Step 4 — Energetics and the Proposed Mechanism¶
This page pulls together the numbers from the previous three steps into a single reaction profile, and states the mechanistic conclusion that the data actually supports at this level of theory.
Summary of electronic energies¶
| Species | E(RB3LYP/6-31G) / Hartree | Status |
|---|---|---|
| Reactants (butadiene + ethene, combined non-bonded job) | −234.5261 | not converged — see Step 1 |
| Transition state | −234.494560 | converged, 1 imaginary frequency |
| Product-side IRC endpoint (proto-cyclohexene) | −234.5177 | not fully relaxed — see Step 3 |
These are illustrative numbers, not final ones
Neither the reactant energy nor the product-side energy above comes from a fully converged stationary point at this stage — the combined reactant optimization hit its step limit (Step 1), and the IRC product-side endpoint was still contracting when the path calculation stopped (Step 3). Both should be reoptimized independently (each as its own opt freq job, each confirmed to have zero imaginary frequencies) before quoting a barrier or reaction energy in a report or paper. The numbers below illustrate the method, not a publication-ready result.
Approximate reaction profile¶
Using the illustrative values above:
| Quantity | Value |
|---|---|
| Forward barrier, ΔE‡ (reactants → TS) | +0.0316 Hartree ≈ +19.8 kcal/mol |
| "Descent" from TS to product-side endpoint | −0.0231 Hartree ≈ −14.5 kcal/mol (endpoint still relaxing) |
The forward barrier of roughly 20 kcal/mol is in the right neighborhood for a Diels–Alder cycloaddition of this type, even at the modest B3LYP/6-31G level used here — but given the caveats above (unconverged reactant geometry, unpolarized basis set with no d-functions), it should be treated as a rough estimate, not a citable number. As noted on the DFT workflow page, reoptimizing all three stationary points with a polarized basis set (e.g. 6-31G(d)) is the natural next refinement.
What the evidence supports¶
Independent of the exact barrier height, three separate pieces of evidence from Steps 2–3 point to the same mechanistic picture:
- One transition state, one imaginary frequency (−534.8 cm⁻¹). The system passes through a single first-order saddle point — there is no evidence of a two-step pathway requiring two separate barriers.
- Equal forming-bond lengths at every point checked (TS: 2.263 vs 2.264 Å; endpoints: 2.870/2.870 Å and 1.637/1.637 Å). Both new σ-bonds form together, not sequentially — ruling out a stepwise diradical or zwitterionic intermediate, which would instead show one short (mostly-formed) bond and one long (unformed) bond at the TS.
- A single, smooth, monotonic IRC path with no additional stationary points, connecting a separating-fragment geometry on one side to a ring-closing geometry on the other.
Proposed mechanism¶
Together, this supports a concerted, single-step, synchronous [4+2] cycloaddition: 1,3-butadiene (held in its reactive s-cis conformation) and ethene approach face-to-face and form both new C–C σ-bonds simultaneously through one pericyclic transition state, directly producing cyclohexene with no discrete intermediate along the way.
Next steps¶
To turn this worked example into a publication-quality study, repeat Steps 1–3 with the following refinements, in the order recommended on the DFT workflow page:
- Reoptimize butadiene and ethene separately (see the pitfall in Step 1), each with its own frequency calculation confirming zero imaginary frequencies.
- Reoptimize the two IRC endpoints from Step 3 as independent stationary points, again confirmed by frequency analysis.
- Repeat the whole sequence with a polarized basis set (e.g. 6-31G(d) or larger) and, if noncovalent interactions matter for the system under study, a dispersion correction.
- Only then compute the final ΔE‡, ΔH‡, ΔG‡, and reaction energy from thermally corrected sums, following the same table format used in Step 2.