Geochemical modeling relies on extensive thermodynamic databases (e.g. the LLNL database, WATEQ4F, MINTEQA2, ThermoChimie) that provide equilibrium constants and related data for chemical reactions. Below, we explain how such databases are created and curated for use in codes like PHREEQC and Geochemist’s Workbench (GWB), focusing on the types of data included, the origins of equilibrium constants (experiment vs. calculation), the role of literature compilations, methods for ensuring internal consistency, and how data conflicts or uncertainties are handled.

Thermodynamic databases typically compile equilibrium constants (log K) and related thermochemical data for a wide range of reactions and species in aqueous geochemistry. Key categories include:

• Aqueous Complexes and Species: Reactions defining dissolved species (e.g. metal-ligand complexes, protonation/deprotonation reactions, redox couples) with their log K values. For example, the formation of a complex like PbCO₃(aq) from Pb²⁺ + CO₃²⁻ would have an equilibrium constant entry. Most databases list thousands of such aqueous complexation reactions.
• Minerals and Solid Phases: Solubility or dissociation reactions for minerals (giving the solubility product K or formation constant). For each mineral, the database provides a reaction (often dissolution into ions) and log K. e.g. CaCO₃ (calcite) ⇌ Ca²⁺ + CO₃²⁻ with a log K (the inverse of calcite’s K_sp). Polymorphs and various solid solutions may also be included, though very complex or ill-defined phases (e.g. certain clays or glassy solids) might be omitted if equilibrium data are unreliable (see Section 5).
• Gases and Volatiles: Equilibria involving gases, often Henry’s law constants or gas dissolution reactions. For example, the dissolution of CO₂ gas (CO₂ (g) + H₂O ⇌ H₂CO₃) or redox gases like O₂ and H₂S are included with log K (or equivalent Henry’s law constant). These entries allow modeling of gas–water equilibrium. Databases usually treat gases as ideal or include equations of state for fugacity corrections at higher pressures.
• Surface Complexes and Ion Exchange: Many databases also include surface complexation reactions (binding of ions to sorbent surfaces) and cation exchange reactions. For instance, the binding of a metal to a ferric oxide surface site (≡FeOH + Pb²⁺ ⇌ ≡FeO–Pb⁺ + H⁺) would have an equilibrium constant. Standard surface reactions for hydrous ferric oxide or clay exchange sites (e.g. from the Dzombak & Morel model) are sometimes integrated. For example, the NIST database includes a set of surface complexation reactions for the Dzombak and Morel Generalized Two-Layer Model. Not all general-purpose databases include sorption data, but specialized ones (like the RES³T sorption database) or extended variants of MINTEQ/PHREEQC do.
• Thermodynamic Parameters: In addition to log K at 25 °C and 1 bar (the usual reference conditions), databases often store auxiliary data used to adjust equilibrium constants for other temperatures or ionic conditions. This can include reaction enthalpies (∆H°) for van ’t Hoff temperature dependence, entropy and heat capacity values, or polynomial coefficients for log K as a function of T. Some files also contain activity coefficient model parameters (e.g. Debye–Hückel B-dot parameters in the LLNL dataset, or Pitzer ion-interaction coefficients in specialized high-ionic-strength databases). These ensure the database is usable across the range of temperatures, pressures, and salinities of interest.

All entries are typically referenced to a standard state (usually infinite dilution for solutes, unit activity of pure minerals, and 1 atm partial pressure for gases at 25 °C) so that the log K values are internally consistent and comparable. The LLNL thermo.com.V8.R6.230 database, for example, contains thousands of aqueous species, minerals, and gases with log K values at 25 °C (and analytical expressions for T dependence), each documented with a reference to its data source.

Compiling a thermodynamic database involves drawing on both laboratory measurements and theoretical models. Empirical (experimental) data underpins most key equilibrium constants, while models and estimation techniques are used to extend or fill gaps where direct data are unavailable:

