Automatic Selection of Integral Thresholds by Extrapolation in Coulomb and Exchange Matrix Constructions

Area of Science:

• Computational chemistry
• Quantum chemistry
• Materials science

Background:

• Accurate computation of Coulomb and exchange matrices is crucial for Hartree-Fock and Kohn-Sham electronic structure methods.
• Existing methods may lack precise control over the accuracy of these fundamental matrices.

Purpose of the Study:

• To develop and demonstrate a method for computing Coulomb and exchange matrices with predetermined accuracy.
• To enable complete error control throughout self-consistent field (SCF) calculations.

Main Methods:

• Utilizing modern algorithms for Coulomb and exchange matrix evaluation.
• Employing an extrapolation method that relates error matrix norm to threshold value (ε = cτ(α)).
• Automatically selecting integral thresholds based on a requested accuracy level.

Main Results:

• Numerical validation showing the relationship between error norm and threshold (ε = cτ(α)).
• Demonstration of the method's effectiveness across diverse systems (protein-like, water clusters, graphene).
• Successful automatic selection of integral thresholds to meet accuracy requirements.

Conclusions:

• The presented method achieves predetermined accuracy for Coulomb and exchange matrices.
• This work is a significant advancement towards full error control in SCF calculations.
• The approach is applicable to various molecular and material systems.