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The quantum method of planes-local pressure definitions for machine learning potentials.

E R Smith1

  • 1Brunel University of London Kingston Lane Uxbridge Middlesex, Uxbridge UB8 3PH, United Kingdom.

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The method of planes (MoP) accurately calculates stress in inhomogeneous fluids, unlike the virial stress tensor. This extension of MoP for machine learning potentials is crucial for non-equilibrium molecular dynamics simulations.

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Area of Science:

  • Computational physics and chemistry
  • Materials science
  • Statistical mechanics

Background:

  • Stress is vital in engineering and molecular modeling.
  • The virial stress tensor is inaccurate for inhomogeneous fluids, essential in fluid dynamics and non-equilibrium molecular dynamics (NEMD) simulations.

Purpose of the Study:

  • To extend the method of planes (MoP) stress calculation to the MACE potential, a machine learning (ML) potential.
  • To validate the MoP for MACE potentials in scenarios like the water-zirconium oxide interface and in non-equilibrium conditions.

Main Methods:

  • Derived local stress for the MACE potential using the Irving and Kirkwood theoretical framework.
  • Applied the method of planes (MoP) to a water-zirconium oxide interface simulation.
  • Demonstrated stress conservation in a control volume bounded by MoP in non-equilibrium simulations.

Main Results:

  • The MoP accurately measures force balance at the water-zirconium oxide interface, where the virial stress tensor fails.
  • The planar stress definition is valid far from equilibrium, showing exact conservation at every time step.
  • The study links stress directly to conservation equations, proving validity in NEMD systems.

Conclusions:

  • The extended MoP provides a valid and accurate method for calculating stress in inhomogeneous fluids using ML potentials.
  • This work is foundational for applying ML in NEMD and molecular fluid dynamics.
  • Open-source code is provided for reproducing results and applying MoP to MACE systems.