Testosterone (a steroid) -

PROBLEM Look at the following structure of estrone, the primary sex hormone in females, and tell whether 4-21 each of the two indicated (red) ring-fusions is cis or trans.
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Testosterone (a steroid) -

Estrone


(80) CHEMISTRY MATTERS -


Molecular Mechanics -

All the structural models in this book are computer-drawn. To make sure they accurately represent bond angles, bond lengths, torsional interactions, and steric interactions, the most stable geometry of each molecule has been calculated on a desktop computer using a commercially available molecular mechanics program based on work by Norman Allinger at the University of Georgia.


Molecular Mechanics -

The idea behind molecular mechanics is to begin with a rough geometry for a molecule and then calculate a total strain energy for that starting geometry, using mathematical equations that assign values to specific kinds of molecular interactions. Bond angles that are too large or too small cause angle strain; bond lengths that are too short or too long cause stretching or compressing strain; unfavorable eclipsing interactions around single bonds cause torsional strain; and nonbonded atoms that approach each other too closely cause steric, or van der Waals, strain.


Molecular Mechanics -

$$
E_{\text {total }}=E_{\mathrm{bond} \text { stretching }}+E_{\text {angle strain }}+E_{\text {torsional strain }}+E_{\text {van der Waals }}
$$


Molecular Mechanics -


Molecular Mechanics -

FIGURE 4.19 Computer programs make it possible to accurately represent molecular geometry. (credit: "Molecular geometry" by Jane Whitney/Flickr, CC BY 4.0)


Molecular Mechanics -

After calculating a total strain energy for the starting geometry, the program automatically changes the geometry slightly in an attempt to lower strain-perhaps by lengthening a bond that is too short or decreasing an angle that is too large. Strain is recalculated for the new geometry, more changes are made, and more calculations are done. After dozens or hundreds of iterations, the calculation ultimately converges on a minimum energy that corresponds to the most favorable, least strained conformation of the molecule.


Molecular Mechanics -

Similar calculations have proven to be particularly useful in pharmaceutical research, where a complementary fit between a drug molecule and a receptor molecule in the body is often the key to designing new pharmaceutical agents (FIGURE 4.20).
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0121.jpg?height=451&width=1061&top_left_y=192&top_left_x=532)


Molecular Mechanics -

FIGURE 4.20 The structure of Tamiflu (oseltamivir), an antiviral agent active against type A influenza, along with a molecular model of its minimum-energy conformation as calculated by molecular mechanics.


Key Terms -

- alicyclic
- angle strain
- axial position (cyclohexane)
- boat cyclohexane
- Bridgehead atom
- chair conformation
- cis-trans isomers
- conformational analysis
- cycloalkanes


Key Terms -


- 1,3-diaxial interaction -

- Equatorial position (cyclohexane)
- polycyclic molecule
- ring-flip (cyclohexane)
- stereoisomer
- steric strain
- torsional strain
- twist-boat conformation


- 1,3-diaxial interaction -


Summary -

Cyclic molecules are so commonly encountered throughout organic and biological chemistry that it's important to understand the consequences of their cyclic structures. Thus, we've taken a close look at cyclic structures in this chapter.


Summary -

Cycloalkanes are saturated cyclic hydrocarbons with the general formula $\mathrm{C}_{n} \mathrm{H}_{2 n}$. In contrast to open-chain alkanes, where nearly free rotation occurs around $\mathrm{C}-\mathrm{C}$ bonds, rotation is greatly reduced in cycloalkanes. Disubstituted cycloalkanes can therefore exist as cis-trans isomers. The cis isomer has both substituents on the same side of the ring; the trans isomer has substituents on opposite sides. Cis-trans isomers are just one kind of stereoisomer-compounds that have the same connections between atoms but different threedimensional arrangements.


Summary -

Not all cycloalkanes are equally stable. Three kinds of strain contribute to the overall energy of a cycloalkane: (1) angle strain is the resistance of a bond angle to compression or expansion from the normal $109^{\circ}$ tetrahedral value, (2) torsional strain is the energy cost of having neighboring $\mathrm{C}-\mathrm{H}$ bonds eclipsed rather than staggered, and (3) steric strain is the repulsive interaction that arises when two groups attempt to occupy the same space.

Cyclopropane ( $115 \mathrm{~kJ} / \mathrm{mol}$ strain) and cyclobutane ( $110.4 \mathrm{~kJ} / \mathrm{mol}$ strain) have both angle strain and torsional strain. Cyclopentane is free of angle strain but has a substantial torsional strain due to its large number of eclipsing interactions. Both cyclobutane and cyclopentane pucker slightly away from planarity to relieve torsional strain.


Summary -

Cyclohexane is strain-free because it adopts a puckered chair conformation, in which all bond angles are near $109^{\circ}$ and all neighboring $\mathrm{C}-\mathrm{H}$ bonds are staggered. Chair cyclohexane has two kinds of positions: axial and equatorial. Axial positions are oriented up and down, parallel to the ring axis, while equatorial positions lie in a belt around the equator of the ring. Each carbon atom has one axial and one equatorial position.


Summary -

Chair cyclohexanes are conformationally mobile and can undergo a ring-flip, which interconverts axial and equatorial positions. Substituents on the ring are more stable in the equatorial position because axial substituents cause 1,3-diaxial interactions. The amount of 1,3-diaxial steric strain caused by an axial substituent depends on its size.


