Real-space solution to the electronic structure problem for nearly a million electrons.

Area of Science:

• Computational materials science
• Quantum chemistry
• Condensed matter physics

Background:

• Investigating the electronic structure of large nanoclusters is crucial for understanding their properties.
• Previous methods were limited in scalability for systems with a high number of atoms and electrons.

Purpose of the Study:

• To perform a large-scale Kohn-Sham density functional theory (KS-DFT) calculation on a silicon nanocluster.
• To demonstrate the efficiency of the real-space approach for electronic structure calculations on high-performance computing platforms.

Main Methods:

• Utilized a real-space, high-order finite-difference method for KS-DFT.
• Employed Chebyshev-filtered subspace iteration for faster eigenspace convergence.
• Implemented blockwise Hilbert space-filling curves for sparse matrix-vector multiplications within the PARSEC code.
• Replaced the orthonormalization + Rayleigh-Ritz step with a generalized eigenvalue problem.

Main Results:

• Successfully calculated the electronic structure of a 20 nm spherical silicon nanocluster (202,617 silicon atoms, 13,836 hydrogen atoms).
• Achieved two Chebyshev-filtered subspace iterations, providing a good approximation of the electronic density of states.
• Demonstrated the scalability of the real-space approach, pushing the limits to nearly 10^6 electrons.

Conclusions:

• The real-space approach is highly effective for large-scale electronic structure calculations.
• This work highlights the potential of modern high-performance computing for tackling complex materials science problems.
• The developed methods enable efficient parallelization for future investigations of large atomic systems.