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Worked Example: Diels–Alder Reaction of 1,3-Butadiene and Ethene

This page walks through a complete, real DFT study of a reaction mechanism, from a reactant guess to a verified transition state to a confirmed reaction path — following the Density Functional Theory (DFT) learning path step by step.

The reaction studied is the textbook [4+2] Diels–Alder cycloaddition between 1,3-butadiene (the diene) and ethene (the dienophile), forming cyclohexene:

        CH2=CH-CH=CH2   +   CH2=CH2   ─────►   cyclohexene
        (1,3-butadiene)      (ethene)

All calculations below were run in Gaussian 09 at the B3LYP/6-31G level of theory, which is exactly the "cheap, first-pass" level recommended in Step 2 of the DFT workflow. The purpose of this example is to show how the workflow is applied and how the resulting numbers are turned into a mechanistic argument — not to produce a publication-quality barrier height. Reoptimizing the stationary points with a polarized basis set (e.g. 6-31G(d)) is the natural next step, as noted on the DFT workflow page.

Level of theory

Setting Value
Functional B3LYP
Basis set 6-31G
Software Gaussian 09
Charge / Multiplicity 0 / 1 (closed-shell singlet)
Optimization method Berny (redundant internal coordinates)
TS search Opt=(CalcFC,TS,NoEigen)
IRC IRC=(MaxPoints=50,CalcFC,StepSize=3)

What this example covers

This worked example is split into four parts. Each part reuses the relevant basic tutorial for the calculation type — this page only shows how the pieces fit together for a real mechanism.

  1. Building and Optimizing the Reactants — constructing the starting geometries and a genuine pitfall encountered when optimizing two non-bonded molecules in a single job.
  2. Locating and Verifying the Transition State — the Berny TS search, the single imaginary frequency, and what the imaginary mode tells us about the mechanism.
  3. Confirming the Path with IRC — following the minimum-energy path downhill from the TS in both directions and connecting it to reactants and product.
  4. Energetics and the Proposed Mechanism — assembling the numbers into an energy profile and stating the mechanistic conclusion the data actually supports.

This example follows the same recommended workflow described on the DFT learning path:

Build Initial Structures
        │
        ▼
Optimize Reactant(s)
        │
        ▼
Optimize Transition State  ──►  Frequency Analysis (1 imaginary mode)
        │
        ▼
IRC Calculation
        │
        ▼
Reoptimize IRC Endpoints
        │
        ▼
Calculate Reaction Energies

This example is deliberately shown "warts and all"

One of the calculations below (the combined reactant optimization) does not converge. Rather than hide that, it is kept in as a worked pitfall — real Gaussian jobs fail for real reasons, and knowing why an optimization stalls is as important as knowing how to read a converged one.

Each stage below builds directly on the corresponding software tutorial. If you have not worked through these yet, start there:

Continue to Step 1 — Building and Optimizing the Reactants →