Time-Dependent Orbital-Free Density Functional Theory: A New Development of the Dynamic Kinetic Energy Potential

Area of Science:

• Computational Physics
• Quantum Chemistry
• Materials Science

Background:

• Time-dependent orbital-free density functional theory (TD-OFDFT) is crucial for simulating electronic dynamics in large metallic systems.
• A key challenge in TD-OFDFT is the accurate representation of the dynamic kinetic energy potential (DKEP), which captures memory effects absent in adiabatic approximations.
• Existing TD-OFDFT methods lack a well-defined total energy, impacting long-time simulation stability.

Purpose of the Study:

• To develop a novel DKEP for TD-OFDFT that incorporates nonlocal spatial and temporal dependencies.
• To address the issue of undefined total energy in TD-OFDFT, ensuring simulation stability.
• To validate the performance of the new TD-OFDFT formalism against established methods.

Main Methods:

• Developed a new DKEP using a density-dependent kernel, nonlocal in space and time.
• Expanded the kernel using Laguerre polynomials and exponential decay functions.
• Determined kernel parameters by fitting TD-OFDFT dipole oscillations to time-dependent Kohn-Sham DFT (TD-KSDFT) results.
• Introduced an energy term within the DKEP to ensure a well-defined total energy.

Main Results:

• The new DKEP successfully incorporates nonlocal effects and memory in TD-OFDFT.
• The inclusion of an energy term resolves the long-standing problem of undefined total energy, enhancing simulation stability.
• Simulations of sodium clusters and a nanorod using the new TD-OFDFT formalism showed good agreement with TD-KSDFT calculations.

Conclusions:

• The developed DKEP represents a significant advancement for TD-OFDFT, enabling more accurate and stable simulations of electronic dynamics.
• This work provides a robust framework for investigating large metallic systems with TD-OFDFT.
• The new method offers a reliable alternative to TD-KSDFT for certain applications, particularly concerning energy conservation and stability.