ThermoCalc Web

Methods

RRHO ideal-gas model with full electronic partition functions. Linear rotors use an exact J-sum; non-linear rotors use the classical rigid-rotor formula. This page explains what is computed and why it’s accurate—implementation details are intentionally brief.

Partition functions

Translation (molar):
qtrans = ((2π m kB T)/h2)3/2 · (kB T / p)
Linear rotation (exact J-sum):
EJ/kB = θr J(J+1), g = (2J+1)
qrot = (1/σ) · ΣJ=0..∞ g · e−EJ/(kBT)
Non-linear rotation (classical rigid-rotor):
qrot = (√π/σ) · T3/2 / √(θAθBθC)
Vibration (harmonic, per mode i):
qvib,i = 1 / (1 − e−θi/T)
Electronic (full multi-state):
qel = Σj gj e−θj/T   (θ0=0 for ground state)

Notation: θi ≡ hνi/kB (vibrational temperatures); θA,B,C are rotational temperatures from A,B,C (cm⁻¹). Symmetry (σ) is applied where appropriate.

Thermodynamic relations

Each contribution uses its own partition function:
S = R ln q + U/T,  U = R ⟨Ē⟩,  Cv = R·Var(Ē)/T²
Cp = Cv + R,  H = U + RT,  G = H − TS

Scope & approximations

  • RRHO: rigid rotor; harmonic oscillator; ideal gas at p° = 1 bar.
  • Rotation: exact J-sum (linear); classical rigid-rotor (non-linear).
  • Vibration: fundamentals with explicit degeneracies; no anharmonic or vib-rot coupling.
  • Electronic: summed over supplied terms (degeneracies & term energies); ground state dominates at 298 K unless otherwise noted.

These choices match common textbook/reference practice at 298 K and deliver room-temperature benchmarks within typical rounding of published tables.

What this page shows vs. Full Service

On this page

  • Transparent formulas and assumptions.
  • Representative 298.15 K validation at p° = 1 bar.
  • Clear notation for each partition-function component.

Full Service

  • Arbitrary T and p ranges, grids, and custom step sizes.
  • Exportable CSV tables for various thermodynamic properties.
  • Per-molecule summaries with units and reference state clearly labeled.

See the Purchase page for details.

Validation 298.15 K

Comparison of ThermoCalc vs. CCCBDB at p° = 1 bar. Δ = (ThermoCalc − CCCBDB). Typical agreement is within ~0.1–0.5% for these species under RRHO.

Compound S° [J·mol⁻¹·K⁻¹] C°p [J·mol⁻¹·K⁻¹]
ThermoCalcCCCBDBΔ ThermoCalcCCCBDBΔ
CO197.65197.66−0.0129.1329.14−0.01
O₂205.13205.15−0.0229.3629.38−0.02
CH₄186.32186.37−0.0535.6435.69−0.05
H₂O188.72188.84−0.1233.4833.60−0.12
NH₃193.12192.77+0.3535.4835.63−0.15

Residual differences from reference data mainly reflect the use of unscaled harmonic vibrational frequencies (anharmonic corrections are not included), as well as small choices in rotor treatment, rounding of fundamentals, and molar-mass conventions. Standard state is p∘ = 1 bar throughout.

Questions or a molecule you want added? Reach out via the Purchase page or info@thermocalc.site — we’re happy to validate more species on request.