Efficient all-electron hybrid density functionals for atomistic simulations beyond 10 000 atoms.

Area of Science:

• Computational Chemistry and Materials Science
• Electronic Structure Theory
• High-Performance Computing

Background:

• Hybrid density functional approximations (DFAs) provide high accuracy for electronic structure simulations.
• A computational bottleneck in hybrid DFAs is the exact exchange evaluation, limiting their application to large systems.
• Existing semilocal DFAs are computationally cheaper but less accurate.

Purpose of the Study:

• To develop a significantly optimized real-space implementation for the exact exchange evaluation in hybrid DFAs.
• To enable large-scale ab initio electronic structure simulations beyond ten thousand atoms.
• To improve the performance and scalability of hybrid DFAs on high-performance computing clusters.

Main Methods:

• Implemented a resolution-of-identity-based real-space method for exact exchange evaluation.
• Utilized refined Message Passing Interface (MPI) parallelization layers and MPI-3 shared memory arrays.
• Applied the optimized code to all-electron simulations under both non-periodic and periodic boundary conditions.

Main Results:

• Achieved substantial improvements in memory efficiency, performance, scalability, and workload distribution.
• Extended the applicability of hybrid DFAs to systems exceeding ten thousand atoms.
• Demonstrated benchmark performance for various chemical systems, including perovskites and ice crystals, up to 30,576 atoms.

Conclusions:

• The optimized implementation drastically reduces the computational cost of exact exchange evaluation.
• This advancement democratizes the use of accurate hybrid DFAs for large-scale materials and molecular simulations.
• Optimizations also benefited other computational parts, such as Hartree potential and force/stress calculations.