Compact representations of Kohn-Sham invariant subspaces.

Area of Science:

• Computational physics
• Quantum chemistry
• Materials science

Background:

• The Kohn-Sham equations are central to density functional theory (DFT) for electronic structure calculations.
• Solving these equations for large systems is computationally intensive, limiting applicability.
• Efficient representations of electronic wave functions are crucial for advancing computational methods.

Purpose of the Study:

• To introduce a novel hierarchical approximate representation for Kohn-Sham equation solutions.
• To enable accurate electronic structure calculations for large-scale systems.
• To facilitate the development of more efficient computational chemistry and physics algorithms.

Main Methods:

• A recursive bisection algorithm is employed to generate localized one-particle wave functions.
• The method creates a hierarchical representation of solutions on subdomains of varying sizes.
• A priori accuracy control is achieved by setting the maximum acceptable error in the 2-norm.

Main Results:

• Demonstrated significant data size reduction for applications to large systems.
• The hierarchical representation accurately approximates Kohn-Sham equation solutions.
• The method's scalability and efficiency were illustrated through practical examples.

Conclusions:

• The proposed method offers a powerful tool for handling large electronic structure problems.
• This approach has direct implications for developing linear-scaling electronic structure methods.
• The technique can accelerate conventional iterative solvers for Kohn-Sham equations.