Skip to content

4.4 Reporting an activation free energy for ammonia inversion

These are unexecuted teaching inputs and starting models. Original diagrams are schematics, not calculated results. Validate version-specific syntax, licensed or authorized data, numerical convergence and the scientific model before using this workflow.

4.4.1 Model, units and provenance

Geometry in Å; electronic energy in hartree; vibrational wavenumbers in cm⁻¹. Check each printed field and keep thermal and standard-state terms distinct.

Shared inputs, conventions and evidence

Original schematic: Reporting an activation free energy for ammonia inversion. No numerical results are claimed.
Original schematic: Reporting an activation free energy for ammonia inversion. No numerical results are claimed.

4.4.2 Unexecuted inputs and explicit deltas

Use the accompanying instructions to identify the parent calculation and placement of every delta; a snippet is not automatically a standalone input. Preserve all blank-line and file-provenance requirements.

4.4.2.1 Input block 1

%oldchk=case14_nh3_ts.chk
%chk=case16_nh3_ts_thermo.chk
%mem=4GB
%nprocshared=2
#p B3LYP/6-31G(d) Freq=ReadFC Geom=AllCheck Guess=Read
   Temperature=298.15 Pressure=1.0

4.4.2.2 Input block 2

%oldchk=case15_nh3_forward_min.chk
%chk=case16_nh3_forward_thermo.chk
%mem=4GB
%nprocshared=2
#p B3LYP/6-31G(d) Freq=ReadFC Geom=AllCheck Guess=Read
   Temperature=298.15 Pressure=1.0

4.4.2.3 Input block 3

%oldchk=case15_nh3_reverse_min.chk
%chk=case16_nh3_reverse_thermo.chk
%mem=4GB
%nprocshared=2
#p B3LYP/6-31G(d) Freq=ReadFC Geom=AllCheck Guess=Read
   Temperature=298.15 Pressure=1.0

4.4.3 Worked investigation

4.4.3.1 Question and intuition

What separates a convincing reaction-path report from a attractive curve? A report must connect validated stationary points, consistent thermodynamic conditions, an unambiguous reference state, and the actual evidence for connectivity. This case assembles the ammonia inversion work from Cases 14–15. The two equivalent minima provide a reference-consistency check, while the TS supplies an activation quantity. Electronic barrier, zero-point-corrected barrier, activation enthalpy, and activation Gibbs energy are different observables within the model, so each needs its own label.

Prerequisites are a validated TS and two unconstrained, frequency-verified IRC endpoint minima. Use case14_nh3_ts.chk, case15_nh3_forward_min.chk, and case15_nh3_reverse_min.chk. Do not use the last IRC points as substitutes for these stationary structures. No new barrier number is supplied in this lesson; the objective is to build a reproducible report using the learner's actual logs and explicitly identify any missing results.

4.4.3.2 Consistent thermochemical reanalysis

The three original jobs already requested 298.15 K and 1 atm. If any condition differs, these separate inputs reanalyze each stored Hessian at the same temperature and pressure. They do not change the geometry or repair an invalid saddle. Each source must contain its completed frequency calculation.

See input block 1 above.

See input block 2 above.

See input block 3 above.

4.4.3.3 Workflow

  1. Create one stationary-point ledger with source filename, charge/multiplicity, method/basis, solvent, optimization status, imaginary-mode count, E, ZPE, H, G, and printed rotational symmetry number. Use identical isotopes, temperature, pressure, and scaling conventions throughout.
  2. Choose one validated pyramidal basin as R and the other as P. Compute ΔE‡ = ETS − ER; Δ(E+ZPE)‡ = (E+ZPE)TS − (E+ZPE)R; ΔH‡ = HTS − HR; and ΔG‡ = GTS − GR. Report differences in kJ mol−1 or kcal mol−1 while retaining the absolute hartree values in the supporting ledger.
  3. Compute ΔGrxn = GP − GR and the reverse barrier GTS − GP. For equivalent ammonia wells, ΔGrxn should be approximately zero and the forward/reverse barriers should agree within numerical precision under the same conventions. This symmetry check is independent of the barrier's absolute accuracy.
  4. Audit entropy and rotational symmetry before interpreting ΔG‡. Check the imaginary umbrella mode is excluded from the TS's vibrational partition function rather than converted into a positive vibration. The TS has five real internal modes for that vibrational contribution, while the minimum has six.
  5. Present the IRC electronic-energy curve separately from a stationary-point Gibbs-energy diagram. Link every plotted point or plateau to its underlying calculation. End with a concise conclusion and limits, including the instructional model chemistry and the absence of an explicit tunneling treatment.

4.4.3.4 Symmetry and entropy without double counting

For the ordinary unlabeled structures, the proper rotational symmetry numbers are 3 for pyramidal C3v NH3 and 6 for planar D3h NH3. Reflection operations are not themselves counted as proper rotations. Do not assume Gaussian printed those values after NoSymm, a slightly distorted geometry, or a particular checkpoint reanalysis; inspect the actual output. If a justified correction from printed σ to the target σ is needed, S(target) = S(printed) − R ln[σ(target)/σ(printed)], so G(target) = G(printed) + RT ln[σ(target)/σ(printed)]. Apply a correction only where it is missing, with the numerical values and reasoning documented.

Rotational symmetry, equivalent wells, and the number of distinct reactive pathways are related statistical questions but are not interchangeable correction buttons. The two NH3 pyramids are equivalent configurations, not two different stable chemical species or a pair of isolable ammonia enantiomers. Define whether the free energy refers to one labeled basin or an ensemble spanning both wells. Do not automatically add a factor of two for seeing two wells, then add another factor of two for forward/reverse IRC branches, on top of symmetry already included in the partition functions. A consistent rate convention must count states and pathways once.

Because this is a unimolecular basin-to-TS comparison, a uniform 1 atm→1 M per-species conversion cancels between reactant and TS. Entropic differences need not vanish, however: vibrational spectra, moments of inertia, and rotational symmetry change. The equivalent endpoints can have the same G while the activation entropy remains nonzero. This is the important distinction between a zero reaction free energy and a zero activation free energy.

4.4.3.5 Optional rate estimate and reporting limits

A classical transition-state estimate for a consistently defined unimolecular process is kTST = (kBT/h) exp(−ΔG‡/RT), with ΔG‡ and R in compatible molar units and k in s−1. Taking a transmission coefficient κ=1 makes this a classical no-recrossing estimate. It is not a prediction of ammonia's tunneling splitting or a guaranteed experimental inversion rate. Ammonia is a particularly clear warning that quantum tunneling can matter; an IRC and harmonic stationary-point thermochemistry alone do not calculate that tunneling physics.

A complete report states the question, input provenance, Gaussian revision, electronic model, phase/solvent, stationary-point tests, mode identity, both endpoint optimizations, standard state, entropy convention, and all reported energy definitions. Write “not determined” for missing quantities rather than filling a blank with a literature number or a schematic height. A single TS pathway establishes the existence of that path at the model level, not its exclusivity or experimental dominance.

EN exercise: Explain how ΔGrxn≈0 can coexist with a positive ΔG‡ and nonzero ΔS‡. Then calculate the symbolic change in a classical rate when ΔG‡ increases by RT ln 2. Identify where adding that same symmetry-derived term twice would introduce a spurious extra factor in the rate.

4.4.5 Sources and further reading