In chemistry, a molecule experiences strain when its chemical
structure undergoes some stress which raises its internal energy in
comparison to a strain-free reference compound. The internal energy of
a molecule consists of all the energy stored within it. A strained
molecule has an additional amount of internal energy which an
unstrained molecule does not. This extra internal energy, or strain
energy, can be likened to a compressed spring. Much like a
compressed spring must be held in place to prevent release of its
potential energy, a molecule can be held in an energetically
unfavorable conformation by the bonds within that molecule. Without
the bonds holding the conformation in place, the strain energy would
1.2 Determining molecular strain
2 Kinds of strain
2.1 Van der Waals strain
2.1.1 Syn-pentane strain
2.1.2 Allylic strain
2.1.3 1,3-diaxial strain
2.2 Torsional strain
2.3 Ring strain
2.3.1 Small rings
2.3.2 Transannular strain
2.3.3 Bicyclic systems
3 See also
The equilibrium of two molecular conformations is determined by the
Gibbs free energy
Gibbs free energy of the two conformations. From this
energy difference, the equilibrium constant for the two conformations
can be determined.
displaystyle ln K_ eq =- frac Delta G^ o RT ,
If there is a decrease in
Gibbs free energy
Gibbs free energy from one state to another,
this transformation is spontaneous and the lower energy state is more
stable. A highly strained, higher energy molecular conformation will
spontaneously convert to the lower energy molecular conformation.
Examples of the anti and gauche conformations of butane.
Enthalpy and entropy are related to
Gibbs free energy
Gibbs free energy through the
equation(at a constant temperature):
displaystyle Delta G^ o =Delta H^ o -TDelta S^ o ,.
Enthalpy is typically the more important thermodynamic function for
determining a more stable molecular conformation. While there are
different types of strain, the strain energy associated with all of
them is due to the weakening of bonds within the molecule. Since
enthalpy is usually more important, entropy can often be ignored.
This isn't always the case; if the difference in enthalpy is small,
entropy can have a larger effect on the equilibrium. For example,
n-butane has two possible conformations, anti and gauche. The anti
conformation is more stable by 0.9 kcal mol−1. We would
expect that butane is roughly 82% anti and 18% gauche at room
temperature. However, there are two possible gauche conformations and
only one anti conformation. Therefore, entropy makes a contribution of
0.4 kcal in favor of the gauche conformation. We find that the
actual conformational distribution of butane is 70% anti and 30%
gauche at room temperature.
Determining molecular strain
Images of cyclohexane and methylcyclopentane.
The heat of formation (ΔHfo) of a compound is described as the
enthalpy change when the compound is formed from its separated
elements. When the heat of formation for a compound is different
from either a prediction or a reference compound, this difference can
often be attributed to strain. For example, ΔHfo for cyclohexane is
-29.9 kcal mol−1 while ΔHfo for methylcyclopentane is
-25.5 kcal mol−1. Despite having the same atoms and
number of bonds, methylcyclopentane is higher in energy than
cyclohexane. This difference in energy can be attributed to the ring
strain of a five-membered ring which is absent in cyclohexane.
Experimentally, strain energy is often determined using heats of
combustion which is typically an easy experiment to perform.
Determining the strain energy within a molecule requires knowledge of
the expected internal energy without the strain. There are two ways do
this. First, one could compare to a similar compound that lacks
strain, such as in the previous methylcyclohexane example.
Unfortunately, it can often be difficult to obtain a suitable
compound. An alternative is to use Benson group increment theory. As
long as suitable group increments are available for the atoms within a
compound, a prediction of ΔHfo can be made. If the experimental ΔHfo
differs from the predicted ΔHfo, this difference in energy can be
attributed to strain energy.
Kinds of strain
Van der Waals strain
Main article: Van der Waals strain
Van der Waals strain, or steric strain, occurs when atoms are forced
to get closer than their Van der Waals radii allow. Specifically, Van
der Waals strain is considered a form of strain where the interacting
atoms are at least four bonds away from each other. The amount on
steric strain in similar molecules is dependent on the size of the
interacting groups; bulky tert-butyl groups take up much more space
than methyl groups and often experience greater steric interactions.
The effects of steric strain in the reaction of trialkylamines and
trimethylboron were studied by Nobel laureate
Herbert C. Brown
Herbert C. Brown et
al. They found that as the size of the alkyl groups on the amine
were increased, the equilibrium constant decreased as well. The shift
in equilibrium was attributed to steric strain between the alkyl
groups of the amine and the methyl groups on boron.
Reaction of trialkylamines and trimethylboron.
There are situations where seemingly identical conformations are not
equal in strain energy. Syn-pentane strain is an example of this
situation. There are two different ways to put both of the bonds the
central in n-pentane into a gauche conformation, one of which is
3 kcal mol−1 higher in energy than the other. When the
two methyl-substituted bonds are rotated from anti to gauche in
opposite directions, the molecule assumes a cyclopentane-like
conformation where the two terminal methyl groups are brought into
proximity. If the bonds are rotated in the same direction, this
doesn't occur. The steric strain between the two terminal methyl
groups accounts for the difference in energy between the two similar,
yet very different conformations.
