Ensemble Time-Dependent Density Functional Theory

Area of Science:

• Computational chemistry
• Quantum mechanics
• Materials science

Background:

• Time-dependent density functional theory (TDDFT) is a standard method for electronic excitation calculations.
• Ensemble DFT (EDFT) is an emerging alternative for ground-state properties.
• A unified time-dependent framework combining TDDFT and EDFT is needed.

Purpose of the Study:

• Introduce ensemble TDDFT (ETDDFT), a novel theory combining TDDFT and EDFT.
• Generalize the Gross-Kohn equation and exchange-correlation kernel for time-dependent ensemble systems.
• Explore new avenues for approximation and application in electronic structure theory.

Main Methods:

• Ensemble generalization of the Gross-Kohn equation.
• Ensemble generalization of TDDFT exchange-correlation kernels.
• Relating coordinate scaling to the adiabatic connection in the context of ETDDFT.

Main Results:

• Developed a practical ETDDFT framework that unifies TDDFT and EDFT.
• Demonstrated the theory's flexibility in constructing approximations.
• Illustrated the application of ETDDFT on the two-site Hubbard model.

Conclusions:

• ETDDFT offers a powerful and versatile approach for studying optical excitations.
• The theory provides a foundation for developing improved approximations in electronic structure calculations.
• ETDDFT is applicable to both perturbative and nonperturbative time-dependent problems.