Tempering stochastic density functional theory

Area of Science:

• Computational Chemistry
• Materials Science
• Quantum Mechanics

Background:

• Stochastic density functional theory (sDFT) is a computational method used to estimate electronic properties.
• sDFT can suffer from significant statistical errors and systematic deviations, limiting its accuracy.
• Accurate and efficient methods are crucial for studying large systems like nanocrystals.

Purpose of the Study:

• To introduce a novel tempering approach, termed t-sDFT, to mitigate statistical errors in sDFT calculations.
• To improve the accuracy of observable expectation values estimated via sDFT.
• To enhance the computational efficiency and reduce systematic deviations in electronic structure calculations.

Main Methods:

• The t-sDFT method rewrites the electronic density as a sum of a dominant "warm" component and smaller "colder" corrections.
• Stochastic orbitals are used, with a significantly larger number allocated to the "warm" component for faster evaluation.
• The approach was tested on large hydrogen-passivated silicon nanocrystals.

Main Results:

• t-sDFT demonstrated a reduction in systematic deviation for energy by over an order of magnitude compared to sDFT.
• Systematic deviations in forces were also effectively quenched.
• Statistical fluctuations were reduced by factors of approximately 4-5 for total energy and 1.5-2 for atomic forces.

Conclusions:

• The tempering approach in t-sDFT significantly reduces both statistical errors and systematic deviations in sDFT calculations.
• t-sDFT offers improved accuracy and efficiency for computational chemistry and materials science applications.
• The fully stochastic nature of t-sDFT allows for integration with other sDFT variants.