Chemistry 125: Lecture 55
February 23, 2011
This
Conjugated Dienes
Theory of Linear and
Cyclic Conjugation
(4n+2) Aromaticity
For copyright
notice see final
page of this file
When does conjugation
make a difference?
Experimental Evidence
Allylic Cation, Anion, Radical
stabilized by ~13 kcal/mole.
Allylic SN1/SN2 Transition States also stabilized.
Diene
Stabilization
DHhydrogenation
(kcal/mole)
-30.2
-29.8
-30.0
-60.0
-60.4
-56.5
Conjugation worth
only ~ 4 kcal/mole
syn
twist
anti
Central “single-bond” twist gives a 6 kcal barrier
(vs. ~ 60 kcal for C=C twist)
6
Energy
kcal/mole
4
2
ps orthogonal at 90°
0
0
45
90
135
Torsional Angle (°)
180
Why is conjugation worth more
in allylic intermediates
than in dienes?
Because we can draw
reasonable resonance structures?
good
bad
Conjugation & Aromaticity
Theory
Simple Hückel MOs
http://www.chem.ucalgary.ca/SHMO/index.html
e.g. J&F Ch. 12-13
Two Ways to Think about Butadiene p System

pp
p

pp
Secondary
mixing is
minor
:

4 Delocalized
p
s
pp
To maximize bonding-orbital overlap
the central AOs are large in 1
and small in 2.
p
pp
or Localized p/p* picture
How different in overall stability?
(because
of poor
E-match)
Average
same as
localized
:

4
p-orbitals
(~3 kcal/mole max)
Very Little
Difference!
Two Ways to Think about Butadiene p System

pp
p

pp
:
4
p-orbitals
:

