Time-dependent density-functional tight-binding method with the third-order expansion of electron density.

Area of Science:

• Computational chemistry
• Quantum chemistry
• Theoretical chemistry

Background:

• Density-functional theory (DFT) is a powerful tool for electronic structure calculations.
• Time-dependent DFT (TD-DFT) extends DFT to excited states.
• Density-functional tight-binding (DFTB) offers a computationally efficient approximation to DFT.

Purpose of the Study:

• To develop a formalism for calculating excitation energies and excited-state gradients using TD-DFTB, including third-order contributions (TD-DFTB3).
• To assess the impact of these third-order terms on excitation energies.
• To evaluate the performance of TD-DFTB3 with optimized parameters for predicting molecular properties.

Main Methods:

• Formulation of excitation energy based on TD-DFT and TD-DFTB2.
• Analytical gradient computation using Z-vector equations.
• Inclusion of third-order energy derivatives with respect to density matrix elements.

Main Results:

• Third-order contributions in TD-DFTB3 showed no significant impact on adiabatic excitation energies for small and medium molecules.
• Optimized DFTB3 parameters led to a slight statistical improvement in predicting adiabatic excitation energies.
• TD-DFTB3 accurately reproduced the experimental fluorescence energy of cresyl violet.

Conclusions:

• TD-DFTB3 provides a robust method for calculating excitation energies and gradients.
• The inclusion of third-order terms offers a refined approach to excited-state calculations.
• TD-DFTB3 demonstrates good predictive power for molecular absorption and fluorescence properties.