1. Conjugated Dienes Theory of Linear and Cyclic Conjugation
Chemistry 125: Lecture 55 February 23, 2011
Conjugated Dienes
Theory of Linear and
Cyclic Conjugation
(4n+2) Aromaticity
This
For copyright notice see final page of this file

2. When does conjugation make a difference? Experimental Evidence
Allylic Cation, Anion, Radical
stabilized by ~13 kcal/mole.
Allylic SN1/SN2 Transition States also stabilized.

3. Conjugation worth only ~ 4 kcal/mole
Diene Stabilization
DHhydrogenation
(kcal/mole)
-30.2
-29.8
-30.0
-60.0
hexadiene 1,4 cis ,4 trans , ,
cHexdiene 1, , diff 0.4±0.2
1,4 pentadiene 60.22
-60.4
Conjugation worth only ~ 4 kcal/mole
-56.5

4. ps orthogonal at 90° twist anti syn Torsional Angle (°) 90 180 135 4590
180
135 45 2 4 6
Energy
kcal/mole
Central “single-bond” twist gives a 6 kcal barrier
(vs. ~ 60 kcal for C=C twist)
based on Raman spectroscopy - Engeln, Consalvo, Reuss, Chemical Physics, 160, 427 (1992)
ps orthogonal at 90°

5. Why is conjugation worth more in allylic intermediates than in dienes?
Because we can draw reasonable resonance structures?
good
bad

6. Conjugation & Aromaticity
Theory
Simple Hückel MOs
e.g. J&F Ch

7. Two Ways to Think about Butadiene  System   



 4
p-orbitals
Secondary mixing is minor
(because of poor E-match)

 :
Averagesame as localized
To maximize bonding-orbital overlap the central AOs are large in 1
and small in 2.
(~3 kcal/mole max)
4 Delocalized
 s
or Localized /p* picture
Very Little
Difference!
How different in overall stability?

8. Two Ways to Think about Butadiene  System4
p-orbitals





     :
4 Delocalized
 
Why ignore this mixing?
Despite better E-match, it does not lower energy.
Orthogonal
(What is gained at two positions is lost at the others)

9. Two Ways to Think about Butadiene  System
How different in overall stability?
Very Little!
(~3 kcal/mole max)
Localized  bond picture
4 Delocalized
  :
Although total energies are nearly the same with and without conjugation, there are substantial differences in HOMO & LUMO energies (Reactivity)
far UV
(167 nm)
nearer UV
(210 nm)
and in HOMO-LUMO gap (Color). :

10. Is There a Limit to 1 Energy for Long Chains?
Overlap
per  bond
(AO product)
1/2
Number of  bonds 1
Total overlap
stabilization
1/2
Chain length 2
Normalized AO size
1/2 4
1/4
1/4 3
3/4 8
1/8
1/8 7
7/8
N.B. We are ignoring the smallish influence of overlap on normalization.
Also we are using our own “overlap stabilization” units, which are twice as large as the conventional “” units you will see in texts. N
1/N
1/N
N-1
(N-1)/N
Yes, the limit is 1, i.e. twice the stabilization of the H2C=CH2  bond.
Similarly, the UMO destabilization limit is twice that of the H2C=CH2  MO.

11. Semicircle Mnemonic for  MO Energy in Conjugated Chains.+1 -1
Radius of circle = 2  stabilization of H2C=CH2
[ limit of ±(N-1)/N ]
Place points denoting length of chain evenly along circumference between upper and lower limit (+1 and -1).
MO Energy (units of 2)
etc.
All odd chains have a non-bonding MO with nodes on alternant carbons. It is the locus of the “odd” electron in the radical, and of + (-) charge in the cation (anion). p
N=2 ethylene
N=3 allyl
N=1 an isolated 2p AO
N=4 1,3-butadiene
As the conjugated chain lengthens, more and more levels are crowded between -1 and +1, and the HOMO-LUMO gap decreases.  
(difference is resonance stabilization
of butadiene vs. 2 isolated ethylenes)
allylic stabilization
(vs. isolated p and )
same 2-electron stabilization
for cation, radical, anion
Color shift toward red.

