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Cyclohexanes
Cyclohexane rings (six atom rings in general) are the most well studied of all ring systems. They have a limited
number of, almost strain free, conformations. Because of their well defined conformational shapes, they are
frequently used to study effects of orientation or steric effects when studying chemical reactions. Additionally, six
atom rings are the most commonly encountered rings in nature. Cyclohexane structures do not choose to be flat.
Slight twists at each carbon atom allow cyclohexane rings to assume much more comfortable conformations, which
we call chair conformations. (Chairs even sound comfortable.) The chair has an up and down shape all around the
ring, sort of like the zig-zag shape seen in straight chains (...time for models!).
C
C
C C
C C
chair conformation
lounge chair - used to kick back and relax while you study your organic chemistry
Cyclohexane rings are flexible and easily allow partial rotations (twists) about the C-C single bonds. There is
minimal angle strain since each carbon can approximately accommodate the 109
o
of the tetrahedral shape. Torsional
strain energy is minimized in chair conformations since all groups are staggered relative to one another. This is
easily seen in a Newman projection perspective. An added new twist to our Newman projections is a side-by-side
view of parallel single bonds. If you look carefully at the structure above or use your model, you should be able to
see that a parallel relationship exists for all C-C bonds across the ring from one another.
There are three sets of parallel C-C bonds in cyclohexane rings. Any 'set' could be used to draw two parallel Newman projections.
Two simultaneous Newman projection views are now possible as shown below. Remember, that any two bonds
on opposite sides of the ring can be used and they can viewed from front or rear directions.
Once the first bond is drawn in a Newman projection of a chair conformation of cyclohexane ring, all of the
other bonds (axial and equatorial) are fixed by the staggered arrangements and the cyclic connections to one another.
Once you have drawn all of the bonds in a Newman projection, you merely fill in the blanks at the end of each line,
based on the substituents that are present (determined from the name or a 2D drawing).
How to draw a Newman projection of a cyclohexane ring.
H
This single bond fixes all of the other bonds in the Newman projection.
Divide front view into thirds.
Stagger back groups relative to front groups.
Draw connections over to parallel Newman projection. Make sure front connects to front and back connects to back.
Add the other two front groups, dividing the front view into thirds and stagger the back groups.
parallel views of Newman projections
Ideal dihedral angles of cyclohexane (the real ones are slightly different)
H
H
H
H
H
H
H
H
dihedral angles 60 o
added on both sides so that it points in an opposite sense to the direction of the parallel lines. These two chair
conformations are the most common shapes of cyclohexane rings, and interconvert with one another (thousands of
times per second).
Two parallel lines, slanting down and slanting up.
add tilted, upside down "V" on one side
add tilted, right side up "V" on one side
add tilted, right side up "V" on the other side
add tilted, upside down "V" on the other side
These two chair conformations will interconvert very rapidly.
An alternate strategy is to draw a slanted V shape first, then add the parallel lines in an opposite direction. Then
the other V shape is added in the opposite direction to the parallel lines. Use whatever works best for you. Make
sure you practice until you can do this with ease.
Alternatively you can draw the slanting "V" shapes first.
add parallel lines
add tilted, right side up "V" on the other side
add tilted, upside down "V" on the other side
These two chair conformations will interconvert very rapidly.
add parallel lines
Our next task is to draw in the axial and equatorial positions. The ring is very helpful to us in this regard. The
ring always points to the axial positions. If a ring carbon atom is in an up position, the axial position is pointing
straight up (on the top of the ring). If a ring carbon atom is in a down position, the axial position is pointing straight
down (on the bottom of the ring). The axial positions can now be added to our chair below.
add axial groups at the up positions (top face), where the ring points up
These two chair conformations will interconvert very rapidly. add axial groups at the up positions (top face)
add axial groups at the down positions (bottom face), where the ring points down
add axial groups at the down positions (bottom face)
The equatorial positions are added last, about the perimeter (or equator) of the ring. The two opposite positions,
in the plane of the paper are the easiest to add since our perspective is a side-on view and they follow the zig-zag
shape we expect in straight chains. Notice that one of these equatorial positions is on the top of the ring and one of
them is on the bottom. They should both be drawn parallel to the ring bonds that are parallel to the plane of the
paper.
Add equatorial positions in the plane of the page.
