Conformational analysis is a comparatively new area of organic chemistry that has been developed well after the theories of organic reactions, bonding in organic compounds and stereochemistry. It was only in the second half of twentieth century that its importance was fully recognized and its central role with respect to bonding, reactivity and stability of organic compounds was appreciated. Fundamental concepts of conformational analysis, a deeper discussion of the conformational analysis of small and common rings and an introduction into the conformational analysis of medium and large rings are presented at a level suitable for an introductory organic chemistry course. This discussion aims to provide a better understanding of the complex relationship among different types of strain, while also discussing the factors that determine stability of a particular conformation. Finally, the unique nature of each class of cycloalkanes is explored.
KeywordsPhysical organic chemistry Conformational analysis Strain Cycloalkanes Medium rings Large rings
In 1874, Van’t Hoff and Le Bell independently proposed that the four valencies of carbon are directed toward the corners of a tetrahedron with the carbon atom at its center [1, 2]. The model was adopted by other chemists, applied to more complex molecules and further developed culminating with Barton’s 1950 paper in which he set foundations of modern conformational analysis .
Configuration of a molecule denotes three-dimensional arrangement of atoms in space. The infinite number of different arrangements of atoms in space that is a result of rotation about a single bond is called conformational isomers, conformers or conformations. Yet another less common term is rotamers.
It is often said that a rotation about a single bond is “free”. The statement is not meant to imply that there is no energy barrier to a rotation, but that rotation is spontaneous at room temperature. Thus, conformations are not actual isomers as they cannot be separated and isolated. They are different shapes of the same molecule. Conformational analysis is the study of kinetic and thermodynamic properties of molecules that are conformation dependent such as the existence of a preferred conformation, energies and populations of different conformational arrangements, and chemical consequences of it.
Strain in acyclic compounds
Before one can carry out conformational analysis of cyclic compounds, it is necessary to introduce fundamental concepts on examples of simple acyclic compounds. Furthermore, stability of a cyclic compound is sometimes estimated or calculated by comparing its energy to the estimated energy of the corresponding acyclic equivalent.
Conformational analysis of ethane
One of the simplest organic compounds that exists in different conformations is ethane. Different conformations of ethane are a result of rotation about the carbon–carbon bond. Obviously, there is an infinite number of such conformations. Fortunately, to carry out conformational analysis of ethane one needs to consider only the two extreme conformations—staggered and eclipsed. In the eclipsed conformation, each of the carbon–hydrogen bonds is in the same plane as the carbon–hydrogen bonds on the neighboring carbon. In a staggered conformation, each of the carbon–hydrogen bonds is in between the two carbon–hydrogen bonds on the neighboring carbon atom. Configuration of an organic compound is usually represented by a perspective formula. For the purpose of conformational analysis, the Newman projection and the sawhorse formula are frequently more suitable.
Similar to the Newman formula, a sawhorse formula is useful if one wants to represent the configuration of the two neighboring atoms (Fig. 1c). One draws an elongated bond connecting these two atoms and, again similar to the Newman projection formula, the substituents on each carbon atom are represented as if the angle between them was 120°—resembling a letter Y or an inverted letter Y.
Conformational analysis of propane
Conformational analysis of butane
Representations of butane
A molecule of ethane has only one type of each staggered and eclipsed conformation. In a more complex molecule, such as butane, one can identify different types of staggered and eclipsed conformations.
Gauche and anti conformers of butane
Rotation about the C2–C3 bond by another 60° results in another eclipsing conformation (the dihedral angle is 120°). This conformation is called anticlinal. It has torsional strain and some steric strain that results from the eclipsing of methyl groups and hydrogen atoms. Since degree of steric strain is lower compared to eclipsing conformation with dihedral angle of 0°, the overall energy of this conformation is somewhat lower.
Rotation by further 60°, results in a staggered conformation where two methyl groups are 180° apart (the dihedral angle is 180°). Therefore, the methyl groups are as far away from each other as possible. This conformation has no strain and is the conformation of the lowest energy. It is called the anti conformation (an abbreviation for antiperiplanar) of butane.
Continuing rotation by another 60° results in a conformation with the dihedral angle of 240°. This conformation is a mirror image of the eclipsed anticlinal conformation with dihedral angle of 120°. Thus, the energies of the two conformations are the same. Rotation by another 60° gives the other gauche conformation—the mirror image of the first one. Rotation by the final 60° completes the full circle and results in the original eclipsing syn conformation.
