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In
chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and chemical compound, compounds made of atoms, molecules a ...
, a
molecule A molecule is a group of two or more atoms that are held together by Force, attractive forces known as chemical bonds; depending on context, the term may or may not include ions that satisfy this criterion. In quantum physics, organic chemi ...
experiences strain when its
chemical structure A chemical structure of a molecule is a spatial arrangement of its atoms and their chemical bonds. Its determination includes a chemist's specifying the molecular geometry and, when feasible and necessary, the electronic structure of the target m ...
undergoes some stress which raises its
internal energy The internal energy of a thermodynamic system is the energy of the system as a state function, measured as the quantity of energy necessary to bring the system from its standard internal state to its present internal state of interest, accoun ...
in comparison to a strain-free reference compound. The
internal energy The internal energy of a thermodynamic system is the energy of the system as a state function, measured as the quantity of energy necessary to bring the system from its standard internal state to its present internal state of interest, accoun ...
of a molecule consists of all the
energy Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...
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 In physics, the elastic potential energy gained by a wire during elongation with a tensile (stretching) or compressive (contractile) force is called strain energy. For linearly elastic materials, strain energy is: : U = \frac 1 2 V \sigma \v ...
, can be likened to a compressed spring.Anslyn and Dougherty, ''Modern Physical Organic Chemistry'', University Science Books, 2006, Much like a compressed spring must be held in place to prevent release of its
potential energy In physics, potential energy is the energy of an object or system due to the body's position relative to other objects, or the configuration of its particles. The energy is equal to the work done against any restoring forces, such as gravity ...
, 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 be released.


Summary


Thermodynamics

The
equilibrium Equilibrium may refer to: Film and television * ''Equilibrium'' (film), a 2002 science fiction film * '' The Story of Three Loves'', also known as ''Equilibrium'', a 1953 romantic anthology film * "Equilibrium" (''seaQuest 2032'') * ''Equilibr ...
of two molecular conformations is determined by the difference in
Gibbs free energy In thermodynamics, the Gibbs free energy (or Gibbs energy as the recommended name; symbol is a thermodynamic potential that can be used to calculate the maximum amount of Work (thermodynamics), work, other than Work (thermodynamics)#Pressure–v ...
of the two conformations. From this energy difference, the
equilibrium constant The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency ...
for the two conformations can be determined. : K_= \exp \left (-\frac \right) \, If there is a decrease in Gibbs free energy from one state to another, this transformation is spontaneous and the lower energy state is more
stable A stable is a building in which working animals are kept, especially horses or oxen. The building is usually divided into stalls, and may include storage for equipment and feed. Styles There are many different types of stables in use tod ...
. A highly strained, higher energy molecular conformation will spontaneously convert to the lower energy molecular conformation.
Enthalpy Enthalpy () is the sum of a thermodynamic system's internal energy and the product of its pressure and volume. It is a state function in thermodynamics used in many measurements in chemical, biological, and physical systems at a constant extern ...
and
entropy Entropy is a scientific concept, most commonly associated with states of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the micros ...
are related to Gibbs free energy through the equation (at a constant
temperature Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measurement, measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making ...
): :\Delta=\Delta-T\Delta\,. 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.Coxon and Norman, ''Principles of Organic Synthesis'', 3rd ed., Blackie Academic & Pro., 1993, We find that the actual conformational distribution of butane is 70% anti and 30% gauche at room temperature.


