general-property-units

Research

Reference guide for energy, force, and stress units across MLIPs, DFT codes, and ASE, including conversion factors.

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Units Reference for Atomistic Simulations

Goal

Provide a single authoritative reference for units of energy, forces, and stress across all MLIPs, DFT codes, and simulation tools used in this project, including the conversions applied internally.

Project Standard

All internal representations follow the ASE (Atomic Simulation Environment) convention:

Quantity	Standard Unit	Notes
Energy	eV	Total energy of the system
Energy per atom	eV/atom	Used for MAE reporting and training labels
Forces	eV/Å	Negative gradient of energy w.r.t. position
Stress	eV/Å³	Voigt notation, 6-component (xx, yy, zz, yz, xz, xy)

MLIP Model Units

Prediction (Inference)

All MLIP wrappers return predictions in ASE standard units through their ASE calculator interface:

Model	Energy	Forces	Stress	Notes
MACE	eV	eV/Å	eV/Å³	Native ASE units
CHGNet	eV	eV/Å	eV/Å³	Native ASE units
UMA (FairChem)	eV	eV/Å	eV/Å³	Native ASE units
M3GNet / TensorNet (MatGL)	eV	eV/Å	eV/Å³	Native ASE units

Training Input Labels

Training labels in training_data.json are stored in ASE standard units (eV, eV/Å, eV/Å³). Conversions to trainer-specific units are handled automatically inside each wrapper:

Trainer	Energy Input	Force Input	Stress Input	Internal Conversion
MACE	eV	eV/Å	eV/Å³	None — trains in eV/Å³
FairChem (UMA)	eV	eV/Å	eV/Å³	None — trains in eV/Å³
MatGL (CHGNet/M3GNet)	eV	eV/Å	GPa (converted)	`eV/Å³ → GPa` in `_prepare_training_data`

[!IMPORTANT] MatGL is the only trainer that requires stress conversion. The conversion from eV/Å³ → GPa is performed automatically inside MATGLWrapper._prepare_training_data(). Users should always provide stress labels in eV/Å³.

Training Output (Saved Metrics)

Each MLIP trainer natively reports MAE in eV. All wrappers apply a ×1000 conversion to save MAE values in meV to training_history.json and plot axes in training_history.png, for human readability and consistent cross-model comparison:

Trainer	Native Energy MAE	Native Force MAE	Native Stress MAE	Saved Unit
MACE	eV/atom	eV/Å	eV/Å³	meV (×1000)
FairChem (UMA)	eV/atom	eV/Å	eV/Å³	meV (×1000)
MatGL (CHGNet/M3GNet)	eV/atom	eV/Å	GPa → eV/Å³	meV (×1000)

The training_history.json keys and their units:

Key	Unit
`energy_mae_train` / `energy_mae_val`	meV/atom
`force_mae_train` / `force_mae_val`	meV/Å
`stress_mae_train` / `stress_mae_val`	meV/Å³
`loss_train` / `loss_val`	Dimensionless (weighted combination)

[!NOTE] For MatGL stress: the trainer computes MAE in GPa internally. The wrapper converts back to eV/Å³ first, then multiplies by 1000 to get meV/Å³, matching the other wrappers.

DFT Code Units

VASP

Quantity	VASP Internal	VASP OUTCAR	Conversion to ASE Standard
Energy	eV	eV	None needed
Forces	eV/Å	eV/Å	None needed
Stress	kB (kilo-Bar)	kB (and GPa)	`kB × 0.1 = GPa`, then `GPa × 0.0062415 = eV/Å³`

[!NOTE] VASP stores stress internally in kB (kilo-Bar). The vasprun.xml parser in pymatgen returns stress in kB. The Atomate2 MCP tool applies the conversion kB → eV/Å³ automatically when convert_units=True (default).

Sign Convention

VASP reports stress with the opposite sign to the physics and ASE convention:

VASP: positive = compressive (pressure-like)
ASE/Physics/MLIPs: positive = tensile

The sign flip is handled during VASP output parsing (e.g. in the atomate2 MCP tool, VASP stress is multiplied by -1 in addition to the unit conversion).

Common Conversion Factors

From	To	Factor	ASE Code
GPa	eV/Å³	0.00624150913	`ase.units.GPa`
eV/Å³	GPa	160.21766208	`1.0 / ase.units.GPa`
kB	GPa	0.1	—
kB	eV/Å³	0.000624150913	`0.1 * ase.units.GPa`
eV	kJ/mol	96.4853	`ase.units.kJ / ase.units.mol`
eV	kcal/mol	23.0605	`ase.units.kcal / ase.units.mol`
Å	Bohr	1.8897259886	`1.0 / ase.units.Bohr`

Quick Reference: Python Conversions

# Env: base-agent
from ase import units

# Stress conversions
stress_GPa = stress_eV_per_A3 / units.GPa        # eV/Å³ → GPa
stress_eV_per_A3 = stress_GPa * units.GPa         # GPa → eV/Å³
stress_eV_per_A3 = stress_kB * 0.1 * units.GPa    # kB → eV/Å³

# Energy conversions
energy_kJ_per_mol = energy_eV * units.kJ / units.mol
energy_kcal_per_mol = energy_eV * units.kcal / units.mol

Constraints

Never mix unit systems within a single workflow.
Always verify stress units when comparing MLIP predictions to DFT references.
Training data JSON files must use eV/Å³ for stress — wrapper-internal conversion handles the rest.
When reporting MAE in papers/docs, specify the unit explicitly (e.g., "Force MAE: 50 meV/Å").

Author: Bowen Deng Contact: GitHub @learningmatter-mit