Conjugated systems — Conjugation & Pericyclic Reactions

Two double bonds in the same molecule can be arranged three ways, and the arrangement changes the chemistry more than the count does. Getting the vocabulary straight first is worth the two minutes, because every reaction in this chapter depends on which of the three you are looking at.

Isolated, conjugated, cumulated

Isolated — the double bonds are separated by two or more sp³ carbons, so their p orbitals never meet. Penta-1,4-diene is the standard example. Each double bond behaves as though the other were not there.
Conjugated — the double bonds alternate with single bonds, so every carbon in the run is sp² and the p orbitals form one continuous overlapping system. Buta-1,3-diene is the simplest case.
Cumulated — the double bonds share a carbon, as in propa-1,2-diene (allene). The central carbon is sp, the two π systems are perpendicular, and they cannot conjugate with each other at all.

Conjugation is not limited to double bonds. A lone pair, a carbocation's empty p orbital, or a radical's half-filled one all conjugate with an adjacent π bond in exactly the same way — which is why allylic and benzylic cations, radicals and anions are so much more stable than their ordinary counterparts. That stabilization is the same delocalization you drew as resonance; conjugation is the orbital picture of it.

Conjugation is worth about 15 kJ/mol, and you can measure it

The claim that a conjugated diene is "more stable" is not a hand-wave. Heats of hydrogenation put a number on it. Hydrogenating but-1-ene releases about 127 kJ/mol. A molecule with two isolated double bonds should therefore release about twice that, roughly 254 kJ/mol — and penta-1,4-diene does.

Buta-1,3-diene releases about 239 kJ/mol. It gives out less energy on the way to the same kind of product, which means it started lower down: it was already about 15 kJ/mol more stable than two isolated double bonds would have been. That difference is the delocalization energy, and it is the whole reason conjugated systems behave differently.

A second, independent piece of evidence sits in the bond lengths. The C2–C3 bond of buta-1,3-diene — formally a single bond — is about 1.47 Å, noticeably shorter than the 1.54 Å of an ordinary C–C single bond and on its way toward the 1.34 Å of a double bond. The π system is genuinely spread across all four carbons, so that "single" bond carries partial double-bond character.

s-cis and s-trans: a conformation, not a configuration

The measurement behind the claim. Hydrogenating one double bond in but-1-ene gives out 127 kJ/mol, and penta-1,4-diene — whose two double bonds are insulated from each other — gives out exactly twice that. Buta-1,3-diene gives out less.Every bar ends at the same kind of product, a saturated alkane, so a shorter bar can only mean a starting material that was already lower in energy. That is the whole experiment: conjugation is not inferred from the drawing, it is weighed. The C2–C3 bond length of 1.47 Å is the second, independent measurement of the same thing.

Because the central C2–C3 bond of a conjugated diene is a single bond, the two ends can rotate about it. The two limiting conformations have their own names, and the s stands for single — it is a rotation, not a double-bond geometry, and nothing about it makes two separate compounds.

s-trans — the two double bonds point in opposite directions across the single bond. This is the more stable conformation and the one most conjugated dienes sit in most of the time.
s-cis — both double bonds point the same way, bringing the two ends of the diene close together. Slightly higher in energy, because the terminal hydrogens crowd each other.

Keep the distinction from cis and trans across a double bond clear. Those describe configurations and cannot interconvert without breaking a π bond; s-cis and s-trans are conformations and interconvert freely at room temperature by rotation. The prefix s is the only thing marking the difference in writing.

The s-cis conformation is the one that matters practically, because the Diels–Alder reaction requires it. A diene that cannot reach s-cis cannot do the reaction at all — which is why a diene locked s-cis inside a ring, like cyclopentadiene, is unusually reactive, and why one locked s-trans is unreactive no matter how electron-rich it is.

Why the ends of the system are where the chemistry happens

Draw the resonance forms of an allylic cation and you find the positive charge on the two ends of the three-carbon system and never in the middle. The same is true of an allylic anion and an allylic radical. This is a general feature of conjugated systems: reactivity appears at the termini, because that is where the coefficients of the relevant orbital are largest.

It is the reason the next section exists. When a conjugated diene is attacked, the intermediate is an allylic cation with two reactive ends, so the nucleophile has two places to go — and the product you get depends on which one it picks.

What carries forward

Three things from this section are load-bearing later. The stability of conjugated systems explains why allylic bromination works, why dienes are thermodynamically favored products of elimination, and eventually why aromatic rings are in a class of their own. The s-cis requirement is the single commonest reason a Diels–Alder does not happen. And the orbital picture — one continuous π system whose energy gap narrows as it lengthens — is exactly what UV-Vis spectroscopy measures, which is the last section of this chapter.