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arxiv: 2606.30892 · v1 · pith:BQBNFBZ5new · submitted 2026-06-29 · ⚛️ physics.chem-ph · cond-mat.stat-mech

Extension of openCOSMO-RS Into a Full Open-Source Equation of State: Implementation, Parameterization, and Benchmarking

Jan Markgraf , D. G. Lisboa Girardi , Irina Smirnova , Simon M\"uller This is my paper

Pith reviewed 2026-07-01 01:12 UTC · model grok-4.3

classification ⚛️ physics.chem-ph cond-mat.stat-mech
keywords openCOSMO-RSCOSMO-SAC-Phiequation of stateactivity coefficientfree volumeopen-source parametersvapor-liquid equilibrium
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The pith

openCOSMO-RS-Phi turns the activity-coefficient model into an equation of state by adding a free-volume pseudo-component

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper implements the COSMO-SAC-Phi extension inside openCOSMO-RS so that pure substances and mixtures are treated as pseudo-mixtures containing an extra hole component that captures free volume. Four parameters per substance are fitted only to vapor-pressure and liquid-molar-volume data and then used unchanged for all mixture calculations. The resulting model reproduces the accuracy of the original closed-source COSMO-SAC-Phi formulation on large pure-compound and binary-mixture benchmarks without any binary interaction parameters. An open parameter set covering roughly 1800 substances is released with the code.

Core claim

Representing each substance as a pseudo-mixture of the real molecules plus an explicit hole pseudo-component converts the COSMO-SAC activity-coefficient framework into a pressure-explicit equation of state whose pure-component parameters transfer directly to mixture calculations without binary adjustments.

What carries the argument

The hole pseudo-component that accounts for free volume and enables the activity-coefficient model to function as a full equation of state.

If this is right

  • Pure-component parameters alone suffice for mixture predictions across the benchmark sets.
  • No binary interaction parameters are introduced or required.
  • The open parameter library of approximately 1800 entries becomes available for community use.
  • The framework supplies a starting point for extending predictive equations of state to electrolyte solutions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same hole construction could be tested on other activity-coefficient models to produce additional open equations of state.
  • Direct comparison of high-pressure mixture densities against the model would test the transferability assumption more stringently than vapor-liquid equilibrium alone.
  • Integration into existing open process-simulation tools would allow pressure-dependent calculations without proprietary components.

Load-bearing premise

The four pure-component parameters fitted to vapor pressure and liquid volume data transfer to all mixture calculations at different pressures without any adjustment or binary parameters.

What would settle it

Systematic deviation between model predictions and experimental vapor-liquid equilibrium data for binary mixtures at elevated pressures when no binary parameters are allowed.

Figures

Figures reproduced from arXiv: 2606.30892 by D. G. Lisboa Girardi, Irina Smirnova, Jan Markgraf, Simon M\"uller.

Figure 1
Figure 1. Figure 1: Comparison of the resulting MAPE of vapor pressure and molar volume from openCOSMO-RS-Phi across different sets [PITH_FULL_IMAGE:figures/full_fig_p014_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Vapor pressure (a) and molar volume (b) for 10 exemplary components. [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a) Resulting MAPE for the molar enthalpy change of vaporization, evaluated across the 107 components of the bench [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a) Resulting MAPE for isobaric molar heat capacities of liquids at saturation, [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: A parity plot of (a) the predicted critical temperature (K) from openCOSMO-RS-Phi compared to experimental critical [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Ratio of • well- and • badly-modeled molecules for the entire dataset, non-self-associating (NSA), and self-associating (SA) fluids. (NSA) and self-associating (SA) components. Consistent with the studies of Piña-Martinez et al. and Ramírez-Vélez et al., openCOSMO-RS-Phi shows lower internal performance for SA fluids than for NSA fluids. However, the ratio of well-modeled to badly modeled compounds should … view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of the resulting MAPE of vapor pressure and molar volume from all components studied across different [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Correlation between COSMO volume and molar-volume MAPE for (a) PC-SAFT and (b) openCOSMO-RS-Phi, with points [PITH_FULL_IMAGE:figures/full_fig_p021_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Molar cavity (a) and hole molar cavity (b) as a function of COSMO volumes. [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparison of the global marks of different EoSs following the methodology proposed in [ [PITH_FULL_IMAGE:figures/full_fig_p024_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: P–x–y diagrams for binary mixtures exhibiting vapor-liquid equilibrium at the specified temperature, calculated with [PITH_FULL_IMAGE:figures/full_fig_p026_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: P–x–y diagrams for three binary mixtures that exhibit a VLLE for the specified temperature calculated with [PITH_FULL_IMAGE:figures/full_fig_p027_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Global phase equilibrium diagram (GPED) for two binary systems calculated with openCOSMO-RS-Phi: (a) N [PITH_FULL_IMAGE:figures/full_fig_p028_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Enthalpy changes of mixing for nine binary systems calculated with openCOSMO-RS-Phi: [PITH_FULL_IMAGE:figures/full_fig_p030_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Isobaric heat capacities of mixing for three binary mixtures calculated with openCOSMO-RS-Phi: [PITH_FULL_IMAGE:figures/full_fig_p031_15.png] view at source ↗
read the original abstract

