Strain (chemistry)
Encyclopedia
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 be released.
of two molecular conformations
is determined by the difference in Gibbs free energy
of the two conformations. From this energy difference, the equilibrium constant for the two conformations can be determined.
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 highly strained, higher energy molecular conformation will spontaneously convert to the lower energy molecular conformation.
Enthalpy
and entropy
are related to Gibbs free energy through the equation
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 say in the equilibrium. For example, n-butane
has two possible conformations, anti and gauche
. The anti conformation is more stable by 0.9 kcal/mol. 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.
(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 while ΔHfo for methylcyclopentane
is -25.5 kcal/mol. 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.
, or steric strain, occurs when nonbonded atoms are forced closer to each other 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 group
s and often experience greater steric interactions.
The effects of steric strain in the reaction of trialkylamines and trimethylboron were studied by 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.
into a gauche conformation, one of which is 3 kcal/mol 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.
ic 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 substituents.
position. When the substituent is axial
, it is brought near to an axial meta hydrogen. The amount of strain is largely dependent on the size of the substituent and can be relieved by forming the other chair conformation which puts 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.
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 3.0 kcal/mol. 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 3.8 kcal/mol 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.
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's 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.
is analogous to a triangle and thus has bond angles of 60o, much lower than the preferred 109.5o of an sp3 hybridized carbon. Furthermore, the hydrogens in cyclopropane are eclipsed. Cyclobutane
experiences similar strain, with bond angles of approximately 88o (it isn't completely planer) and eclipsed hydrogens. The strain energy of cyclopropane and cyclobutane are 27.5 and 26.3 kcal/mol, respectively. Cyclopentane experiences much less strain, mainly due to torsional strain from eclipsed hydrogens, and has a strain energy of 6.2 kcal/mol.
across from each other are brought into proximity and experience Van der Waals strain.
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.
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
, a molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...
experiences strain when its chemical structure
Chemical structure
A chemical structure includes molecular geometry, electronic structure and crystal structure of molecules. Molecular geometry refers to the spatial arrangement of atoms in a molecule and the chemical bonds that hold the atoms together. Molecular geometry can range from the very simple, such as...
undergoes some stress which raises its internal energy
Internal energy
In thermodynamics, the internal energy is the total energy contained by a thermodynamic system. It is the energy needed to create the system, but excludes the energy to displace the system's surroundings, any energy associated with a move as a whole, or due to external force fields. Internal...
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
Strain energy
In a molecule, strain energy is released when the constituent atoms are allowed to rearrange themselves in a chemical reaction or a change of chemical conformation in a way that:* angle strain,* torsional strain,* ring strain and/or steric strain,...
, can be likened to a compressed spring
Spring (device)
A spring is an elastic object used to store mechanical energy. Springs are usually made out of spring steel. Small springs can be wound from pre-hardened stock, while larger ones are made from annealed steel and hardened after fabrication...
. Much like a compressed spring must be held in place to prevent release of its potential energy
Potential energy
In physics, potential energy is the energy stored in a body or in a system due to its position in a force field or due to its configuration. The SI unit of measure for energy and work is the Joule...
, a molecule can be held in an energetically unfavorable conformation by the bonds
Chemical bond
A chemical bond is an attraction between atoms that allows the formation of chemical substances that contain two or more atoms. The bond is caused by the electromagnetic force attraction between opposite charges, either between electrons and nuclei, or as the result of a dipole attraction...
within that molecule. Without the bonds holding the conformation in place, the strain energy would be released.
Thermodynamics
The equilibriumChemical equilibrium
In a chemical reaction, chemical equilibrium is the state in which the concentrations of the reactants and products have not yet changed with time. It occurs only in reversible reactions, and not in irreversible reactions. Usually, this state results when the forward reaction proceeds at the same...
of two molecular conformations
Conformational isomerism
In chemistry, conformational isomerism is a form of stereoisomerism in which the isomers can be interconverted exclusively by rotations about formally single bonds...
is determined by the difference in Gibbs free energy
Gibbs free energy
In thermodynamics, the Gibbs free energy is a thermodynamic potential that measures the "useful" or process-initiating work obtainable from a thermodynamic system at a constant temperature and pressure...
of the two conformations. From this energy difference, the equilibrium constant for the two conformations can be determined.
If there is a decrease in Gibbs free energy from one state to another, this transformation is spontaneous
Spontaneous process
A spontaneous process is the time-evolution of a system in which it releases free energy and moves to a lower, more thermodynamically stable energy state...
and the lower energy state is more stable. A highly strained, higher energy molecular conformation will spontaneously convert to the lower energy molecular conformation.
Enthalpy
Enthalpy
Enthalpy is a measure of the total energy of a thermodynamic system. It includes the internal energy, which is the energy required to create a system, and the amount of energy required to make room for it by displacing its environment and establishing its volume and pressure.Enthalpy is a...
and entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
are related to Gibbs free energy through the equation
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 say in the equilibrium. For example, n-butane
Butane
Butane is a gas with the formula C4H10 that is an alkane with four carbon atoms. The term may refer to any of two structural isomers, or to a mixture of them: in the IUPAC nomenclature, however, butane refers only to the unbranched n-butane isomer; the other one being called "methylpropane" or...
has two possible conformations, anti and gauche
Alkane stereochemistry
Alkane stereochemistry concerns the stereochemistry of alkanes.Alkane conformers are one of the subjects of alkane stereochemistry.-Conformations:...
