Efficient preconditioning of the electronic structure problem in large scale ab initio molecular dynamics simulations

Area of Science:

• Computational chemistry
• Materials science
• Quantum mechanics

Background:

• Electronic structure calculations are crucial for understanding material properties.
• Large-scale simulations often face computational bottlenecks.
• Existing preconditioning methods can be computationally expensive.

Purpose of the Study:

• To develop an improved preconditioning scheme for electronic structure calculations.
• To reduce the computational cost of preconditioner construction.
• To accelerate molecular dynamics (MD) simulations.

Main Methods:

• Developed a preconditioner using the full Kohn-Sham matrix without computationally intensive diagonalisation.
• Introduced a modified Hotelling's iterative inversion for preconditioner matrix inversion.
• Applied filtering of small elements during sparse matrix multiplication for linear scaling.

Main Results:

• Achieved a significant reduction in preconditioner construction cost.
• Demonstrated a 2-5 fold speedup per MD step for systems of hundreds to thousands of atoms.
• Maintained rapid convergence and robustness in simulations.

Conclusions:

• The improved preconditioning scheme offers a substantial speedup for large-scale electronic structure calculations.
• This method effectively addresses computational bottlenecks in molecular dynamics simulations.
• The approach is robust and efficient for practical applications in computational materials science.