Extended Lagrangian formulation of charge-constrained tight-binding molecular dynamics.

Area of Science:

• Computational materials science
• Condensed matter physics
• Theoretical chemistry

Background:

• Molecular dynamics simulations are crucial for understanding material properties.
• Accurate energy conservation and efficient computation are key challenges.
• Enforcing local charge neutrality requires complex self-consistent field optimizations.

Purpose of the Study:

• To apply the extended Lagrangian Born-Oppenheimer molecular dynamics (MD) formalism to a tight-binding model.
• To achieve precise, long-term energy conservation in microcanonical trajectories.
• To reduce the number of self-consistent field (SCF) optimizations per time step.

Main Methods:

• Utilized the extended Lagrangian Born-Oppenheimer MD formalism.
• Implemented a tight-binding model with local charge neutrality constraint.
• Performed microcanonical MD simulations of a metallic cluster using an sd-valent titanium model.
• Investigated the effects of weak dissipation on auxiliary degrees of freedom.

Main Results:

• Achieved precise, long-term energy conservation in MD simulations.
• Demonstrated a reduced number of SCF optimizations at each time step.
• Successfully optimized chemical potential and atomwise potential energy shifts.
• Illustrated capabilities with simulations of a titanium metallic cluster.

Conclusions:

• The extended Lagrangian formalism offers efficient and accurate MD simulations under charge neutrality constraints.
• Time reversal symmetry is restored in electronic degree propagation.
• The method provides a robust framework for studying material dynamics.