• Laboratory Measurements: Wherever possible, log K values are taken from experimental studies – such as solubility experiments for minerals, titrations for complex formation constants, or calorimetric measurements of reaction enthalpies. For example, critical solubility constants in the carbonate system (e.g. calcite, aragonite, dolomite) were determined by carefully controlled experiments and are adopted from sources like Plummer & Busenberg (1982). These measured values at 25 °C form the baseline of most databases. Similarly, stability constants for aqueous complexes might come from critical compilations of potentiometric or spectroscopic studies (e.g. the NIST stability constant database, or older compilations by Martell and Smith).
• First-Principles Calculations: In some cases, especially for species that are difficult to study experimentally, researchers use quantum chemistry or molecular simulations to estimate thermodynamic properties. Ab initio calculations can predict gas-phase energies and with solvation models yield approximate free energies of aqueous species. However, such first-principles predictions often lack the accuracy of experimental data for complex ions in solution. Thus, direct quantum-calculated log K values are relatively rare in these databases; at best, they guide data selection or provide preliminary values when experiments are not feasible.
• Semi-Empirical Models (HKF Equation of State): A powerful approach for generating and extrapolating thermodynamic data is the Helgeson–Kirkham–Flowers (HKF) model. The revised HKF equations of state allow calculation of standard Gibbs energies (and hence equilibrium constants) for aqueous species over wide ranges of temperature and pressure (up to 1000 °C, 5 kbar). The catch is that HKF requires numerous species-specific parameters (e.g. apparent molal volumes, heat capacity coefficients). Many of these parameters cannot be measured directly for each species, but correlations and empirical trends (established by Helgeson, Shock, Sverjensky and co-workers) enable estimation of missing values. In practice, a researcher might fit HKF parameters to whatever experimental data do exist (such as solubilities at several temperatures) and then use HKF to calculate log K at other conditions. The LLNL database and SUPCRT programs leverage this approach: they store standard-state thermodynamic properties (∆G°, ∆H°, heat capacity coefficients) for each species, which were obtained by fitting both high-temperature experimental data and known 25 °C values via HKF. The HKF model thus extends the database beyond the laboratory conditions, but its reliability still ultimately hinges on experimental verification of at least some data points.
• Activity Models (Pitzer, SIT): While activity coefficient models (Pitzer equations, Specific Ion Interaction theory, etc.) are not used to derive fundamental log K, they are crucial for applying thermodynamic data to real-world conditions (e.g. brines). The Pitzer model, for example, uses virial coefficients fitted to experimental osmotic and activity data. Many high-ionic-strength databases (like the PHREEQC pitzer.dat or the ThermoChimie extension for brines) include these Pitzer parameters. Thus, one could say part of the “thermodynamic data” (namely effective equilibrium constants in salt solutions) is computed from models – but the models themselves are calibrated using experimental measurements. In essence, Pitzer and similar models extrapolate experimental log K values from pure water to concentrated solutions.
• Estimations and Analogies: In some cases, database compilers must estimate a value by analogy or systematic trends. For example, if a stability constant for a Pb(II) complex is unknown, one might infer it from a Zn(II) or Cd(II) analog or use Linear Free Energy Relationships (LFER) if applicable. Group additivity or correlations (like those found by Shock and Helgeson for HKF parameters) can provide educated guesses. However, such estimates are clearly flagged or used sparingly, and ideally replaced when real data become available.

In summary, the bulk of the thermodynamic constants in databases come from laboratory data, especially at standard conditions. Theoretical and semi-empirical models are invaluable for extending those data to other temperatures, pressures, or ionic strengths, and for providing stopgap values when experiments are lacking. Notably, major projects developing databases for nuclear waste disposal explicitly combine literature data with new experimental work to fill gaps – for instance, the ThermoChimie project states that its data are “mainly derived from comprehensive literature studies and supplemented by an experimental program when required”. This underscores that even today, critical equilibrium constants often must be measured, with calculation serving as a complementary tool.

Creating a comprehensive database requires mining the literature for thermodynamic data and carefully evaluating disparate sources. Typically, developers gather published values for equilibrium constants, enthalpies, and related thermochemical properties from journals, reports, and prior databases. The process involves critical review and selection to ensure the final dataset is as reliable and self-consistent as possible:

