Multipole-based integral estimates for the rigorous description of distance dependence in two-electron integrals

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• Standard ab initio methods often use Schwarz screening for electron integrals.
• Schwarz screening neglects the 1/R distance decay of charge distributions, limiting accuracy.
• Efficient screening is crucial for large-scale quantum chemical calculations.

Purpose of the Study:

• To develop a rigorous and tight upper bound for four-center two-electron integrals.
• To introduce a screening method that accounts for 1/R distance decay.
• To improve the efficiency of ab initio calculations, particularly for electron correlation.

Main Methods:

• Derivation of multipole-based integral estimates (MBIE).
• Formulation of screening criteria valid for all angular momenta and multipole orders.
• Application of dipole-limited expansion for Hartree-Fock and density-functional theories.
• Integration with continuous fast multipole methods.

Main Results:

• MBIE provides rigorous upper bounds, improving upon Schwarz screening by including 1/R decay.
• Dipole-limited MBIE offers tight estimates with negligible computational overhead.
• Significant speedups observed: 2.1x for exchange and 1.3x for Coulomb parts in large systems.
• MBIE effectively exploits the 1/R4 decay of electron-correlation effects.

Conclusions:

• MBIE is a highly effective and efficient screening method for quantum chemistry.
• The method enhances computational performance in ab initio and correlated calculations.
• MBIE is well-suited for exploiting distance decay in electron correlation, enabling larger system studies.