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arxiv: 2605.18264 · v1 · pith:CTQGTHTMnew · submitted 2026-05-18 · 🌌 astro-ph.EP · astro-ph.IM· astro-ph.SR

FastChem 4: New chemical elements and improved convergence behaviour

Daniel Kitzmann , Joachim W. Stock , A. Beate C. Patzer This is my paper

Pith reviewed 2026-05-20 00:15 UTC · model grok-4.3

classification 🌌 astro-ph.EP astro-ph.IMastro-ph.SR
keywords chemical equilibriumcondensation sequencesexoplanet atmospheresbrown dwarfscarbon-rich chemistrynumerical methodssilicon monoxide
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The pith

FastChem 4 stabilizes chemical equilibrium calculations for non-solar abundances and identifies silicon monoxide as a condensate in a limited range.

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

FastChem 4 updates an open-source code for calculating chemical equilibrium in the atmospheres of exoplanets, brown dwarfs, and similar objects. The main changes involve a new multidimensional Newton method for the gas-phase solver and a reformulation of the equations using logarithmic element densities. These allow the code to converge reliably even with strongly non-solar elemental abundances and to run in double precision at low temperatures. The condensate part also receives better regularization and a combined solver. The result is faster and more stable computations that reproduce known solar condensation sequences while showing different behavior in carbon-rich mixtures.

Core claim

The central claim is that the new solver methods and expanded chemical network enable robust calculations across a wide range of elemental compositions. This leads to the discovery that silicon monoxide forms as a stable condensate under carbon-rich conditions within a limited pressure-temperature window, consistent with recent observations.

What carries the argument

The multidimensional Newton-method in logarithmic element densities for the gas-phase solver, which improves convergence and eliminates the need for quad-precision arithmetic.

If this is right

  • The code achieves a strong increase in computational performance and stability.
  • It reproduces the classical solar-composition condensation sequence.
  • Marked shifts in the condensation sequence appear under carbon-rich conditions.
  • Silicon monoxide remains stable as a condensate over a limited pressure-temperature range.

Where Pith is reading between the lines

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

  • The stability of silicon monoxide as a condensate could explain certain spectral features seen in brown dwarf atmospheres.
  • Improved handling of non-solar abundances may help model the chemistry of exoplanets with unusual compositions inferred from observations.
  • Future extensions could incorporate even more elements or couple the equilibrium solver to atmospheric dynamics models.

Load-bearing premise

The tabulated thermochemical data for the 44 elements and 1311 species are assumed to be accurate enough that any errors in the Gibbs energies would not change the reported condensation sequences or the stability range for silicon monoxide.

What would settle it

A mismatch between the predicted pressure-temperature range for silicon monoxide condensation and direct spectroscopic observations of carbon-rich brown dwarfs would falsify the stability result.

Figures

Figures reproduced from arXiv: 2605.18264 by A. Beate C. Patzer, Daniel Kitzmann, Joachim W. Stock.

Figure 1
Figure 1. Figure 1: , which shows the number of iterations needed across the pressure-temperature (p-T) range used by Stock et al. (2018). In contrast to those calculations, we adopted solar elemental abun￾dances but set the carbon-to-oxygen (C/O) ratio equal to one. To remain comparable with the earlier calculations, only gas-phase species were considered, thus neglecting condensation [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Improved convergence behaviour as implemented in FastChem. The left panel depicts the number of iterations and employs the same colour scale as in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Element abundances of various elements in the solar photosphere (xphot) and CI chondrites (xCI) from Asplund et al. (2021). The elements labelled in blue are part of the original FastChem release (Stock et al. 2018, 2022). Elements that are added to FastChem as part of this study are coloured in red, while remaining elements are depicted in yellow. For elements where no photospheric abundance is available,… view at source ↗
Figure 4
Figure 4. Figure 4: Overview of the elements included in FastChem in the form of the periodic table. Elements coloured in blue are part of the previous versions of FastChem (Stock et al. 2018, 2022; Kitzmann et al. 2024), while those in cyan are additionally available in the data set by Hoeijmakers et al. (2019) that contains only atoms as well as singly and doubly ionised gas-phase species. Elements for which new molecules a… view at source ↗
Figure 5
Figure 5. Figure 5: Results of the FastChem calculations across a wide p-T range. The panels on the left show results for solar elemental abundances, while those on the right correspond to a carbon-rich composition with a C/O ratio of 2. For each element, the plots display the dominant gas-phase and condensate species, that is, the species containing the largest fraction of the element, as a function of pressure and temperatu… view at source ↗
read the original abstract

