Robust Periodic Fock Exchange with Atom-Centered Gaussian Basis Sets.

Area of Science:

• Computational chemistry
• Solid-state physics

Background:

• Periodic Fock exchange calculations are crucial for accurate electronic structure.
• Divergence issues arise with finite k-point sampling in periodic calculations.
• Gaussian-type orbitals (GTOs) offer computational advantages but require careful implementation in periodic systems.

Purpose of the Study:

• To implement and validate a robust periodic Fock exchange for atom-centered GTOs.
• To compare the minimum image convention (MIC) and truncated Coulomb interaction (TCI) schemes for divergence removal.
• To assess the stability and accuracy of these methods for Hartree-Fock calculations.

Main Methods:

• Implementation of periodic Fock exchange using GTOs.
• Comparison of MIC and TCI schemes with k-meshes.
• Analysis of four-center integrals and their impact on exchange and density matrices.
• Hartree-Fock calculations for semiconducting and insulating systems.

Main Results:

• TCI scheme introduces artifacts in GTO integrals, affecting exchange and density matrices.
• MIC scheme avoids these artifacts, leading to more stable self-consistent field convergence.
• Both MIC and TCI provide comparable energies for large supercells or k-meshes.
• The implemented GTO-based method shows excellent agreement with plane-wave codes.

Conclusions:

• The minimum image convention (MIC) is the preferred method over TCI for periodic Fock exchange with GTOs due to improved stability.
• The robust implementation is validated against other GTO-based methods and plane-wave codes.
• This work provides a reliable computational tool for electronic structure calculations in periodic systems.