• Sources of Data: Literature sources include peer-reviewed papers, monographs (e.g. NIST compilation of stability constants), government reports (such as USGS or DOE publications), and previously compiled databases. For example, the LLNL database (thermo.com.V8.R6) was built by Wolery and coworkers by converting the earlier EQ3/6 data collection and adding many values from new literature. The MINTEQA2 database (EPA) was based largely on the earlier WATEQ and other USGS datasets. In practice, each new generation of database draws heavily on its predecessors, then updates parts of it with newer or more specialized studies.
• Critical Evaluation and Selection: When multiple literature values exist for the same constant, compilers must judge which to use. They consider the experimental methods (Was the measurement direct or indirect? At what conditions? Were interfering equilibria accounted for?), the reputation of the data source (e.g. critical review vs. single study), and consistency with related data. Often, critical reviews and expert panel evaluations are preferred. For instance, the NEA Thermochemical Data Base project convenes expert committees to review all published data for an element and recommend a best value with an uncertainty. Such vetted values carry more weight than any single study.
• Example – WATEQ4F Compilation: The WATEQ4F database (Ball & Nordstrom, 1991) illustrates literature-based curation. In updating earlier USGS databases, they incorporated “the most precise and internally consistent sets of data available” for important systems. For carbonates and sulfates, they adopted equilibrium constants from Plummer & Busenberg (1982) and Busenberg et al. (1984), which were comprehensive studies of those mineral systems. They also took uranium complexation data from the thorough review by Grenthe et al. (1992). At the same time, they identified and corrected errors from prior compilations (e.g. mis-reported Al–sulfate complex constants were fixed). This example shows how compilers merge data from multiple references, favoring well-reviewed sources and fixing mistakes along the way.
• Consistency and Expert Judgment: Literature data rarely agree perfectly. Compilers look for patterns and try to resolve discrepancies. They might perform fresh calculations using raw thermochemical data from sources (e.g. recalculating a log K from reported ∆G° of formation) to double-check. If one source’s data for a whole set of related reactions yields consistent results except for one outlier, that outlier might be rejected in favor of values that maintain consistency. In some cases, new measurements are sought: for example, if an important species lacks consensus in literature, database projects may trigger new experiments (as ThermoChimie does).
• Referencing and Documentation: A rigorous database will document the source of each value for transparency. The LLNL and MINTEQ databases list literature references for each reaction in comments, and projects like NEA TDB publish volumes detailing the rationale for chosen values. This traceability is crucial so that users know the pedigree of the data and can consult original sources if needed. It also helps future compilers update values by providing a paper trail for each datum.

In summary, literature data form the backbone of thermodynamic databases. Through critical compilation, comparison, and expert review, the compilers integrate many disparate measurements into one coherent dataset. The process is akin to making a consensus dataset from sometimes-conflicting studies, guided by chemical understanding and quality of sources.

A paramount concern in building a thermodynamic database is internal consistency – the requirement that all the data work together without thermodynamic contradictions. Internal consistency means that all equilibrium constants and thermodynamic parameters derive from a single, coherent set of standard-state properties. In practice, achieving this involves:

• Common Reference States and Conventions: All data must share the same baseline. This includes standard reference states for elements (e.g. graphite vs diamond for carbon, etc.), unit conventions (1 bar vs 1 atm), and a consistent temperature (usually 25 °C) for tabulated values. If one source defines log K relative to a different standard state, it must be converted. For example, older data might use 1 atm as standard pressure; modern databases convert these to 1 bar values where needed. Similarly, the convention for the aqueous proton is often that the free energy of formation of H⁺(aq) is zero at 25 °C, which ensures pH = 0 corresponds to 1 M H⁺. All entries must adhere to such choices uniformly.
• Thermochemical Relationships: The laws of thermodynamics impose relationships among properties – for instance, ∆G° and ∆H° must relate through ∆S°, and multiple reaction equilibria that form a cycle should multiply to identity. Compilers check that the dataset does not violate these principles. If mineral A ↔ B + C and B ↔ D + E are both in the database, the implied A ↔ D + E + C reaction should yield a log K that equals the sum of the others. Violations indicate inconsistency. A known issue is that mixing data from different sources can introduce subtle inconsistencies because each source might have used slightly different fundamental constants (gas constant, Faraday constant, atomic weights, etc.) or reference states. Thus, developers often prefer to derive as many reactions as possible from a core set of formation free energies to enforce consistency.
• Use of Formation Data: One strategy is to start with a set of standard-state thermodynamic properties for individual species (elements, aqueous ions, minerals) that is internally consistent, and then calculate all reaction log K from those. For example, Helgeson et al. (1978) developed an internally consistent set of ∆G°_f, ∆H°_f, S°, and C_p values for hundreds of species. If one adopts that set, then any reaction written between those species will have a log K that is thermodynamically consistent with any other reaction. The LLNL database essentially follows this approach: it stores Gibbs energies of formation and heat capacity polynomials for species, fitted such that they reproduce key experimental equilibria, and then all other reactions can be derived (and were validated against experiments). Ensuring internal consistency might mean adjusting a formation free energy slightly so that a critical equilibrium (for which high-quality data exist) is matched exactly, and thereby other related equilibria are brought into alignment. This was done, for instance, in the NEA reviews – they would sometimes re-optimize a cluster of reactions to enforce consistency and adjust one or two values by small amounts.
• Consistent Temperature Dependence: Internal consistency is not just at 25 °C, but across temperatures. If a database includes enthalpies or heat capacity data, using them to calculate log K at 50 °C should give a result that agrees with any direct experimental measurement at 50 °C. This is another check. Many databases only provide 25 °C log K and a ∆H°, implicitly assuming ∆H° is constant with T (which is an approximation). More advanced ones provide full temperature-dependent formulas. In either case, curators test the database by comparing computed values against known data at various temperatures. If mismatches occur, the data may be adjusted for better consistency.
• Cross-Checks and Balancing: When assembling the database, compilers perform cross-checks. For example, they may compare ∆G° derived from a mineral’s solubility vs. ∆G° derived from calorimetric data to ensure they match within uncertainties (discrepancies hint at problems). They avoid mixing data that are fundamentally incompatible; if two sources conflict strongly, they might choose one source’s entire dataset to maintain coherence rather than mix-and-match. As Nordstrom and Munoz (1994) note, one must recognize if data are on different “scales” and avoid merging them blindly.

