Efficient implementations of analytic energy gradient for mixed-reference spin-flip time-dependent density functional...

Area of Science:

• Quantum Chemistry
• Computational Spectroscopy
• Theoretical Chemistry

Background:

• Spin-contamination in spin-flip time-dependent density functional theory (SF-TDDFT) affects the accuracy of calculated electronic states.
• Accurate characterization of singlet and triplet states is crucial for understanding photophysical processes and reaction mechanisms.

Purpose of the Study:

• To develop and implement analytic energy gradients for collinear mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT).
• To address and overcome the spin-contamination issues present in standard SF-TDDFT.
• To enhance the accuracy and practicality of computational methods for studying electronic states.

Main Methods:

• Derivation and implementation of analytic energy gradients for individual singlet and triplet states within the MRSF-TDDFT framework.
• Introduction of dimensional-transformation matrices to simplify equation derivations and maintain computational efficiency.
• Comparison of MRSF-TDDFT results with SF-TDDFT for optimized structures and energies.

Main Results:

• MRSF-TDDFT effectively eliminates problematic spin-contamination found in SF-TDDFT.
• Calculations using MRSF-TDDFT yield significantly different optimized structures and energies compared to SF-TDDFT due to reduced spin-contamination.
• The method simplifies the identification of minimum energy conical intersections by clearly separating singlet and triplet states.

Conclusions:

• MRSF-TDDFT demonstrates superior accuracy and practicality compared to SF-TDDFT for electronic structure calculations.
• The method is well-suited for various "black-box" applications, including minimum-energy optimization, reaction path following, and molecular dynamics simulations.
• MRSF-TDDFT represents a significant advancement for theoretical studies involving excited electronic states.