All-electron time-dependent density functional theory with finite elements: time-propagation approach.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Time-dependent density functional theory (TDDFT) is crucial for understanding electronic dynamics.
• Accurate modeling requires efficient methods to handle complex electron interactions.
• Existing methods may face limitations in treating both core and valence electrons simultaneously.

Purpose of the Study:

• To introduce a novel all-electron method for TDDFT.
• To enable the study of linear and nonlinear electronic responses.
• To improve the computational treatment of electron behavior under external fields.

Main Methods:

• Utilizing hierarchical nonuniform finite-element bases.
• Employing a time-propagation approach for dynamic simulations.
• Developing a preconditioner for the propagation equation.
• Implementing stable absorbing boundary conditions, including a novel perfectly matched layer-inspired type.

Main Results:

• The presented method successfully treats both valence and core electrons.
• It accurately captures linear and nonlinear responses to external fields.
• The new absorbing boundary conditions enhance simulation stability and accuracy.

Conclusions:

• The developed all-electron TDDFT method offers a robust framework for electronic structure dynamics.
• It provides a powerful tool for investigating complex electronic phenomena.
• The advancements in numerical techniques improve the reliability of computational simulations in quantum chemistry.