Energy window stochastic density functional theory.

Area of Science:

• Computational chemistry
• Condensed matter physics
• Materials science

Background:

• Linear scaling density functional theory (DFT) is crucial for electronic structure properties of nanometer-scale systems.
• Stochastic DFT offers linear or sublinear scaling without density matrix sparsity, but often requires many stochastic orbitals to minimize statistical fluctuations.

Purpose of the Study:

• Introduce a novel stochastic DFT approach to efficiently reduce statistical fluctuations.
• Integrate the new method with an embedded fragmentation scheme for enhanced applicability.

Main Methods:

• Developed a new stochastic DFT by dividing the occupied space into energy windows.
• Projected stochastic orbitals using a single expansion onto all energy windows simultaneously.
• Applied the method to bulk silicon in a large supercell to demonstrate noise reduction.

Main Results:

• Achieved significant reduction in statistical noise for certain observable properties.
• Demonstrated the method's effectiveness on bulk silicon, showing noise reduction for forces and electron density.
• Provided theoretical analysis explaining noise reduction for specific ground-state properties.

Conclusions:

• The new stochastic DFT method efficiently reduces statistical noise, particularly for ground-state properties like forces and electron density.
• The approach is compatible with embedded fragmentation schemes, broadening its utility.
• This advancement offers a more accurate and efficient way to study electronic structures of nanoscale materials.