GGchem Equilibrium Chemistry Models

• GGchem equilibrium chemistry models are defined as thermo-chemical solvers that compute gas-phase abundances from elemental and thermodynamic conditions, including optional condensation.
• They employ a law-of-mass-action formulation with element conservation and a robust low-temperature numerical strategy, converging efficiently even below 100 K.
• The framework demonstrates that equilibrium condensation alters gas composition, affecting opacity calculations, cloud modeling, and atmospheric retrievals.

GGchem, from “Gleich-Gewichts-Chemie”, is a thermo-chemical equilibrium code for computing the composition of astrophysical and planetary gases, with optional equilibrium condensation, over a temperature range extending down to $100\,\mathrm{K}$. In the literature it functions both as a standalone equilibrium solver and as a chemistry backbone inside larger atmosphere and retrieval frameworks. Its defining role is to map specified thermodynamic conditions and elemental abundances into equilibrium gas abundances, ionic populations, electron densities, and, when enabled, condensate stability, thereby supplying the chemical state needed for opacity calculations, cloud modeling, and atmosphere structure calculations (Woitke et al., 2017). Later work embedded GGchem directly into self-consistent atmosphere grids such as MSG and into retrieval pipelines such as TauREx 3.1, while other studies used it to connect bulk composition to silicate mineralogy in polluted white dwarfs (Jørgensen et al., 2024, Al-Refaie et al., 2021, Rogers et al., 22 Jul 2025).

1. Origins, scope, and species inventory

GGchem was introduced as a fast and versatile equilibrium code intended for local thermodynamic equilibrium applications in stellar atmospheres, brown dwarfs, giant exoplanet atmospheres, cool stars, AGB star winds, cloud formation environments, and cold planetary or planet-forming environments where condensation matters. Its original motivation was that spectroscopy, radiative transfer, atmospheric structure, and dust formation all depend sensitively on equilibrium composition, while many older equilibrium datasets and fitting formulae become unreliable below a few hundred kelvin (Woitke et al., 2017).

The code treats both pure gas-phase equilibrium and gas-plus-condensate phase equilibrium. The paper reports a gas-phase inventory of 24 elements,

$$\mathrm{H, He, Li, C, N, O, F, Na, Mg, Al, Si, P, S, Cl, K, Ca, Ti, V, Cr, Mn, Fe, Ni, Zr, W},$$

and describes a molecular inventory that appears in two slightly different counts: 552 molecules and ions in the summary, and 568 molecules in Sect. 3, reflecting different selection stages. For condensation chemistry, the data comprise 257 condensates, including 38 liquids; the main solar-abundance phase-equilibrium model uses 190 condensed species alongside 388 gas-phase species (Woitke et al., 2017).

This broad inventory is one reason GGchem is frequently treated as an equilibrium “backbone” rather than merely a lookup-table generator. In later atmosphere work, however, the exact way GGchem is embedded varies. MSG, for example, uses GGchem for gas-phase equilibrium while delegating cloud condensates to StaticWeather, whereas TauREx 3.1 exposes GGchem itself as a callable equilibrium solver inside the retrieval loop (Jørgensen et al., 2024, Al-Refaie et al., 2021).

2. Thermodynamic formulation and numerical strategy

GGchem solves equilibrium primarily through a law-of-mass-action formulation coupled to elemental conservation, rather than by direct minimization of a scalar Gibbs free-energy functional. For a molecule $\mathrm{A_aB_bC_c}$, the equilibrium relation is written as

$$p_{\rm A_aB_bC_c} = k_p({\rm A_aB_bC_c},T)\;p_{\rm A}^a\,p_{\rm B}^b\,p_{\rm C}^c ,$$

with

$$k_p({\rm A_aB_bC_c},T) = \big(p^\circ\big)^{1-a-b-c} \exp\left(-\frac{\Delta G^\circ}{RT}\right) .$$

Element conservation is enforced through

$$\epsilon_k\,n_{\langle {\rm H}\rangle} = \sum_i s_{i,k}\,n_i ,$$

and charge conservation is handled by treating charge as an additional pseudo-element with $\epsilon_{\rm el}=0$ (Woitke et al., 2017).

