Efficient Hybrid-Functional-Based Force and Stress Calculations for Periodic Systems with Thousands of Atoms

Area of Science:

• Computational Chemistry
• Materials Science
• Solid State Physics

Background:

• Hybrid functionals are crucial for accurate electronic structure calculations.
• Evaluating exact-exchange energy contributions, especially forces and stresses, is computationally demanding.
• Efficient algorithms are needed for large-scale material simulations.

Purpose of the Study:

• To present an efficient linear-scaling algorithm for analytical force and stress evaluation from exact-exchange energy.
• To enable accurate structural relaxation of large material systems using hybrid functionals.
• To benchmark the algorithm's performance and demonstrate its utility.

Main Methods:

• Formulation within numerical atomic orbital (NAO) basis sets.
• Utilizing the localized resolution-of-identity (LRI) technique for Coulomb integrals.
• Exploiting sparsity of expansion coefficients for linear-scaling behavior.
• Massively parallel implementation for large-scale computations.

Main Results:

• Achieved linear-scaling computational cost for exact-exchange force and stress evaluation.
• Demonstrated efficient structural relaxation for bulk materials with thousands of atoms.
• Validated the algorithm's performance through benchmark calculations and case studies.
• Showcased improved accuracy of hybrid functionals for perovskite materials under strain.

Conclusions:

• The developed algorithm provides a significant speedup for hybrid functional calculations.
• It enables accurate and efficient structural optimization of large and complex material systems.
• The method enhances the understanding of material properties, such as lone pair behavior in perovskites under strain.