Tempering stochastic density functional theory

We introduce a tempering approach with stochastic density functional theory (sDFT), labeled t-sDFT, which reduces the statistical errors in the estimates of observable expectation values. This is achieved by rewriting the electronic density as a sum of a warm component complemented by colder correction(s). Since the warm component is larger in magnitude but faster to evaluate, we use many more stochastic orbitals for its evaluation than for the smaller-sized colder correction(s). This results in a significant reduction in the statistical fluctuations and systematic deviation compared to sDFT for the same computational effort. We demonstrate the method's performance on large hydrogen-passivated silicon nanocrystals, finding a reduction in the systematic deviation in the energy by more than an order of magnitude, while the systematic deviation in the forces is also quenched. Similarly, the statistical fluctuations are reduced by factors of approximate to 4-5 for the total energy and approximate to 1.5-2 for the forces on the atoms. Since the embedding in t-sDFT is fully stochastic, it is possible to combine t-sDFT with other variants of sDFT such as energy-window sDFT and embedded-fragmented sDFT. Published under an exclusive license by AIP Publishing.

Automated summary

The t-sDFT method reduces statistical errors in estimating observable expectation values by decomposing the electronic density into a warm component and a colder correction, with a significant improvement compared to sDFT under the same computational effort. The method demonstrates improved performance for large hydrogen-passivated silicon nanocrystals, reducing systematic deviation in energy and forces while also decreasing statistical fluctuations.