Current density partitioning in time-dependent current density functional theory.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Theoretical Physics

Background:

• Solving the many-electron problem in molecules is computationally intensive.
• Time-dependent fields introduce complex electron dynamics.
• Fragment-based methods offer a potential solution for complex systems.

Purpose of the Study:

• To adapt time-dependent current density functional theory for fragment-based calculations.
• To develop a method for solving the many-electron problem of molecules in time-dependent electromagnetic fields.
• To establish mappings between fragment properties and total system electron dynamics.

Main Methods:

• Utilizing time-dependent current density functional theory.
• Treating molecules as non-interacting subsystems evolving under an auxiliary electromagnetic potential (partition 4-potential).
• Expressing the partition electromagnetic (EM) 4-potential using real EM potentials and a gluing potential for exchange-correlation and inter-fragment interactions.

Main Results:

• Demonstrated one-to-one mappings between the auxiliary potential, fragment current densities, and total current density.
• Proved the zero-force theorem for the fragmented system.
• Established a variational formulation using action functionals.

Conclusions:

• The developed fragment-based approach accurately captures electron dynamics in time-dependent fields.
• This method provides a computationally tractable way to study molecular systems under external electromagnetic influences.
• The theoretical framework is illustrated with a simple model of a charged particle in a ring.