Main article: Allylic strain
Allylic methyl and ethyl groups are close together.
Allylic strain, or A1,3 strain is closely associated to syn-pentane
strain. An example of allylic strain can be seen in the compound
2-pentene. It's possible for the ethyl substituent of the olefin to
rotate such that the terminal methyl group is brought near to the
vicinal methyl group of the olefin. These types of compounds usually
take a more linear conformation to avoid the steric strain between the
1,3-diaxial strain is another form of strain similar to syn-pentane.
In this case, the strain occurs due to steric interactions between a
substituent of a cyclohexane ring ('α') and gauche interactions
between the alpha substituent and both methylene carbons two bonds
away from the substituent in question (hence, 1,3-diaxial
interactions). When the substituent is axial, it is brought near to an
axial gamma hydrogen. The amount of strain is largely dependent on the
size of the substituent and can be relieved by forming into the major
chair conformation placing the substituent in an equatorial position.
The difference in energy between conformations is called the A value
and is well known for many different substituents. The
A value is a
thermodynamic parameter and was originally measured along with other
methods using the
Gibbs free energy
Gibbs free energy equation and, for example, the
Oppenauer oxidation equilibrium
for the measurement of axial versus equatorial values of
cyclohexanone/cyclohexanol (0.7 kcal mol−1).
Further information: Alkane stereochemistry
Torsional strain is the resistance to bond twisting. In cyclic
molecules, it is also called Pitzer strain.
Torsional strain occurs when atoms separated by three bonds are placed
in an eclipsed conformation instead of the more stable staggered
conformation. The barrier of rotation between staggered conformations
of ethane is approximately 2.9 kcal mol−1. It was
initially believed that the barrier to rotation was due to steric
interactions between vicinal hydrogens, but the Van der Waals radius
of hydrogen is too small for this to be the case. Recent research has
shown that the staggered conformation may be more stable due to a
hyperconjugative effect. Rotation away from the staggered
conformation interrupts this stabilizing force.
More complex molecules, such as butane, have more than one possible
staggered conformation. The anti conformation of butane is
approximately 0.9 kcal mol−1 (3.8 kJ mol−1)
more stable than the gauche conformation. Both of these staggered
conformations are much more stable than the eclipsed conformations.
Instead of a hyperconjugative effect, such as that in ethane, the
strain energy in butane is due to both steric interactions between
methyl groups and angle strain caused by these interactions.
Main article: Ring strain
According to the
VSEPR theory of molecular bonding, the preferred
geometry of a molecule is that in which both bonding and non-bonding
electrons are as far apart as possible. In molecules, it is quite
common for these angles to be somewhat compressed or expanded compared
to their optimal value. This strain is referred to as angle strain, or
Baeyer strain. The simplest examples of angle strain are small
cycloalkanes such as cyclopropane and cyclobutane, which are discussed
below. Furthermore, there is often eclipsing in cyclic systems which
cannot be relieved.
Strain of some common cycloalkane ring-sizes
Strain energy (kcal mol−1)
Strain energy (kcal mol−1)
In principle, angle strain can occur in acyclic compounds, but the
phenomenon is rare.
Cyclohexane is considered a benchmark in determining ring strain in
cycloalkanes and it is commonly accepted that there is little to no
strain energy. In comparison, smaller cycloalkanes are much higher
in energy due to increased strain.
Cyclopropane is analogous to a
triangle and thus has bond angles of 60°, much lower than the
preferred 109.5° of an sp3 hybridized carbon. Furthermore, the
hydrogens in cyclopropane are eclipsed.
similar strain, with bond angles of approximately 88° (it isn't
completely planar) and eclipsed hydrogens. The strain energy of
cyclopropane and cyclobutane are 27.5 and 26.3 kcal mol−1,
Cyclopentane experiences much less strain, mainly due
to torsional strain from eclipsed hydrogens, and has a strain energy
of 6.2 kcal mol−1.
Ring strain can be considerably higher in bicyclic systems. For
example, bicyclobutane, C4H6, is noted for being one of the most
strained compounds that is isolatable on a large scale; its strain
energy is estimated at 63.9 kcal mol−1
(267 kJ mol−1).
Main article: Transannular strain
Perhaps surprisingly, medium-sized rings (7–13 carbons) experience
more strain energy than cyclohexane. This transannular strain, also
known as Prelog strain, occurs when the cyclic molecules attempt to
avoid angle and torsional strain. In doing so, ring substituents
across from each other are brought into proximity and experience Van
der Waals strain.
Main article: Bicyclic molecule
The amount of strain energy in bicyclic systems is commonly the sum of
the strain energy in each individual ring. This isn't always the
case, as sometimes the fusion of rings induces some extra strain.
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