When condensation is enabled, GGchem imposes phase equilibrium by supersaturation constraints. For a condensate $j$,

$S_j = \frac{p_j}{p_j^{\rm vap}(T)} ,$

with stable condensates satisfying $S_j=1$ and unstable ones $$\mathrm{H, He, Li, C, N, O, F, Na, Mg, Al, Si, P, S, Cl, K, Ca, Ti, V, Cr, Mn, Fe, Ni, Zr, W},$$0. For minerals lacking a corresponding gas molecule, the code evaluates a generalized supersaturation ratio directly from gas-phase atomic partial pressures. In practice, condensation is implemented by reducing the gas-phase elemental abundances until all selected condensates satisfy phase equilibrium, while non-selected condensates remain sub-saturated (Woitke et al., 2017).

A central contribution of the original paper is the low-temperature numerical strategy. GGchem switches to quadruple precision arithmetic below $$\mathrm{H, He, Li, C, N, O, F, Na, Mg, Al, Si, P, S, Cl, K, Ca, Ti, V, Cr, Mn, Fe, Ni, Zr, W},$$1 and uses a hierarchical pre-iteration scheme based on the elemental abundance hierarchy before a final Newton–Raphson solve. If $$\mathrm{H, He, Li, C, N, O, F, Na, Mg, Al, Si, P, S, Cl, K, Ca, Ti, V, Cr, Mn, Fe, Ni, Zr, W},$$2 rather than $$\mathrm{H, He, Li, C, N, O, F, Na, Mg, Al, Si, P, S, Cl, K, Ca, Ti, V, Cr, Mn, Fe, Ni, Zr, W},$$3 is specified, the code iterates on the mean molecular weight and typically converges in 1–5 calls to the chemistry solver. With a good initial guess from a nearest-neighbor database, the phase-equilibrium solve usually converges in fewer than 10 iterations (Woitke et al., 2017).

The benchmark against TEA is particularly important for how GGchem is positioned in later literature. In a 24-element pure gas-phase benchmark at $$\mathrm{H, He, Li, C, N, O, F, Na, Mg, Al, Si, P, S, Cl, K, Ca, Ti, V, Cr, Mn, Fe, Ni, Zr, W},$$4 bar and $$\mathrm{H, He, Li, C, N, O, F, Na, Mg, Al, Si, P, S, Cl, K, Ca, Ti, V, Cr, Mn, Fe, Ni, Zr, W},$$5–$$\mathrm{H, He, Li, C, N, O, F, Na, Mg, Al, Si, P, S, Cl, K, Ca, Ti, V, Cr, Mn, Fe, Ni, Zr, W},$$6, GGchem and TEA agreed to roughly $$\mathrm{H, He, Li, C, N, O, F, Na, Mg, Al, Si, P, S, Cl, K, Ca, Ti, V, Cr, Mn, Fe, Ni, Zr, W},$$7 dex where species inventories overlapped, but TEA failed to converge below $$\mathrm{H, He, Li, C, N, O, F, Na, Mg, Al, Si, P, S, Cl, K, Ca, Ti, V, Cr, Mn, Fe, Ni, Zr, W},$$8 even with 2000 iterations. GGchem required about $$\mathrm{H, He, Li, C, N, O, F, Na, Mg, Al, Si, P, S, Cl, K, Ca, Ti, V, Cr, Mn, Fe, Ni, Zr, W},$$9 CPU s per point, falling to $\mathrm{A_aB_bC_c}$0 CPU s per point above $\mathrm{A_aB_bC_c}$1, and was estimated to be more than $\mathrm{A_aB_bC_c}$2 times faster under that benchmark (Woitke et al., 2017).

