Stochastic Optimally-Tuned Ranged-Separated Hybrid Density Functional Theory

TL;DR

This paper introduces a stochastic formulation of range-separated hybrid density functional theory that reduces computational effort while maintaining high accuracy in quasiparticle energy calculations for large systems.

Contribution

It presents a novel stochastic approach to optimally-tuned range-separated hybrid DFT, enabling efficient and accurate large-scale electronic structure calculations.

Findings

Accurate quasiparticle energies for silicon nanocrystals exceeding 3000 electrons.

Excellent agreement with stochastic GW for fundamental band gaps.

Low statistical errors in total energy calculations for large systems.

Abstract

We develop a stochastic formulation of the optimally-tuned range-separated hybrid density functional theory which enables significant reduction of the computational effort and scaling of the non-local exchange operator at the price of introducing a controllable statistical error. Our method is based on stochastic representations of the Coulomb convolution integral and of the generalized Kohn-Sham density matrix. The computational cost of the approach is similar to that of usual Kohn-Sham density functional theory, yet it provides much more accurate description of the quasiparticle energies for the frontier orbitals. This is illustrated for a series of silicon nanocrystals up to sizes exceeding 3000 electrons. Comparison with the stochastic GW many-body perturbation technique indicates excellent agreement for the fundamental band gap energies, good agreement for the band-edge quasiparticle excitations, and very low statistical errors in the total energy for large systems. The present approach has a major advantage over one-shot GW by providing a self-consistent Hamiltonian which is central for additional post-processing, for example in the stochastic Bethe-Salpeter approach.