Excitation Energies in Time-Dependent (Current-) Density-Functional Theory: A Simple Perspective

Area of Science:

• Quantum Chemistry
• Computational Physics

Background:

• Density-functional theory (DFT) is a powerful quantum mechanical modeling method.
• Calculating excitation energies is crucial for understanding material properties and chemical reactions.

Purpose of the Study:

• To provide a pedagogical explanation of calculating excitation energies using time-dependent density-functional theory (TDDFT).
• To derive the single-pole approximation (SPA) for excitation energies in an alternative manner.
• To extend the SPA to time-dependent current-density-functional theory (TDCDFT).

Main Methods:

• Utilizing density matrices of two-level systems for a simplified approach.
• Applying time-dependent density-functional theory (TDDFT) for excitation energy calculations.
• Deriving the single-pole approximation (SPA) through an alternative method.

Main Results:

• A clear, pedagogical method for calculating excitation energies with TDDFT is presented.
• The well-established single-pole approximation (SPA) for excitation energies is derived.
• The SPA is successfully extended to the framework of time-dependent current-density-functional theory (TDCDFT).

Conclusions:

• The study offers an accessible explanation of TDDFT for excitation energies.
• The alternative derivation of the SPA enhances understanding of excitation energy approximations.
• The extension to TDCDFT broadens the applicability of these methods for complex systems.