Analytical excited state gradients for time-dependent density functional theory plus tight binding (TDDFT + TB)

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Photoluminescent mechanisms are crucial for various applications, including photocatalysis, biology, and electronics.
• Analyzing excited state potential energy surfaces (PESs) with traditional methods like time-dependent density functional theory (TDDFT) is computationally intensive for large systems.
• Faster approximations like TDDFT + TB can reproduce TDDFT results efficiently, especially for large nanoparticles.

Purpose of the Study:

• To develop an efficient analytical approach for calculating the derivative of vertical excitation energy within the TDDFT + TB framework.
• To enable more effective exploration of excited state potential energy surfaces (PESs) for photochemical processes.
• To provide a computationally feasible method for studying photoluminescent properties of large systems.

Main Methods:

• Derivation of the analytical gradient for vertical excitation energy using the Z-vector method.
• Utilizing an auxiliary Lagrangian to characterize excitation energy and its derivatives.
• Solving for Lagrange multipliers after incorporating derivatives of Fock, coupling, and overlap matrices into the auxiliary Lagrangian.
• Implementation of the method within the Amsterdam Modeling Suite.

Main Results:

• Successfully derived the analytical gradient for vertical excitation energy in TDDFT + TB.
• Demonstrated the method's proof of concept by analyzing emission energies and optimized excited state geometries.
• Achieved efficient excited state PES exploration for small organic molecules and noble metal nanoclusters.

Conclusions:

• The developed analytical gradient in TDDFT + TB offers a computationally efficient alternative for exploring excited state PESs.
• This method significantly accelerates the study of photoluminescent mechanisms in large systems compared to traditional TDDFT.
• The approach is validated for organic molecules and nanoclusters, paving the way for broader applications in photochemistry and materials science.