Stability of the Long-Range Corrected Exchange-Correlation Functional and the Proca Procedural Functional in...

Area of Science:

• Computational Physics
• Quantum Chemistry
• Materials Science

Background:

• Excitonic effects in solids are crucial for optical absorption spectra.
• Time-dependent density-functional theory (TDDFT) describes these effects.
• Long-range corrected (LRC) functionals have been extended to real-time TDDFT for exciton dynamics.

Purpose of the Study:

• To investigate the numerical stability of the time-dependent LRC approach.
• To understand the origins of instabilities in LRC-based exciton dynamics simulations.
• To develop a robust numerical stabilization scheme for the time-dependent LRC method.

Main Methods:

• Employed a two-dimensional model solid for numerical simulations.
• Utilized the time-dependent Kohn-Sham equation with an LRC vector potential.
• Analyzed the connection between exciton binding energy and numerical stability.

Main Results:

• Instabilities in the time-dependent LRC approach increase with exciton binding energy.
• These instabilities stem from time-averaged violations of the zero-force theorem.
• A simple and robust numerical stabilization scheme was successfully developed.

Conclusions:

• The study identifies the root cause of numerical instabilities in time-dependent LRC TDDFT.
• A new stabilization method is proposed and justified, enhancing the reliability of simulations.
• This work validates and explains the efficacy of the Proca procedural functional for stabilizing LRC vector potentials.