In summary, maintaining internal consistency often means deriving all log K from a selected set of fundamental data and applying uniform models/standards. Projects like the NEA TDB explicitly mandate that selections must be consistent with each other and basic thermodynamic requirements. Similarly, Ball & Nordstrom (1991) emphasized internal consistency by taking data from coherent sources (e.g. selecting all carbonate constants from one study) and by not mixing incongruent values. The benefit of an internally consistent database is that it behaves predictably in simulations: no subset of reactions will produce a thermodynamic cycle that yields a free energy “loop error.” Achieving this consistency is challenging and is one reason why databases are curated by experts over years.

Even after careful selection, compilers face conflicting data and uncertainties. Here’s how discrepancies are resolved and uncertainties managed:

• Conflict Resolution: When different sources report different log K for the same reaction, the database maintainers weigh the options. They might choose the value from the most direct experimental measurement or from the source deemed most reliable (e.g. a critical review or recent high-precision study). Sometimes a compromise is made by adjusting a value to intermediate between reported values, especially if it improves consistency with related reactions. In other cases, one value is clearly an outlier (due to experimental error) and is rejected. For example, if one study reported an unusually high stability for a rare complex that causes mass balance issues with other species, compilers may exclude that data until confirmed. The WATEQ4F team explicitly did not include equilibrium constants for many silicate minerals (smectites, illites, etc.) because those phases “have not demonstrated reversible, equilibrium solubility behavior” – i.e. any available K_sp was deemed unreliable. Instead of forcing dubious data into the database, they noted the lack and left such minerals out or marked them as non-attainment of equilibrium. This policy prevents the inclusion of values that could skew modeling results.
• Data Updates and Corrections: As new data become available, databases are periodically updated. Discrepancies can be resolved by new experiments that clarify which earlier value was correct. For instance, if two sources disagreed on a mineral solubility, a new study might support one of them, leading to the database being updated with the new consensus value. Obvious errors discovered (like typos or miscalculations in sources or in transcribing data) are corrected and documented. In the WATEQ4F manual, Ball and Nordstrom list specific corrections (such as fixing two Al–sulfate reactions where an earlier source had errors).
• Handling Uncertainty: Every equilibrium constant has an uncertainty range, though databases typically provide a single “best-fit” value. Some specialized databases (e.g. NEA TDB) do quantify uncertainties and even provide upper/lower bounds or error estimates for each value in their documentation. The NEA guidelines outline how to assign and propagate uncertainty for recommended data. In more general databases like LLNL or PHREEQC files, uncertainties aren’t explicitly listed for each entry in the working data file, but the sources (if consulted) often provide error bars. Database compilers aim for consistency usually within the uncertainty of the data. They sometimes reduce the number of significant figures for a log K to reflect its uncertainty. The WATEQ4F authors note that the number of significant digits given varies because “uncertainties in thermodynamic data are reaction-specific.”. For example, well-studied reactions might have log K known to ±0.01, whereas a poorly constrained one might be ±0.5, so they wouldn’t list an unwarranted precision. By acknowledging uncertainty, users are cautioned which results are more tentative. Some programs allow sensitivity analyses by varying log K within reasonable bounds to see the effect on predictions.
• Internal Flags and Comments: Where data are suspect or based on estimation, compilers often include comments in the database. For instance, an entry might note “(estimated)” or provide a footnote in documentation that a particular constant is from analogue estimation. This alerts users that the value carries extra uncertainty. In cases of conflicting data that cannot be resolved definitively, one approach is to maintain multiple alternative datasets – e.g. a “default” database vs. an alternate one with a different set of constants (such as PHREEQC’s phreeqc.dat vs. minteq.dat vs. llnl.dat, which differ in their sources). Users can then choose a database and should report which one was used, as results can differ significantly when different thermodynamic datasets are employed.
• Example – Uranium(IV) Phosphate Complexes: In the WATEQ4F compilation, they noted a specific gap: “Data for aqueous uranium(IV) phosphate complexes are not given… reliable data are not available at this time (Grenthe et al., 1992)”. Instead of including rough guesses, they left these reactions out. This reflects a conservative strategy: it’s better to omit or disable a reaction than to include a highly uncertain constant that could mislead modeling. The absence is documented so that when trustworthy data emerge (and indeed later NEA work did address U(IV) species), the database can be updated.
• Quality Control and Peer Review: Many databases undergo internal QA/QC and sometimes external review. For instance, the NEA TDB undergoes peer review of its recommended values. The LLNL database, being widely used, has been examined by many researchers who sometimes spot inconsistencies, leading to community-driven corrections (as noted in GWB forums where transcription errors in LLNL were corrected against original sources).

