Strain (chemistry)

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.

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.

:<math> K_{\rm eq}= \exp \left (-\frac{\Delta {G^\circ{RT} \right) \,</math>

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.

thumb|right|upright=1.2|alt=Examples of the anti and gauche conformations of butane.|Examples of the anti and gauche conformations of butane.

Enthalpy and entropy are related to Gibbs free energy through the equation (at a constant temperature):

:<math>\Delta{G^\circ}=\Delta{H^\circ}-T\Delta{S^\circ}\,.</math>

Enthalpy is typically the more important thermodynamic function for determining a more stable molecular conformation. We find that the actual conformational distribution of butane is 70% anti and 30% gauche at room temperature.

Determining molecular strain

thumb|left|upright=1.4|alt=Images of cyclohexane and methylcyclopentane.|Images of cyclohexane and methylcyclopentane.

The standard heat of formation (ΔfH°) 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, ΔfH° for cyclohexane is -29.9 kcal mol−1 while ΔfH° for methylcyclopentane is -25.5 kcal mol−1. 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 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.

thumb|center|upright=1.8|alt=Reaction of trialkylamines and trimethylboron.|Reaction of trialkylamines and trimethylboron.

Syn-pentane strain

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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.

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. 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. 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 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 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. (Figure 2)

thumb|Figure 1 Bthumb|Figure 2 B

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|+Strain of some common cycloalkane ring-sizes

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.