Determining molecular strain

The standard heat of formationf''H''°) of a compound is described as the enthalpy change when the compound is formed from its separated elements.Levine, ''Physical Chemistry'', 5th ed., McGraw-Hill, 2002, 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, Δf''H''° for
cyclohexane Cyclohexane is a cycloalkane with the molecular formula . Cyclohexane is non-polar. Cyclohexane is a colourless, flammable liquid with a distinctive detergent-like odor, reminiscent of cleaning products (in which it is sometimes used). Cyclohexan ...
is -29.9 kcal mol−1 while Δf''H''° for
methylcyclopentane Methylcyclopentane is an organic compound with the chemical formula CH3C5 H9. It is a colourless, flammable liquid with a faint odor. It is a component of the naphthene fraction of petroleum usually obtained as a mixture with cyclohexane. It is m ...
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 In organic chemistry, ring strain is a type of instability that exists when bonds in a molecule form angles that are abnormal. Strain is most commonly discussed for small rings such as cyclopropanes and cyclobutanes, whose internal angles ar ...
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 Methylcyclohexane (cyclohexylmethane) is an organic compound with the molecular formula is CH3C6H11. Classified as saturated hydrocarbon, it is a colourless liquid with a faint odor. Methylcyclohexane is used as a solvent. It is mainly converted ...
example. Unfortunately, it can often be difficult to obtain a suitable compound. An alternative is to use
Benson group increment theory Benson group-increment theory (BGIT), group-increment theory, or Benson group additivity uses the experimentally calculated heat of formation for individual groups of atoms to calculate the entire heat of formation for a molecule under investigatio ...
. As long as suitable group increments are available for the atoms within a compound, a prediction of Δf''H''° can be made. If the experimental Δf''H''° differs from the predicted Δf''H''°, this difference in energy can be attributed to strain energy.


Kinds of strain


Van der Waals strain

Van der Waals strain Van der Waals strain is strain resulting from Van der Waals repulsion when two substituents in a molecule approach each other with a distance less than the sum of their Van der Waals radii. Van der Waals strain is also called Van der Waals repul ...
, 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.Brown, Foote, and Iverson, ''Organic Chemistry'', 4th ed., Brooks/Cole, 2005, 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 group In organic chemistry, a methyl group is an alkyl derived from methane, containing one carbon atom bonded to three hydrogen atoms, having chemical formula (whereas normal methane has the formula ). In formulas, the group is often abbreviated a ...
s and often experience greater steric interactions. The effects of steric strain in the reaction of trialkylamines and
trimethylboron Trimethylborane (TMB) is a toxic, pyrophoric gas with the formula B(CH3)3 (which can also be written as Me3B, with Me representing methyl). Properties As a liquid it is colourless. The strongest line in the infrared spectrum is at 1330 cm� ...
were studied by Nobel laureate 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 group In organic chemistry, an alkyl group is an alkane missing one hydrogen. The term ''alkyl'' is intentionally unspecific to include many possible substitutions. An acyclic alkyl has the general formula of . A cycloalkyl group is derived from a cy ...
s of the amine and the methyl groups on boron.


Syn-pentane strain

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.


Allylic strain

Allylic strain 250 px, Allylic strain in an olefin. Allylic strain (also known as A1,3 strain, 1,3-allylic strain, or A-strain) in organic chemistry is a type of strain energy resulting from the interaction between a substituent on one end of an olefin (a synony ...
, or A1,3 strain is closely associated to syn-pentane strain. An example of
allyl In organic chemistry, an allyl group is a substituent with the structural formula . It consists of a methylene bridge () attached to a vinyl group (). The name is derived from the scientific name for garlic, . In 1844, Theodor Wertheim isolated a ...
ic strain can be seen in the compound 2-pentene. It's possible for the ethyl substituent of the
olefin In organic chemistry, an alkene, or olefin, is a hydrocarbon containing a carbon–carbon double bond. The double bond may be internal or at the terminal position. Terminal alkenes are also known as α-olefins. The International Union of Pu ...
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 substituents.