4 Delocalized
p
pp
:
:

p
pp
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)
Two Ways to Think about Butadiene p System
nearer
UV
far
UV
(210 nm)
(167 nm)
:
Although total energies are
nearly the same with and
without conjugation, there
are substantial differences
in HOMO & LUMO energies
(Reactivity)
and in HOMO-LUMO gap
(Color).
:
:
:
4 Delocalized
p
(~3 kcal/mole max)
Localized p bond picture
How different in overall stability? Very Little!
Is There a Limit to 1 Energy for Long Chains?
Chain
length
Normalized
AO size
Overlap
per p
bond
Number
Total
of p
overlap
bonds stabilization
(AO product)
2
1/2
1/2
1
1/2
4
1/4
1/4
3
3/4
8
1/8
1/8
7
7/8
1/N
1/N
N.B. We are ignoring the smallish
influence of overlap on normalization.
Also we are using our own “overlap
N
stabilization” units, which are twice as
large as the conventional “” units you
Yes,
the limit is 1, i.e. twice the
will see
in texts.
N-1 (N-1)/N
stabilization of the H2C=CH2 p bond.
Similarly, the UMO destabilization limit is twice that of the H2C=CH2 p MO.
MO Energy (units of 2)
+1
Semicircle Mnemonic for p MO
Energy in Conjugated Chains.
Radius of circle = 2  stabilization of pH2C=CH2
[ limit of ±(N-1)/N ]
Place points denoting length of chain
evenly along circumference between
upper and lower limit (+1 and -1).
0
-1
p
N=2 an
N=3
N=1
ethylene
allyl
isolated 2p AO
N=4
1,3-butadiene
etc.
All odd chains
have
a nonAs
the
conjugated
chain
lengthens,
(difference
is resonance
stabilization
bonding
MO
with
nodes
on
p
p
more
and
more
levels
are
crowded
of butadiene
vs. 2 isolated
ethylenes)
alternant
carbons.
It is the
between -1 and +1, and the HOMOlocus
of the
“odd” electron
p andgap
p)
allylic stabilization (vs. isolated
LUMO
decreases.
in the radical, and of + (-)
same 2-electron stabilization
Color
shiftintoward
red. (anion).
charge
the cation
for cation, radical, anion
AROMATICITY
Cyclic Conjugation
worth ~30 kcal !
~78
observed 49
~22-24
predicted
26
Conjugation
worth ~2 kcal
54
28
Heats of Hydrogenation
(kcal/mole)
Cf. J&F 13.5a pp. 580-581
Bringing the ends of a conjugated chain
together to form a ring gives a lowest
p 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
0 nodes
E = +1/2
2 nodes
2 nodes
Energy Shifts on “Ring Formation”
Shifts Alternate (because of node parity).
+1
MO Energy (units of 2)
unfavorable
favorable
0
unfavorable
End to End
Interaction
-1
favorable
On bringing the ends of a chain together,
odd-numbered p MOs (1, 3, 5, etc.) decrease in energy
(favorable terminal overlap for 0,2,4… nodes), while
even-numbered p MOs (2, 4, 6, etc.) increase in energy
(unfavorable terminal overlap for 1,3,5… nodes).
Thus having an odd number of occupied p MOs
(more odd-numbered than even-numbered)
insures overall p stabilization of ring (compared to chain).
[though there may be strain in the  bonds]
an odd number
of e-pairs
Hückel’s Rule:
4n+2 p electrons is unusually
favorable in a conjugated ring.
(where n in an integer)
.
.
0
Same radius as for open chain
.
..
.
Inscribe regular polygon
with point down.
Read MO energies
on vertical scale.
reactive SOMOs !
3 cyclopropenyl
4 cyclobutadiene
6 benzene
4n “Antiaromatic”!
Stabilized
slightly
destabilized
Cation (vs.
strongly
stabilized
hexatriene)
:
: : ::
-1
:
.
.
::
MO Energy (units of 2)
+1
open-chain p energies from semicircle mnemonic
Circle Mnemonic for p MO
Energy in Conjugated Rings.
.
(vs. butadiene)
+
(vs. allyl )
•
There
is always
an MO at
Anion
destabilized
Radical
less
stabilized
(vs.-1.
allyl•)
Generalization of
Aromaticity:
4n+2 Stability
Transition State “Aromaticity”
Cycloadditions &
Electrocyclic Reactions
e.g. J&F Sec. 13.6 pp. 582-595
Heteroaromatic Compounds
N
O
H
Pyridine
H
Furan
H
YY
H
H
N
H
H
Pyrrole
Imidazole
H
H
N.B. Single denotes contribution of 1 e to p
system (redundant with double bond).
(occurs in
amino acid
histidine)
N
H
H
H
N
H
HH
Relay for long-range
proton transfer by enzymes
X
X-
e.g. J&F Sec. 13.9 pp. 598-601
Furan
4 ABNs
2 ABNs
0 anti-bonding nodes
(N.B. must click “Show Orbitals” to update
energies after changing structure)
SHMo2
(Simple Hückel Molecular Orbital Program)
Crude p calculation shows heterocycle analogy.
identical shape
energy
N
lower energy N
node
highonNN
density
larger on N
N
lower energy
Benzene
Pyridine
Cyclodecapentaene  Naphthalene
(SHMo2)
same as
ethylene
same as
butadiene
same as
cyclodecapentaene
& butadiene
Another Criterion of Aromaticity
is the PMR Chemical Shift
(coming soon, Chapter 15)
Generalized Aromaticity
H
H
H
H
H
OH-
H
We’ll cover this frame on Friday. I’ve left it
in because it is fair game for Monday’s exam.
H
pKa 15
vs. 16 for H2O
H
cyclo-C7H8
R
H
H
H
6 p electrons (4n+2)
cyclo-C7H7- pKa 39 (despite more resonance structures)
e.g. J&F Sec. 13.6 p. 591
8 p electrons (4n, antiaromatic)
R
H
Ph3C+
+
R
R
unusually
stable cation
(triply benzylic)
Same for cyclo-C7H8
(cycloheptatrienyl
+
+
R
Ph3CH
R
even more stable
2 p electrons (4n+2)
e.g. J&F Sec. 13.6pp. 587, 592
cyclo-C7H7+
6 p electrons (4n+2)
“tropylium”)
End of Lecture 55
February 23, 2011
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J. M. McBride, Chem 125. License: Creative Commons BY-NC-SA 3.0