Sublinear scaling for time-dependent stochastic density functional theory.

Area of Science:

• Computational Physics
• Quantum Chemistry
• Materials Science

Background:

• Time-dependent density functional theory (TDDFT) is crucial for understanding electronic properties.
• Calculating correlation energy and absorption spectra can be computationally intensive.
• Stochastic methods offer potential for more efficient quantum mechanical calculations.

Purpose of the Study:

• To develop a novel stochastic approach for time-dependent density functional theory (TDDFT).
• To compute the absorption cross section and random phase approximation (RPA) correlation energy efficiently.
• To assess the performance of the method for silicon nanocrystals.

Main Methods:

• Time-propagation of a limited set of stochastic orbitals.
• Projection of orbitals onto the occupied space.
• Propagation using time-dependent Kohn-Sham equations.
• Implementation using real-space grids for silicon nanocrystals.

Main Results:

• A small number of stochastic orbitals (≈16) yield meaningful results for absorption spectra and RPA correlation energy.
• The stochastic approach provides an exact representation of electron density with an infinite number of orbitals.
• The algorithm exhibits sublinear scaling with computational time and memory.

Conclusions:

• The developed stochastic TDDFT approach is efficient and accurate for calculating key electronic properties.
• This method provides a computationally feasible alternative for studying complex systems.
• The sublinear scaling suggests scalability for larger systems and future applications.