In conclusion, curators of thermodynamic databases strive to reconcile conflicting information by relying on the best science available and by being transparent about data quality. Uncertainties are managed by choosing consistent data sets, updating values when new evidence warrants, and sometimes simply by informing users of the data limitations. Thanks to these efforts, modern geochemical databases like LLNL, PHREEQC’s compilations, and ThermoChimie are internally coherent and based on the best-available thermodynamic data, making them reliable foundations for modeling. They are living documents, periodically refined as the science advances, with the ultimate goal of accurately representing chemical equilibria in geochemical systems.

• Delany & Lundeen (1991) – LLNL Thermochemical Database (EQ3/6 data0); Ball & Nordstrom (1991) – WATEQ4F Manual
• NEA Thermochemical Database Project – guidelines for data selection
• Shock et al. (1997) and Sverjensky et al. (1997) – development of HKF parameters
• PHREEQC Documentation and Earth Science Reviews (2022) – comparisons of common databases;
• Dzombak & Morel (1990) – surface complexation data;
• ThermoChimie overview (2020).

• Delany, J. M., & Lundeen, S. R. (1991). LLNL Thermochemical Database. EQ3/6 data0. Lawrence Livermore National Laboratory. Link (archived)
• Ball, J. W., & Nordstrom, D. K. (1991). User’s manual for WATEQ4F, with revised thermodynamic database and test cases for calculating speciation of major, trace, and redox elements in natural waters. U.S. Geological Survey Open-File Report 91-183. https://pubs.usgs.gov/of/1991/0183/report.pdf
• OECD Nuclear Energy Agency (NEA). Thermodynamic Database Project (TDB). https://www.oecd-nea.org/dbtdb/
• Shock, E. L., Helgeson, H. C., & Sverjensky, D. A. (1997). Calculation of the thermodynamic and transport properties of aqueous species at high pressures and temperatures: Standard partial molal properties of inorganic neutral species. Geochimica et Cosmochimica Acta, 61(5), 907–950. https://doi.org/10.1016/S0016-7037(96)00339-0
• Sverjensky, D. A., Shock, E. L., & Helgeson, H. C. (1997). Prediction of the thermodynamic properties of aqueous metal complexes to 1000 °C and 5 kb. Geochimica et Cosmochimica Acta, 61(7), 1359–1412. https://doi.org/10.1016/S0016-7037(97)00009-4
• Parkhurst, D. L., & Appelo, C. A. J. (2013). Description of Input and Examples for PHREEQC Version 3. U.S. Geological Survey Techniques and Methods, book 6, chapter A43. https://pubs.usgs.gov/tm/06/a43/
• Dzombak, D. A., & Morel, F. M. M. (1990). Surface Complexation Modeling: Hydrous Ferric Oxide. Wiley-Interscience. https://www.wiley.com/en-us/Surface+Complexation+Modeling%3A+Hydrous+Ferric+Oxide-p-9780471517685
• ThermoChimie Database – Andra, Thermochemical Data for Nuclear Waste Disposal. https://www.thermochimie-tdb.com/