Step 2 — Locating and Verifying the Transition State

Basic tutorial

This step assumes familiarity with the Transition State Optimization tutorial, including why a TS search needs an initial Hessian (CalcFC) and how the Berny algorithm follows a mode of negative curvature. Only the parts specific to this reaction are covered here.

Building the TS guess

A chair/boat-like guess was built with the diene and the dienophile approaching face-to-face, close enough that the terminal diene carbons and the ethene carbons are within bonding distance — but not yet bonded. This is reflected in the connectivity section of the input, which lists the forming bonds with a half-integer bond order (0.5):

%nprocshared=1
%mem=2GB
%chk=diels-alder-ts.chk
# opt=(calcfc,ts,noeigen) freq b3lyp/6-31g geom=connectivity

Title Card Required

0 1
 C   0.00662774  2.54373293  -1.41771995
 ...(16 atoms total)...

 1 2 1.5 9 1.0 10 1.0 11 0.5
 2 3 1.5 8 1.0
 3 4 1.5 7 1.0
 4 5 1.0 6 1.0 12 0.5
 ...
 11 12 1.5 13 1.0 14 1.0
 12 15 1.0 16 1.0

The 1.5 bond orders along the diene and ethene backbones reflect the partial delocalization expected at a pericyclic TS; the 0.5 orders on atoms 1–11 and 4–12 mark the two forming σ-bonds. Opt=(CalcFC,TS,NoEigen) tells Gaussian to compute an initial force constant matrix analytically, optimize toward a first-order saddle point, and not to abort if the initial Hessian does not already show a single negative eigenvalue (useful for TS guesses built by hand rather than generated by QST2/QST3).

Convergence

The job reports two successful stationary-point searches in the log — the geometry optimization itself, followed by the frequency calculation restarting from the optimized geometry to compute the Hessian at the true stationary point:

    -- Stationary point found.
 ...
    -- Stationary point found.
 Normal termination of Gaussian 09 at Fri Jul 17 12:55:21 2026.
 ...
 Normal termination of Gaussian 09 at Fri Jul 17 12:56:27 2026.

Geometry at the saddle point

The two forming C–C bonds are essentially identical in length:

Bond (forming)	Length / Å
C1–C11	2.263
C4–C12	2.264

The diene backbone (C1–C2–C3–C4) is also perfectly planar in the TS (dihedral = 0.0°), i.e. still locked in the reactive s-cis conformation required for the [4+2] overlap.

The near-equal forming-bond lengths are the geometric signature of a synchronous, concerted transition state: both new σ-bonds are forming to essentially the same extent, rather than one bond forming well ahead of the other (which would point toward a stepwise, diradical-like mechanism instead).

Frequency verification

A valid transition state must have exactly one imaginary vibrational frequency, corresponding to the reaction coordinate. The frequency job confirms this:

 Low frequencies --- -534.8182   -4.3154   -0.0009   -0.0008    0.0005   11.4562
 Low frequencies ---   19.3145  139.8392  205.3829
 ******    1 imaginary frequencies (negative Signs) ****** 

Property	Value
Imaginary frequency	−534.8 cm⁻¹
Number of imaginary frequencies	1

Animating this mode shows the two terminal diene carbons (atoms 1, 4) and the two ethene carbons (atoms 11, 12) moving toward and away from each other in phase — exactly the motion that forms both new σ-bonds simultaneously. This is consistent with the synchronous picture already suggested by the equal forming-bond lengths above.

Only one imaginary frequency — why it matters

If a second imaginary frequency had appeared, the structure would be a higher-order saddle point (e.g. a rotational transition state superimposed on the bond-forming motion), not the TS connecting reactants to product, and the geometry would need to be re-guessed. See Transition State Verification Using Frequency Analysis for the underlying theory.

Thermochemistry at the TS

Because the frequency calculation converged, a full thermochemical correction is available at 298.15 K / 1 atm:

Quantity	Value (Hartree)
Electronic energy	−234.494560
Zero-point correction	+0.141692
Thermal correction to Energy	+0.147998
Thermal correction to Enthalpy	+0.148942
Thermal correction to Gibbs Free Energy	+0.112198
Sum, E + ZPE	−234.352868
Sum, E + thermal free energy (G)	−234.382362

These corrected values will be needed once the reactants and product are also reoptimized with a matching frequency calculation (see the caveat in Step 1 and the summary in Step 4).

---

← Back to Step 1 — Reactants · Continue to Step 3 — IRC Verification →