Even though anti conformation is the lowest energy conformation of butane, at room temperature butane does not exist exclusively in the anti conformation. There are two gauche conformations and one anti. Thus, probability factors favor a gauche conformation. Furthermore, a mixture of conformations is favored since it has greater entropy compared to a single conformation. Preference for a mixture and the increased proportion of gauche conformation increases with temperature.
Types of strain
Bond strain—stretching or compression of chemical bonds. This type of strain is rather severe and is not encountered very often in organic compounds. To minimize bond strain, a molecule adopts conformations that have other, less energy-demanding, types of strain.
Torsional strain (eclipsing strain, Pfitzer strain) is caused by eclipsing interactions. Torsional strain is considerably higher compared to steric or angle strain, which are explained next.
Steric strain (Van der Waals strain, Prelog strain) is caused by atoms forced too close to each other. Transannular strain (Prelog strain) is a form of steric strain characteristic of medium rings.
Angle strain (Bayer strain, classical strain) is a result of deviation from the ideal bond angle. Compared to other types of strain, increase in energy of a conformation caused by angle strain is relatively low. As a result, a molecule can accommodate relatively large deviation from an ideal bond angle and still be stable.
Any cyclic molecule tends to assume such a conformation in which the sum of the four types of strain is minimal. Since bond strain is considerably higher than the rest, it is relatively rare in cyclic compounds. If possible, a molecule will assume a conformation that exhibits one or more of the other three types of strain to avoid bond strain. Therefore, in most cases the overall strain is the interplay of the remaining three types of strain that are responsible for the energy of a particular conformation.
Classification of cyclic compounds
Cyclic compounds are classified, according to the number of atoms in the ring and properties, as small rings with 3 or 4 atoms, common rings with 5–7, medium rings 8–11, and large rings with 12 or more. Rings of similar size exhibit similar properties.
Small rings are rigid and highly strained. They are characterized both by a large deviation from the ideal tetrahedral valency angle—a high angle strain, and eclipsing interactions—a high torsional strain. Common rings are characterized by the tetrahedral valency angles and having substituents pointing only “out” of the ring. Medium rings are characterized by a specific type of steric strain called transannular interactions. It is a strain caused by substituents pointing “into” the ring. Large rings usually exhibit very little strain and resemble the corresponding open-chain compounds.
Sometimes small and common rings are grouped together into classical rings while medium and large rings are grouped into many-membered rings. Classical rings are relatively easy to form. Even though some may be rather strained, entropy of formation is favorable as the two ends of the chain are close together. Many-membered rings are considerably more difficult to prepare due to unfavorable entropy of activation.
Conformations of cyclohexane
It may be convenient to start analysis of cycloalkanes with cyclohexane rather than a chronological examination of the rings from the smallest to the largest. Cyclohexane is the smallest ring that exhibits no strain and types of bonds and conformations of cyclohexane form the basis of conformational analysis of other rings.
In a hypothetical “planar cyclohexane” C–C–C bond angles would be larger (120°) than tetrahedral. Furthermore, such conformation would exhibit 12 pairs of eclipsing C–H interactions. Instead, cyclohexane ring puckers to relieve both the torsional and the angle strain. In fact, one of the resulting puckered cyclohexane conformations has no strain at all. The two extreme conformations of cyclohexane are chair and boat. Chair conformation is the one without strain (Fig. 15b). In a chair conformation all of the bond angles are tetrahedral angles and all of the C–H bonds are in staggered conformations.
Axial and equatorial bonds of cyclohexane
Bond angles of cyclohexane
Drawing of the chair conformations of cyclohexane
One should start by drawing a five-atom chain in a zigzag conformation a. The conformation resembles letter M. One should keep in mind that the drawing should represent a side-on perspective view of the ring. Thus, the angles in the chain should actually be 135°–150°. Next, one draws another five-atom chain parallel to the first one in a form of a letter W as in b. The starting point is approximately one half bond length below the midpoint of the first bond in M. The first bond in W should be parallel to the second bond in M. Then, the second atom of the first chain should be connected to the second atom of the second chain and the second last atom of the first chain should be connected to the second last atom of the second chain c. As an aid in determining which atoms to connect, one can place hydrogen atoms at the ends of each chain and then connect the terminal carbon atoms d. The resulting drawing depicts all carbon–carbon bonds and four of the six equatorial carbon–hydrogen bonds. The remaining two equatorial bonds are parallel to the two C–C bonds just drawn e. The axial bonds are parallel to the edge of the paper as in f. Sequence g–l shows the drawing of the alternate chair conformation. One should start by drawing a five-atom chain in a zigzag conformation g (identical to a). Next, one draws another five-atom chain parallel to the first one in a form of a letter W with the starting point now approximately one half bond length below the midpoint of the last bond in M (h). The rest of the drawing follows the same process as for the first chair. The second atom of the first chain should be connected to the second atom of the second chain and the second last atom of the first chain should be connected to the second last atom of the second chain (i), terminal bonds are labeled as the equatorial hydrogens (j) and the remaining two equatorial bonds are drawn parallel to the two C–C bonds just drawn (k). The axial bonds are parallel to the edge of the paper as in l.
