Stochastic Optimally-Tuned Ranged-Separated Hybrid Density Functional Theory

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.

7 pages, 3 figures

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Cited by in corpus (17)

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• Swift $GW$ beyond $10,000$ electrons using fractured stochastic orbitals
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• Simulations of nonradiative processes in semiconductor nanocrystals
• Stochastic Resolution-of-the-Identity Auxiliary-Field Quantum Monte Carlo: Scaling Reduction without Overhead
• Equilibrium configurations of large nanostructures using the embedded saturated-fragments stochastic density functional theory
• Spontaneous charge carrier localization in extended one-dimensional systems
• Decomposition and embedding in the stochastic $GW$ self-energy
• Stochastic Time-Dependent DFT with Optimally Tuned Range-Separated Hybrids: Application to Excitonic Effects in Large Phosphorene Sheets
• Stochastically Realized Observables for Excitonic Molecular Aggregates
• Optimized Attenuated Interaction: Enabling Stochastic Bethe-Salpeter Spectra for Large Systems
• Plane-Wave-Based Stochastic-Deterministic Density Functional Theory for Extended Systems
• Dopant levels in large nanocrystals using stochastic optimally tuned range-separated hybrid density functional theory
• GW with hybrid functionals for large molecular systems
• Efficient Langevin dynamics for "noisy" forces
• Tuning the range separation parameter in periodic systems
• Stochastic GW calculations for molecules