Chemical equilibrium calculations are a key ingredient for modelling and interpreting spectroscopic observations of (exo)planets, brown dwarfs, cool stars, and protoplanetary disks. As these applications increasingly probe non-solar elemental abundances and previously underrepresented elements, equilibrium chemistry solvers must be both numerically robust and capable of handling complex chemical systems. Here we present FastChem 4, a major update to the open-source FastChem equilibrium chemistry code. We extend the gas-phase solver with a multidimensional Newton-method that mitigates the slow convergence previously encountered for strongly non-solar elemental abundances. We further reformulate the gas-phase equations in logarithmic element densities, removing the dependence on quad-precision arithmetic and allowing FastChem to be applied at low temperatures on any platform supporting double precision. The condensate solver is upgraded with adaptive Levenberg-Marquardt regularisation, a perturbed-Hessian fallback, and a combined gas-condensate Newton solver. These changes lead to a strong increase in computational performance and stability. The thermochemical data is expanded using thermochemical data from the NIST-JANAF tables and the Barin compilation, and now comprises 800 gas-phase molecules and ions and 511 condensates spanning 44 elements. We apply the updated code to a wide pressure-temperature grid for both solar and carbon-rich (C/O = 2) elemental compositions. The resulting grids reproduce the classical solar-composition condensation sequence and reveal the marked shifts that occur under carbon-rich conditions. We also find that silicon monoxide is stable as a condensate over a limited pressure-temperature range, consistent with recent JWST observations of brown dwarfs. FastChem 4 is released under the GPLv3 licence, together with a pre-compiled Python package.

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

3 major / 2 minor

Summary. The manuscript presents FastChem 4, a major update to the open-source FastChem chemical equilibrium code. It introduces a multidimensional Newton solver for the gas phase, reformulates equations in logarithmic element densities to eliminate quad-precision requirements, and upgrades the condensate solver with adaptive Levenberg-Marquardt regularization, perturbed-Hessian fallback, and a combined gas-condensate Newton method. The thermochemical database is expanded to 800 gas-phase species and 511 condensates spanning 44 elements using NIST-JANAF and Barin data. Application to pressure-temperature grids for solar and C/O=2 compositions reproduces the classical solar condensation sequence, shows marked shifts under carbon-rich conditions, and identifies a limited P-T domain where SiO is stable as a condensate, consistent with recent JWST observations of brown dwarfs. The code is released under GPLv3 with a pre-compiled Python package.

Significance. If the numerical improvements and reported sequences hold, this provides a more robust and broadly applicable tool for equilibrium chemistry modeling of exoplanet atmospheres, brown dwarfs, cool stars, and disks, especially for non-solar abundances and underrepresented elements. The open-source release with Python package and the explicit demonstration of SiO stability as a potential observational link are strengths that support wider use and reproducibility.

major comments (3)
  1. [Results, P-T grid application] In the section presenting the P-T grids and SiO stability (results on carbon-rich and solar sequences): the reported limited pressure-temperature range where SiO appears as a stable condensate depends directly on the Gibbs energies for the new SiO condensate entry from the Barin compilation. No sensitivity test to plausible variations in formation enthalpy or heat capacity is shown, which is load-bearing for the claim of consistency with JWST observations.
  2. [Thermochemical data expansion] In the methods description of the expanded thermochemical data: the addition of 511 new condensates and 800 gas species assumes NIST-JANAF and Barin tables are free of systematic errors across the full P-T range of interest. No cross-validation against FastChem 3 results for the overlapping species subset or against an independent equilibrium code is reported, preventing isolation of data error from the claimed solver improvements.
  3. [Solver improvements and performance] In the section on solver upgrades and performance: the abstract and text claim a 'strong increase in computational performance and stability,' yet no quantitative benchmarks (e.g., iteration counts, failure rates, or wall-time ratios on the same grids) comparing version 3 to version 4 are provided for the tested solar and C/O=2 cases.
minor comments (2)
  1. [Figures] Figure captions for the condensation sequences should explicitly state the exact elemental abundances and pressure range used to allow direct reproduction.
  2. [Abstract] The abstract states performance gains qualitatively; adding a sentence with specific metrics (e.g., factor of X speedup or reduction in non-convergent cases) would strengthen the summary.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough and constructive review of our manuscript. We address each of the major comments point by point below, indicating where revisions will be made to improve the paper.

read point-by-point responses

  1. Referee: [Results, P-T grid application] In the section presenting the P-T grids and SiO stability (results on carbon-rich and solar sequences): the reported limited pressure-temperature range where SiO appears as a stable condensate depends directly on the Gibbs energies for the new SiO condensate entry from the Barin compilation. No sensitivity test to plausible variations in formation enthalpy or heat capacity is shown, which is load-bearing for the claim of consistency with JWST observations.

