Step 3 — Confirming the Path with IRC¶
Basic tutorial
This step assumes familiarity with the Intrinsic Reaction Coordinate (IRC) tutorial, including why the IRC follows the mass-weighted steepest-descent path from the saddle point. Only the parts specific to this reaction are covered here.
Why an IRC is necessary¶
Finding a stationary point with one imaginary frequency confirms that a structure is a transition state — it does not by itself prove that this particular saddle point connects the diene + ethene reactants to the cyclohexene product rather than to some other pair of structures. The IRC settles that question by following the minimum-energy path downhill from the TS in both directions.
Input¶
The IRC was started directly from the optimized TS geometry, using the analytic force constants computed at the TS (CalcFC) and a comparatively large step size to cover a wide stretch of the path in a limited number of points:
%nprocshared=1
%mem=2GB
%chk=diels-alder-irc-100points.chk
# irc=(maxpoints=50,calcfc,stepsize=3) b3lyp/6-31g geom=connectivity
Title Card Required
0 1
C 0.44156300 -1.43944900 -0.49183300
...(TS geometry, 16 atoms)...
MaxPoints=50 requests up to 50 points in each direction (forward and reverse), so the completed path can contain up to 100 points plus the TS itself. StepSize=3 sets a relatively large mass-weighted step, trading some path resolution for the ability to travel far from the TS in a reasonable number of points.
Completion¶
Maximum number of steps reached.
Calculation of REVERSE path complete.
Reaction path calculation complete.
Total number of points: 100
Total number of gradient calculations: 101
Total number of Hessian calculations: 1
Normal termination of Gaussian 09 at Wed Jul 22 20:38:06 2026.
Both directions ran to their full point allowance (50 + 50 = 100 points) and terminated normally. Note the phrase "Maximum number of steps reached" rather than "path follows to a minimum" — this means the path was stopped because it hit the point limit, not because it reached a flat region. The two end points below are therefore not yet fully relaxed minima; they still need to be reoptimized as ordinary stationary points (see the note at the end of this page).
Energy profile along the path¶
Gaussian reports the energy of every IRC point relative to the TS electronic energy (−234.494560 Hartree). A representative subset of the 100-point path:
| Point | Reaction coordinate | Energy relative to TS (Hartree) | Side |
|---|---|---|---|
| 1 | −4.291 | −0.08288 | reactant-side endpoint |
| 20 | −2.660 | −0.04415 | reactant-side |
| 40 | −0.944 | −0.00578 | reactant-side, close to TS |
| 51 | 0.000 | 0.00000 | TS |
| 60 | 0.772 | −0.00253 | product-side, close to TS |
| 80 | 2.489 | −0.01420 | product-side |
| 101 | 4.291 | −0.02314 | product-side endpoint |
The energy decreases smoothly and monotonically away from the TS on both sides, with no additional maxima, shoulders, or discontinuities along the 100-point path. That is exactly what a single-step, concerted mechanism should look like: one saddle point, one continuous downhill path to reactants in one direction and to product in the other, with no intermediate stationary points in between.
Geometric confirmation: the forming bonds¶
Tracking the two forming C–C bond lengths (C1–C11 and C4–C12) along the path makes the picture concrete:
| Point | C1–C11 / Å | C4–C12 / Å | Interpretation |
|---|---|---|---|
| 1 (reactant-side endpoint) | 2.870 | 2.870 | fragments separating, no bond |
| 51 (TS) | 2.263 | 2.264 | forming bonds, ~equal length |
| 101 (product-side endpoint) | 1.637 | 1.637 | contracting toward a single C–C bond |
Two details confirm the mechanism directly:
- The two distances stay equal to each other at every point shown, including the TS and both endpoints — the reaction is synchronous: both σ-bonds form (and break, in reverse) together, not one after the other.
- Moving away from the TS toward the reactant side, the distance increases (2.263 → 2.870 Å), i.e. the fragments separate — consistent with butadiene and ethene drifting apart. Moving toward the product side, the distance decreases (2.264 → 1.637 Å) toward a normal C–C single bond (~1.54 Å in cyclohexene), i.e. the ring is closing.
1.637 Å is not yet a finished single bond
A fully relaxed sp³ C–C single bond is closer to 1.54 Å. The product-side endpoint at 1.637 Å is still contracting when the IRC job stops (consistent with "Maximum number of steps reached" above), which is exactly why the next step in the DFT workflow is to reoptimize the IRC endpoints as independent geometry optimizations. Only after that reoptimization should the endpoint energies be treated as the true reactant and product minima.
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