Data repository for:

• "Chemical potentials from structure factors: I. Neutral multi-component mixtures" — arXiv:2608.08357
• "Chemical potentials from structure factors: II. Charged multi-component mixtures" — arXiv:2608.30060

This repository computes composition-dependent chemical potentials of multicomponent mixtures directly from NPT molecular dynamics (MD) simulations using the extended-S0 method.

extended-S0 workflow:

NPT MD  →  S_αβ(k)  →  S^0 = S(k→0)  →  Γ (chemical-potential derivatives)  →  ∫ → μ_i 
                       (OZ/BC fit)          (S0_multi)                       (GPR_grad)

1. Run NPT MD simulations over a grid of compositions.
2. Compute partial structure factors, Sαβ(k), from the trajectories.
3. Extrapolate S_αβ(k) to k→0 to obtain S_αβ^0 (the examples use the OZ matrix fit).
4. Calculate chemical-potential derivatives using the S0_multi package.
5. Integrate the chemical-potential derivatives using the GPR_grad package with one or more reference chemical potentials.
6. Optional: use GPR_grad's CUR point selection to identify additional compositions to simulate, as demonstrated for the Fe–Cu–Ni liquid alloy example.

extended-S0 for charged systems

For charged systems, we follow the same general workflow. However, step 3 is modified to use the Bare Coulomb (BC) fit, and charges need to be included when using the S0_multi package.

Table of contents

• LiquidAlloyFeCuNi/ — MD inputs, simulated S0 data, and stationary GP regression models for the Fe-Cu-Ni system.
• Paracetamo-Water-Ethanol/ — MD inputs, simulated S0 data, and non-stationary GP regression models for the paracetamol–water–ethanol system.
• Molten_Salts/ — MD inputs, simulated S0 data, Bare Coulomb(BC) fits, GP regression models, and structural analysis
• HalideAqueousElectrolyte/ MD inputs, simulated S0 data, Bare Coulomb(BC) fits, and GP regression model
• moltenSalt-MACELES/ MACELES MLIP trained on molten chloride salts, used for every Molten_Salts/ trajectory

1. Requirements

Requirements for S0_multi and GPR_grad. Additional requirements listed for each example.

• Python 3.10+
• NumPy
• PyTorch

The notebooks and analysis scripts import the current source versions of these companion packages directly:

Package	Role	Source
S0_multi (szero)	Converts fitted S0 values into the Γ matrix of chemical-potential derivatives.	GitHub
GPR_grad (gpr_grad)	PyTorch Gaussian-process regression with function-value and gradient observations; includes CUR point selection.	GitHub

For environment setup, companion-package paths, local tests, and external inputs needed for recalculation, see REPRODUCIBILITY.md.