A Sparse Self-Consistent Field Algorithm and Its Parallel Implementation: Application to Density-Functional-Based...

Area of Science:

• Computational Chemistry
• Materials Science
• Quantum Mechanics

Background:

• Solving self-consistent problems is crucial in Hartree-Fock and density functional theory.
• Traditional methods face computational challenges with large systems.
• Efficient algorithms are needed to leverage modern computing architectures.

Purpose of the Study:

• To present a novel algorithm and its parallel implementation for solving self-consistent problems.
• To exploit matrix sparsity using local molecular orbitals.
• To efficiently utilize symmetric multiprocessing (SMP) computer architectures.

Main Methods:

• Developed a parallel algorithm leveraging local molecular orbitals for sparse matrices.
• Implemented the algorithm to optimize performance on SMP systems.
• Applied the method within the density-functional-based tight binding (DFTB) framework.

Main Results:

• Enabled single-point calculations on systems with millions of atoms on large SMP machines.
• Achieved significant acceleration for intermediate systems (1,000-100,000 atoms) on standard servers.
• Demonstrated controlled error in total energy due to orbital coefficient cutoffs, below SCF convergence criteria.

Conclusions:

• The presented algorithm offers a scalable and efficient solution for large-scale electronic structure calculations.
• The parallel implementation effectively utilizes modern SMP architectures.
• This approach significantly advances the feasibility of accurate calculations for very large molecular systems.