. The anti conformation is more stable by 0.9 kcal/mol. 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
The heat of formationStandard enthalpy change of formation
The standard enthalpy of formation or standard heat of formation of a compound is the change of enthalpy that accompanies the formation of 1 mole of a substance in its standard state from its constituent elements in their standard states...
(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
Cyclohexane
Cyclohexane is a cycloalkane with the molecular formula C6H12. Cyclohexane is used as a nonpolar solvent for the chemical industry, and also as a raw material for the industrial production of adipic acid and caprolactam, both of which being intermediates used in the production of nylon...
is -29.9 kcal/mol while ΔHfo for methylcyclopentane
Alkyl cycloalkane
Alkyl cycloalkanes are chemical compounds with an alkyl group with a single ring of carbons to which hydrogens are attached according to the formula...
is -25.5 kcal/mol. 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
Ring strain
In organic chemistry, ring strain is the tendency of a cyclic molecule, such as cyclopropane, to destabilize when its atoms are in non-favorable high energy spatial orientations...
of a five-membered ring which is absent in cyclohexane. Experimentally, strain energy is often determined using heats of combustion
Heat of combustion
The heat of combustion is the energy released as heat when a compound undergoes complete combustion with oxygen under standard conditions. The chemical reaction is typically a hydrocarbon reacting with oxygen to form carbon dioxide, water and heat...
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
Methylcyclohexane is a colourless liquid with a faint benzene-like odour. Its molecular formula is C7H14. Methylcyclohexane is used in organic synthesis and as a solvent for cellulose ethers. It is a component of jet fuel and is also a component of correction fluids.-Structure:Monosubstituted...
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
Benson Group Increment Theory , or Group Increment Theory, uses the experimentally calculated heat of formation for individual groups of atoms to calculate the entire heat of formation for a molecule under investigation...
. 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.
Van der Waals strain
Van der Waals strainVan der Waals strain
In chemistry, 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 repulsion and is related to steric hindrance...
, or steric strain, occurs when nonbonded atoms are forced closer to each other than their Van der Waals radii
Van der Waals radius
The van der Waals radius, r, of an atom is the radius of an imaginary hard sphere which can be used to model the atom for many purposes. It is named after Johannes Diderik van der Waals, winner of the 1910 Nobel Prize in Physics, as he was the first to recognise that atoms had a finite size and to...
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
Butyl
In organic chemistry, butyl is a four-carbon alkyl radical or substituent group with general chemical formula -C4H9, derived from either of the two isomers of butane....
take up much more space than methyl group
Methyl group
Methyl group is a functional group derived from methane, containing one carbon atom bonded to three hydrogen atoms —CH3. The group is often abbreviated Me. Such hydrocarbon groups occur in many organic compounds. The methyl group can be found in three forms: anion, cation and radical. The anion...
s and often experience greater steric interactions.
The effects of steric strain in the reaction of trialkylamines and trimethylboron were studied by 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.
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-pentanePentane
Pentane is an organic compound with the formula C5H12 — that is, an alkane with five carbon atoms. The term may refer to any of three structural isomers, or to a mixture of them: in the IUPAC nomenclature, however, pentane means exclusively the n-pentane isomer; the other two being called...
into a gauche conformation, one of which is 3 kcal/mol 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
Cyclopentane
Cyclopentane is a highly flammable alicyclic hydrocarbon with chemical formula 510 and CAS number 287-92-3, consisting of a ring of five carbon atoms each bonded with two hydrogen atoms above and below the plane. It occurs as a colorless liquid with a petrol-like odor. Its melting point is −94 °C...
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, or A1,3 strain is closely associated to syn-pentane strain. An example of allylAllyl
An allyl group is a substituent with the structural formula H2C=CH-CH2R, where R is the connection to the rest of the molecule. It is made up of a methylene , attached to a vinyl group . The name is derived from the Latin word for garlic, Allium sativum. Theodor Wertheim isolated an allyl...
ic strain can be seen in the compound 2-pentene. It's possible for the ethyl
Ethyl group
In chemistry, an ethyl group is an alkyl substituent derived from ethane . It has the formula -C2H5 and is very often abbreviated -Et.Ethylation is the formation of a compound by introduction of the ethyl functional group, C2H5....
substituent of the olefin to rotate such that the terminal methyl group is brought near to the vicinal
Vicinal (chemistry)
In chemistry vicinal stands for any two functional groups bonded to two adjacent carbon atoms. For example the molecule 2,3-dibromobutane carries two vicinal bromine atoms and 1,3-dibromobutane does not....
