GPU algorithms for density matrix methods on MOPAC: linear scaling electronic structure calculations for large...

Area of Science:

• Computational chemistry
• Quantum chemistry
• Materials science

Background:

• Density matrix purification methods are essential for accurate electronic structure calculations in complex chemical systems.
• The efficiency of these methods is often limited by the performance of underlying linear algebra operations, particularly matrix-matrix multiplication.
• Existing methods struggle with large systems due to computational bottlenecks.

Purpose of the Study:

• To develop and implement a parallel central processing unit (CPU) and graphics processing unit (GPU) matrix-matrix multiplication algorithm (SP2) for accelerating density matrix purification.
• To integrate the SP2 algorithm into MOPAC's MOZYME method for enhanced semiempirical calculations.
• To evaluate the accuracy and performance of the GPU-accelerated SP2 algorithm.

Main Methods:

• Implementation of a parallel matrix-matrix multiplication algorithm (SP2) utilizing the symmetrical variable block row (SVBR) format.
• Integration of the SP2 algorithm within MOPAC's MOZYME method, including LMO Fock matrix assembly and atomic integral calculations.
• Leveraging the NVIDIA/CUDA platform for GPU acceleration and performance testing on a water cluster system.

Main Results:

• The implemented SP2 algorithm demonstrates accuracy and significant speed improvements.
• GPU acceleration achieved speedups of up to 40 times compared to single-threaded versions for a water cluster system (42,312 orbitals).
• The GPU-accelerated SP2 enables faster calculations for semiempirical wavefunctions and single-point energies for large molecules (>100,000 orbitals).

Conclusions:

• The parallel CPU and GPU SP2 algorithm offers a substantial acceleration for electronic structure calculations.
• This advancement allows for more rigorous calculations (stricter SCF criteria) on localized charged molecular systems.
• The developed method significantly reduces computation time for large molecular systems, making advanced calculations more accessible.