1,3-diaxial strain

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 Cyclohexane is a cycloalkane with the molecular formula . Cyclohexane is non-polar. Cyclohexane is a colourless, flammable liquid with a distinctive detergent-like odor, reminiscent of cleaning products (in which it is sometimes used). Cyclohexan ...
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 400px, The A-value for a methyl group is 1.74 as derived from the chemical equilibrium above. This means it costs of energy to have a methyl group in the axial position compared to the equatorial position. A-values are numerical values used i ...
and is well known for many different substituents. The
A value 400px, The A-value for a methyl group is 1.74 as derived from the chemical equilibrium above. This means it costs of energy to have a methyl group in the axial position compared to the equatorial position. A-values are numerical values used i ...
is a thermodynamic parameter and was originally measured along with other methods using the
Gibbs free energy In thermodynamics, the Gibbs free energy (or Gibbs energy as the recommended name; symbol is a thermodynamic potential that can be used to calculate the maximum amount of Work (thermodynamics), work, other than Work (thermodynamics)#Pressure–v ...
equation and, for example, the
Meerwein–Ponndorf–Verley reduction The Meerwein–Ponndorf–Verley (MPV) reduction in organic chemistry is the reduction of ketones and aldehydes to their corresponding alcohols utilizing aluminium alkoxide catalysis in the presence of a sacrificial alcohol. The advantages of the ...
/
Oppenauer oxidation Oppenauer oxidation, named after , is a gentle method for selectively oxidizing secondary alcohols to ketones. The reaction is the opposite Meerwein–Ponndorf–Verley reduction. The alcohol is oxidized with aluminium isopropoxide in excess ...
equilibrium for the measurement of axial versus equatorial values of cyclohexanone/cyclohexanol (0.7 kcal mol−1).


Torsional strain

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 In chemistry an eclipsed conformation is a conformation in which two substituents X and Y on adjacent atoms A, B are in closest proximity, implying that the torsion angle X–A–B–Y is 0°. Such a conformation can exist in any open chain, ...
instead of the more stable
staggered conformation In organic chemistry, a staggered conformation is a chemical conformation of an ethane-like moiety abcX–Ydef in which the substituents a, b, and c are at the maximum distance from d, e, and f; this requires the torsion angles to be 60°. I ...
. The barrier of rotation between staggered conformations of
ethane Ethane ( , ) is a naturally occurring Organic compound, organic chemical compound with chemical formula . At standard temperature and pressure, ethane is a colorless, odorless gas. Like many hydrocarbons, ethane is List of purification methods ...
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 Ethane ( , ) is a naturally occurring Organic compound, organic chemical compound with chemical formula . At standard temperature and pressure, ethane is a colorless, odorless gas. Like many hydrocarbons, ethane is List of purification methods ...
, the strain energy in
butane Butane () is an alkane with the formula C4H10. Butane exists as two isomers, ''n''-butane with connectivity and iso-butane with the formula . Both isomers are highly flammable, colorless, easily liquefied gases that quickly vaporize at ro ...
is due to both steric interactions between methyl groups and angle strain caused by these interactions.


Ring strain

According to the
VSEPR theory Valence shell electron pair repulsion (VSEPR) theory ( , ) is a conceptual model, model used in chemistry to predict the geometry of individual molecules from the number of electron pairs surrounding their central atoms. It is also named the Gill ...
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 or Pitzer strain in cyclic systems. These and possible transannular interactions were summarized early by H.C. Brown as internal strain, or I-Strain.
Molecular mechanics Molecular mechanics uses classical mechanics to model molecular systems. The Born–Oppenheimer approximation is assumed valid and the potential energy of all systems is calculated as a function of the nuclear coordinates using Force field (chemi ...
or force field approaches allow to calculate such strain contributions, which then can be correlated e.g. with reaction rates or equilibria. Many reactions of alicyclic compounds, including equilibria, redox and solvolysis reactions, which all are characterized by transition between sp2 and sp3 state at the reaction center, correlate with corresponding strain energy differences SI (sp2 -sp3). The data reflect mainly the unfavourable vicinal angles in medium rings, as illustrated by the severe increase of
ketone In organic chemistry, a ketone is an organic compound with the structure , where R and R' can be a variety of carbon-containing substituents. Ketones contain a carbonyl group (a carbon-oxygen double bond C=O). The simplest ketone is acetone ( ...
reduction rates with increasing SI (Figure 1). Another example is the solvolysis of bridgehead tosylates with steric energy differences between corresponding bromide derivatives (sp3) and the
carbenium ion The carbenium ion is a kind of cation, positive ion with the structure RR′R″C+, that is, a chemical species with carbon atom having three covalent bonds, and it bears a +1 formal charge. Carbenium ions are a major subset of carbocations, whic ...
as sp2- model for the
transition state In chemistry, the transition state of a chemical reaction is a particular configuration along the reaction coordinate. It is defined as the state corresponding to the highest potential energy along this reaction coordinate. It is often marked w ...
. (Figure 2) In principle, angle strain can occur in acyclic compounds, but the phenomenon is rare.


