Zero Excitation Energy Theorem and the Spin-Flip Kernel.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Theoretical Physics

Background:

• Time-dependent density functional theory (TDDFT) is a powerful method for calculating electronic excited states.
• Accurate calculation of excited states, particularly spin-flip excitations, remains a challenge.
• Existing methods may lack accuracy or efficiency for certain types of excited states.

Purpose of the Study:

• To establish the zero excitation energy theorem for TDDFT with open-shell reference states.
• To derive a method for constructing spin-flip kernels from spin-conserving kernels.
• To develop a computationally efficient and stable approach for spin-flip excited-state calculations.

Main Methods:

• Establishing the zero excitation energy theorem within TDDFT.
• Deriving an identity connecting spin-conserving and spin-flip kernels.
• Proposing a method to construct the spin-flip kernel from the spin-conserving kernel.
• Implementing and testing the spin-flip TDDFT approach.

Main Results:

• The zero excitation energy theorem holds exactly in TDDFT but approximately in the Tamm-Dancoff approximation.
• A novel method for constructing the spin-flip kernel from the spin-conserving kernel was developed.
• The proposed method is numerically stable, preserves energy degeneracy, and is applicable to collinear functionals.
• Spin-flip TDDFT demonstrated comparable efficiency to spin-conserving TDDFT in numerical tests.

Conclusions:

• The zero excitation energy theorem provides a theoretical foundation for accurate spin-flip excitation calculations.
• The developed method offers an efficient and practical approach for routine spin-flip TDDFT calculations.
• The ease of implementation makes this method particularly valuable for existing TDDFT software.