FRECKLL: 1D Chemical Kinetics for Exoplanet Atmospheres

• FRECKLL is a 1D chemical kinetics framework that evolves atmospheric chemistry to steady state by solving continuity and transport equations.
• It utilizes advanced numerical methods like K-fold distillation to minimize computational error and significantly reduce evaluation times.
• The framework supports multiple chemical networks, including full and reduced C/H/O/N schemes and an extended C/H/O/N/S module, with direct integration into TauREx 3.1.

FRECKLL, “Full and Reduced Exoplanet Chemical Kinetics distiLLed”, is a Python 1‑D chemical‑kinetics framework for exoplanet atmospheres that was introduced to evolve large chemical networks efficiently and to make full disequilibrium chemistry usable in forward modelling and Bayesian retrievals (Al-Refaie et al., 2022). In the literature it functions as a one‑dimensional kinetic or photochemical model that solves coupled continuity and transport equations, includes vertical mixing and photodissociation, and returns steady‑state vertical abundance profiles that can be passed directly to TauREx 3.1; the same framework has subsequently been used with the full and reduced Venot C/H/O/N networks, an extensively validated C/H/O/N update, and a later C/H/O/N/S extension (Al-Refaie et al., 2022, Veillet et al., 2023, Veillet et al., 17 May 2025).

1. Software identity and conceptual role

FRECKLL is described as a Python 1‑D chemical kinetics code for exoplanet atmospheres and, in later work, as the Python version of the code used in Venot et al. (2020), with identical results and greatly improved computational time (Al-Refaie et al., 2022, Veillet et al., 2023). Its scientific role is to take a prescribed atmospheric structure—typically a pressure grid, a temperature profile, elemental abundances, a stellar UV field, and a parameterization of vertical mixing—and evolve the chemistry until a steady state is reached. In this sense, FRECKLL is the chemical engine linking bulk composition and transport assumptions to vertically resolved molecular abundances.

A central distinction in the subsequent literature is that FRECKLL is a solver rather than a fixed abundance grid. Retrieval studies emphasize that it is “not a pre-computed abundance grid but an external disequilibrium code called via the TauREx 3.1 plugin interface”; at each likelihood evaluation, TauREx passes the current atmospheric state, and FRECKLL solves the time-dependent chemical kinetics until a steady state is reached, returning the vertical mixing ratios (Bardet et al., 15 Jun 2025). This architecture makes FRECKLL a general host for different validated reaction networks rather than a single immutable chemistry prescription.

The code appears in two closely related operational modes. In forward modelling studies, FRECKLL is run to generate steady‑state abundance profiles and those profiles are then passed to TauREx 3.1 to compute synthetic transmission spectra (Veillet et al., 2023, Veillet et al., 17 May 2025). In retrieval studies, the same calculation is executed “on the fly” inside each model evaluation, so that parameters such as metallicity, C/O, and $K_{zz}$ are constrained through a full disequilibrium chemistry calculation rather than through equilibrium chemistry or altitude‑independent mixing ratios (Bardet et al., 15 Jun 2025).

2. Governing equations and numerical method

FRECKLL evolves the standard 1D continuity equation for each species $i$,

$$\frac{\partial n_i}{\partial t} = P_i - L_i - \frac{\partial \Phi_i}{\partial z},$$

where $n_i$ is the number density, $P_i$ and $L_i$ are chemical and photochemical production and loss terms, and $\Phi_i$ is the vertical flux (Al-Refaie et al., 2022, Veillet et al., 17 May 2025). In the general formulation described in the code paper, the vertical flux includes molecular diffusion and eddy diffusion,

$$\phi_i = -n_i D_i \left( \frac{1}{n_i}\frac{\partial n_i}{\partial z} + \frac{1}{H_i} + \frac{1}{T}\frac{\partial T}{\partial z} \right) - n_i K_{zz}\left(\frac{1}{y_i}\frac{\partial y_i}{\partial z} \right),$$

where $D_i$ is the molecular diffusion coefficient, $H_i$ the scale height, $i$0 the mixing ratio, and $i$1 the eddy diffusion coefficient (Al-Refaie et al., 2022). In later retrieval implementations, transport is often parameterized explicitly through a constant eddy diffusion coefficient,

$i$2

with $i$3 (Bardet et al., 15 Jun 2025, Jaziri et al., 20 Jul 2025).

