Reactive Intermediate Chemistry

718 STRAINED HYDROCARBONS: STRUCTURES, STABILITY, AND REACTIVITY

1. INTRODUCTION: BAEYER STRAIN THEORY; THE ORIGIN AND TYPES OF STRAIN

Molecules that are distorted from their normal geometry usually have an increased energy that may lead to increased reactivity. Such destabilization is commonly referred to as ‘‘strain.’’ The concept of strain was first introduced by Adolph von Baeyer in 1874.1 He noted that whereas there were many compounds with fiveor six-membered rings, there were few examples of smaller or larger rings. He proposed that the other ring sizes would lead to deformed bond angles, and thus be ‘‘strained.’’ We now know that this is correct for threeand four-membered rings. However, he thought all rings were planar, and it was subsequently shown that essentially all saturated rings, except cyclopropane, are nonplanar. Rings with more than six atoms have some strain, but they have components other than bond angle deformation. Here, torsional strain and steric strain become particularly important.

Strained hydrocarbons range from being quite stable thermally and relatively unreactive (cyclobutane) to being transient intermediates. The following will be concerned with the factors that control stability and reactivity.

2. STRAIN ENERGIES

The energies of molecules vary over a wide range making it difficult to compare them. Strain energies allow a direct comparison of deviations in energy from ‘‘normal’’ values, independent of molecular size. The following will summarize calculations of strain energies.

2.1. Experimental Data

The energy of a molecule is usually given as the heat (enthalpy) of formation from the elements in their normal state (graphite for carbon, diatomic gases for hydrogen, oxygen, nitrogen and fluorine, etc.). It may be derived from the heat of combustion, which is a standard calorimetric measurement. Consider cyclohexane. The heat of combustion in the gas phase is given by

C6H12ðlÞ þ 9O2ðgÞ ! 6CO2ðgÞ þ 6H2OðlÞ H ¼ 944:7 kcal=mol

where the negative sign indicates that the reaction is exothermic. This result may be compared with the combustion of the elements

6CðsÞ þ 6H2ðgÞ ! 6CO2ðgÞ þ 6H2OðlÞ H ¼ 974:2 kcal=mol

The difference between these quantities, 29:5 kcal/mol, is the heat of formation of cyclohexane and the negative sign indicates that it is more stable than the elements

that it contains. These data are available for many strained hydrocarbons.2 Unfortunately, the measurement of heats of combustion is no longer an active area of experimental thermochemistry, and energies of new compounds are now commonly estimated using theoretical calculations.

The heats of formation of alkenes may sometimes be obtained by combining heats of hydrogenation with the heat of formation of the saturated product. This procedure has been used to obtain heats of formation of many strained alkenes.3 The heats of hydrogenation are usually measured in solution, and may differ somewhat from the value appropriate for the gas phase. Thus, the heats of formation of alkenes obtained in this way have a somewhat higher uncertainty than those obtained from heats of combustion.

2.2. Calculated Energies

Molecular mechanics (MM)4 is useful for estimating heats of formation for many compounds that have modest bond angle deformation. Here, one starts with an approximate geometry, and the MM program calculates the bond lengths, angles, torsional angles, and nonbonded distances. The deviations from ‘‘standard’’ values are calculated, along with the energies associated with the deviations. Then, a systematic search is carried out for the lowest energy conformation that can be reached from the starting geometry. This procedure allows the energy of the molecule to be estimated, and for molecules that do not deviate markedly from normal geometrical parameters, this procedure is usually capable of providing satisfactory estimates of the heats of formation. In common with all methods for geometry optimization, only the nearest local minimum will be found, and a number of different starting points must be examined for flexible molecules such as cyclooctane in order to locate the global minimum.5

However, MM is not generally useful for compounds that have more severe angle deformation or other unusual structural features. Ab initio molecular orbital (MO) calculations are not subject to this limitation. Here, again, an approximate geometry is used as the starting point, and geometry optimization will lead to the nearest local minimum. Satisfactory results are usually obtained when moderately high level calculations are carried out. The simplest procedure is a Hartree–Fock (HF) calculation, but it has the disadvantage that the electron–electron repulsions that are generated in the course of the calculation are too large because they do not recognize that electrons will tend to stay out of each others way because of their mutual repulsion. A better calculation takes this into account, and is described as correcting for electron correlation.6

It is now practical to carry out these calculations for a wide variety of molecules, and here the use of density functional theory (DFT)7 and particularly the hybrid functionals such as B3LYP has proven to be particularly useful. A basis set (equivalent to a set of atomic orbitals) such as 6-311þG* appears to be generally satisfactory. Greater accuracy may be obtained using more advanced methods such as the G28 or CBSQ9 model chemistries. The calculations also provide estimates of the vibrational frequencies from which the zero-point energies may be obtained.