Interconversions of cyclohexane conformations
There are two chair conformations of cyclohexane. The two conformations are mirror images of each other and, therefore, have the same energy. At room temperature cyclohexane molecules undergo an interconversion (a “flip”) from one chair conformation to another. In cyclohexane interconversion of configuration proceeds through a mechanism described as an inversion.
Cyclohexane is not strain free
Cyclohexane is commonly referred to as being a strain-free ring in its chair conformation. However, strictly speaking that is not the case. Cyclohexane exhibits some steric strain. Obviously four carbon sequences in a cyclohexane chair are forced into gauche conformations. Therefore, the same type of strain present in a gauche conformation of butane is present in cyclohexane. Even though we understand that the chair conformation of cyclohexane is not entirely strain free, it is a commonly used “strain-free” standard to which stabilities of other cycloalkanes are compared.
A definition of what is strain free and what represents an appropriate comparison is not always clear. For example, in hexane gauche conformation is predominant as there are many gauche conformations and only one anti. Thus, when comparing cyclohexane with a hexane, one can say that it has about the same energy and is strain free. However, cyclohexane has a considerably higher energy compared to an all-anti conformation of hexane.
Conformations of disubstituted cyclohexanes: cis–trans isomerism
Fused six-membered rings: decalin
A bent bond results in a reduced angle strain, but, since the orbital overlap is not as good as in an ordinary σ bond, the bond is considerably weaker. While strength of an ordinary carbon–carbon bond (for example carbon–carbon bond in ethane) is ca. 83–85 kcal mol−1 (345–355 kJ mol−1), the strength of carbon–carbon bond in cyclopropane is only ca. 65 kcal mol−1 (272 kJ mol−1). Energy of a carbon–carbon π orbital is ca. 60–65 kcal mol−1 (251–272 kJ mol−1). This is an important consideration since sometimes the reactivity of cyclopropane resembles that of an alkene. In fact, there is a view that a double bond can be considered to be a two-carbon ring. Unlike other cycloalkanes, and alkanes in general, cyclopropane is very reactive since a reaction that results in a ring opening relieves both the angle and the torsional strain.
While cyclopropane exhibits considerable strain, there is one type of strain that is absent. Since all C–H bonds on different carbons are 1,2 relative to each other, in cyclopropane 1,3-repulsive interactions are not possible. All other cycloalkanes exhibit 1,3-repulsive interactions.
One can identify two types of C–H bonds in cyclobutane: pseudoaxial and pseudoequatorial (Fig. 35). Pseudoaxial are parallel to the imaginary axis of the ring, while pseudoequatorial are distributed around the rings “equator”. Pseudoaxial and pseudoequatorial bonds of cyclobutane resemble to axial and equatorial bonds of cyclohexane. As in cyclohexane, conformation with substituents in pseudoequatorial positions is more stable except that the energy differences are smaller.
As in the case of cyclobutane, a molecule of cyclopentane is not planar. The overall strain is reduced by twisting of the molecule out of the plane, but the angle strain is increased since valency angles become considerably smaller than 108°. Thus, in cyclobutane and cyclopentane puckering of the molecule results in an increased angle strain. The C–C–C bond angle is already smaller than the ideal tetrahedral angle and puckering further reduces it. As the resulting structure is no longer symmetrical, bond angles vary from 102° to 106° . Preferred conformations of cyclopentane are the envelope and the half-chair (also called the “twist” form). In an envelope conformation four carbon atoms are in the same plane and one is either above or below it. In a half-chair conformation, three carbon atoms are in a single plain, while two non-adjacent carbon atoms are either above or below it. Thus, when one places a model of an envelope conformation on the table, four hydrogen atoms (shown in bold and underlined) will rest on the table top. When one places a model of a half-chair conformation on the table, three hydrogen atoms will rest on the table top. Note that either of the two conformations still has some torsional strain as in cyclopentane some eclipsing interactions cannot be avoided. In conclusion, cyclopentane has torsional strain and a very small angle strain.