3. Condensation sequences and their chemical consequences

A defining feature of GGchem equilibrium models is that condensation is not merely an auxiliary solid-state output; it substantially alters the gas composition itself. In the solar-abundance condensation sequence at $\mathrm{A_aB_bC_c}$3 bar, the first stable condensate is metallic tungsten, $\mathrm{A_aB_bC_c}$4, at $\mathrm{A_aB_bC_c}$5, followed by $\mathrm{A_aB_bC_c}$6 at $\mathrm{A_aB_bC_c}$7, $\mathrm{A_aB_bC_c}$8 at $\mathrm{A_aB_bC_c}$9, $$p_{\rm A_aB_bC_c} = k_p({\rm A_aB_bC_c},T)\;p_{\rm A}^a\,p_{\rm B}^b\,p_{\rm C}^c ,$$0 at $$p_{\rm A_aB_bC_c} = k_p({\rm A_aB_bC_c},T)\;p_{\rm A}^a\,p_{\rm B}^b\,p_{\rm C}^c ,$$1, and later the major magnesium silicates $$p_{\rm A_aB_bC_c} = k_p({\rm A_aB_bC_c},T)\;p_{\rm A}^a\,p_{\rm B}^b\,p_{\rm C}^c ,$$2 at $$p_{\rm A_aB_bC_c} = k_p({\rm A_aB_bC_c},T)\;p_{\rm A}^a\,p_{\rm B}^b\,p_{\rm C}^c ,$$3 and $$p_{\rm A_aB_bC_c} = k_p({\rm A_aB_bC_c},T)\;p_{\rm A}^a\,p_{\rm B}^b\,p_{\rm C}^c ,$$4 at $$p_{\rm A_aB_bC_c} = k_p({\rm A_aB_bC_c},T)\;p_{\rm A}^a\,p_{\rm B}^b\,p_{\rm C}^c ,$$5 (Woitke et al., 2017).

The resulting equilibrium dust-to-gas ratio is smaller than the frequently assumed canonical value until volatile ices condense. After the major refractory condensates form, the dust/gas mass ratio reaches about $$p_{\rm A_aB_bC_c} = k_p({\rm A_aB_bC_c},T)\;p_{\rm A}^a\,p_{\rm B}^b\,p_{\rm C}^c ,$$6, and after sulfur condenses as $$p_{\rm A_aB_bC_c} = k_p({\rm A_aB_bC_c},T)\;p_{\rm A}^a\,p_{\rm B}^b\,p_{\rm C}^c ,$$7 the equilibrium value is about $$p_{\rm A_aB_bC_c} = k_p({\rm A_aB_bC_c},T)\;p_{\rm A}^a\,p_{\rm B}^b\,p_{\rm C}^c ,$$8. The commonly assumed $$p_{\rm A_aB_bC_c} = k_p({\rm A_aB_bC_c},T)\;p_{\rm A}^a\,p_{\rm B}^b\,p_{\rm C}^c ,$$9 is achieved only after $$k_p({\rm A_aB_bC_c},T) = \big(p^\circ\big)^{1-a-b-c} \exp\left(-\frac{\Delta G^\circ}{RT}\right) .$$0 and $$k_p({\rm A_aB_bC_c},T) = \big(p^\circ\big)^{1-a-b-c} \exp\left(-\frac{\Delta G^\circ}{RT}\right) .$$1 condense; the paper states that ice formation increases condensate mass by a factor of about 2.5 and condensate volume by about 6 (Woitke et al., 2017).

The same condensation sequence drives major changes in the gas-phase carbon-to-oxygen ratio. Starting from a solar value of about $$k_p({\rm A_aB_bC_c},T) = \big(p^\circ\big)^{1-a-b-c} \exp\left(-\frac{\Delta G^\circ}{RT}\right) .$$2, silicate condensation raises the gas-phase C/O to about $$k_p({\rm A_aB_bC_c},T) = \big(p^\circ\big)^{1-a-b-c} \exp\left(-\frac{\Delta G^\circ}{RT}\right) .$$3 by removing oxygen into solids while leaving carbon almost entirely gaseous. Below roughly $$k_p({\rm A_aB_bC_c},T) = \big(p^\circ\big)^{1-a-b-c} \exp\left(-\frac{\Delta G^\circ}{RT}\right) .$$4, additional hydration of silicates by phyllosilicate formation increases the gaseous C/O further to about $$k_p({\rm A_aB_bC_c},T) = \big(p^\circ\big)^{1-a-b-c} \exp\left(-\frac{\Delta G^\circ}{RT}\right) .$$5. The paper emphasizes that this effect can bias atmospheric interpretations if Mg-, Si-, and Fe-bearing condensate chemistry is neglected (Woitke et al., 2017).

A related result is that carbon remains gaseous throughout the modeled solar-abundance sequence down to $$k_p({\rm A_aB_bC_c},T) = \big(p^\circ\big)^{1-a-b-c} \exp\left(-\frac{\Delta G^\circ}{RT}\right) .$$6: at $$k_p({\rm A_aB_bC_c},T) = \big(p^\circ\big)^{1-a-b-c} \exp\left(-\frac{\Delta G^\circ}{RT}\right) .$$7 bar, not a single carbon atom condenses in the equilibrium model presented there. The authors explicitly note that this conclusion could change if missing organic solids and liquids were added, which marks one of the stated limits of the available condensate inventory (Woitke et al., 2017).

