Time-dependent density-functional theory for nonadiabatic electronic dynamics.

Area of Science:

• Quantum mechanics
• Computational chemistry
• Condensed matter physics

Background:

• Studying the dynamics of electrons and nuclei in interacting systems is computationally challenging.
• Existing methods often rely on approximations for electron-electron interactions and nuclear motion.

Purpose of the Study:

• To develop a formalism for exactly reproducing time-dependent density matrices in interacting electron-nuclear systems.
• To enable the construction of rigorous time-dependent density-functional theories (TD-DFT) for nonadiabatic dynamics.

Main Methods:

• The study proposes a method to exactly map the density matrix of an interacting system to a system with arbitrary electron-electron interactions.
• This mapping is valid given the initial density matrix and coupled nuclear degrees of freedom.

Main Results:

• The time-dependent single-electron and nuclear density matrix of an interacting system can be exactly reproduced.
• The Runge-Gross and van Leeuwen theorems are recovered as special cases in the adiabatic limit.

Conclusions:

• The developed formalism provides a rigorous foundation for TD-DFT in studying nonadiabatic electronic dynamics.
• This approach offers a pathway to more accurate simulations of complex quantum systems.