13.2: Dienes
- Page ID
- 366319
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Now that we have discussed allyl systems, in which electrons are conjugated over three atoms, what if we extended the conjugation to four atoms? How would that change the molecular orbital description?
1,3-Butadiene is the simplest conjugated four-atom system. It exists in two different forms, s-cis and s-trans, with the latter more favorable by 2.8 kcal/mol because of steric strain.
One peculiar thing about 1,3-butadiene is that there is restricted bond rotation about the C2-C3 bond. This is odd since there is normally free rotation about the \(σ\)-bond (except, as you’ve seen, in cases like DMF). Well, maybe there is something similar going on. If butadiene were really just two isolated double bonds, then there should be free rotation, but because there is restricted rotation, somehow these double bonds are interacting with each other.
Let’s look at the molecular orbital diagram for 1,3-butadiene.
If you take a look at the \(ψ\)1 and \(ψ\)2 wavefunctions, you might notice that the size of the bonding interaction in \(ψ\)1 between C2-C3 is stronger than the antibonding interaction between C2-C3 in \(ψ\)2. So, they don’t fully cancel each other out, meaning there is net bonding between C2-C3. This would not be the case if the coefficients in \(ψ\)1 were all equal – they MUST be larger at C2-C3. This should make sense now because the barrier to rotation between s-cis and s-trans is 6.5 kcal/mol.
Besides explaining the restricted bond rotation between C2-C3, why is this important? Here’s a thought question: if butadiene is acting like a nucleophile, then it is the HOMO that reacts. So, which carbons react? Of course, the ones at the ends, which have greater electron density (larger coefficients).
What are the effects of conjugation (or more and more conjugation)?
1. Conjugated systems have greater stability than nonconjugated systems. This is a thermodynamic effect.
2. Conjugated systems are more reactive than nonconjugated systems. This is a kinetic effect. The LUMO of conjugated systems is lower, so it more readily reacts with a nucleophile (it is more electrophilic). The HOMO of conjugated systems is higher, so it more readily reacts with an electrophile (it is more nucleophilic).
3. As you add more and more conjugation, the HOMO goes up (kinetic effect, more nucleophilic), the LUMO comes down, but the \(ψ\)1 always goes down (thermodynamic effect, more stable). This is the essence of UV-Vis spectroscopy. Electronic transitions occur from \(π\) --> \(π^{*}\). As more conjugation lowers the HOMO-LUMO gap, the wavelength needed to promote that transition gets longer. Eventually, it becomes so long that it becomes visible. This gives rise to the color we see on leaves in the fall due to conjugated dienes in lycopene and carotene.
4. Dienes react with electrophiles like HX or X2 like any normal \(π\)C-C bond, but because the intermediate carbocation can undergo resonance stabilization, there is the possibility of obtaining not only the 1,2-addition product, but also the 1,4-addition product. Usually the 1,2-addition product predominates, especially under cold temperatures and short reaction time, indicating that it is under kinetic control. At higher temperatures and longer reaction time, the 1,4-product predominates, indicating that it is under thermodynamic control.