4. Embedding GGchem in self-consistent atmosphere models

The most explicit recent atmosphere implementation is MSG, a grid of self-consistent 1D model atmospheres spanning $$k_p({\rm A_aB_bC_c},T) = \big(p^\circ\big)^{1-a-b-c} \exp\left(-\frac{\Delta G^\circ}{RT}\right) .$$8–$$k_p({\rm A_aB_bC_c},T) = \big(p^\circ\big)^{1-a-b-c} \exp\left(-\frac{\Delta G^\circ}{RT}\right) .$$9, built by iteratively coupling MARCS, StaticWeather, and GGchem. Within MSG, GGchem is not used as the final condensate solver; it is used “solely” to calculate gas-phase particle densities from local temperature, pressure, and gas-phase elemental abundances, while StaticWeather computes the solid-state condensates and cloud evolution (Jørgensen et al., 2024).

In that framework GGchem computes concentrations of all neutral and singly ionized atoms, electrons, molecules, and molecular ions for 22 elements,

$$\epsilon_k\,n_{\langle {\rm H}\rangle} = \sum_i s_{i,k}\,n_i ,$$0

using an additional database of 543 molecules, molecular ions, and cations. The outputs supply the gas composition needed for opacities and also the true electron pressure used by the atmosphere solver (Jørgensen et al., 2024).

A central numerical result of MSG is that GGchem enables convergence in a regime where classical MARCS electron-pressure iteration becomes unstable. For warmer models the atmosphere iteration can converge using electron pressure as an independent variable, but for cooler models the coupling to GGchem makes it possible to converge effectively on gas pressure instead. The paper attributes this to the fact that at low temperatures the physically correct electron pressure becomes so small that it is numerically fragile as an iteration variable, while GGchem can still provide the true $$\epsilon_k\,n_{\langle {\rm H}\rangle} = \sum_i s_{i,k}\,n_i ,$$1 needed for the opacity and thermodynamic calculations (Jørgensen et al., 2024).

Cloudy MSG models make the GGchem role even clearer. StaticWeather computes cloud formation, growth, settling, sublimation, and depletion; the resulting layer-dependent gas-phase elemental abundances are then passed back to GGchem, which recomputes the post-depletion gas-phase equilibrium composition. The paper states explicitly that “the gas-phase equilibrium chemistry is always computed after we have computed the gas-phase element depletions from cloud formation.” This produces a cloud-consistent gas chemistry rather than a fixed pre-cloud composition field (Jørgensen et al., 2024).

5. Retrieval backends, benchmarking, and common failure modes

GGchem entered comparative retrieval studies most clearly through TauREx 3.1, where it was integrated via the taurex_ggchem plugin and could be invoked with chemistry_type = ggchem; equilibrium condensation could be activated with equilibrium_condensation = True. In that setting GGchem was compared directly with ACE and FastChem under otherwise identical forward-model and sampler machinery, which separated chemistry-backend effects from radiative-transfer and inference-code effects (Al-Refaie et al., 2021).

The principal conclusion of that comparison is often summarized as a statement about solver equivalence under matched assumptions. Like-for-like equilibrium retrievals with ACE, FastChem, and GGchem recovered the correct parameters to less than 1% of the truth. By contrast, when the chemical assumptions were mismatched—missing elements, fixed elemental ratios, or incorrect condensation treatment—metallicity and other parameters could deviate by 20% while maintaining extremely low uncertainties below 1%, creating false confidence (Al-Refaie et al., 2021).

The distinction between plain GGchem and GGchem with condensation is therefore not a minor implementation switch but a physically consequential model choice. In the heavy-element cases studied there, enabling condensation reduced gas-phase TiO strongly and VO mildly through sequestration from condensation; against a heavy+condensation truth, GGchem without condensation drove the metallicity to the prior ceiling and forced very low C/O, whereas GGchem with condensation recovered the truth accurately. The paper uses this result to argue that the dominant source of bias is not the equilibrium solver implementation itself, but the chemical assumptions encoded in the selected equilibrium model (Al-Refaie et al., 2021).

That same study also quantifies the computational cost of making GGchem more chemically complete inside a retrieval loop. Mean retrieval times were reported as 10.52 minutes for GGchem C/H/O/N, 30.2 minutes for GGchem heavy chemistry, and 540.43 minutes for GGchem heavy chemistry with condensation. The slowdown was attributed specifically to equilibrium condensation on the CPU, which became a significant fraction of the forward-model time (Al-Refaie et al., 2021).

