Simple preconditioning for time-dependent density functional perturbation theory.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Time-dependent density functional theory (TD-DFT) is widely used for studying electronic excitations.
• The linear-response regime of TD-DFT relies on solving the Sternheimer equation.
• Traditional methods face challenges with ill-conditioning and convergence near resonant frequencies.

Purpose of the Study:

• To address the limitations of the Sternheimer method in TD-DFT calculations.
• To develop a more efficient and robust approach for solving linear-response equations.
• To improve the convergence properties and accuracy of electronic excitation calculations.

Main Methods:

• A novel preconditioning strategy is proposed for the Sternheimer equation.
• The Sternheimer equation is solved directly as a linear equation using iterative Krylov subspace methods.
• The preconditioner utilizes information from a limited number of unoccupied Kohn-Sham states with minimal implementation changes.

Main Results:

• The proposed method overcomes the ill-conditioning issues of the Sternheimer equation.
• Faster convergence is achieved compared to traditional iterative techniques.
• The method demonstrates improved performance over a wider frequency range.

Conclusions:

• The preconditioning strategy offers a significant improvement for TD-DFT electronic excitation calculations.
• This approach enhances the efficiency and applicability of linear-response TD-DFT.
• The method provides a practical solution for overcoming convergence challenges in computational chemistry.