Self-averaging stochastic Kohn-Sham density-functional theory.

Area of Science:

• Computational physics
• Quantum chemistry
• Materials science

Background:

• Kohn-Sham density functional theory (KS-DFT) is a cornerstone for electronic structure calculations.
• Traditional KS-DFT faces computational challenges, particularly with large systems and density matrix sparseness.

Purpose of the Study:

• To reformulate KS-DFT as a statistical theory for improved computational efficiency.
• To develop a method that achieves sublinear scaling for electronic structure calculations.
• To overcome limitations associated with density matrix calculations in KS-DFT.

Main Methods:

• Formulating KS-DFT as a statistical theory using a trace formula for electron density.
• Utilizing correlated stochastic densities and focusing on energy per electron convergence.
• Demonstrating the approach on silicon nanocrystals, bypassing density matrix computation.

Main Results:

• Achieved the first report of sublinear scaling KS-DFT electronic structure calculations.
• Demonstrated insensitivity to density matrix sparseness, crucial for systems like silicon nanocrystals.
• Showcased seamless convergence to the thermodynamic limit through self-averaging.

Conclusions:

• The statistical formulation of KS-DFT offers a significant advancement in computational efficiency and applicability.
• This novel approach promises to extend the reach of KS-DFT to larger and more complex systems.
• The method represents a paradigm shift in understanding and performing electronic structure calculations.