Stochastic density functional theory: Real- and energy-space fragmentation for noise reduction

Area of Science:

• Computational Materials Science
• Quantum Chemistry
• Condensed Matter Physics

Background:

• Stochastic density functional theory (sDFT) offers linear scaling for ground-state properties of materials but introduces statistical noise.
• Accurate calculation of forces from sDFT is essential for structural determination, but is hindered by statistical fluctuations.
• Previous embedding schemes reduced noise by fragmenting systems in real or energy space, but further reduction is needed for chemical accuracy.

Purpose of the Study:

• To develop and demonstrate a novel approach for significantly reducing statistical noise in sDFT calculations.
• To improve the accuracy of ground-state properties, including electron density, total energy, and nuclear forces, obtained via sDFT.
• To enhance the reliability of sDFT for studying extended materials, particularly for applications requiring precise structural information.

Main Methods:

• Combined existing real-space and energy-window embedding schemes within sDFT.
• Introduced a new embedding approach utilizing overlapped fragments and energy windows.
• Applied the combined and new methods to calculate ground-state properties for a G-center in bulk silicon.

Main Results:

• The novel embedding approach significantly lowered statistical noise in sDFT calculations.
• Demonstrated substantial noise reduction for key ground-state observables: electron density, total energy, and forces on nuclei.
• The combined embedding strategy proved effective for improving the accuracy of sDFT predictions.

Conclusions:

• The developed embedding schemes provide a powerful strategy to mitigate statistical errors in sDFT.
• This noise reduction is critical for achieving chemical accuracy and enabling reliable structural predictions using sDFT forces.
• The new approach enhances the applicability of sDFT for complex material systems.