Conformational analysis of medium and large rings
Diamond lattice method for identifying low-energy conformations of cycloalkanes
The diamond lattice method can be applied to six-membered and larger rings as the smallest ring that can be superimposed on the diamond lattice is cyclohexane (Fig. 44b). Therefore, any smaller ring must exhibit angle strain. Furthermore, only rings with an even number of carbon atoms can form a closed path on a diamond lattice. As a result, all odd-membered rings must exhibit some torsional strain. We already encountered such situation with cycloheptane.
Even-membered rings can be classified into two types: those with 4n and those with 4n + 2 carbon atoms. Only rings with 4n + 2 carbon atoms can have a completely strain-free conformation. An example is cyclohexane (n = 1). Cyclodecane (n = 2) is an exception. As a medium-sized ring, it exhibits steric (transannular) strain. Cyclotetradecane and larger n + 2 rings are essentially strain free. Other rings with even number of carbon atoms (4n) exhibit some strain and for them the diamond lattice conformation is not always optimal. Among the large rings, those with odd number of carbon atoms exhibit the most strain.
While diamond lattice approach may represent a good starting point in conformational analysis of medium and large rings, nowadays its importance has decreased and we rely more on experimental (IR and Raman spectroscopies, X-ray diffraction, electron diffraction, low-temperature 1H and 13C NMR) and theoretical approaches such as molecular mechanics (MM), molecular orbital (MO) and molecular dynamics (MD) methods.
Common features of medium rings
Compounds with 8–11 atoms in a ring are classified as medium rings. Conformational analysis of medium rings is complex. They are not simply intermediate between common and large rings. They have some specific features that are characteristic only of them. Common and large rings generally differ little in chemical behavior compared to their open-chain counterparts.
Perhaps the most distinguishing feature of medium-sized rings is the difficulty in synthesizing them. Due to the both unfavorable enthalpy and entropy of activation ring closure reactions that result in formation of medium rings are difficult to carry out.
Ring strain of cycloalkanes
Strain per CH2
Finally, there is a specific type of transannular reactions (reactions across the ring) that only medium-sized rings undergo. Such reactions are a consequence of conformations of medium rings. Their intraannular hydrogen substituents readily undergo 1,3- and 1,5-hydride shift resulting in rearranged products.
In summary, medium rings are characterized by three principal phenomena: low formation tendency, high strain and transannular reactions. Cycloheptane exhibits strain energy close to that of the medium rings. However, compared to eight- to eleven-membered rings, it is easy to prepare. Thus, it is classified as a common ring. On the other hand, cyclododecane, while difficult to prepare, has low strain energy. Therefore, it is a large ring.
Both from the names and from the actual conformations, one can infer that the elements of cyclohexane conformations are present in medium and larger rings. As the number of atoms in the ring increases, the number of conformations sharply increases. There is no formula or an algorithm to determine the number of conformations from the number of ring atoms.
While in small and common rings there was an attempt to identify and study all the conformations regardless of their energies, in medium and large rings an effort is made to clearly distinguish between a conformation, which is a local minimum on an energy diagram, and a transition state, which is a local maximum. While most efforts were placed in identification of all of the conformations of individual rings, study of transition states is also important. They represent pathways for interconversion of individual conformations, allowing one to identify the nature of the conformational “flip” (such as pseudorotation or inversion), the energies involved and hence how likely is that a particular conformation will be interconverted into another. Study of the transition states is also important when considering their reactivity and biomedical properties (such as interactions with enzymes and receptors).
Cyclooctane is the smallest member of the class of medium rings. It exhibits all of the typical properties of a medium ring: difficulty in cyclizing, transannular strain, transannular reactions and lack of single lowest energy structure. A total of 10 different conformations have been identified [24, 25]. In fact, an additional conformation was reported , but it was apparently identical to the one already known . Complexities of conformational analysis of cyclooctane are a very good illustration of the challenges encountered when dealing with medium and large rings.
As a medium ring, cyclooctane also undergoes transannular reactions (reactions across the ring), which are covered later.
Odd-membered medium and large rings have been studied somewhat less extensively compared to even-membered rings. Cyclononane has the highest strain of all medium ring cycloalkanes. Dale wrote that “On the basis of thermochemical strain cyclononane can be considered the most typical medium-sized ring. It can also be considered the smallest macrocyclic alkane inasmuch as torsion angles larger than 120° start to play a role, and since the greater mobility of the ring permits conformational conversions to take place in more localized step processes rather than as synchronous changes of the whole ring” .
