A diagonalization-free optimization algorithm for solving Kohn-Sham equations of closed-shell molecules.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Kohn-Sham equations are central to density functional theory.
• Standard self-consistent field (SCF) methods can face convergence issues.
• Eigendecomposition is computationally intensive for large systems.

Purpose of the Study:

• Introduce a novel local optimization algorithm for Kohn-Sham equations.
• Improve computational efficiency and reliability in electronic structure calculations.
• Provide an alternative to traditional SCF methods, especially in challenging cases.

Main Methods:

• Direct minimization of the energy functional with Grassmann Manifold constraints.
• Avoidance of eigendecomposition.
• Optimization for one Kohn-Sham matrix evaluation per iteration.

Main Results:

• Algorithm shows high reliability where SCF iterations fail.
• Achieves competitive performance with DIIS-accelerated SCF.
• Randomization of initial approximation leads to global minimum convergence in most cases.

Conclusions:

• The presented local optimization algorithm offers a robust and efficient alternative for solving Kohn-Sham equations.
• It is particularly advantageous for large-scale computations and problematic convergence scenarios.
• Further development could enhance its guarantee of global minimum convergence.