Effective electron displacements: a tool for time-dependent density functional theory computational spectroscopy.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• The Delta-r (Δr) metric, previously defined within time-dependent density functional theory (TD-DFT), quantifies electronic excitations.
• Existing metrics may not be effective for all types of electronic transitions, such as those in centrosymmetric systems or Rydberg excitations.

Purpose of the Study:

• To extend the Δr metric by incorporating electronic position variances.
• To introduce a new metric, Gamma (Γ), applicable to a broader range of electronic transitions.
• To enhance the interpretability of electronic transitions using Natural Transition Orbitals (NTOs).

Main Methods:

• Extension of the Δr metric to include the difference in electronic position variances between occupied and virtual orbitals.
• Development of the Γ metric within the TD-DFT framework.
• Application of Natural Transition Orbitals (NTOs) to the Γ metric.

Main Results:

• The new Γ metric successfully analyzes electronic transitions in centrosymmetric systems and Rydberg excitations, where Δr is less effective.
• The Γ-NTO approach provides an intuitive visualization of local electron density changes during transitions.
• Γ values offer insights into the performance of different functionals (GGA, hybrid) for various transition types.

Conclusions:

• The Γ metric represents a significant advancement in analyzing electronic excitations, expanding the applicability of TD-DFT.
• The Γ-NTO method offers a powerful tool for understanding the nature of electronic transitions and evaluating computational methods.
• The study establishes a framework for defining a 'confidence radius' for functional performance in TD-DFT calculations.