Strain (chemistry)

Last updated May 14, 2022

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.^[1] 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.

Summary

Thermodynamics

The equilibrium 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.

K_{\rm {eq}}=\exp \left(-{\frac {\Delta {G^{\circ }}}{RT}}\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 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 (at a constant temperature):

\Delta {G^{\circ }}=\Delta {H^{\circ }}-T\Delta {S^{\circ }}\,.

Enthalpy is typically the more important thermodynamic function for determining a more stable molecular conformation.^[1] 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.^[1] 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.^[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.^[2] 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 formation (Δ_fH°) of a compound is described as the enthalpy change when the compound is formed from its separated elements.^[3] 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, Δ_fH° for cyclohexane is -29.9 kcal mol⁻¹ while Δ_fH° for methylcyclopentane is -25.5 kcal mol⁻¹.^[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 Δ_fH° can be made. If the experimental Δ_fH° differs from the predicted Δ_fH°, this difference in energy can be attributed to strain energy.

Kinds of strain

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.^[4]^: 5 Specifically, Van der Waals strain is considered a form of strain where the interacting atoms are at least four bonds away from each other.^[5] 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 et al.^[6] 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. Alkylamine.png — Reaction of trialkylamines and trimethylboron.

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.^[1] 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 methyl and ethyl groups are close together. Allyl2.png — Allylic methyl and ethyl groups are close together.

Allylic strain, or A^1,3 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 substituents.^[1]

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 ('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).^[4]^: 10 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 equation and, for example, the Meerwein–Ponndorf–Verley reduction/Oppenauer oxidation equilibrium for the measurement of axial versus equatorial values of cyclohexanone/cyclohexanol (0.7 kcal mol⁻¹).^[7]

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 is approximately 2.9 kcal mol⁻¹.^[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.^[8] 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.^[1] 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.

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.^[9] 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.^[10] Molecular mechanics 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).^[11] The data reflect mainly the unfavourable vicinal angles in medium rings, as illustrated by the severe increase of ketone 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 as sp2- model for the transition state.^[12] (Figure 2)

Strain of some common cycloalkane ring-sizes^[1]
Ring size	Strain energy (kcal mol⁻¹)	Ring size	Strain energy (kcal mol⁻¹)
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

In principle, angle strain can occur in acyclic compounds, but the phenomenon is rare.

Small rings

Cyclohexane is considered a benchmark in determining ring strain in cycloalkanes and it is commonly accepted that there is little to no strain energy.^[1] 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. Cyclobutane 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.^[1] Cyclopentane experiences much less strain, mainly due to torsional strain from eclipsed hydrogens: its preferred conformations interconvert by a process called pseudorotation.^[4]^: 14

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).^[13]^[14]

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, 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.^[1] This isn't always the case, as sometimes the fusion of rings induces some extra strain.

Strain in allosteric systems

In synthetic allosteric 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.^[15]

Related Research Articles

In organic chemistry, an alkane, or paraffin, is an acyclic saturated hydrocarbon. In other words, an alkane consists of hydrogen and carbon atoms arranged in a tree structure in which all the carbon–carbon bonds are single. Alkanes have the general chemical formula C_nH_2n+2. The alkanes range in complexity from the simplest case of methane, where n = 1, to arbitrarily large and complex molecules, like pentacontane or 6-ethyl-2-methyl-5-(1-methylethyl) octane, an isomer of tetradecane.

Stereoisomerism When molecules have the same atoms and bond structure but differ in 3D orientation

In stereochemistry, stereoisomerism, or spatial isomerism, is a form of isomerism in which molecules have the same molecular formula and sequence of bonded atoms (constitution), but differ in the three-dimensional orientations of their atoms in space. This contrasts with structural isomers, which share the same molecular formula, but the bond connections or their order differs. By definition, molecules that are stereoisomers of each other represent the same structural isomer.

In organic chemistry, the cycloalkanes are the monocyclic saturated hydrocarbons. In other words, a cycloalkane consists only of hydrogen and carbon atoms arranged in a structure containing a single ring, and all of the carbon-carbon bonds are single. The larger cycloalkanes, with more than 20 carbon atoms are typically called cycloparaffins. All cycloalkanes are isomer of Alkene.

Cyclohexane conformation Structures of cyclohexane

In organic chemistry, cyclohexane conformations are any of several three-dimensional shapes adopted by molecules of cyclohexane. Because many compounds feature structurally similar six-membered rings, the structure and dynamics of cyclohexane are important prototypes of a wide range of compounds.

