Exact subsystem time-dependent density-functional theory.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• Time-dependent density functional theory (TDDFT) is a powerful tool for calculating electronic excitation energies.
• Subsystem TDDFT methods aim to reduce computational cost by dividing the system into smaller parts.
• Projection-based embedding (PbE) is a technique used to embed a subsystem within a larger environment.

Purpose of the Study:

• To develop an exact subsystem theory for TDDFT calculations.
• To accurately restore supermolecular TDDFT excitation energies using a subsystem approach.
• To address limitations in previous subsystem TDDFT formalisms.

Main Methods:

• Coupled subsystem time-dependent density functional theory (subsystem TDDFT).
• Projection-based embedding (PbE) for subsystem calculations.
• Careful treatment of kernel contributions due to enforced orthogonality in the TDDFT eigenvalue problem.

Main Results:

• The proposed subsystem TDDFT-PbE method exactly reproduces supermolecular TDDFT excitation energies.
• Numerical validation was performed on the helium dimer and fluoroethane molecule.
• Deviations and incorrect transition ordering were observed with a previously proposed symmetric approximation.

Conclusions:

• The developed coupled subsystem TDDFT-PbE formalism provides an exact method for electronic excitation energy calculations.
• Accurate handling of kernel contributions is critical for the exactness of the subsystem approach.
• The findings highlight potential inaccuracies in approximate symmetric eigenvalue treatments for subsystem TDDFT.