Photochemistry enters through depth-dependent photolysis rates. In the sulfur-network application, these are written as

$i$4

and the photolysis loss term for species $i$5 has rate $i$6 (Veillet et al., 17 May 2025). The later retrieval literature describes the same conceptual structure: photodissociation rates depend on the stellar UV spectrum, atmospheric attenuation, and absorption cross sections (Bardet et al., 15 Jun 2025).

The distinctive numerical innovation of FRECKLL is its use of “distillation” in computing reaction rates, minimizing error bounds to the minimum allowed by double precision values, $i$7 (Al-Refaie et al., 2022). The motivation is the catastrophic cancellation that arises when large production and loss terms nearly balance. FRECKLL therefore uses K‑fold accurate summation based on error‑free transformations of pairwise sums, rather than relying on standard pairwise summation in numpy.sum (Al-Refaie et al., 2022). This numerical choice is not a peripheral implementation detail: in the HD 209458 b benchmark given in the code paper, pairwise summation required about 128 minutes, 467,335 RHS evaluations, and 2,179 Jacobian evaluations, whereas K‑fold distillation with $i$8 completed the same run in about 5 minutes with 2,682 RHS evaluations and 158 Jacobian evaluations (Al-Refaie et al., 2022).

Time integration is performed with stiff ODE solvers from ODEPACK. The code paper identifies VODE and DLSODES as the solvers used in FRECKLL (Al-Refaie et al., 2022), while later retrieval applications explicitly state that “continuity equations of each species evolve the stiff ordinary differential equation (ODE) solver VODE package” until a steady state is reached (Bardet et al., 15 Jun 2025). Initial conditions are typically thermochemical equilibrium abundances, computed with ACE in the code paper and described more generally as an equilibrium initialization in later applications (Al-Refaie et al., 2022, Bardet et al., 15 Jun 2025).

3. Chemical networks, validation, and operating domain

FRECKLL is designed to host both full and reduced chemical schemes. The initial release packaged the Venot et al. (2020) full and reduced networks, and later studies embedded successively larger validated networks without changing the basic FRECKLL role as the 1D disequilibrium solver (Al-Refaie et al., 2022, Veillet et al., 2023, Veillet et al., 17 May 2025).

Network or application	Size	FRECKLL role
Full Venot2020 (Al-Refaie et al., 2022)	108 species; 1906 reactions; 55 photodissociations	Full C/H/O/N disequilibrium kinetics
Reduced Venot2020 (Al-Refaie et al., 2022)	44 species; 582 reactions; no photodissociations	Faster kinetics without photochemistry
V23 C/H/O/N network (Veillet et al., 2023)	174 species; 1293 reactions mostly reversible	Extensively validated CHON network
C/H/O/N/S extension (Veillet et al., 17 May 2025)	226 species; 1692 mostly reversible reactions	Sulfur-enabled disequilibrium kinetics

The validated CHON network introduced in 2023 was aimed at conditions between $i$9–$$\frac{\partial n_i}{\partial t} = P_i - L_i - \frac{\partial \Phi_i}{\partial z},$$0 K and $$\frac{\partial n_i}{\partial t} = P_i - L_i - \frac{\partial \Phi_i}{\partial z},$$1–$$\frac{\partial n_i}{\partial t} = P_i - L_i - \frac{\partial \Phi_i}{\partial z},$$2 bar, with cautious extrapolation at lower temperature values (Veillet et al., 2023). It was built from recent combustion mechanisms and validated against 1618 combustion and pyrolysis experiments; when embedded in FRECKLL, it altered HCN by up to four orders of magnitude and substantially modified CO$$\frac{\partial n_i}{\partial t} = P_i - L_i - \frac{\partial \Phi_i}{\partial z},$$3 profiles relative to the previous network (Veillet et al., 2023). The later sulfur extension explicitly targeted the full C/H/O/N/S system for $$\frac{\partial n_i}{\partial t} = P_i - L_i - \frac{\partial \Phi_i}{\partial z},$$4–$$\frac{\partial n_i}{\partial t} = P_i - L_i - \frac{\partial \Phi_i}{\partial z},$$5 K, $$\frac{\partial n_i}{\partial t} = P_i - L_i - \frac{\partial \Phi_i}{\partial z},$$6–$$\frac{\partial n_i}{\partial t} = P_i - L_i - \frac{\partial \Phi_i}{\partial z},$$7 bar, and any atomic composition, and was validated on 1606 experimental measurements from combustion and pyrolysis of H$$\frac{\partial n_i}{\partial t} = P_i - L_i - \frac{\partial \Phi_i}{\partial z},$$8S, CH$$\frac{\partial n_i}{\partial t} = P_i - L_i - \frac{\partial \Phi_i}{\partial z},$$9SH, CS$n_i$0, and OCS (Veillet et al., 17 May 2025).