In chemistry, conformational isomerism is a form of stereoisomerism in which the isomers can be interconverted just by rotations about formally single bonds. While any two arrangements of atoms in a molecule that differ by rotation about single bonds can be referred to as different conformations, conformations that correspond to local minima on the potential energy surface are specifically called conformational isomers or conformers. Conformations that correspond to local maxima on the energy surface are the transition states between the local-minimum conformational isomers. Rotations about single bonds involve overcoming a rotational energy barrier to interconvert one conformer to another. If the energy barrier is low, there is free rotation and a sample of the compound exists as a rapidly equilibrating mixture of multiple conformers; if the energy barrier is high enough then there is restricted rotation, a molecule may exist for a relatively long time period as a stable rotational isomer or rotamer. When the time scale for interconversion is long enough for isolation of individual rotamers, the isomers are termed atropisomers. The ring-flip of substituted cyclohexanes constitutes another common form of conformational isomerism.

Alkane stereochemistry concerns the stereochemistry of alkanes. Alkane conformers are one of the subjects of alkane stereochemistry.

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 are substantially smaller than the idealized value of approximately 109°. Because of their high strain, the heat of combustion for these small rings is elevated.

Pentane interference or syn-pentane interaction is the steric hindrance that the two terminal methyl groups experience in one of the chemical conformations of n-pentane. The possible conformations are combinations of anti conformations and gauche conformations and are anti-anti, anti-gauche⁺, gauche⁺ - gauche⁺ and gauche⁺ - gauche⁻ of which the last one is especially energetically unfavorable. In macromolecules such as polyethylene pentane interference occurs between every fifth carbon atom. The 1,3-diaxial interactions of cyclohexane derivatives is a special case of this type of interaction, although there are additional gauche interactions shared between substituents and the ring in that case. A clear example of the syn-pentane interaction is apparent in the diaxial versus diequatorial heats of formation of cis 1,3-dialkyl cyclohexanes. Relative to the diequatorial conformer, the diaxial conformer is 2-3 kcal/mol higher in energy than the value that would be expected based on gauche interactions alone. Pentane interference helps explain molecular geometries in many chemical compounds, product ratios, and purported transition states. One specific type of syn-pentane interaction is known as 1,3 allylic strain or.

Hyperconjugation Concept in organic chemistry

In organic chemistry, hyperconjugation refers to the delocalization of electrons with the participation of bonds of primarily σ-character. Usually, hyperconjugation involves the interaction of the electrons in a sigma (σ) orbital with an adjacent unpopulated non-bonding p or antibonding σ* or π* orbitals to give a pair of extended molecular orbitals. However, sometimes, low-lying antibonding σ* orbitals may also interact with filled orbitals of lone pair character (n) in what is termed negative hyperconjugation. Increased electron delocalization associated with hyperconjugation increases the stability of the system. In particular, the new orbital with bonding character is stabilized, resulting in an overall stabilization of the molecule. Only electrons in bonds that are in the β position can have this sort of direct stabilizing effect — donating from a sigma bond on an atom to an orbital in another atom directly attached to it. However, extended versions of hyperconjugation can be important as well. The Baker–Nathan effect, sometimes used synonymously for hyperconjugation, is a specific application of it to certain chemical reactions or types of structures.

In organic chemistry, transannular strain is the unfavorable interactions of ring substituents on non-adjacent carbons. These interactions, called transannular interactions, arise from a lack of space in the interior of the ring, which forces substituents into conflict with one another. In medium-sized cycloalkanes, which have between 8 and 11 carbons constituting the ring, transannular strain can be a major source of the overall strain, especially in some conformations, to which there is also contribution from large-angle strain and Pitzer strain. In larger rings, transannular strain drops off until the ring is sufficiently large that it can adopt conformations devoid of any negative interactions.

In organic chemistry, a ring flip is the interconversion of cyclic conformers that have equivalent ring shapes that results in the exchange of nonequivalent substituent positions. The overall process generally takes place over several steps, involving coupled rotations about several of the molecule's single bonds, in conjunction with minor deformations of bond angles. Most commonly, the term is used to refer to the interconversion of the two chair conformers of cyclohexane derivatives, which is specifically referred to as a chair flip, although other cycloalkanes and inorganic rings undergo similar processes.

In organic chemistry, the anomeric effect or Edward-Lemieux effect is a stereoelectronic effect that describes the tendency of heteroatomic substituents adjacent to a heteroatom within a cyclohexane ring to prefer the axial orientation instead of the less hindered equatorial orientation that would be expected from steric considerations. This effect was originally observed in pyranose rings by J. T. Edward in 1955 when studying carbohydrate chemistry.