    Authors: We agree that the stability range of SiO as a condensate is sensitive to the thermochemical data adopted from the Barin tables. To strengthen this aspect of the manuscript, we will add a sensitivity test in the revised version. Specifically, we will vary the standard enthalpy of formation and heat capacity data for SiO within estimated uncertainties (e.g., ±5-10 kJ/mol for enthalpy) and demonstrate how this affects the P-T domain of stability. This will provide a more robust basis for the claimed consistency with JWST observations of brown dwarfs. revision: yes

  2. Referee: [Thermochemical data expansion] In the methods description of the expanded thermochemical data: the addition of 511 new condensates and 800 gas species assumes NIST-JANAF and Barin tables are free of systematic errors across the full P-T range of interest. No cross-validation against FastChem 3 results for the overlapping species subset or against an independent equilibrium code is reported, preventing isolation of data error from the claimed solver improvements.

    Authors: We acknowledge the importance of validating the thermochemical database to distinguish between improvements due to the new solver and potential data differences. In the revised manuscript, we will include a cross-validation section comparing equilibrium compositions from FastChem 4 with those from FastChem 3 for the subset of species present in both versions, using identical P-T conditions and elemental abundances. We will also discuss any discrepancies and their origins. A comparison with an independent code such as TEA or GGchem could be added if space permits, but the primary validation will be against the previous FastChem version. revision: yes

  3. Referee: [Solver improvements and performance] In the section on solver upgrades and performance: the abstract and text claim a 'strong increase in computational performance and stability,' yet no quantitative benchmarks (e.g., iteration counts, failure rates, or wall-time ratios on the same grids) comparing version 3 to version 4 are provided for the tested solar and C/O=2 cases.

    Authors: We appreciate this observation regarding the lack of quantitative performance metrics. Although the improvements are described in the text, we will add quantitative benchmarks in the revised manuscript. This will include a table or figure presenting average iteration counts, convergence success rates, and relative wall-clock times for FastChem 3 versus FastChem 4 on the same solar and C/O=2 P-T grids. These metrics will directly support the claims of enhanced performance and stability. revision: yes

Circularity Check

0 steps flagged

No circularity in FastChem 4 code update and condensation results

full rationale

The paper describes numerical upgrades to the FastChem equilibrium solver (multidimensional Newton, logarithmic element densities, adaptive Levenberg-Marquardt) and the addition of external thermochemical data from NIST-JANAF and Barin tables for 800 gas species and 511 condensates. The reported solar and C-rich condensation sequences, including the limited P-T domain for SiO stability, are direct numerical outputs from applying the updated solver to these independent input tables. No step reduces a claimed result to a fitted parameter or self-citation by construction; the consistency note with JWST observations functions as an external cross-check rather than an input. The derivation chain is therefore self-contained against external benchmarks and data sources.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work relies on standard numerical analysis results for Newton convergence and on the accuracy of external thermochemical tables. No new physical entities are postulated and no parameters appear to be fitted to the target data.

axioms (2)
  • domain assumption Newton's method converges to the physical solution for the chosen initial guesses and regularization schedule across the full P-T-abundance domain.
    Invoked when the authors state that the multidimensional Newton method mitigates slow convergence for strongly non-solar abundances.
  • domain assumption Gibbs free energies tabulated in NIST-JANAF and Barin compilations are accurate enough for all 44 elements and 1311 species at the pressures and temperatures considered.
    The expanded database is taken directly from these sources without additional validation reported in the abstract.

pith-pipeline@v0.9.0 · 5853 in / 1634 out tokens · 45212 ms · 2026-05-20T00:15:19.607825+00:00 · methodology

discussion (0)

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    FN, FNO, FNO2, FNO3, FNa,FNi i, FO, FOTi, OFO, FOO FP, FP –, FP+, FPS, FS, FS –, FS+, FSi, FTi,FZn i, F2, F2Fe, F2H2, F2H2Si, F2K–, F2K2, F2Mg, F2Mg+, F2N, cis-F2N2,trans-F 2N2 F2Na–, F2Na2, F2O, F2OS, F2OSi, F2OTi, F2O2, F2O2S, F2P, F2P–, F2P+, F2S, F2S–, F2S+, FS2F, SSF2 F2Si, F2Ti, F3Fe, F3HSi, F3H3, F3N, F3NO, F3OP, F3P, F3PS, F3S, F3S–, F3S+, F3Si, F...

    work page 1973