A Well-Tempered Hybrid Method for Solving Challenging Time-Dependent Density Functional Theory (TDDFT) Systems.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Spectroscopy

Background:

• Time-dependent Hartree-Fock (TDHF) and time-dependent density functional theory (TDDFT) are efficient methods for electronic resonance calculations.
• Standard iterative eigenvalue solvers struggle with convergence in spectrally dense regions, common in X-ray absorption spectroscopy (XAS).
• The generalized preconditioned locally harmonic residual (GPLHR) method offers better convergence but increases computational cost.

Purpose of the Study:

• To develop a hybrid solver that balances computational efficiency with robust convergence for electronic resonance calculations.
• To improve the performance of eigenvalue solvers in challenging spectral regions encountered in XAS.

Main Methods:

• A novel hybrid method is proposed, adapting to specific computational problems.
• The hybrid method integrates the strengths of standard and GPLHR solvers.
• A modification to the GPLHR algorithm adaptively selects the shift parameter.

Main Results:

• The proposed hybrid method enhances computational performance.
• Superior convergence properties, similar to GPLHR, are achieved.
• Adaptive shift parameter selection in GPLHR ensures convergence for states above a specified energy threshold.

Conclusions:

• The hybrid approach offers a computationally efficient and robust solution for electronic resonance calculations.
• This method is particularly beneficial for X-ray absorption spectroscopy (XAS) applications.
• Adaptive parameter selection further optimizes the convergence and reliability of the solver.