Structure optimization with stochastic density functional theory.

Area of Science:

• Computational Chemistry
• Materials Science
• Condensed Matter Physics

Background:

• Linear-scaling methods are crucial for large-scale electronic structure calculations in density functional theory (DFT).
• Existing linear-scaling DFT methods often require density matrix localization or embedding, limiting their scope.
• Stochastic DFT (sDFT) offers linear/sub-linear scaling without these limitations but suffers from fluctuating observables.

Purpose of the Study:

• To develop and evaluate structure optimization techniques for stochastic density functional theory (sDFT).
• To address the challenge of fluctuating nuclear forces in sDFT for accurate structural determination.
• To assess the computational efficiency of different stochastic optimization algorithms within sDFT.

Main Methods:

• Integration of advanced noise-reduction schemes for sDFT.
• Implementation and comparison of stochastic gradient descent (SGD) and its variants (e.g., SGD with momentum).
• Application of Hessian-based stochastic optimization algorithms, specifically the stochastic Broyden-Fletcher-Goldfarb-Shanno (BFGS) method.

Main Results:

• Successful implementation of structure optimization directly within the sDFT framework.
• Comparative analysis of SGD-based and Hessian-based stochastic optimization methods.
• Detailed assessment of computational efficiency across different optimization parameters and supercell sizes for bulk silicon.

Conclusions:

• The combination of noise reduction and stochastic optimization enables reliable structure optimization in sDFT.
• Performance evaluation provides insights into the practical applicability of these methods for large systems.
• This work paves the way for efficient and accurate prediction of ground-state properties for extended materials using sDFT.