720 STRAINED HYDROCARBONS: STRUCTURES, STABILITY, AND REACTIVITY

Correction for the differences in zero-point energies may be important when examining energy changes for reactions.

The heat of formation of a compound may be derived from the results of these calculations in several different ways. First, it is possible to calculate a set of group equivalents using the same level of theory as used for the compound in question.10 Then,

H ¼ 627:5 ðEcalc nCH3 ECH3 þ nCH2 ECH2 þ nCHECH þ Þ

where Ecalc is the calculated energy, n is the number of groups of a given type, E is the corresponding group equivalent, and 627.5 is the conversion factor from atomic units (used in the calculations) to kilocalories per mole (kcal/mol). This procedure often can give estimated heats of formation with an uncertainly of 1–2 kcal/mol. The heats of formation of some of the cycloalkanes in Figure 15.1 were estimated in this fashion using B3LYP/6-311þG* calculated energies.

A second procedure makes use of heats of atomization. The heat of atomization of carbon is the energy of converting graphite to carbon atoms. With diatomic molecules such as hydrogen, nitrogen, oxygen, and fluorine, it is the energy required to convert them into atoms. The heats of atomization for most elements in their normal form are known from experimental data.11

Figure 15.1. Heats of formation and strain energies of cyclic hydrocarbons in kilocalories per mole. The values given to 0.1 kcal/mol are experimental values (Refs. 2, 3, 17) and have an uncertainty of 0.5–1.0 kcal/mol. The values given as integers are calculated values (B3LYP/6-311þG*) and have an uncertainty of 3 kcal/mol.

Figure 15.1 (Continued)

The heat of atomization of a compound may also be derived from the calculated energy and the calculated heats of atomization of the elements.12 The difference between the heats of atomization of the compound and that of its constituent elements gives the heat of formation of the compound.

A third method makes use of an isodesmic reaction,13 which is a balanced reaction in which the number and types of groups are as similar as possible on the two sides of the equation. Consider the following example:

1

The energy change for the reaction may be estimated using the calculated energies of the component molecules. The heats of formation of all of the molecules except bicyclo[2.2.0]hexane (1) are well known, and having the calculated energy change for the overall reaction, its heat of formation may be estimated. The calculated energy change is 47 kcal/mol, and combined with the experimental heats of formation of cyclohexane, ethane and methane, it leads to a heat of formation of 1 of 33 kcal/mol. This value may be compared with the value 30 kcal/mol obtained from the heat of hydrogenation of 1 and the heat of formation of cyclohexane.

2.3. Models for Strain Energy Calculations

The strain energy (SE) of a molecule is the difference between its heat of formation and the heat of formation of a ‘‘suitable unstrained model.’’ Different choices of

722 STRAINED HYDROCARBONS: STRUCTURES, STABILITY, AND REACTIVITY

TABLE 15.1. Franklin Group Equivalentsa

a Hf at 25 C.

models may lead to different strain energies. Since the strain energies are not absolute quantities, all that is needed is a consistent, easily applied model. One of the simplest is derived from the Franklin group equivalents.14 These are the heats of formation at 25 C of various structural groups such as CH3, CH2, CH, C and olefinic groups (Table 15.1). By taking the appropriate sum of these equivalents, one obtains an unstrained model.

As an example, the heat of formation of cyclopentane in the gas phase is18.4 kcal/mol. The Franklin group equivalent for CH2 is 4.93 kcal/mol, and thus an unstrained model for cyclopentane is five times this quantity or 24.6 kcal/ mol. The difference between the two values gives the strain energy as 6.2 kcal/ mol. The strain energies given in Figure 15.1 were obtained in this way.

The strain energies may similarly be derived from the ab initio calculated energies by obtaining calculated group equivalents corresponding to the level of theory used. In the simplest approximation, the value for an unstrained CH2 group might be taken as the difference in energy between butane and pentane, that for a CH3 group would be one-half the energy of butane minus the CH2 equivalent. The CH equivalent could be obtained by subtracting three times the CH3 equivalent from the energy of isobutane. Other group equivalents may be obtained in a similar fashion.

A more detailed calculation would include the zero-point energies and the change in energy on going from 0 to 298 K. However, this usually has only a small effect on the calculated strain energies. Taking cyclopentane as an example, the B3LYP/6-311þG* energy is 196.59878 hartrees (1H ¼ 627.51 kcal/mol), and the difference between butane and pentane is 39.32190 H. Subtracting five times the latter from the calculated energy of cyclopentane, and converting to kilocalories per mole gives 6.7 kcal/mol as the strain energy, in good agreement with the value derived from the experimental heat of formation.

