Efficient evaluation of exact exchange for periodic systems via concentric atomic density fitting

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Accurate electronic structure description in periodic systems is vital for materials science.
• Exact Hartree-Fock (HF) exchange is computationally demanding in ab initio and hybrid density functional methods.
• Existing methods for HF exchange in periodic systems face computational challenges.

Purpose of the Study:

• To develop an efficient formulation for periodic exact Hartree-Fock (HF) exchange.
• To reduce the computational cost of HF exchange calculations in periodic systems.
• To improve the accuracy of electronic structure calculations for periodic materials.

Main Methods:

• Linear combination of atomic orbitals (LCAO) representation.
• Concentric atomic density fitting approximation for HF exchange.
• Domain-free local density fitting approach.
• Real two-center multipole expansions and spheropole-compensated unit cell densities for Coulomb contribution.

Main Results:

• Significant reduction in computational cost for exact exchange compared to conventional methods.
• Sub-millihartree/atom errors in absolute HF energies.
• Good cancellation of fitting errors in relative energies.
• Demonstrated efficiency and accuracy of the novel formulation.

Conclusions:

• The proposed method offers an efficient and accurate way to compute periodic HF exchange.
• This advancement facilitates more reliable ab initio and hybrid density functional calculations for periodic systems.
• The approach addresses key computational bottlenecks in electronic structure theory for materials.