Embedding theory for excited states.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Electronic Structure Theory

Background:

• Embedding theories are crucial for studying large quantum systems by dividing them into subsystems.
• Density Functional Theory (DFT) and Wave Function Theory (WFT) are leading methods for electronic structure calculations.
• Accurately describing excited states in complex systems remains a significant challenge.

Purpose of the Study:

• To formally assess the correctness of DFT-in-DFT and WFT-in-DFT embedding approaches for ground and excited states.
• To investigate the inherent approximations and systematic improvements in these embedding methods.
• To explore the potential of WFT-in-DFT for reliable excited-state calculations.

Main Methods:

• Utilizing the Perdew and Levy embedding technique.
• Deriving and analyzing the equations of motion for DFT-in-DFT.
• Formally demonstrating the capabilities of WFT-in-DFT for excited-state properties.

Main Results:

• Both DFT-in-DFT and WFT-in-DFT embedding methods are formally validated for ground and a subset of excited states.
• The standard DFT-in-DFT approach yields coupled Euler-Lagrange equations without further approximations.
• WFT-in-DFT provides a systematic pathway for describing excited states originating from the embedded subsystem.

Conclusions:

• Embedding theories, specifically DFT-in-DFT and WFT-in-DFT, are rigorously applicable to excited-state investigations.
• WFT-in-DFT presents a promising avenue for accurate excited-state calculations, particularly when excitations are localized.
• Further research into practical implementations of WFT-in-DFT for excited states is warranted.