Converging Time-Dependent Density Functional Theory Calculations in Five Iterations with Minimal Auxiliary...

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Krylov space methods are essential for solving large eigenvalue problems in quantum chemistry.
• Preconditioners significantly enhance the convergence speed of these iterative methods.
• Time-dependent density functional theory (TDDFT) relies on efficient computational techniques.

Purpose of the Study:

• To design and evaluate a novel preconditioner for TDDFT calculations.
• To improve the efficiency of solving linear systems in quantum chemistry.
• To accelerate the convergence of excitation energies and polarizabilities.

Main Methods:

• Systematic design of a new preconditioner based on the TDDFT-ris semiempirical model.
• Retuning of empirical scaling factors and angular momenta of a minimal auxiliary basis.
• Inclusion of d-functions in the auxiliary basis, resulting in the "rid" preconditioner.

Main Results:

• The "rid" preconditioner demonstrates an average convergence in 5-6 iterations.
• This represents a 2-3 fold speedup compared to conventional diagonal preconditioners.
• The "rid" preconditioner achieves results comparable to existing methods without compromising accuracy.

Conclusions:

• The "rid" preconditioner offers a significant improvement in computational efficiency for TDDFT.
• It is a broadly applicable and effective tool for quantum chemistry simulations.
• The developed preconditioner accelerates convergence without affecting the quality of the final results.