Add equatorial positions in the plane of the page.
equatorial bond on the bottom
equatorial bond on the bottom
equatorial bond on the top
equatorial bond on the top
Axial and equatorial positions switch places in the two conformations.
= axial position
= equatorial position
= axial position
= equatorial position
The other equatorial positions require slightly better artistic skills. To represent the equatorial positions coming
out of the plane of the page, toward the viewer, wedges are drawn; if projecting behind the page, away from the
viewer, dashed lines are drawn. These bonds will be parallel to bonds in the ring already drawn and in fact they have
an anti relationship with those parallel bonds (use models). Use the ring bonds to guide you in drawing the
equatorial bonds in the ring.
Heavy lines indicate parallel equatorial and ring bonds (above). Use the ring bonds to help you draw the equatorial bonds and then add the proper 3D perspective as simple lines, wedged lines or dashed lines (below).
C
C C
C
C
C C
C C
C
C
C C
C C
C
C
C
C
C C
C
C
C
C
C
C C
C Equatorial positions in the two chair C conformations of a cyclohexane ring.
C
C C
C
C
C
C
C
C C
C C
Equatorial and axial positions in the two chair conformations of a cyclohexane ring.
conformations rapidly interconvert
This is what you need to be able to draw to analyze six atom rings.
bold lines indicate parallel bonds
bold lines indicate parallel bonds
If you practice this several times, you should be able to generate a chair cyclohexane structure in seconds.
Substituents can be added as indicated from a chemical name. These two chair conformations are the most common
and comfortable of all the conformational possibilities available to a cyclohexane ring. Almost all of your work with
cyclohexanes will involve chair conformations.
Boat and Twist Boat Conformations
There are additional conformations of cyclohexane rings: boat, twist boat and half-chair conformations. These
are high potential energy conformations that are encountered when one chair rotates to the other chair conformation.
chair 1 (^) half chair 1 boat half chair 2 chair 2
0
2
4
6
8
10
12
twist boat 1 twist boat 2
PE
Energy changes of cyclohexane conformations.
Background thermal energy is about 20 kcal/mole, more than enough to make all of these conformations accesible.
5.0 ^ 6.4 5.
(^11) 11
However, we will view the interconversion of the two cyclohexane conformations, simplistically, as chair 1 in
equilibrium with chair 2 via the boat conformation.
Chair 1 Chair 2
Boat
van der Waals strain, (flag pole interactions)
All groups are staggered, which allows maximum stabilization.
Groups along parallel bonds in the ring are eclipsed, which increases torsional strain. Groups pointing into the center of the ring on the carbon atoms pointing up crowd one another, which increases van der Waals strain.
All groups are staggered, which minimizes torsional strain energy.
Equilibration, back and forth, between the two chair conformations is rapid at room temperature and occurs on
the order of 80,000 times per second. At lower temperatures interconversion is much slower (there is less thermal
background energy). At -
o
C the interconversion occurs about 40 times per second, at -
o
C interconversion
occurs about once every 23 minutes and at -
o
C it is estimated to occur once every 23 years. The equilibration can
occur in either of two directions as shown below.
chair 1
boat 1
boat 2
chair 2
a
a
b
b
b
a
b
a
Notice that all axial positions (top and bottom) become equatorial positions with the flip-flop of two chairs. Of
course, all equatorial positions become axial positions at the same time.
chair 1
axial on top becomes equatorial on top
transition via "boat"
axial on bottom becomes equatorial on bottom
equatorial on top becomes axial on top
chair 2
= axial
= equatorial = axial
= equatorial
Since the two chair conformations are so much more stable than the boat or half chair over 99.99% of the
molecules are in one of the two chair conformations. If all of the ring substituents are hydrogen atoms, there should
nearly be a 50/50 mixture of two indistinguishable chair structures.
K =
boat
chair
chair 1
K = chair 2
G
2.3RT
G
2.3RT
(6400 cal/mole)
(2.3)(2 cal/mol-K)(298 K)
= 10-4.60^ = 2.1x10-5^ =
(0 cal/mole)
(2.3)(2 cal/mol-K)(298 K)
= 10^0 = =
Real molecules actually exist that illustrate most of the cyclohexane conformations mentioned, above, as
substructures (chair, boat and twist boat). Adamantane has four chair cyclohexane rings in its complicated tricyclic
arrangement. Twistane has a good example of a twist boat conformation and is isomeric with adamantane.