This sequence of embedded networks shows that FRECKLL is chemically modular but validation-sensitive. The code has hosted a reduced network without photochemistry, a full C/H/O/N network with 108 species, a larger extensively validated C$n_i$1–C$n_i$2 CHON network, and a sulfur-enabled extension with explicit C/S and N/S coupling (Al-Refaie et al., 2022, Veillet et al., 2023, Veillet et al., 17 May 2025). A plausible implication is that FRECKLL’s scientific output is determined jointly by the solver and the network selection: the transport–photochemistry machinery is stable across studies, while the chemically important pathways can change substantially when the embedded network changes.

4. Coupling to TauREx 3.1 and retrieval workflow

A defining characteristic of FRECKLL is its direct coupling to TauREx 3.1. The original code paper introduced a TauREx 3.1 plugin and demonstrated retrievals on simulated JWST spectra using the full and reduced Venot2020 networks (Al-Refaie et al., 2022). Later work generalized this into full atmospheric retrievals in which FRECKLL is called during every forward-model evaluation rather than through precomputed interpolation (Bardet et al., 15 Jun 2025).

In the hot-Jupiter re-analysis, TauREx 3.1 samples a 5-point temperature–pressure profile, metallicity $n_i$3, C/O ratio, a constant $n_i$4, the transit radius at 10 bar, and, in some emission runs, altitude-independent free abundances of TiO and VO (Bardet et al., 15 Jun 2025). The atmospheric structure is built on 80 pressure levels from $n_i$5 to $n_i$6 bar with 20 layers per decade; heavy elements are scaled by $n_i$7, carbon is adjusted to achieve the chosen C/O while oxygen is fixed to Lodders 2010 solar values, and FRECKLL then computes initial equilibrium abundances, integrates the kinetic ODE system with VODE until steady state, and returns vertically resolved mixing ratios for all 108 species (Bardet et al., 15 Jun 2025). TauREx subsequently extracts the opacity species needed for radiative transfer and computes the model spectrum.

Other FRECKLL studies use different vertical discretizations and boundary regimes while preserving the same code role. The CHON and sulfur forward-modelling studies use pressure–temperature profiles discretized into 130 layers, spanning deep to upper-atmosphere pressures and then feeding the steady-state profiles to TauREx 3.1 for transmission calculations (Veillet et al., 2023, Veillet et al., 17 May 2025). The K2‑18 b study instead evaluates a precomputed 3D grid of FRECKLL models over metallicity, C/O, and $n_i$8, again coupling the resulting profiles to TauREx 3 for transmission spectra (Jaziri et al., 20 Jul 2025).

The TauREx coupling also exposes FRECKLL’s chemical domain boundaries. In the hot-Jupiter retrieval paper, TiO and VO are not included in the FRECKLL network and are treated separately as altitude-independent “free” abundances inserted only into the TauREx radiative-transfer calculation (Bardet et al., 15 Jun 2025). In the K2‑18 b grid, the chemical network is limited to C$n_i$9 and C$P_i$0 H/C/N/O species, with no S or P chemistry and no condensation (Jaziri et al., 20 Jul 2025). These examples establish that FRECKLL provides the disequilibrium chemistry backbone, but that chemically absent species must be treated externally or omitted.

5. Scientific applications and inferred chemistry

The first major post-introduction application of FRECKLL was the integration of the validated V23 C/H/O/N network for GJ 436 b, GJ 1214 b, HD 189733 b, and HD 209458 b (Veillet et al., 2023). In that study, FRECKLL showed that the nitrogen-chemistry update was impactful on abundance profiles, particularly for HCN, with differences up to four orders of magnitude, while CO$P_i$1 profiles were also significantly affected (Veillet et al., 2023). For GJ 436 b at solar metallicity, the V23 profiles produced by FRECKLL lead to a new CO$P_i$2 absorption feature around $P_i$3m with an amplitude of about 100 ppm, while the HCN feature at about $P_i$4m disappears; the same study explicitly framed FRECKLL as the one-dimensional disequilibrium chemistry model that translates updated combustion-derived kinetics into observable transmission spectra (Veillet et al., 2023).