12. AROMATICITY Cyclic Conjugation worth ~30 kcal ! ~78 predicted ~22-2454 26
observed 49
Conjugation worth ~2 kcal 28
Heats of Hydrogenation
(kcal/mole)
Cf. J&F 13.5a pp

13. Bringing the ends of a conjugated chain together to form a ring gives a lowest  MO with an additional bond. (much more effective than adjusting AO sizes)
Lowest MO will have energy = -N/N = -1
In a conjugated ring peripheral nodes must come in even numbers. e.g. cyclopropenyl
E = -1
E = +1/2
E = +1/2
0 nodes
2 nodes
2 nodes

14. Energy Shifts on “Ring Formation”
Shifts Alternate (because of node parity). +1 -1
MO Energy (units of 2)
unfavorable
favorable
unfavorable
End to End Interaction
favorable

15. On bringing the ends of a chain together,
odd-numbered  MOs (1, 3, 5, etc.) decrease in energy
(favorable terminal overlap for 0,2,4… nodes), while
even-numbered  MOs (2, 4, 6, etc.) increase in energy (unfavorable terminal overlap for 1,3,5… nodes).
Thus having an odd number of occupied  MOs (more odd-numbered than even-numbered) insures overall  stabilization of ring (compared to chain).
[though there may be strain in the  bonds]
Hückel’s Rule: 4n+2  electrons is unusually favorable in a conjugated ring.
an odd number of e-pairs
(where n in an integer)

16. Circle Mnemonic for  MO Energy in Conjugated Rings.+1 -1
MO Energy (units of 2)
open-chain  energies from semicircle mnemonic
Same radius as for open chain
Stabilized
(vs. hexatriene) : :
4n “Antiaromatic”!
slightly destabilized
(vs. butadiene)
Inscribe regular polygon with point down.
Cation strongly stabilized
(vs. allyl+) :
Radical less stabilized (vs. allyl•) .
Read MO energies on vertical scale. : . .
Anion de stabilized • -
reactive SOMOs !
3 cyclopropenyl
4 cyclobutadiene
6 benzene : :
There is always an MO at -1.

17. Generalization of Aromaticity: 4n+2 Stability Transition State “Aromaticity” Cycloadditions & Electrocyclic Reactions
e.g. J&F Sec pp

18. Heteroaromatic Compounds
Pyridine H O
Furan Y- H X H X- Y H N
Pyrrole H H N
Imidazole
(occurs in amino acid histidine)
Relay for long-range
proton transfer by enzymes
N.B. Single denotes contribution of 1 e to  system (redundant with double bond).
e.g. J&F Sec pp

19. Furan
4 ABNs
2 ABNs
0 anti-bonding nodes

20. SHMo2 (Simple Hückel Molecular Orbital Program)
(N.B. must click “Show Orbitals” to update
energies after changing structure)
SHMo2 (Simple Hückel Molecular Orbital Program)
Crude  calculation shows heterocycle analogy. N N
identical shape
energy
lower energy
node on N
high N density N
Benzene
Pyridine
larger on N
lower energy

21. Cyclodecapentaene  Naphthalene (SHMo2)
same as
ethylene
same as
cyclodecapentaene
& butadiene
same as
butadiene

22. Another Criterion of Aromaticity is the PMR Chemical Shift (coming soon, Chapter 15)

23. Generalized AromaticityH H
OH-
We’ll cover this frame on Friday. I’ve left it
in because it is fair game for Monday’s exam.
pKa 15
vs. 16 for H2O
6  electrons (4n+2)
cyclo-C7H cyclo-C7H7- pKa 39 (despite more resonance structures)
8  electrons (4n, antiaromatic)
e.g. J&F Sec p. 591 R H
+ Ph3C+
+ Ph3CH R +
even more stable
unusually stable cation (triply benzylic)
2  electrons (4n+2)
Same for cyclo-C7H cyclo-C7H7+
(cycloheptatrienyl “tropylium”)
e.g. J&F Sec. 13.6pp. 587, 592
6  electrons (4n+2)

24. End of Lecture 55 February 23, 2011
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