Stochastic Density Functional Theory

Eran Rabani
University of California, Berkeley (UC Berkeley)

Stochastic density functional theory (sDFT) is becoming a valuable tool for studying ground-state properties of extended materials. The computational complexity of describing the Kohn–Sham orbitals is replaced by introducing a set of random (stochastic) orbitals leading to linear and often sub-linear scaling of certain ground-state observables at the account of introducing a controlled statistical error. Schemes to reduce the noise are essential, for example, for determining the structure using the forces obtained from sDFT as well as controlling the bias resulting for the self-consistency of the Kohn-Sham equations.

In this talk, I will review our recent efforts to mitigate the statistical fluctuations using embedding schemes, based on fragmenting the system either in real space or slicing the occupied space into energy windows, allowing for a significant reduction in the statistical fluctuations. As demonstrated for G-center in bulk silicon, the new approach significantly lowers the noise for ground-state properties, such as the electron density, total energy per electron, and forces on the nuclei. Combined with a stochastic minimization algorithm, only a few tens of stochastic orbitals are needed to determine the ground state structure to within chemical accuracy, for systems with tens of thousands of electrons. Furthermore, we discussed the advantages of using sDFT to describe warm dense matter, particularly, at elevated temperatures, prohibitive for deterministic DFT due to the partial occupation of a very large number of high-energy Kohn-Sham eigenstates.

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