Small rings

Cyclohexane Cyclohexane is a cycloalkane with the molecular formula . Cyclohexane is non-polar. Cyclohexane is a colourless, flammable liquid with a distinctive detergent-like odor, reminiscent of cleaning products (in which it is sometimes used). Cyclohexan ...
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 Cyclopropane is the cycloalkane with the molecular formula (CH2)3, consisting of three methylene groups (CH2) linked to each other to form a triangular ring. The small size of the ring creates substantial ring strain in the structure. 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.
Cyclobutane Cyclobutane is a cycloalkane and organic compound with the formula (CH2)4. Cyclobutane is a colourless gas and is commercially available as a liquefied gas. Derivatives of cyclobutane are called cyclobutanes. Cyclobutane itself is of no commerc ...
experiences 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, respectively.
Cyclopentane Cyclopentane (also called C pentane) is a highly flammable alicyclic compound, alicyclic hydrocarbon with chemical formula C5H10, C5H10 and CAS number 287-92-3, consisting of a ring of five carbon atoms each bonded with two hydrogen atoms above and ...
experiences much less strain, mainly due to torsional strain from eclipsed hydrogens: its preferred conformations interconvert by a process called pseudorotation. 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).


Transannular strain

Medium-sized rings (7–13 carbons) experience more strain energy than cyclohexane, due mostly to deviation from ideal vicinal angles, or Pitzer strain. Molecular mechanics calculations indicate that transannular strain, also known as
Prelog strain In organic chemistry, transannular strain (also called Prelog strain after chemist Vladimir Prelog) is the unfavorable interactions of ring substituents on non-adjacent carbons. These interactions, called transannular interactions, arise from a ...
, does not play an essential role. Transannular reactions however, such as 1,5-shifts in cyclooctane substitution reactions, are well known.


Bicyclic systems

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.


Strain in allosteric systems

In synthetic
allosteric In the fields of biochemistry and pharmacology an allosteric regulator (or allosteric modulator) is a substance that binds to a site on an enzyme or receptor distinct from the active site, resulting in a conformational change that alters the p ...
systems there are typically two or more conformers with stability differences due to strain contributions. Positive cooperativity for example results from increased binding of a substrate A to a conformer C2 which is produced by binding of an effector molecule E. If the conformer C2 has a similar stability as another equilibrating conformer C1 a fit induced by the substrate A will lead to binding of A to C2 also in absence of the effector E. Only if the stability of the conformer C2 is significantly smaller, meaning that in absence of an effector E the population of C2 is much smaller than that of C1, the ratio K2/K1 which measures the efficiency of the allosteric signal will increase. The ratio K2/K1 can be related directly to the strain energy difference between the conformers C1 and C2; if it is small higher concentrations of A will directly bind to C2 and make the effector E inefficient. In addition, the response time of such allosteric switches depends on the strain of the conformer interconversion transitions state.H.-J. Schneider. ''Org. Biomol. Chem.'' 2016,14, 7994. https://pubs.rsc.org/en/content/articlepdf/2016/ob/c6ob01303a


See also

*
Strain (materials science) In mechanics, strain is defined as relative deformation, compared to a position configuration. Different equivalent choices may be made for the expression of a strain field depending on whether it is defined with respect to the initial or th ...


References

{{DEFAULTSORT:Strain (Chemistry) Stereochemistry