Self-consistent predictor/corrector algorithms for stable and efficient integration of the time-dependent Kohn-Sham...

Area of Science:

• Computational Chemistry
• Quantum Mechanics

Background:

• Time-dependent density functional theory (TDDFT) describes electron density evolution after perturbation.
• Traditional linear-response TDDFT has limitations for broad-band spectra and large density of states systems.

Purpose of the Study:

• Introduce efficient predictor/corrector algorithms for integrating the time-dependent Kohn-Sham (TDKS) equation.
• Improve computational efficiency and stability in real-time TDDFT simulations.

Main Methods:

• Developed and implemented predictor/corrector algorithms for density matrix propagation.
• Introduced a self-consistent extension of the modified-midpoint algorithm.
• Focused on integrating the TDKS equation with a time-dependent effective Hamiltonian.

Main Results:

• The new algorithms facilitate larger time steps, increasing computational efficiency.
• Demonstrated improved performance compared to traditional methods, especially for complex systems.
• Implemented on-the-fly divergence detection for simulation stability.

Conclusions:

• Real-time TDDFT with predictor/corrector algorithms offers a more efficient approach for calculating spectra.
• These methods enhance the stability and reliability of electronic structure calculations.
• The developed algorithms are beneficial for studying systems with large densities of states and core-excited states.