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Adiabatic motion and statistical mechanics via mass-zero constrained dynamics.

Sara Bonella1, Alessandro Coretti, Rodolphe Vuilleumier

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This study extends mass-zero constrained dynamics for simulating complex molecular systems. The improved algorithm ensures accurate Born-Oppenheimer dynamics and scales efficiently for large systems.

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Area of Science:

  • Computational Chemistry
  • Theoretical Physics
  • Materials Science

Background:

  • The shell model for polarization dynamics requires efficient numerical methods.
  • Constrained molecular dynamics with zero mass for fast degrees of freedom offers stability and reversibility.

Purpose of the Study:

  • To extend mass-zero constrained dynamics for additional conditions on fast degrees of freedom.
  • To adapt the method for first principles molecular dynamics.
  • To analyze the statistical mechanics of the mass-zero constrained dynamical system.

Main Methods:

  • Implementing constrained molecular dynamics to enforce null forces on zero-mass degrees of freedom.
  • Adapting the algorithm for problems with specific conditions on fast degrees of freedom.
  • Analyzing the statistical mechanics to recover Born-Oppenheimer probability density.

Main Results:

  • The extended mass-zero constrained dynamics successfully handles additional conditions, including first principles molecular dynamics.
  • The statistical mechanics analysis confirms the recovery of the Born-Oppenheimer probability density.
  • Test calculations on solid sodium demonstrate the method's effectiveness and favorable scaling.

Conclusions:

  • Mass-zero constrained dynamics is a versatile and efficient method for simulating complex dynamical systems.
  • The extension enables accurate first principles molecular dynamics and captures essential statistical properties.
  • The algorithm's scalability makes it suitable for large-scale materials simulations.