Cyclic compound Molecule with a ring of bonded atoms

A cyclic compound is a term for a compound in the field of chemistry in which one or more series of atoms in the compound is connected to form a ring. Rings may vary in size from three to many atoms, and include examples where all the atoms are carbon, none of the atoms are carbon, or where both carbon and non-carbon atoms are present. Depending on the ring size, the bond order of the individual links between ring atoms, and their arrangements within the rings, carbocyclic and heterocyclic compounds may be aromatic or non-aromatic; in the latter case, they may vary from being fully saturated to having varying numbers of multiple bonds between the ring atoms. Because of the tremendous diversity allowed, in combination, by the valences of common atoms and their ability to form rings, the number of possible cyclic structures, even of small size numbers in the many billions.

In the study of conformational isomerism, the Gauche effect is an atypical situation where a gauche conformation is more stable than the anti conformation (180°).

Allylic strain in organic chemistry is a type of strain energy resulting from the interaction between a substituent on one end of an olefin with an allylic substituent on the other end. If the substituents are large enough in size, they can sterically interfere with each other such that one conformer is greatly favored over the other. Allyic strain was first recognized in the literature in 1965 by Johnson and Malhotra. The authors were investigating cyclohexane conformations including endocyclic and exocylic double bonds when they noticed certain conformations were disfavored due to the geometry constraints caused by the double bond. Organic chemists capitalize on the rigidity resulting from allylic strain for use in asymmetric reactions.

A-Values are numerical values used in the determination of the most stable orientation of atoms in a molecule, as well as a general representation of steric bulk. A-values are derived from energy measurements of the different cyclohexane conformations of a monosubstituted cyclohexane chemical. Substituents on a cyclohexane ring prefer to reside in the equatorial position to the axial. The difference in Gibbs free energy (ΔG) between the higher energy conformation and the lower energy conformation is the A-value for that particular substituent.

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 investigation. This can be a quick and convenient way to determine theoretical heats of formation without conducting tedious experiments. The technique was developed by professor Sidney William Benson of the University of Southern California. It is further described in Heat of formation group additivity.

Isomer Chemical compounds with the same molecular formula but different atomic arrangements

In chemistry, isomers are molecules or polyatomic ions with identical molecular formulae — that is, same number of atoms of each element — but distinct arrangements of atoms in space. Isomerism is existence or possibility of isomers.

Carbohydrate conformation refers to the overall three-dimensional structure adopted by a carbohydrate (saccharide) molecule as a result of the through-bond and through-space physical forces it experiences arising from its molecular structure. The physical forces that dictate the three-dimensional shapes of all molecules—here, of all monosaccharide, oligosaccharide, and polysaccharide molecules—are sometimes summarily captured by such terms as "steric interactions" and "stereoelectronic effects".

Macrocyclic stereocontrol refers to the directed outcome of a given intermolecular or intramolecular chemical reaction, generally an organic reaction, that is governed by the conformational or geometrical preference of a carbocyclic or heterocyclic ring, where the ring containing 8 or more atoms.

References

1 2 3 4 5 6 7 8 9 10 11 12 13 Anslyn and Dougherty, Modern Physical Organic Chemistry, University Science Books, 2006, ISBN 978-1-891389-31-3
↑ Coxon and Norman, Principles of Organic Synthesis, 3rd ed., Blackie Academic & Pro., 1993, ISBN 978-0-7514-0126-4
↑ Levine, Physical Chemistry, 5th ed., McGraw-Hill, 2002, ISBN 978-0-07-253495-5
1 2 3 Dragojlovic, Veljko (2015). "Conformational analysis of cycloalkanes" (PDF). Chemtexts. 1 (3). doi:10.1007/s40828-015-0014-0. S2CID 94348487.
↑ Brown, Foote, and Iverson, Organic Chemistry, 4th ed., Brooks/Cole, 2005, ISBN 978-0-534-46773-9
↑ Brown, H. C.; Johannesen, R. B. (1952). "Dissociation of the Addition Compounds of Trimethlboron with n-Butyl- and Neopentyldimethylamines; Interaction of Trimethylboron and Boron Trifluoride with highly hindered bases". J. Am. Chem. Soc. 75: 16–20. doi:10.1021/ja01097a005.
↑ Eliel, E.L., Wilen, S.H., The Stereochemistry of Organic Compounds, Wiley-Interscience, 1994.
↑ Weinhold, F. (2001). "Chemistry: A New Twist on Molecular Shape". Nature . 411 (6837): 539–541. doi:10.1038/35079225. PMID 11385553. S2CID 9812878.
↑ Wiberg, K. (1986). "The Concept of Strain in Organic Chemistry". Angew. Chem. Int. Ed. Engl. 25 (4): 312–322. doi:10.1002/anie.198603121.
↑ H. C. Brown , R.S. Fletcher, R.B. Johannes J. Am. Chem. Soc.1951, 73, 212. https://pubs.acs.org/doi/pdf/10.1021/ja01145a072 DOI: 10.1021/ja01145a072 ; H.C. Brown, G. Ham J. Am. Chem. Soc.1956, 78 , 2735 https://pubs.acs.org/doi/pdf/10.1021/ja01593a024
↑ H.-J. Schneider , G. Schmidt , F. Thomas J. Am. Chem. Soc.1983, 105, 3556. https://pubs.acs.org/doi/pdf/10.1021/ja00349a031
↑ P. Müller, J. Mareda , D. Milin J. Phys.Org. Chem., 1995, 8, 507. https://onlinelibrary.wiley.com/doi/epdf/10.1002/poc.610080802
↑ Wiberg, K. B. (1968). "Small Ring Bicyclo[n.m.0]alkanes". In Hart, H.; Karabatsos, G. J. (eds.). Advances in Alicyclic Chemistry. Vol. 2. Academic Press. pp. 185–254. ISBN 9781483224213.
↑ Wiberg, K. B.; Lampman, G. M.; Ciula, R. P.; Connor, D. S.; Schertler, P.; Lavanish, J. (1965). "Bicyclo[1.1.0]butane". Tetrahedron . 21 (10): 2749–2769. doi:10.1016/S0040-4020(01)98361-9.
↑ H.-J. Schneider. Org. Biomol. Chem.2016,14, 7994. https://pubs.rsc.org/en/content/articlepdf/2016/ob/c6ob01303a

