TY - JOUR

T1 - Tempering stochastic density functional theory

AU - Nguyen, Minh

AU - Li, Wenfei

AU - Li, Yangtao

AU - Rabani, Eran

AU - Baer, Roi

AU - Neuhauser, Daniel

N1 - Publisher Copyright:
© 2021 Author(s).

PY - 2021/11/7

Y1 - 2021/11/7

N2 - 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 ≈4-5 for the total energy and ≈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.

AB - 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 ≈4-5 for the total energy and ≈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.

UR - http://www.scopus.com/inward/record.url?scp=85120749242&partnerID=8YFLogxK

U2 - 10.1063/5.0063266

DO - 10.1063/5.0063266

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C2 - 34852484

AN - SCOPUS:85120749242

SN - 0021-9606

VL - 155

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

IS - 20

M1 - 204105

ER -