Additional Problems -


Visualizing Chemistry -

PROBLEM Name the following cycloalkanes:


Visualizing Chemistry -


Visualizing Chemistry -

PROBLEM Name the following compound, identify each substituent as axial or equatorial, and tell whether the
4-23 conformation shown is the more stable or less stable chair form (green $=\mathrm{Cl}$ ):
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0122.jpg?height=348&width=454&top_left_y=845&top_left_x=429)


Visualizing Chemistry -

PROBLEM A trisubstituted cyclohexane with three substituents-red, green, and blue-undergoes a ring-flip
4-24 to its alternate chair conformation. Identify each substituent as axial or equatorial, and show the positions occupied by the three substituents in the ring-flipped form.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0122.jpg?height=291&width=1007&top_left_y=1383&top_left_x=429)

PROBLEM The following cyclohexane derivative has three substituents-red, green, and blue. Identify each
4-25 substituent as axial or equatorial, and identify each pair of relationships (red-blue, red-green, and blue-green) as cis or trans.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0122.jpg?height=282&width=400&top_left_y=1862&top_left_x=429)


Visualizing Chemistry -

PROBLEM Glucose exists in two forms having a 36:64 ratio at equilibrium. Draw a skeletal structure of each,
4-26 describe the difference between them, and tell which of the two you think is more stable (red = 0).
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0123.jpg?height=405&width=959&top_left_y=197&top_left_x=432)


Visualizing Chemistry -

PROBLEM Draw three isomers of trans-1,2-dichlorocyclobutane, and label them as either constitutional 4-31 isomers or stereoisomers.


Visualizing Chemistry -

Glucose


Visualizing Chemistry -

PROBLEM Draw 1,3,5-trimethylcyclohexane using a hexagon to represent the ring. How many cis-trans 4-33 stereoisomers are possible?


Cycloalkane Conformation and Stability -

PROBLEM Hydrocortisone, a naturally occurring hormone produced in the adrenal glands, is often used to
4-34 treat inflammation, severe allergies, and numerous other conditions. Is the indicated -OH group axial or equatorial?
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0124.jpg?height=259&width=766&top_left_y=193&top_left_x=422)


Hydrocortisone


PROBLEM A 1,2-cis disubstituted cyclohexane, such as cis-1,2-dichlorocyclohexane, must have one group 4-35 axial and one group equatorial. Explain.

PROBLEM A 1,2-trans disubstituted cyclohexane must have either both groups axial or both groups equatorial. 4-36 Explain.


PROBLEM Why is a 1,3-cis disubstituted cyclohexane more stable than its trans isomer? 4-37

PROBLEM Which is more stable, a 1,4-trans disubstituted cyclohexane or its cis isomer?
4-38
PROBLEM cis-1,2-Dimethylcyclobutane is less stable than its trans isomer, but cis-1,3-dimethylcyclobutane is
4-39 more stable than its trans isomer. Draw the most stable conformations of both, and explain.
PROBLEM From the data in Figure 4.13 and Table 4.1, estimate the percentages of molecules that have their
4-40 substituents in an axial orientation for the following compounds:
(a) Isopropylcyclohexane
(b) Fluorocyclohexane
(c) Cyclohexanecarbonitrile, $\mathrm{C}_{6} \mathrm{H}_{11} \mathrm{CN}$


PROBLEM Assume that you have a variety of cyclohexanes substituted in the positions indicated. Identify
4-41 the substituents as either axial or equatorial. For example, a 1,2-cis relationship means that one substituent must be axial and one equatorial, whereas a 1,2-trans relationship means that both substituents are axial or both are equatorial.
(a) 1,3-Trans disubstituted (b) 1,4-Cis disubstituted (c) 1,3-Cis disubstituted
(d) 1,5-Trans disubstituted
(e) 1,5-Cis disubstituted (f) 1,6-Trans disubstituted


Cyclohexane Conformational Analysis
PROBLEM Draw the two chair conformations of cis-1-chloro-2-methylcyclohexane. Which is more stable, and
4-42 by how much?
PROBLEM Draw the two chair conformations of trans-1-chloro-2-methylcyclohexane. Which is more stable? 4-43


PROBLEM Galactose, a sugar related to glucose, contains a six-membered ring in which all the substituents
4-44 except the -OH group, indicated below in red, are equatorial. Draw galactose in its more stable chair conformation.
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Galactose


Menthol -

PROBLEM There are four cis-trans isomers of menthol (Problem 4-45), including the one shown. Draw the
4-46 other three.
PROBLEM The diaxial conformation of cis-1,3-dimethylcyclohexane is approximately $23 \mathrm{~kJ} / \mathrm{mol}(5.4 \mathrm{kcal} / \mathrm{mol})$
4-47 less stable than the diequatorial conformation. Draw the two possible chair conformations, and suggest a reason for the large energy difference.


Menthol -

PROBLEM Approximately how much steric strain does the 1,3-diaxial interaction between the two methyl
4-48 groups introduce into the diaxial conformation of cis-1,3-dimethylcyclohexane? (See Problem 4-47.)


Menthol -

PROBLEM In light of your answer to Problem 4-48, draw the two chair conformations of
4-49 1,1,3-trimethylcyclohexane and estimate the amount of strain energy in each. Which conformation is favored?


Menthol -

PROBLEM One of the two chair structures of cis-1-chloro-3-methylcyclohexane is more stable than the other
4-50 by $15.5 \mathrm{~kJ} / \mathrm{mol}(3.7 \mathrm{kcal} / \mathrm{mol})$. Which is it? What is the energy cost of a 1,3 -diaxial interaction between a chlorine and a methyl group?


General Problems -

PROBLEM We saw in Problem 4-20 that cis-decalin is less stable than trans-decalin. Assume that the
4-51 1,3-diaxial interactions in cis-decalin are similar to those in axial methylcyclohexane [that is, one $\mathrm{CH} 2 \leftrightarrow \mathrm{H}$ interaction costs $3.8 \mathrm{~kJ} / \mathrm{mol}(0.9 \mathrm{kcal} / \mathrm{mol})]$, and calculate the magnitude of the energy difference between cis- and trans-decalin.