Accelerating Fock Build via Hybrid Analytical-Numerical Integration

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Self-consistent field (SCF) and time-dependent density functional theory (TDDFT) calculations are computationally intensive, particularly for large molecules.
• Accelerating the Fock build, which involves calculating Coulomb (J) and exchange (K) matrices, is crucial for improving computational efficiency.

Purpose of the Study:

• To develop and implement a hybrid analytical-numerical integration scheme to accelerate the Fock build in SCF and TDDFT calculations.
• To improve the efficiency of calculations for large molecules with extended basis sets.

Main Methods:

• A hybrid approach combining analytical and numerical integration for the Coulomb matrix (J) evaluation, termed analytic-MECP (aMECP).
• A revised chain-of-spheres (COSX) algorithm for the exchange matrix (K) evaluation, termed analytic-COSx (aCOSx).
• Density matrix decomposition into atomic density matrices and remaining parts for selective analytical and numerical treatment.

Main Results:

• The combination of aMECP and aCOSx achieves high accuracy for ground-state SCF calculations with minimal energy error ($$).
• The hybrid scheme demonstrates significant efficiency gains for large molecules and extended basis sets.
• For TDDFT excitation energies, medium and coarse grids for MECP and COSx, respectively, are sufficient.

Conclusions:

• The proposed analytic-MECP and analytic-COSx hybrid Fock build scheme offers a substantial acceleration of SCF and TDDFT calculations.
• This method is particularly beneficial for large molecular systems, enabling more feasible and efficient quantum chemical computations.
• The accuracy and efficiency of the hybrid approach pave the way for broader applications in computational chemistry.