The heats of formation and the strain energies of a group of experimentally known hydrocarbon systems are summarized in Figure 15.1. It can be seen that the strain energies cover a very wide range, with many of them greater than the strength of a carbon–carbon bond (90 kcal/mol).15

Strained alkenes may have a combination of the strain in the basic ring system, and the added strain that results from the introduction of the double bond. Thus, it is convenient to define olefinic strain (OS)16 that may be given as the difference in heat of hydrogenation of the alkene in question and that of a similarly substituted

724 STRAINED HYDROCARBONS: STRUCTURES, STABILITY, AND REACTIVITY

repulsions in cyclooctane are removed by converting it into cyclooctene and the olefinic strain is 6 kcal/mol.

There is a group of alkenes in which the olefinic strain has relatively large negative values. These alkenes are termed hyperstable,16 and are expected to be relatively unreactive. One example is bicyclo[4.4.4]tetradec-1-ene (2) with a predicted OS of 14 kcal/mol.

2

3. STRUCTURES OF STRAINED HYDROCARBONS

3.1. Angle Deformation

Bond angle deformation is one of the more common sources of strain. A C C C bond in an open-chain alkane has an angle of 111 . For relatively small angular deviations, the increase in energy would approximately be given by

E ¼ 12 kj j2 ¼ 0:0175 j2

where kj is the bending force constant and j is the change in angle from the

ing to E ¼ 3:2 kcal/mol. This value is less than the observed strain energy because cyclopentane also has significant torsional strain (see below).

With cyclopropane, the conventional C C C bond angle is 60 , which is too small to be accommodated by any bonding model. Coulson and Moffitt18 showed that the bonds in cyclopropane are bent and have an interorbital angle of 104 (Fig. 15.3). This leads to high p-orbital character in the C C bonds, and correspondingly higher s-orbital character in the C H bonds. Clearly, a conventional description of bond angle deformation is not appropriate for compounds having three-membered rings. Cyclobutane is much closer to a conventional hydrocarbon.

The strain energies of cyclopropane (26.5 kcal/mol) and cyclobutane (26 kcal/ mol) are nearly the same despite the apparent much greater bond angle deformation with the former. One reason is that the weak C C bonds in cyclopropane are compensated in part by the stronger C H bonds. The increased strength results from the greater s character, and it is known that C H bond strengths increase with

The paracyclophanes (8) have a strong repulsive steric interaction between the two parallel aromatic rings, which leads to considerable deformation of the rings.28

8

Compounds with n as small as 2 have been prepared. With a substituent on one of the rings they are chiral and have been resolved.29 When the chains are longer, it is possible for one benzene ring to rotate, leading to racemization, and when n ¼ 4 resolution was not possible indicating that rotation of a benzene ring is no longer strongly hindered.30

Although tri-tert-butylethylene has been prepared,31 it has not as yet been possible to prepare tetra-tert-butylethylene, which should have very severe repulsive interactions between the tert-butyl groups. There are many other examples of intramolecular steric interactions that lead to increased strain energies.32 Intermolecular steric interactions can lead to reduced reactivity.26

3.5. Twisted Double Bonds

It is relatively difficult to twist a double bond because this would lead to a disruption of the p bond. As a result, compounds with twisted double bonds are relatively rare. One notable series of such compounds are the trans-cycloalkenes. The smallest one that can exist at room temperature is trans-cyclooctene. The difference in energy between cisand trans-cyclooctane was determined from the heats of hydrogenation and is 11 kcal/mol.33 trans-Cycloheptene has been observed at a low temperature,34 and there are indications that trans-cyclohexene is a transient intermediate in a reaction.35 When the ring is larger, as with cyclodecene,36 the normal tendency for the trans alkene to have the lower energy is again found. The OS values for these compounds are given in Table 15.2, and the examples with large positive values have been found to be relatively reactive toward electrophiles and in cycloaddition reactions.16

The structures of these compounds are interesting (Table 15.2). The cis compounds have both H C C H and C C C C torsional angles close to 0 . The trans compounds have calculated H C C H torsional angles close to 180 , but the C C C C torsional angles increasingly deviate from 180 as the size of the ring is decreased, indicating that the p bonds are becoming pyramidalized. The calculated H C C H torsional angles are in agreement with the electron diffraction study of trans-cyclooctene37 and with the NMR coupling constant for trans-cycloheptene.34 It is difficult to determine the angle between the p-orbitals of the double bond in these cases38 since bonds that are deformed are generally bent,39 and so the simple geometric angles are not very useful.