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[Anslyn-1] 1 2 3 4 5 6 7 8 9 10 11 12 13 Anslyn and Dougherty, Modern Physical Organic Chemistry, University Science Books, 2006, ISBN 978-1-891389-31-3

[Coxon-2] Coxon and Norman, Principles of Organic Synthesis, 3rd ed., Blackie Academic & Pro., 1993, ISBN 978-0-7514-0126-4

[Levine-3] Levine, Physical Chemistry, 5th ed., McGraw-Hill, 2002, ISBN 978-0-07-253495-5

[Dragojlovic-4] 1 2 3 Dragojlovic, Veljko (2015). "Conformational analysis of cycloalkanes" (PDF). Chemtexts. 1 (3). doi:10.1007/s40828-015-0014-0. S2CID 94348487.

[Brown-5] Brown, Foote, and Iverson, Organic Chemistry, 4th ed., Brooks/Cole, 2005, ISBN 978-0-534-46773-9

[BrownandJohannesen-6] Brown, H. C.; Johannesen, R. B. (1952). "Dissociation of the Addition Compounds of Trimethlboron with n-Butyl- and Neopentyldimethylamines; Interaction of Trimethylboron and Boron Trifluoride with highly hindered bases". J. Am. Chem. Soc. 75: 16–20. doi:10.1021/ja01097a005.

[7] Eliel, E.L., Wilen, S.H., The Stereochemistry of Organic Compounds, Wiley-Interscience, 1994.

[Weinhold-8] Weinhold, F. (2001). "Chemistry: A New Twist on Molecular Shape". Nature . 411 (6837): 539–541. doi:10.1038/35079225. PMID 11385553. S2CID 9812878.

[Wiberg-9] Wiberg, K. (1986). "The Concept of Strain in Organic Chemistry". Angew. Chem. Int. Ed. Engl. 25 (4): 312–322. doi:10.1002/anie.198603121.

[10] H. C. Brown , R.S. Fletcher, R.B. Johannes J. Am. Chem. Soc.1951, 73, 212. https://pubs.acs.org/doi/pdf/10.1021/ja01145a072 DOI: 10.1021/ja01145a072 ; H.C. Brown, G. Ham J. Am. Chem. Soc.1956, 78 , 2735 https://pubs.acs.org/doi/pdf/10.1021/ja01593a024

[11] H.-J. Schneider , G. Schmidt , F. Thomas J. Am. Chem. Soc.1983, 105, 3556. https://pubs.acs.org/doi/pdf/10.1021/ja00349a031

[12] P. Müller, J. Mareda , D. Milin J. Phys.Org. Chem., 1995, 8, 507. https://onlinelibrary.wiley.com/doi/epdf/10.1002/poc.610080802

[13] Wiberg, K. B. (1968). "Small Ring Bicyclo[n.m.0]alkanes". In Hart, H.; Karabatsos, G. J. (eds.). Advances in Alicyclic Chemistry. Vol. 2. Academic Press. pp. 185–254. ISBN 9781483224213.

[14] Wiberg, K. B.; Lampman, G. M.; Ciula, R. P.; Connor, D. S.; Schertler, P.; Lavanish, J. (1965). "Bicyclo[1.1.0]butane". Tetrahedron . 21 (10): 2749–2769. doi:10.1016/S0040-4020(01)98361-9.

[15] H.-J. Schneider. Org. Biomol. Chem.2016,14, 7994. https://pubs.rsc.org/en/content/articlepdf/2016/ob/c6ob01303a

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