The sulfur extension broadened that role by embedding a validated C/H/O/N/S network and using FRECKLL to model GJ 436 b, GJ 1214 b, HD 189733 b, HD 209458 b, WASP‑39 b, and WASP‑107 b (Veillet et al., 17 May 2025). In those calculations, the coupling between carbon and sulfur chemistry was found to be impactful on both abundance profiles and observables, with CH$P_i$5S identified as a key species and CS$P_i$6 found to be probably much higher than anticipated in current kinetic networks for exoplanets (Veillet et al., 17 May 2025). FRECKLL predicted CS$P_i$7 abundances 2–3 orders of magnitude higher between 1 and $P_i$8 bar in GJ 436 b and GJ 1214 b, greater than 1 ppm in HD 189733 b, and as much as 7 orders of magnitude higher in WASP‑107 b than in the comparison sulfur network; the corresponding TauREx 3.1 transmission spectra from 1–25 $P_i$9m at $L_i$0 showed strong CS$L_i$1 features around $L_i$2m and $L_i$3m, weaker CH$L_i$4 bands at $L_i$5m and $L_i$6m in some planets, the disappearance of the HCN feature at $L_i$7m in HD 189733 b, and the absence of the NH$L_i$8 feature at $L_i$9m in WASP‑107 b (Veillet et al., 17 May 2025).

In retrieval mode, FRECKLL has been used to reassess the chemical structure of ten hot-Jupiter atmospheres from HST/WFC3 eclipse and transit spectra (Bardet et al., 15 Jun 2025). There, the disequilibrium approach significantly altered retrieved metallicity and C/O ratios compared to equilibrium models, retrievals reconciled transit and eclipse temperature profiles in deeper atmospheric layers but not in upper layers, and the results were highly dependent on spectral resolution and retrieval priors (Bardet et al., 15 Jun 2025). The study also quantified the computational burden of on-the-fly kinetics: the full set of runs required 874,207 CPU hours (Bardet et al., 15 Jun 2025). A central scientific conclusion was that equilibrium/free and FRECKLL models can fit the WFC3 data similarly well while yielding very different inferred compositions.

FRECKLL has also been applied to the temperate sub-Neptune K2‑18 b through a grid of 10,440 non-equilibrium models spanning metallicity, C/O ratio, and $\Phi_i$0 (Jaziri et al., 20 Jul 2025). Using a fixed pressure–temperature profile and JWST NIRISS+NIRSpec data, that study reported a best-fit metallicity of 280.7, a polynomial-fitted central value $\Phi_i$1 at $\Phi_i$2, a $\Phi_i$3 lower limit C/O $\Phi_i$4, and no preferred $\Phi_i$5 anywhere between $\Phi_i$6 and $\Phi_i$7 (Jaziri et al., 20 Jul 2025). The best disequilibrium model exceeded a flat spectrum by more than $\Phi_i$8, CH$\Phi_i$9 was robustly detected, CO$$\phi_i = -n_i D_i \left( \frac{1}{n_i}\frac{\partial n_i}{\partial z} + \frac{1}{H_i} + \frac{1}{T}\frac{\partial T}{\partial z} \right) - n_i K_{zz}\left(\frac{1}{y_i}\frac{\partial y_i}{\partial z} \right),$$0 remained uncertain, and the authors used FRECKLL to argue that a gas-rich mini-Neptune interpretation is at least as plausible as a strictly Hycean one (Jaziri et al., 20 Jul 2025).

6. Limitations, uncertainties, and research directions

Across the literature, FRECKLL remains a 1D vertical framework. Retrieval applications describe 1D vertical columns, plane-parallel geometry, and globally averaged or limb-averaged pressure–temperature structures, with no 2D or 3D dynamics and no horizontal transport (Bardet et al., 15 Jun 2025). The K2‑18 b analysis makes the same simplification through a single fixed pressure–temperature profile and a constant $$\phi_i = -n_i D_i \left( \frac{1}{n_i}\frac{\partial n_i}{\partial z} + \frac{1}{H_i} + \frac{1}{T}\frac{\partial T}{\partial z} \right) - n_i K_{zz}\left(\frac{1}{y_i}\frac{\partial y_i}{\partial z} \right),$$1, while explicitly neglecting condensation and clouds in the chemistry calculation (Jaziri et al., 20 Jul 2025). These are not incidental restrictions: they define the regime in which FRECKLL currently translates chemistry into observables.

