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

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.