Variation in abundance of conformations of cyclononane with temperature
Dale (“Wedge”) representations of medium and large rings
With cyclononane both the perspective drawings and the nomenclature of various conformations get somewhat confusing. Side-on perspective views suitable for representation of smaller rings make it difficult to visualize and analyze a larger ring conformation. There is also an issue with nomenclature. Naming is now less descriptive as it is rather difficult to draw conformation from a given name, or assign a unique unambiguous name to a conformation. Furthermore, there is considerable possibility for confusion as in the case of TCB, TBC and SCB.
Each conformation is designated by a series of numbers within square brackets. Each number gives the number of bonds in one side, starting with the shortest and the direction of the ring is chosen so that the following number is the smallest possible . For example, each “side” of TBC conformation has three bonds and the Dale notation is . In SCB conformation the shortest side has two bonds, the shortest next to it three and the last one four. Hence, the notation is . The sum of the numbers gives the ring size.
According to Dale convention, based on the number of sides, conformations of medium and large rings can be classified as triangular, quadrangular and quinquangular. All of the cyclononane conformations we examined are triangular. Quadrangular conformations are commonly encountered in even-membered large rings while quinquangular in odd-membered large rings.
The most studied and perhaps the most interesting medium-sized ring is that of cyclodecane. It is a very good illustration of the uniqueness of medium rings. For example, it is the only ring that has 4n + 2 carbon atoms that exhibit significant strain.
There are 18 conformations of cyclodecane . 13C NMR studies have shown that at a low-temperature BCB is the principal conformer . At room temperature, cyclodecane exists as a mixture of a rather large number of conformations. The six lowest energy conformations are shown in Fig. 62 [27, 36].
The most interesting features of medium-sized rings are the phenomena of transannular interactions and the transannular reactions. Transannular interactions have been covered when dealing with each individual cycloalkane. In medium-sized rings, transannular reactions take place between atoms on opposite sides of the ring.
Large rings are highly flexible. Properties of large rings resemble those of the corresponding open-chain compounds. As the rings get sufficiently large, they assume conformations of extended rectangles composed of two long parallel chains linked by two bridges of minimum length . Disubstituted derivatives do not exhibit cis–trans isomerism since the rotation about carbon–carbon bonds in larger rings is free and the individual carbon atoms can rotate without affecting the rest of the ring. The number of conformations increases rapidly with the increasing ring size. For even-membered rings the number of possible diamond lattice conformations also increases and all large rings have more than one diamond lattice conformation.
As expected, complexity of conformational situation increases with the ring size. Conformational analysis becomes more complex and there are fewer studies available. However, one can still draw some general conclusions. With the increase in ring size the number of possible conformations sharply increases and finding all reasonable conformations becomes a problem . Larger rings are likely to exist as mixtures of several conformations. Even-membered rings exhibit low strain and tend to be mixtures of various quadrangular conformations. Odd-membered rings are more strained and are usually more complex mixtures of a larger number of various, mainly quadrangular and quinquangular, conformations.
Cycloheptadecane presents an interesting problem for conformational analysis. Since it is a large odd-membered ring, there is no obvious low-energy conformation. Cycloheptadecane is a challenging target and search for all of its conformations has been used as a test for validity of a particular search method [29, 52, 53]. There is an extremely large number of conformational minima and 264 conformations in the range of 0–3 kcal mol−1 have been identified . Conformation shown in Fig. 77b has been identified as the preferred conformation of cycloheptadecane [53, 54].
Conformational analysis is an indispensible tool for elucidation of the properties and behavior of organic molecules. Molecules should not be considered to be static “frozen” species as implied by molecular models. To fully understand three-dimensional structure of molecules, one has to consider their flexibility, thermal motion and a possibility of a bond rotation. Furthermore, conformational analysis should be related to chemical thermodynamics and in particular theory of intermediates and transition states. Finally, in the case of medium and large rings, the role of entropy cannot be neglected.
In a typical organic chemistry course, conformational analysis of cycloalkanes is restricted to small and common rings. Medium and large rings are present in numerous natural products and pharmacologically active compounds. Thus, not only a thorough understanding, but also an ability to apply conformational analysis is essential to comprehend biological properties of organic compounds and interactions in complex systems.
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