6. Extensions, adjacent frameworks, and interpretive boundaries

A recent non-atmospheric application illustrates how GGchem equilibrium models are used outside standard stellar or exoplanet retrieval problems. In polluted white dwarfs, GGchem was used to test whether the bulk Mg/Si ratio of accreted rocky material predicts whether circumstellar dust is more olivine- or pyroxene-dominated. Those calculations assumed Gibbs free-energy minimization with gas-phase and condensation chemistry at $$\epsilon_k\,n_{\langle {\rm H}\rangle} = \sum_i s_{i,k}\,n_i ,$$2; the detailed comparison shown in the paper is at $$\epsilon_k\,n_{\langle {\rm H}\rangle} = \sum_i s_{i,k}\,n_i ,$$3, with Mg, Fe, and O fixed at Bulk Earth-like values and Si varied to scan $$\epsilon_k\,n_{\langle {\rm H}\rangle} = \sum_i s_{i,k}\,n_i ,$$4. The reported trend is that increasing Mg/Si favors forsterite $$\epsilon_k\,n_{\langle {\rm H}\rangle} = \sum_i s_{i,k}\,n_i ,$$5, enstatite $$\epsilon_k\,n_{\langle {\rm H}\rangle} = \sum_i s_{i,k}\,n_i ,$$6 peaks near $$\epsilon_k\,n_{\langle {\rm H}\rangle} = \sum_i s_{i,k}\,n_i ,$$7 $$\epsilon_k\,n_{\langle {\rm H}\rangle} = \sum_i s_{i,k}\,n_i ,$$8, and lower Mg/Si leads to more silica-bearing condensates. The observed white-dwarf sample showed a tentative correlation between photospheric Mg/Si and dust mineralogy, with weighted Pearson coefficients $$\epsilon_k\,n_{\langle {\rm H}\rangle} = \sum_i s_{i,k}\,n_i ,$$9 for Mg/Si versus peak wavelength and $\epsilon_{\rm el}=0$0 for Mg/Si versus pyroxene/olivine band ratio (Rogers et al., 22 Jul 2025).

Several recent equilibrium frameworks occupy adjacent but distinct positions relative to GGchem:

Framework	Equilibrium formulation as described	Relation to GGchem
GGchem	Law of mass action plus element conservation, with optional equilibrium condensation and supersaturation constraints (Woitke et al., 2017)	Baseline equilibrium code
easyCHEM	Gibbs free-energy minimization in the NASA CEA lineage; benchmarked against CEA with identical results (Lei et al., 2024)	Adjacent equilibrium framework, not GGchem
NEXOCHEM in XODIAC	Built-in equilibrium solver, but the internal numerical method is not specified in the XODIAC paper (Ghosh et al., 7 Dec 2025)	Equilibrium initializer inside a photochemical model
Burrows/Sharp table-based Y-dwarf chemistry	Premixed thermochemical-equilibrium opacity tables following Sharp (2007) and Burrows (1999) (Lacy et al., 2023)	Conceptually similar equilibrium backbone, but explicitly not GGchem

A recurring misconception is therefore to treat any local thermochemical-equilibrium baseline, any rainout chemistry setup, or any cloud-consistent gas-abundance table as “GGchem.” The cited literature does not support that equivalence. Some models use GGchem directly; others use Gibbs-minimization solvers in the CEA tradition; still others interpolate premixed equilibrium tables or include equilibrium only as initialization for kinetics. The shared physical target is thermochemical equilibrium, but the solver architecture, condensate treatment, and interface to transport, cloud microphysics, or retrieval machinery remain model-specific (Lei et al., 2024, Ghosh et al., 7 Dec 2025, Lacy et al., 2023).

In that sense, “GGchem equilibrium chemistry models” refers both to the original low-temperature equilibrium solver and to a family of later modeling workflows that either embed GGchem itself or are evaluated against it. What remains distinctive in the GGchem lineage is the combination of low-temperature robustness down to $\epsilon_{\rm el}=0$1, explicit equilibrium condensation, and the recognition—demonstrated repeatedly in atmosphere, retrieval, and mineralogy contexts—that refractory chemistry changes the gas composition rather than merely accompanying it (Woitke et al., 2017).