The Staggered Mesh Method: Accurate Exact Exchange Toward the Thermodynamic Limit for Solids

Area of Science:

• Computational Physics
• Materials Science
• Quantum Chemistry

Background:

• Hartree-Fock (HF) exchange energy convergence is slow in periodic systems as system size increases.
• Accurate calculation of HF exchange energy is crucial for predicting material properties.
• Existing methods like regular and truncated Coulomb methods face limitations in finite-size scaling.

Purpose of the Study:

• To evaluate the effectiveness of the staggered mesh method for accelerating finite-size convergence of exact exchange energy.
• To compare the staggered mesh method with existing approaches for periodic systems.
• To assess the performance of computationally cheaper variants: non-SCF and split-SCF staggered mesh.

Main Methods:

• Implementation and application of the staggered mesh method for Fock exchange energy calculations.
• Comparison with regular and truncated Coulomb methods on insulators and semiconductors.
• Numerical tests on simple solids to evaluate convergence of various material properties.

Main Results:

• The staggered mesh method demonstrably expedites the finite-size convergence rate for exact exchange energy.
• This improvement was observed across various insulators and semiconductors, outperforming regular and truncated Coulomb methods.
• Computationally cheaper non-SCF and split-SCF staggered mesh variants also showed enhanced convergence.
• The method improved convergence for band gaps, bulk moduli, lattice dimensions, energies, and phonon force constants.

Conclusions:

• The staggered mesh method offers a significant improvement for calculating exchange energy in periodic systems.
• It provides a more efficient pathway to achieve convergence towards the thermodynamic limit for key material properties.
• The method and its variants represent a valuable advancement for computational materials science and quantum chemistry.