TERRA Database Integration

This document describes the integration of the TERRA thermodynamic database (developed by Boris Trusov) into Prometheus.

Database Overview

The TERRA database consists of binary files (terra.bas for metadata and terra_a.bas for coefficients) containing approximately 2,600 chemical species. It uses a unique polynomial form for the reduced Gibbs energy (Φ*).

Conversion Logic

TERRA uses a 7-coefficient polynomial for the reduced Gibbs energy G*(x), where x = T / 10000 is the normalised temperature:

\[G^*(x) = f_1 + f_2 \ln x + f_3 x^{-2} + f_4 x^{-1} + f_5 x + f_6 x^2 + f_7 x^3\]

To integrate this into Prometheus these coefficients are converted into the standard NIST Shomate form (with t = T / 1000):

\[C_p^\circ(t) = A + Bt + Ct^2 + Dt^3 + E/t^2\]

Coefficient Mapping

Shomate

TERRA Relation

Notes

A

f₂

Constant Cₚ term

B

0.2 · f₅

Linear T term

C

0.06 · f₆

Quadratic T term

D

0.012 · f₇

Cubic T term

E

200.0 · f₃

Inverse quadratic term

F

(H_meta − 10000·f₄ − shift) / 1000

Enthalpy constant (with reference shift)

G

f₁ + f₂ − f₂ ln(10)

Entropy constant

Enthalpy Reference Shift

TERRA uses H(0) as its reference point for enthalpy. NASA and Prometheus use H(298.15 K). A dynamic stoichiometric back-substitution is applied:

  1. Dynamic discovery — for each of the 79 unique elements and the electron (e⁻) in the database, the parser identifies the most stable reference substance (lowest raw Gibbs energy at 298.15 K).

  2. Reference calculation — the raw enthalpy at 298.15 K is computed for each reference substance using the TERRA polynomials and metadata offsets.

  3. Universal shift — for every species in the database (including ions), the weighted sum of element-specific reference enthalpies is subtracted based on the species’ full elemental composition.

  4. Consistency — all standard elements have H_f°(298.15) = 0, and all species (neutral and ionic) are correctly aligned with the NASA-9/JANAF reference scale used throughout Prometheus.

Accuracy Verification

A comparison of over 1,400 overlapping species at 298.15 K shows excellent agreement with NASA-9/CEA:

Property

Typical Deviation

Enthalpy (H)

< 0.1 kJ/mol (common species)

Entropy (S)

< 0.1 J/(mol·K)

Heat Capacity (Cₚ)

< 0.05 J/(mol·K)

Reduced Gibbs (G/RT)

< 0.05

Note

Differences in large hydrocarbons or isomers are expected due to varying standard-state definitions between databases.

Usage in Prometheus

The database is available as prometheus/thermo_data/terra.json. Load it via SpeciesDatabase by passing the terra_path argument. Species originating from this database carry the [TERRA] source attribution.