Analytic energy gradients of spin-adapted open-shell time-dependent density functional theory

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Time-dependent density functional theory (TD-DFT) is widely used for excited-state calculations.
• Unrestricted TD-DFT (U-TD-DFT) is often applied to open-shell systems but can yield spin-contaminated states.
• Spin-adapted TD-DFT (X-TD-DFT) has emerged as a more accurate alternative for open-shell systems.

Purpose of the Study:

• To demonstrate that X-TD-DFT can be used for geometry optimization and dynamics simulations of excited states in open-shell systems.
• To show that X-TD-DFT offers computational efficiency comparable to U-TD-DFT.
• To validate the accuracy of X-TD-DFT for excited states of open-shell molecules.

Main Methods:

• Analytic energy gradients for X-TD-DFT were derived.
• Modifications were made to U-TD-DFT energy gradient calculations.
• Restricted open-shell Kohn-Sham orbitals were employed.

Main Results:

• X-TD-DFT achieves accuracy similar to conventional TD-DFT for closed-shell systems.
• X-TD-DFT calculations show no computational overhead compared to U-TD-DFT.
• Analytic energy gradients for X-TD-DFT were successfully obtained with minor modifications to U-TD-DFT methods.

Conclusions:

• X-TD-DFT is a viable and efficient replacement for U-TD-DFT in excited-state geometry optimizations and dynamics simulations of open-shell systems.
• The method provides accurate results without significant computational cost.
• This advancement facilitates more reliable theoretical studies of open-shell molecular systems.