Time-dependent potential-functional embedding theory.

Area of Science:

• Quantum mechanics
• Computational chemistry
• Materials science

Background:

• Accurate simulation of ultrafast quantum dynamics in large systems remains computationally challenging.
• Existing methods often require uniform computational approaches across the entire system, limiting efficiency.
• A need exists for hybrid methods that can treat different parts of a system with varying levels of theory.

Purpose of the Study:

• Introduce a novel theoretical framework, time-dependent potential-functional embedding theory (TD-PFET).
• Enable the use of diverse time-dependent quantum mechanical methods for different subsystems within a unified approach.
• Provide a first-principles method for seamless treatment of subsystem interactions in quantum dynamics.

Main Methods:

• Formulation of TD-PFET based on the time-dependent quantum mechanics variational principle.
• Development of a potential-functional approach where the system's action is a functional of the time-dependent embedding potential.
• Proof of the uniqueness of the time-dependent embedding potential using the Runge-Gross theorem and derivation of its integral equation.

Main Results:

• Demonstrated TD-PFET for a Na4 cluster, treating each atom as a subsystem.
• Propagated subsystems using time-dependent Kohn-Sham density functional theory (TDDFT) with the adiabatic local density approximation (ALDA).
• Achieved excellent agreement between TD-PFET results and direct TDDFT calculations on the entire cluster.

Conclusions:

• TD-PFET offers a viable and accurate approach for simulating quantum dynamics in complex systems.
• The method allows for computational efficiency by employing different quantum mechanical methods for different subsystems.
• TD-PFET is expected to be valuable for studying ultrafast quantum dynamics in condensed matter systems.