Speeding Up Hartree-Fock in JuliaChem with Density Fitting

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• High-Performance Computing

Background:

• The restricted Hartree-Fock (RHF) method is a cornerstone of quantum chemistry for molecular electronic structure calculations.
• The computational cost of RHF scales steeply with system size, particularly the Fock matrix construction step.
• Density Fitting (DF) approximations offer a route to reduce this computational scaling.

Purpose of the Study:

• To implement and optimize the Density Fitting (DF) approximation within the restricted Hartree-Fock (RHF) method in the JuliaChem computational chemistry code.
• To leverage graphics processing units (GPUs) for accelerating the DF-RHF calculations.
• To develop a novel, adaptive DF-RHF algorithm for improved performance across different system sizes.

Main Methods:

• Integration of a symmetry-adapted, integral-screening Density Fitting (DF) algorithm into the JuliaChem RHF implementation.
• Adaptation of DF-RHF techniques for parallel execution on GPUs, exploiting their matrix multiplication capabilities.
• Development of an adaptive algorithm that dynamically selects between two DF-RHF approaches based on the number of basis functions.

Main Results:

• Significant reduction in the time required to compute the Fock matrix using the implemented DF-RHF method.
• Achieved up to a 2× speedup in Fock build times compared to existing state-of-the-art GPU DF-RHF implementations.
• Demonstrated the portability and performance of JuliaChem's CPU and GPU DF-RHF implementations across diverse hardware architectures.

Conclusions:

• The developed JuliaChem GPU DF-RHF implementation offers substantial performance gains for electronic structure calculations.
• The adaptive algorithm and direct operation on screened matrices contribute to the observed speedup.
• The high portability of the Julia code facilitates benchmarking and application on various computational platforms.