Accelerating Hartree-Fock and Density Functional Theory Calculations Using Tensor Hypercontraction.

Area of Science:

• Computational chemistry
• Quantum chemistry
• Materials science

Background:

• Self-consistent field (SCF) methods like Hartree-Fock and Density Functional Theory are crucial in computational chemistry.
• Accelerating these computationally intensive methods is essential for studying larger and more complex systems.

Purpose of the Study:

• To develop and implement a novel tensor hypercontraction (THC) approach for accelerating SCF calculations.
• To achieve a more efficient Fock matrix construction with reduced computational scaling.

Main Methods:

• Development of a tensor hypercontraction (THC) construction with O(N^3) formal scaling.
• Implementation of an empirically O(N^2) scaling Fock matrix construction that avoids recalculating two-electron repulsion integrals.
• Utilization of a density-difference ansatz for accurate energy calculations.

Main Results:

• The THC implementation achieves a 2-4x speedup over existing integral-direct methods.
• Achieved errors below 1 kcal/mol for relative energies in protein systems up to 3000 basis functions.
• Demonstrated the effectiveness of using a linear solver for optimizing matrix factors in THC.

Conclusions:

• The developed THC method significantly accelerates SCF calculations.
• This approach enables accurate and efficient computation of electronic structures for large molecular systems.
• The optimization strategy using linear solvers has broad applicability for THC methods.