Fast periodic Gaussian density fitting by range separation

Area of Science:

• Computational chemistry
• Materials science
• Quantum mechanics

Background:

• Periodic Gaussian density fitting (GDF) is crucial for accurate electronic structure calculations.
• Existing GDF methods can be computationally intensive, especially for large systems or dense k-point meshes.

Purpose of the Study:

• To introduce an efficient and accurate implementation of periodic Gaussian density fitting.
• To improve the computational scaling of GDF for periodic systems.

Main Methods:

• Range-separation of the Coulomb kernel into short-range (real space) and long-range (reciprocal space) components.
• Implementation of algorithmic optimizations for evaluating three-center integrals.
• Development of range-separated Gaussian density fitting (RSGDF).

Main Results:

• RSGDF demonstrates sublinear to linear scaling with the number of k-points for common mesh sizes.
• Achieved approximately ten-fold speedups compared to previous GDF methods for 3D solids.
• Introduced minimal precision loss, with errors around 10^-5 E_h in Hartree-Fock energy.

Conclusions:

• RSGDF offers a significant computational advantage for periodic electronic structure calculations.
• The method provides a balance between computational efficiency and accuracy.
• Precision can be systematically improved by adjusting auxiliary basis set size with minimal overhead.