Norbornane has a boat conformation locked into its rigid bicyclic framework with a bridging CH 2 holding the boat
shape in place. Each of these is highlighted below. Your models can help you see this a lot more clearly than these
pictures.
Adamantane
Every face is a chair conformation.
chair
chair
chair
chair (from back)
Twistane - has a twist boat conformation
twist boat
boat
Norbornane - has a boat conformation
side view front view
We have previously seen that a CH 3 /CH 3 gauche interaction raises the potential energy about 0.8 kcal/mole.
CH 3
CH 3
CH 3
CH 3
anti CH 3 /CH 3 = 0 kcal/mole gauche CH 3 /CH 3 = 0.8 kcal/mole
gauche
Two such relationships should raise the energy by approximately (2)x(0.8 kcal/mole) = 1.6 kcal/mole. The
actual value observed for an axial CH 3 in cyclohexane relative to equatorial is 1.7 kcal/mole, very close to what we
expect.
chair 1
half chair 1
boat
half chair 2
PE
Energy changes of methylcyclohexane conformations.
chair 2
G = 1.
kcal
mole
chair 2
K = chair 1
G 2.3RT
(1700 cal/mole)
(2.3)(2 cal/mol-K)(298 K)
= 10-1.2^ = 0.058 =
axial CH 3
equatorial CH 3
The two gauche interactions of axial R substituents and the ring carbon atoms in cyclohexane structures, are
called 1,3-diaxial interactions. In the axial position, the substituent R, is forced close to the other two axial groups
on the same side of the ring. Since these are both three atoms away from the ring carbon atom with the R
substituent, the 1,3-diaxial descriptor is appropriate.
1,3-diaxial interaction
( two gauche interactions)
H
R
H
1
2
3
2'
3'
Problem 2 - Which boat conformation would be a more likely transition state in interconverting the two chair
conformations of methylcyclohexane...or are they equivalent? Explain your answer.
R
R
first
first
boat 2
boat 1
R
flip "R"
side down
flip non-"R"
side up
A wide range of substituents has been studied and almost all show a preference for the equatorial position.
Several examples are listed in the table below. The actual energy difference between equatorial substituents and
axial substituents is often called the A value (axial strain). Larger A values indicate a greater equatorial preference
for the substituent due to larger destabilizing 1,3-diaxial interactions (or double gauche interactions).
S
S = substituent group
(table of energy values below)
S
equatorial
PE
axial
equatorial
axial
Go^ =
Substituent Go^ (A value) Substituent Go^ (A value)
-H 0.0 -CH 2 OH 1.
-CH 3 1.7 -CH 2 Br 1.
-CH 2 CH 3 1.8 -CF 3 2.
-CH(CH 3 ) 2 2.1 -O 2 CCH 2 CH 3 1.
-C(CH 3 ) 3 > 5.0 -OH 0.
-F 0.3 -OCH 3 0.
-Cl 0.5 -SH 1.
-Br 0.5 -SCH 3 1.
-I 0.5 -SC 5 H 6 1.
-CH=CH 2 1.7 -SOCH 3 1.
-CH=C=CH 2 1.5 -SO 2 CH 3 2.
-CCH 0.5 -SeC 6 H 5 1.
-CN 0.2 -TeC 6 H 5 0.
-C 6 H 5 (phenyl) 2.9 -NH 2 1.2(C 6 H 5 CH 3 ), 1.7(H 2 O)
-CH 2 C 6 H 5 (benzyl) 1.7 -N(CH 3 ) 2 1.5 (C 6 H 5 CH 3 ), 2.1(H 2 O)
-CO 2 H 0.6 -NO 2 1.
-CO 2 2.0 -HgBr 0.
-CHO 0.7 -HgCl -0.
-MgBr 0.
inward pointing hydrogen as its preferred conformation. When the substituent is t -butyl (R = CH 3 , R = CH 3 , R =
CH 3 ), there is no such option. All possible orientations of an axial t -butyl point a CH 3 toward the center of the ring,
which is extremely destabilizing (easy to see with a model) and chair 1 is overwhelmingly preferred.
Even though an equatorial substituent is preferred for all of the examples above, both chair conformations are
present in rapid equilibrium. What varies is the percent of each chair conformation that is present. Even with
t -butyl as the substituent, a tiny fraction of cyclohexane rings will have a transient, axial t -butyl (see the table
above).
