Efficient Hartree-Fock exchange algorithm with Coulomb range separation and long-range density fitting.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Electron repulsion integrals are computationally intensive in quantum chemistry.
• Conventional methods face scaling challenges (N4) for large molecular systems.
• Accurate calculation of Coulomb potentials is crucial for electronic structure methods.

Purpose of the Study:

• To develop a more efficient and accurate method for calculating electron repulsion integrals.
• To reduce the computational cost of Hartree-Fock calculations for large molecules.
• To improve the accuracy of density fitting methods for Coulomb potentials.

Main Methods:

• Separating the Coulomb potential into short-range and long-range components.
• Utilizing analytical algorithms for short-range interactions due to Gaussian-type orbital locality.
• Approximating long-range Coulomb integrals using the density fitting method with a small auxiliary basis.

Main Results:

• The range-separated density fitting method significantly reduces computational effort compared to conventional schemes.
• Achieved more than twice the overall performance for large molecules in Hartree-Fock calculations.
• Demonstrated higher accuracy than conventional density fitting methods, reducing energy errors to < 0.1 μEh/atom.

Conclusions:

• Range separation combined with long-range density fitting offers a computationally efficient and accurate approach for large molecular systems.
• This method overcomes limitations of traditional integral evaluation and density fitting techniques.
• Enables highly accurate Hartree-Fock energy calculations with reduced computational cost.