Stochastic Optimally Tuned Range-Separated Hybrid Density Functional Theory.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Density Functional Theory (DFT) is a cornerstone of electronic structure calculations.
• Range-separated hybrid functionals offer improved accuracy but are computationally expensive.
• Accurate calculation of quasiparticle energies, especially for frontier orbitals, is crucial for understanding material properties.

Purpose of the Study:

• To develop a computationally efficient stochastic formulation of optimally tuned range-separated hybrid DFT.
• To enable accurate calculation of quasiparticle energies for large systems, such as silicon nanocrystals.
• To provide a self-consistent Hamiltonian for advanced postprocessing techniques.

Main Methods:

• Stochastic representations of the Coulomb convolution integral.
• Stochastic representations of the generalized Kohn-Sham density matrix.
• Application to silicon nanocrystals up to over 3000 electrons.

Main Results:

• Significant reduction in computational effort and scaling of the nonlocal exchange operator.
• Accurate description of quasiparticle energies for frontier orbitals, comparable to stochastic GW methods.
• Excellent agreement for fundamental band gaps and good agreement for band edge excitations.
• Very low statistical errors in total energy for large systems.

Conclusions:

• The stochastic range-separated hybrid DFT approach offers a balance between computational cost and accuracy.
• It provides a viable and efficient alternative to traditional methods for large quantum systems.
• The self-consistent Hamiltonian enables further sophisticated calculations, enhancing its utility.