Solid Free Energy

This skill calculates the absolute free energy of a crystalline solid using Frenkel-Ladd switching, which is a specific form of Thermodynamic Integration (TI).

Thermodynamic integration computes the free energy difference between two states by integrating the derivative of the Hamiltonian along a continuous coupling path. In this skill, the path interpolates between a physical MLIP Hamiltonian (the target state) and a harmonic Einstein-crystal reference (where the exact absolute free energy is analytically known).

Goal

Compute the Helmholtz free energy $F$ of a pre-equilibrated periodic solid at a target temperature, and optionally the Gibbs free energy $G = F + PV$ if pressure is supplied.

Prerequisites

• A pre-equilibrated periodic solid structure in an ASE-readable format such as CIF or POSCAR.
• The transferable MLIP wrapper stack must be available in the target repo via src.utils.mlips.loader.load_wrapper(...).
• ASE and pymatgen must be installed in the relevant conda environment.

[!IMPORTANT] This skill only performs the Frenkel-Ladd free-energy workflow. It does not relax the structure, build a supercell, equilibrate the volume, perform alchemical switching, or apply center-of-mass corrections.

Choosing a Foundation Potential

Frenkel-Ladd switching is an MD-based free-energy method, so both energy and force stability matter.

[!IMPORTANT]

• Prefer materials models intended for PES or MD use, such as MACE-OMAT-0-small, MACE-MH-1, CHGNet-MatPES-*, or TensorNet-MatPES-*.
• Use smaller or faster models for long switching trajectories when practical.
• Avoid changing model family between preparation and Frenkel-Ladd unless you intentionally want a different free-energy reference.

Refer to the foundation-potentials skill for model selection guidance.

Preparing Inputs

This skill assumes the input structure is already appropriate for the target thermodynamic state point. For production workflows, the most useful upstream skills are:

• mat-db-mp: Retrieve a starting bulk crystal structure from Materials Project.
• mat-equation-of-state: Estimate an equilibrium cell volume and generate a better-relaxed starting point before finite-temperature sampling.
• mat-lammps-md: Equilibrate a larger periodic cell at the target temperature or pressure using the same MLIP family.
• mat-md-monitors: Check MD stability, thermostat behavior, volume drift, and equilibration while preparing the input trajectory.
• mat-phonon: Screen for imaginary modes or other vibrational-instability warnings before running an expensive free-energy workflow.

Calculation Workflow

Run the standalone Frenkel-Ladd script:

# Env: mace-agent
python .agents/skills/mat-solid-free-energy/scripts/run_frenkel_ladd.py \
    --structure path/to/pre_equilibrated_structure.cif \
    --name my_solid \
    --calculator mace \
    --model-name MACE-OMAT-0-small \
    --temperature 300 \
    --pressure-gpa 0.0 \
    --output-dir research/my_folder/frenkel_ladd

Key Parameters

• --structure: Pre-equilibrated periodic solid at the target state point.
• --calculator: MLIP backend: mace, fairchem, or matgl.
• --model-name: Model name or checkpoint path.
• --task-name: Optional task head for multitask models.
• --temperature: Temperature in K.
• --pressure-gpa: Optional pressure in GPa. If provided, the script also reports Gibbs free energy.
• --msd-equilibration-steps: NVT equilibration before MSD collection.
• --msd-production-steps: NVT production used to estimate per-atom spring constants.
• --equilibration-steps: Harmonic-reference equilibration between forward and backward switching.
• --switching-steps: Number of MD steps in each switching direction.
• --switching-type: linear or polynomial. Default is the smoother polynomial schedule.
• --record-interval: Record every N MD steps.

Default Production Settings

The script defaults are:

• timestep_fs = 1.0
• thermostat_damping_fs = 100.0
• msd_equilibration_steps = 1000
• msd_production_steps = 10000
• equilibration_steps = 5000
• switching_steps = 25000
• switching_type = polynomial
• record_interval = 1
• symmetrize_spring_constants = True

Output Files

• frenkel_ladd_results.json: Summary including Helmholtz free energy, optional Gibbs free energy, dissipated energy, calculator metadata, and settings.
• frenkel_ladd_traces.npz: Raw recorded arrays:
  • lambda_steps
  • forward_energy_contributions
  • backward_energy_contributions
  • spring_constants
  • mean_squared_displacement
• input_structure.cif: Copy of the starting structure.
• final_structure.cif: Final structure after backward switching.

Example

See examples/Si_MACE/ for a minimal silicon example using MACE with reduced step counts for demonstration.

# Env: mace-agent
python .agents/skills/mat-solid-free-energy/scripts/run_frenkel_ladd.py \
    --structure .agents/skills/mat-solid-free-energy/examples/Si_MACE/Si.cif \
    --name Si_demo \
    --calculator mace \
    --model-name MACE-OMAT-0-small \
    --temperature 300 \
    --msd-equilibration-steps 50 \
    --msd-production-steps 200 \
    --equilibration-steps 100 \
    --switching-steps 500 \
    --record-interval 5 \
    --output-dir research/frenkel_ladd/Si_demo

[!NOTE] The example is a smoke-test style demonstration. For production free-energy work, start from a genuinely pre-equilibrated structure and use the heavier default settings or stricter settings appropriate for your system.

Constraints

• Environment:
  • mace-agent for MACE models
  • fairchem-agent for FairChem/UMA models
  • matgl-agent for MatGL/CHGNet models
• Periodic solids only: This method is intended for bulk crystalline solids, not molecules or non-periodic clusters.
• Pre-equilibrated input required: The script assumes the supplied structure already represents the desired thermodynamic state point.
• Quality control: Inspect abs(dissipated_energy) / num_atoms. Values much larger than about 0.05 eV/atom suggest poor switching reversibility and should be treated with caution.
• Cost: Frenkel-Ladd calculations are expensive because they require long MD trajectories in both switching directions.

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Author: Juno Nam Contact: GitHub @recisic