Extended Lagrangian free energy molecular dynamics.

Area of Science:

• Computational physics and chemistry
• Materials science
• Quantum mechanics

Background:

• First principles molecular dynamics (FPMD) simulations are crucial for understanding material properties.
• Simulations at finite electronic temperatures are essential for accurately modeling real-world systems.
• Existing methods can be computationally expensive and face challenges with stability and efficiency.

Purpose of the Study:

• To develop novel extended free energy Lagrangians for FPMD simulations.
• To enable stable and efficient calculations at finite electronic temperatures.
• To provide accurate force expressions for both plane-wave pseudopotential and local orbital methods.

Main Methods:

• Proposed extended free energy Lagrangians for FPMD.
• Utilized stable geometric schemes for integrating electronic degrees of freedom.
• Developed efficient expressions for nuclear and electronic forces in local orbital representations.
• Implemented a rapidly converging recursive Fermi operator expansion for density matrix construction.
• Derived an efficient Pulay force expression valid for fractional occupations.

Main Results:

• The extended Lagrangian approach ensures free energy conservation during simulations.
• Local orbital methods yield simple and numerically efficient force expressions.
• The recursive Fermi operator expansion avoids costly eigenvalue calculations.
• An efficient Pulay force expression is demonstrated for finite electronic temperatures.

Conclusions:

• The proposed extended free energy Lagrangians offer a stable and efficient framework for FPMD at finite electronic temperatures.
• These methods are well-suited for both plane-wave pseudopotential and local orbital calculations, particularly the latter due to reduced complexity.
• The advancements facilitate more accurate and computationally feasible simulations of materials under realistic conditions.