Spin-adapted open-shell time-dependent density functional theory. III. An even better and simpler formulation

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Standard time-dependent density functional theory (TD-DFT) methods struggle with spin contamination in high spin open-shell systems.
• Restricted open-shell TD-DFT (RO-TD-DFT) is limited to singlet excitations, while unrestricted TD-DFT (U-TD-DFT) suffers from severe spin contamination.
• Spin-adapted TD-DFT (S-TD-DFT) addresses spin contamination but its accuracy is limited by approximate exchange-correlation functionals violating spin degeneracy conditions (SDC).

Purpose of the Study:

• To develop a more accurate and computationally efficient method for calculating excited states of high spin open-shell systems.
• To overcome the limitations of existing S-TD-DFT methods, particularly the violation of spin degeneracy conditions by approximate functionals.
• To introduce a hybrid approach that combines the strengths of S-TD-DFT and spin-adapted random phase approximation (S-RPA).

Main Methods:

• Development of a hybrid formalism, X-TD-DFT, combining S-TD-DFT and S-RPA.
• The proposed X-TD-DFT formalism maintains spin degeneracy conditions, leveraging the Wigner-Eckart theorem.
• X-TD-DFT is conceptualized as an S-RPA correction to the exchange-correlation kernel of U-TD-DFT.

Main Results:

• X-TD-DFT effectively eliminates spin contamination in the calculation of excited states for high spin open-shell systems.
• The new method demonstrates significantly improved accuracy compared to S-TD-DFT for low-lying excited states, as exemplified by N(2)(+).
• X-TD-DFT achieves these improvements with a substantially reduced computational cost.

Conclusions:

• X-TD-DFT offers a robust and efficient solution for calculating excited states in high spin open-shell systems.
• The method successfully addresses the spin contamination issue and improves accuracy by maintaining spin degeneracy conditions.
• X-TD-DFT is recommended for routine computational studies of excited states in challenging high spin open-shell systems.