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

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This study explains calculating excitation energies using time-dependent density-functional theory (TDDFT) with two-level systems. It also derives and extends the single-pole approximation for excitation energies.

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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.