Dual-Grid and Mixed-Precision Methods for Accelerating Plane-Wave Hybrid Functional Electronic Structure Calculations

Area of Science:

• Condensed-matter physics and materials science
• Computational materials science
• Electronic structure theory

Background:

• Hybrid functionals incorporating exact Hartree-Fock exchange (HFX) are essential for accurate electronic structure predictions in materials.
• HFX calculations are computationally intensive, posing a bottleneck for large-scale simulations in density functional theory (DFT).

Purpose of the Study:

• To enhance the computational efficiency of plane-wave hybrid functional calculations.
• To enable larger and more complex material system simulations using DFT.

Main Methods:

• Introduction of dual-grid and mixed-precision techniques based on adaptively compressed exchange (ACE) and interpolative separable density fitting (ISDF) low-rank approximations.
• Dual-grid method reduces grid size by employing a smaller cutoff energy for HFX calculations.
• Mixed-precision method utilizes single precision for HFX construction while maintaining double precision for other DFT processes.

Main Results:

• Dual-grid and mixed-precision techniques significantly accelerate plane-wave hybrid functional calculations by several times.
• These methods achieve this acceleration with an acceptable trade-off in accuracy compared to original low-rank approximations.
• Successful demonstration of large-scale calculations (up to 8,000 silicon atoms) using a hybrid MPI/OpenMP parallel implementation.

Conclusions:

• The developed dual-grid and mixed-precision techniques offer a computationally efficient approach for HFX calculations in DFT.
• These advancements facilitate more extensive and accurate electronic structure studies of materials.
• The methods pave the way for tackling larger material systems and complex electronic structure problems.