Its chemical completeness is likewise study-dependent. The hot-Jupiter retrieval implementation omits species outside the H–He–C–O–N system, so TiO and VO are handled separately as free opacities rather than as kinetically evolved species (Bardet et al., 15 Jun 2025). The K2‑18 b application is limited to C$$\phi_i = -n_i D_i \left( \frac{1}{n_i}\frac{\partial n_i}{\partial z} + \frac{1}{H_i} + \frac{1}{T}\frac{\partial T}{\partial z} \right) - n_i K_{zz}\left(\frac{1}{y_i}\frac{\partial y_i}{\partial z} \right),$$2 and C$$\phi_i = -n_i D_i \left( \frac{1}{n_i}\frac{\partial n_i}{\partial z} + \frac{1}{H_i} + \frac{1}{T}\frac{\partial T}{\partial z} \right) - n_i K_{zz}\left(\frac{1}{y_i}\frac{\partial y_i}{\partial z} \right),$$3 chemistry, with no S or P, and therefore cannot represent higher-order hydrocarbon polymerization or sulfur-bearing tracers (Jaziri et al., 20 Jul 2025). Even within the sulfur-enabled version, some key reactions remain based on analogy rather than ab initio calculations, the H$$\phi_i = -n_i D_i \left( \frac{1}{n_i}\frac{\partial n_i}{\partial z} + \frac{1}{H_i} + \frac{1}{T}\frac{\partial T}{\partial z} \right) - n_i K_{zz}\left(\frac{1}{y_i}\frac{\partial y_i}{\partial z} \right),$$4S thermal decomposition rate still relies on an effective scheme with $$\phi_i = -n_i D_i \left( \frac{1}{n_i}\frac{\partial n_i}{\partial z} + \frac{1}{H_i} + \frac{1}{T}\frac{\partial T}{\partial z} \right) - n_i K_{zz}\left(\frac{1}{y_i}\frac{\partial y_i}{\partial z} \right),$$5, and the N/S chemistry is explicitly described as not yet as fully developed as the C/S chemistry (Veillet et al., 17 May 2025). Earlier CHON work similarly cautions that upper-atmosphere predictions can be sensitive to barrierless radical–radical recombinations and extrapolated rates outside the validated range (Veillet et al., 2023).

Computational cost and external inputs are persistent constraints. The full on-the-fly kinetic retrievals are extremely expensive, and the 10-hot-Jupiter study identifies stellar UV assembly, prior sensitivity, and limited HST wavelength coverage as direct limitations on what FRECKLL-enabled retrievals can robustly infer (Bardet et al., 15 Jun 2025). The K2‑18 b work makes the same point from the perspective of JWST: only CH$$\phi_i = -n_i D_i \left( \frac{1}{n_i}\frac{\partial n_i}{\partial z} + \frac{1}{H_i} + \frac{1}{T}\frac{\partial T}{\partial z} \right) - n_i K_{zz}\left(\frac{1}{y_i}\frac{\partial y_i}{\partial z} \right),$$6 is robustly detected, $$\phi_i = -n_i D_i \left( \frac{1}{n_i}\frac{\partial n_i}{\partial z} + \frac{1}{H_i} + \frac{1}{T}\frac{\partial T}{\partial z} \right) - n_i K_{zz}\left(\frac{1}{y_i}\frac{\partial y_i}{\partial z} \right),$$7 remains unconstrained, and high C/O may be entangled with unmodeled aerosols (Jaziri et al., 20 Jul 2025).

The stated development trajectory is toward broader spectral leverage and broader chemistry. The retrieval literature points to JWST as the natural regime in which disequilibrium chemistry should become substantially more diagnostic than with HST/WFC3 alone (Bardet et al., 15 Jun 2025). The K2‑18 b study highlights future JWST NIRSpec G395H and ELT/ANDES observations as especially important for constraining CO, CO$$\phi_i = -n_i D_i \left( \frac{1}{n_i}\frac{\partial n_i}{\partial z} + \frac{1}{H_i} + \frac{1}{T}\frac{\partial T}{\partial z} \right) - n_i K_{zz}\left(\frac{1}{y_i}\frac{\partial y_i}{\partial z} \right),$$8, H$$\phi_i = -n_i D_i \left( \frac{1}{n_i}\frac{\partial n_i}{\partial z} + \frac{1}{H_i} + \frac{1}{T}\frac{\partial T}{\partial z} \right) - n_i K_{zz}\left(\frac{1}{y_i}\frac{\partial y_i}{\partial z} \right),$$9O, NH$D_i$0, and minor organics (Jaziri et al., 20 Jul 2025). The sulfur-network work, in turn, shows that extending FRECKLL to validated C/H/O/N/S kinetics can qualitatively alter predicted abundances and spectra, implying that further extensions to additional elements and more comprehensive coupling chemistry are likely to be central to its next phase of use (Veillet et al., 17 May 2025).