Average excitation energies from time-dependent density functional response theory

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Physics

Background:

• Time-dependent density functional response theory (TD-DFRT) often inaccurately predicts Rydberg and charge-transfer excitation energies, particularly within the local (spin) density approximation (LDA/LSDA).
• Existing TD-DFRT methods require explicit correction of the exchange-correlation potential to address these inaccuracies.

Purpose of the Study:

• To develop and validate an occupation number averaging scheme for TD-DFRT in the frequency domain.
• To improve the prediction accuracy of excitation energies, specifically Rydberg and charge-transfer types, without modifying the exchange-correlation potential.
• To investigate the dependence of excitation energies on the fraction of excited electrons in molecular systems.

Main Methods:

• Adapted the working equations of TD-DFRT to handle arbitrary differences in orbital occupation numbers.
• Utilized the nonsymmetric matrix form of Casida's formulation of TD-DFRT.
• Applied the scheme to closed-shell and open-shell molecular systems, analyzing excitation energy dependence on electron fraction.

Main Results:

• The proposed occupation number averaging scheme demonstrates good performance in predicting excitation energies.
• Results are consistent with previous findings using the real-time propagation approach.
• The method shows promise for improving excitation energy calculations within the LDA/LSDA framework.

Conclusions:

• The occupation number averaging scheme offers a viable method to enhance TD-DFRT accuracy for excitation energies.
• Calculating average excitation energies may be a key strategy for improving predictions from LDA/LSDA.
• The study discusses techniques for treating singlet, triplet, and doublet states within this modified scheme.