Multipole-based distance-dependent screening of Coulomb integrals.

Area of Science:

• Computational chemistry
• Quantum chemistry

Background:

• Two-electron repulsion integrals (ERIs) are fundamental in electronic structure calculations.
• Efficient computation of ERIs is crucial for large-scale quantum chemistry simulations.

Purpose of the Study:

• To develop a new, rigorous upper bound estimate for ERIs.
• To apply this estimate for accelerating the calculation of the Fock exchange matrix.

Main Methods:

• Utilizing a multipole expansion of charge distributions.
• Deriving an upper bound for ERIs in local atomic basis sets.
• Implementing the estimate to screen negligible contributions in Fock matrix construction.

Main Results:

• A new rigorous upper bound for two-electron repulsion integrals (ERIs) is derived.
• The scheme is applicable to any formalism using ERIs.
• Screening negligible contributions accelerates exchange matrix construction by up to a factor of two.
• No further approximations are introduced beyond the ERI estimate.

Conclusions:

• The proposed multipole-based ERI estimate offers a computationally efficient approach.
• Significant acceleration in Fock exchange matrix construction is achieved without compromising accuracy.
• This method provides a valuable tool for large-scale quantum chemical calculations.