The COSMO-SAC-Phi model developed by Soares et al. extends the COSMO-SAC activity-coefficient framework into a full equation of state by explicitly accounting for pressure effects. In this approach, pure substances and mixtures are represented as pseudo-mixtures consisting of the actual number of moles and an additional pseudo-component that describes free volume, or holes. In this work, we implement this extension within the openCOSMO-RS framework and evaluate it using a large and diverse set of molecules and binary systems. The resulting equation of state includes an extensive open-source parameter set with around 1800 pure-component entries, made freely available to the academic community. The four pure-component parameters were fitted to vapor-pressure and liquid-molar volume data for each substance. Model performance was assessed against two benchmark equation-of-state databases, one for pure compounds and one for binary mixtures, without introducing any binary interaction parameters. The resulting openCOSMO-RS-Phi model reproduces the accuracy of the original COSMO-SAC-Phi formulation while providing a fully open-source and accessible implementation for the scientific community. Beyond its immediate utility, it also establishes a foundation for future development of predictive EoS for electrolyte solutions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper extends the openCOSMO-RS framework to a full equation of state (openCOSMO-RS-Phi) by representing substances and mixtures as pseudo-mixtures that include a hole pseudo-component to account for free volume and pressure effects. Four pure-component parameters per substance are fitted to vapor-pressure and liquid-molar-volume data for ~1800 compounds; the resulting model is evaluated on pure-component and binary-mixture benchmark databases without any binary interaction parameters and is claimed to reproduce the accuracy of the original COSMO-SAC-Phi formulation while providing a fully open-source implementation and parameter set.

Significance. If the parameter transfer to mixtures holds, the work supplies a large, freely available open-source EoS parameter database and implementation that lowers barriers for the community and provides a foundation for extensions such as electrolyte solutions. The explicit open release of both code and ~1800 fitted parameters is a concrete strength that supports reproducibility.

major comments (2)
  1. [Abstract] Abstract: the claim that the model 'reproduces the accuracy of the original COSMO-SAC-Phi formulation' on binary mixtures is presented without any quantitative error statistics, RMSE values, data-exclusion rules, or direct comparison of error bars against the reference model; this absence prevents assessment of whether the central transfer claim is supported.
  2. [Parameterization and Benchmarking sections] The four pure-component parameters are fitted exclusively to vapor-pressure and liquid-volume data; the manuscript asserts that these parameters transfer without adjustment or binary terms to mixture calculations at varying pressures, yet reports no hold-out test, cross-validation on mixture data, or refitting experiment that would falsify the transfer assumption.
minor comments (1)
  1. Notation for the hole pseudo-component and its volume fraction should be defined explicitly on first use to avoid ambiguity with standard COSMO-RS segment notation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

Thank you for the referee's insightful comments. We have carefully considered each point and provide our responses below. We agree that enhancements to the abstract and additional clarifications in the text are warranted.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that the model 'reproduces the accuracy of the original COSMO-SAC-Phi formulation' on binary mixtures is presented without any quantitative error statistics, RMSE values, data-exclusion rules, or direct comparison of error bars against the reference model; this absence prevents assessment of whether the central transfer claim is supported.

    Authors: We acknowledge that the abstract would benefit from quantitative support for the claim. In the revised version, we will include key RMSE values for vapor pressure, liquid volume, and mixture properties, along with a note on the databases used and a direct comparison to the COSMO-SAC-Phi results where possible. This will allow readers to assess the reproduction of accuracy. revision: yes

  2. Referee: [Parameterization and Benchmarking sections] The four pure-component parameters are fitted exclusively to vapor-pressure and liquid-volume data; the manuscript asserts that these parameters transfer without adjustment or binary terms to mixture calculations at varying pressures, yet reports no hold-out test, cross-validation on mixture data, or refitting experiment that would falsify the transfer assumption.

    Authors: The fitting is indeed limited to pure-component properties. The transferability is tested by applying the model to an independent set of binary mixture data from the benchmark database, without any adjustments or binary parameters. This evaluation on mixture data not used in parameterization serves as validation of the transfer. We will revise the manuscript to explicitly state this and include any available error statistics comparing to the reference model. If the referee suggests specific additional experiments, we can consider them, but the current benchmarking provides evidence for the claim. revision: partial

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper fits four pure-component parameters to vapor-pressure and liquid-molar volume data per substance, then assesses performance on separate benchmark databases for pure compounds and binary mixtures without binary interaction parameters. The central claim of reproducing COSMO-SAC-Phi accuracy (Soares et al.) is an external comparison, not a reduction to the fitted inputs by construction. No quoted step equates mixture predictions to the pure-component fits, renames a fit as a prediction, or relies on load-bearing self-citation; the mixture benchmark serves as an independent test, making the derivation self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central claim rests on the COSMO-SAC activity-coefficient framework plus the specific pseudo-mixture construction for free volume; four fitted parameters per compound are introduced without independent physical derivation.

free parameters (1)
  • four pure-component parameters per substance
    Explicitly stated as fitted to vapor-pressure and liquid-molar volume data for each of the ~1800 entries.
axioms (2)
  • domain assumption Pure substances and mixtures can be represented as pseudo-mixtures consisting of the actual number of moles and an additional pseudo-component that describes free volume or holes.
    This is the core modeling choice taken from Soares et al. and invoked to extend the activity-coefficient model into an equation of state.
  • domain assumption The COSMO-SAC activity-coefficient framework remains valid when pressure effects are introduced via the pseudo-component.
    The paper builds directly on the prior COSMO-SAC-Phi formulation without re-deriving the underlying combinatorial and residual contributions.
invented entities (1)
  • pseudo-component representing free volume (holes) no independent evidence
    purpose: To account for pressure dependence inside the equation of state.
    Introduced as an additional component in every pure-substance and mixture calculation; no independent experimental signature is provided beyond the fitted pure-component data.

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Reference graph

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