Problem 3 – a. Propose an explanation for why ethenyl (-CH=CH 2 ) has a larger preference for the equatorial
position than ethynyl (-CCH).
substituent = C^ C^ H^ C
H
C
H
H
= attachment to the ring
ethynyl ethenyl
b. Propose an explanation for why ethenyl (-CH=CH 2 ) has a smaller preference for the equatorial position than
phenyl (-C 6 H 5 ).
substituent = C
H
C
H
H
= attachment to the ring
ethenyl phenyl
C C
C
C C
C
H H
H
H H
c. Benzyl would seem to be a larger group than phenyl, but has a smaller A value. Propose a possible explanation.
substituent = = attachment to the ring
benzyl phenyl
C C
C
C C
C
H H
H
H H
C C
C
C C
C
H 2 C
H H
H
H H
Disubstituted Cyclohexanes
Here is an excellent example of why memorization does not work in organic chemistry. Not only is it easier to
learn a limited number of basic principles and logically use them in newly encountered situations, it is down right
impossible to memorize every possible situation you might encounter.
When we add a second substituent to monosubstituted cyclohexane rings, the possibilities increase
tremendously. Seven flat ring structures are drawn below, which just emphasize the top and bottom positions on the
ring. Flat structures can be drawn as time average approximations between two interconverting chairs, although in
actuality none of the structures are flat. These structures are only used as a short hand to show that substituents are
on the same side or are on opposite sides. In biochemistry they are sometimes called Haworth projections and
commonly used with cyclic sugar molecules.
R 1
R 2 R 2
R 2
R 2
R 1 R 1
R 2
R 1 R 1
R 2
R 1 R 1
R 2
1,1-di "R" cis -1,2-di "R" trans -1,2-di "R" cis -1,3-di "R" trans -1,3-di "R"^ cis -1,4-di "R"^ trans -1,4-di "R"
R 1 = R 2 R 1 R 2 gauche interactions are possible when substituents are 1,2-substituted
Even though we have gone from a single monosubstituted cyclohexane to seven disubstituted cyclohexane rings,
the situation is even more complicated yet! Just as our monosubstituted cyclohexane had two chair conformations,
there are two possible chair conformations for each of the flat structures shown above. In some cases the two
conformations are equivalent in energy, but in other cases one conformation is preferred.
We need a systematic method of analysis or we will quickly become hopelessly lost in the wilderness of flip-
flopping cyclohexane rings. I recommend the following strategy for every cyclohexane analysis.
Possible systematic approach to Analyze Cyclohexane Conformations
1. Draw the cyclohexane ring framework as a bond-line formula (chair).
2. Add both axial and equatorial positions. Axials point straight up or down in alternating fashion (the ring points
to the axial positions). Equatorials are off to the side (use the axial positions to guide you as to top and bottom
positions). Both alternate on top or bottom of the face of the ring as you move around the ring. Use parallel
bonds in the ring to guide you where to draw the equatorial bonds.
3. Add in the necessary substituents according to the name of the structure (fill in the blank). It is generally easier
to visualize substituents drawn on the extreme left or extreme right carbon atoms of the ring because those
bonds will be in the plane of the paper, so these are good places to draw your first substituent.
4. Draw the other conformation by flipping one side up and flip the other side down. All of the axial and
equatorial positions will interchange, but the top will still be the top and the bottom will still be the bottom.
5. In addition to 1,3-diaxial interactions look for an extra gauche interactions when substituents are substituted 1,
(vicinal substitution). We will use gauche values from the table in Topic 5 (page 13) or 0.8 if not available.
6. Evaluate which is the preferred conformation using the available energy values. Use H to calculate a ratio.
K = 10
- G
2.3RT (^) 10
- H
2.3RT
Example 1 cis 1,4-dimethylcyclohexane
1.Draw the bond line formula of a chair.
2. Add axial and equatorial positions (ring points axial).
3. Add the indicated substituents. Generally the easiest positions to fill are the positions on the far left and far right
carbon atoms (1 and 4, just above), since their representation is drawn in the plane of the page. At least the first
substituent should be drawn at one of these positions and then fill in any other substituent(s) as required.