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 ring and a hydrogen at the metaArene substitution patterns
Arene substitution patterns are part of organic chemistry IUPAC nomenclature and pinpoint the position of substituents other than hydrogen in relation to each other on an aromatic hydrocarbon.- Ortho, meta, and para substitution :...
position. When the substituent is axial
Cyclohexane conformation
A cyclohexane conformation is any of several three-dimensional shapes that a cyclohexane molecule can assume while maintaining the integrity of its chemical bonds....
, it is brought near to an axial meta hydrogen. The amount of strain is largely dependent on the size of the substituent and can be relieved by forming the other chair conformation which puts the substituent in an equatorial position. The difference in energy between conformations is called the A value
A value
thumb|400px|right| The A-value for a [[methyl]] group is 1.74 as derived from the [[chemical equilibrium]] above. This means it costs 1.74 [[kcal/mol]] of energy to have a methyl group in the axial position compared to the equatorial position....
and is well known for many different substituents.
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 instead of the more stable staggered conformation. The barrier of rotation between staggered conformations of ethane
Ethane
Ethane is a chemical compound with chemical formula C2H6. It is the only two-carbon alkane that is an aliphatic hydrocarbon. At standard temperature and pressure, ethane is a colorless, odorless gas....
is approximately 3.0 kcal/mol. 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
Hyperconjugation
In organic chemistry, hyperconjugation is the interaction of the electrons in a sigma bond with an adjacent empty non-bonding p-orbital or antibonding π orbital or filled π orbital, to give an extended molecular orbital that increases the stability of the system...
. 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 3.8 kcal/mol 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
Ethane is a chemical compound with chemical formula C2H6. It is the only two-carbon alkane that is an aliphatic hydrocarbon. At standard temperature and pressure, ethane is a colorless, odorless gas....
, the strain energy in butane
Butane
Butane is a gas with the formula C4H10 that is an alkane with four carbon atoms. The term may refer to any of two structural isomers, or to a mixture of them: in the IUPAC nomenclature, however, butane refers only to the unbranched n-butane isomer; the other one being called "methylpropane" or...
is due to both steric interactions between methyl groups and angle strain caused by these interactions.
Angle strain
According to the VSEPR theoryVSEPR theory
Valence shell electron pair repulsion theory is a model in chemistry used to predict the shape of individual molecules based upon the extent of electron-pair electrostatic repulsion. It is also named Gillespie–Nyholm theory after its two main developers...
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's 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.
Ring strain
Cyclic structures differ from acyclic structures in that atoms located in the ring are constrained and, except in cyclohexanes, cannot assume the preferred bond angles. Furthermore, there is often eclipsing in cyclic systems which cannot be relieved. The following table lists some common rings and their associated strain.| Number of carbons in ring | Strain energy (kcal/mol) | Number of carbons in ring | Strain energy (kcal/mol) |
|---|---|---|---|
| 3 | 27.5 | 10 | 12.4 |
| 4 | 26.3 | 11 | 11.3 |
| 5 | 6.2 | 12 | 4.1 |
| 6 | 0.1 | 13 | 5.2 |
| 7 | 6.2 | 14 | 1.9 |
| 8 | 9.7 | 15 | 1.9 |
| 9 | 12.6 | 16 | 2.0 |
Small Rings
Cyclohexane is considered a benchmark in determining ring strain in cycloalkanes and it is commonly accepted that here is little to no strain energy. In comparison, smaller cycloalkanes are much higher in energy due to increased strain. CyclopropaneCyclopropane
Cyclopropane is a cycloalkane molecule with the molecular formula C3H6, consisting of three carbon atoms linked to each other to form a ring, with each carbon atom bearing two hydrogen atoms...
is analogous to a triangle and thus has bond angles of 60o, much lower than the preferred 109.5o of an sp3 hybridized carbon. Furthermore, the hydrogens in cyclopropane are eclipsed. Cyclobutane
Cyclobutane
Cyclobutane is an organic compound with the formula 4. Cyclobutane is a colourless gas and commercially available as a liquefied gas. Derivatives of cyclobutane are called cyclobutanes...
experiences similar strain, with bond angles of approximately 88o (it isn't completely planer) and eclipsed hydrogens. The strain energy of cyclopropane and cyclobutane are 27.5 and 26.3 kcal/mol, respectively. Cyclopentane experiences much less strain, mainly due to torsional strain from eclipsed hydrogens, and has a strain energy of 6.2 kcal/mol.
Transannular strain
Perhaps surprisingly, medium sized rings (between 7-13 carbons) experience more strain energy than cyclohexane. This transannular strain occurs when the cycloalkanes attempt to avoid angle and torsional strain. In doing so, methylene groupsMethylene
Methylene is a chemical species in which a carbon atom is bonded to two hydrogen atoms. Three different possibilities present themselves:* the -CH2- substituent group: e.g., dichloromethane ....
across from each other are brought into proximity and experience Van der Waals strain.
Bicyclic systems
The amount of strain energy in bicyclic systemsBicyclic molecule
A bicyclic molecule is a molecule that features two fused rings. Bicyclic molecules occur widely in organic and inorganic compounds.Fusion of the rings can occur in three ways:...
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.