Speeding up Hartree-Fock and Kohn-Sham calculations with first-order corrections

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Self-consistent field (SCF) calculations, including Hartree-Fock and Kohn-Sham methods, are fundamental to quantum chemistry.
• These methods can be computationally intensive, limiting their application to larger systems or complex problems.
• Improving the efficiency of SCF calculations is crucial for advancing computational chemistry research.

Purpose of the Study:

• To develop and present novel approaches for enhancing the efficiency of Hartree-Fock and Kohn-Sham SCF calculations.
• To introduce a first-order energy correction scheme to reduce computational cost.
• To evaluate the accuracy and performance of these new methods across various computational settings.

Main Methods:

• Implementation of a first-order energy correction during the final iteration of SCF calculations.
• Testing the approach with conventional and local density fitting (DF) SCF methods, varying auxiliary basis sets and fitting metrics.
• Application to seminumerical SCF methods using different integration grid qualities and incorporating occupied orbital resolution of identity (RI) exchange construction.

Main Results:

• The proposed energy correction effectively diminishes errors in SCF calculations.
• Significant speedups, up to 80%, were achieved across various tested methods and configurations.
• The enhanced efficiency did not lead to a significant loss of accuracy in total energies, reaction energies, or molecular geometries.

Conclusions:

• The novel approaches offer a substantial improvement in the computational efficiency of Hartree-Fock and Kohn-Sham SCF calculations.
• These methods provide a practical way to accelerate electronic structure calculations without compromising accuracy.
• The findings are expected to benefit a wide range of applications in computational and theoretical chemistry.