Development and Implementation of Excited-State Gradients for Local Hybrid Functionals

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Local hybrid functionals offer a tunable approach to modeling electronic structure.
• Accurate prediction of excited-state properties is crucial for understanding molecular behavior.

Purpose of the Study:

• To implement and assess time-dependent density functional theory (TD-DFT) excited-state gradients for local hybrid functionals.
• To evaluate the performance of this new method for predicting excited-state structural parameters and vibrational frequencies.

Main Methods:

• Development of a fully variational auxiliary Lagrangian for excitation energy.
• Derivation of third-order functional derivatives for hyper-kernel and kernel-gradients.
• Application of a semi-numerical integration scheme for implementation.

Main Results:

• Achieved competitive accuracy for excited-state bond lengths (MAE 1.2 pm) and vibrational frequencies (MAE 81 cm^-1).
• Demonstrated excellent performance for adiabatic triplet excitation energies (MAE 0.08 eV).
• Identified conceptual advantages and disadvantages of the local hybrid scheme for excited-state gradients.

Conclusions:

• The developed TD-DFT excited-state gradients for local hybrid functionals provide a robust and accurate tool for computational chemistry.
• This method shows significant promise for studying excited-state properties of molecules, particularly for triplet states.