems using a plane-wave basis set.

Main Results:

• Achieved a significant reduction in time complexity from O(N_e^2 N_k) to O(N_e N_k^2) for hybrid functional calculations.
• Demonstrated substantially lower prefactor and memory consumption compared to standard methods.
• Successfully incorporated k-point sampling into the ACE-ISDF framework for reciprocal space.

Conclusions:

• The ACE-ISDF algorithm offers a computationally efficient approach for hybrid functional calculations in periodic systems.
• This method significantly lowers computational cost and memory requirements, making larger systems tractable.
• The integration of k-point sampling is key to extending these approximations to reciprocal space.