H
H 3 C
(^1 2 )
cis = same side, so both CH 3 groups should be on the same side (top side as written in this example). If you turned the structure over, the two methyl groups would still be on the same side, but that side would be the bottom.
CH 3
H
H 3 C H
(^1 2 )
One CH 3 is axial and one CH 3 is equatorial, but both are on the same side.
1,4 substitution tells us that the second substituent goes here.
Newman Projections
CH 3
H
H
CH 3
H
H
H
H
H 3 C
H
1 2
3
4
(^6 ) 2 3
4
6 5
H
H
H
H
CH 3
H
HH
H
H
H H
H
H
CH 3
H
H
H
H
H
C 4 C 5 and C 2 C 1
Newman projections:
One axial methyl and one equatorial methyl
chair 1 chair 2
CH 3
H 3 C
CH 3
One axial methyl and one equatorial methyl
anti gauche^ gauche anti
Example 2 trans -1,2-dimethylcyclohexane
1. See above.
2. Add axial and equatorial positions wherever substituents are present (the ring points to axial).
3. Add the indicated substituents.
H
H 3 C
trans = opposite side, so the second
CH 3 should be on the bottom side
since we drew the first CH 3 on the
top side.
H
H 3 C
Both CH 3 groups are
equatorial, but are on
the opposite sides.
1,2 substitution tells
us that the second
substituent goes here.
H
CH 3
4 & 5. Draw the other conformation and estimate the energy expense of each conformation.
H
H 3 C
H
CH 3
CH 3
H
H
CH 3
flip
down
flip
up
0 axial substituents
1 gauche interaction = 0.
2 axial substituents (opposite sides) = 2(1.7) = 3.
0 gauche interaction
kcal
mole
kcal
mole
6. Chair 1 has a gauche relationship between the two CH 3 substituents, which increases energy of that conformation
by +0.8 kcal/mole.
H 3 C
One gauche CH 3
interaction.
7. The potential energy difference between the two conformations is (3.4 – 0.8) = 2.6 kcal/mole. Use this value to
calculate Kequilibrium.
H
H
H
H
H
H
H 3 C
H
H 3 C
H
1 2
3
4
(^6 ) 2 3
4
6 5
H
H
CH 3
H
CH 3
H
H
H
H
H H
H
H
H
H
H
H
CH 3
C 4 C 5 and C 2 C 1
Newman projections:
chair 1 chair 2
CH 3
H 3 C
H
both methyls equatorial with gauch interaction
H 3 C
both methyls axial, anti
7. The potential energy difference between the two conformations is (5.0 – 1.7) = 3.3 kcal/mole. Use this value to
calculate Kequilibrium.
chair 1
half chair 1
boat
half chair 2
PE
Energy changes of trans -1-t-butyl-3-methylcyclohexane conformations.
chair 2
G > 5.
kcal
mole
chair 2
chair 1
K = = 10
G
2.3RT
( 3,300 cal/mole)
(2.3)(2 cal/mol-K)(298 K)
-0.
G = 1.
kcal
mole
Gchange = (5.0 - 1.7) = 3.
kcal
mole
Problem 4 – Draw all isomers of dimethylcyclohexane and evaluate their relative energies and estimate an equilibrium
distribution for the two chair conformations. Use the given energy values for substituted cyclohexane rings. If the two
substituents on the ring were different, all 14 conformations below would have different energies!
Potential
Energy
kcal
mole
A B
G = 2x(1.7) = 3.
trans -1,
C D
cis -1,
E F
trans -1,
G H
cis -1,
I J
trans -1,
K L
cis -1,
M N
One axial methyl group increases the potential energy by 1.7 kcal/mole,
Two axial methyl groups, on the same side (cis), increase the potential energy by 5.5 kcal/mole,
1,2 gauche methyl groups increase the potential energy by 0.8 kcal/mole.
Problem 5 - Both cis and trans 1-bromo-3-methylcyclohexane can exist in two chair conformations. Evaluate the
relative energies of the two conformations in each isomer (use the energy values from the table presented earlier).
Estimate the relative percents of each conformation at equilibrium using the difference in energy of the two
conformations from you calculations. Draw each chair conformation in 3D bond line notation and as a Newman
projection using the C 1 C 6 and C 3 C 4 bonds to sight down.
Br CH 3
1-bromo-3-methylcyclohexane
