Ch. 2 Textbook

2.1 Newman Projection

　It was understood that the rotation about C-C single bond of ethane and related molecules to cause the change of molecular shape. It is necessary, however, to prepare a set of rules beforehand in order to express the change of three-dimensional structure in a two-dimensional way.

Schematic Drawings

　The first step to express molecular structure in a two-dimensional way is use of schematic drawings; i.e., to draw molecular structure as it looks. In order to stress the three-dimensional nature, several conventions are used. dash and wedge drawings are some examples.

(a) perspective (b) dash and wedge drawing

Fig. 2.1 Schematic drawings of ethane.

It is impossible, however, for these drawings to reproduce the exact shape of the molecules. As we have learned before, the dihedral angle defined by four atoms, H-C-C-H, is a very good parameter of molecular structure. It is not practical, however, to draw such a figure Fig. 1.8 as for a large compound. In order to solve the problem a method of drawing molecular structure was proposed by the American chemist M. S. Newman in the middle of 20th century. The characteristic point of this method is that the dihedral angle is clearly demonstrated. The way of drawing a Newman projection is exemplified with ethane. The molecule (or rather, molecular model) of ethane is projected against the wall behind the molecule along the direction of C-C bond. On the wall, the shadow of six hydrogens and two carbons should appear. However, since the projection is made along the C-C bond, the two carbon atoms overlapped and only one carbon in front can be seen and the other is behind the front one. To avoid this inconvenience, the front carbon is now designated as a dot, while a large circle represents the carbon behind. The dihedral angle is defined by the angle made by two bond, CA-HA and CB-HB on the Newman projection. The angle is positive if the overlapping of CA-HA bond with CB-HB bond is achieved by moving the former clockwise, while the angle is negative if the same process requires an anticlock movement of CA-HA bond. In Fig. 2.2, two conformations of ethane 1 and 2 given in Fig. 1.8 are shown.

Fig. 2.2 Newman projection of ethane

▶(Back to Q.2.1 as necessary)

2.2 Conformational analysis of ethane

　Then how we can describe the relation between 1 and 2? They are stereoisomers each other since the spatial relation among eight atoms forming each ethane is different. The difference is, however, not the same one observed for 14 and 15 of Ch. 1. (comment: these are two enantiomers of CHFClBr) 14 and 15 are not interconvertible without breakage and reunion of some chemical bonds. On the other hand, 1 and 2 in this chapter are interconvertible by rotation about the bond without bond breakage. In such a case 1 and 2 are refereed to having a different conformation.

▶(Back to Q.2.2 as necessary)

How can we distinguish conformations 1 and 2? Rotation about C-C bond will cause a change in the tortion angleφ and consequently the distance between HA and HB. If the distance between two hydrogen atoms(or between a hydrogen atom and an alkyl group, or between two alkyl groups) becomes short, the potential energy of the molecule will increase because the steric repulsion will increase. When the tortion angleφ = 0o, 120o and 240o , it becomes maximal; when the tortion angleφ = 60o, 180oand 300o, it becomes minimal. Thus, the plot of φ with the potential energy will give the tortion angle-potential energy curve given in Fig. 2.3 　A study of the change of molecular structure and energy caused by a rotation of C-C (and other) single bond is referred to conformational analysis.

Fig. 2.3 The tortion angle-potential energy curve of ethane.

▶go to S2.1 conformational analysis

Potential energy of ethane is maximal when φ =0o, 120o and 240o, and minimal when φ = 60o, 180o and 300o. The structure for the former is referred to staggered, 4 and that for the latter to eclipsed. 3.

　The potential energy difference between two forms is ca 12 kJ mol－1 (2.86 kcal mol－1) Conformations corresponding to the structure with maximal or minimal energy are referred to conformational isomer or simply conformer. In this book we use conformer since this term.

▶go to S2.2 Eclipsed and Staggered Forms

▶(Back to Q2.3 as necessary)

2.3 Conformational Analysis of Butane

　Although propane has much the same tortion angle-energy curve with ethane, a considerably different result will be obtained when the conformational analysis for butane is attempted in relation to the rotation of central C-C bond. When the potential energy of the molecule is plotted against the tortion angle made by two C-CH3 bonds, there are obtained two conformers with maximum energy(A and C of Fig. 2.4) and two conformers with minimum energy(B and D of Fig. 2.4).

Fig. 2.4 The tortion angle-potential energy curve of butane.

　The Newman projection corresponding to conformers A-D are shown below(5-8). In the case of ethane, staggered and eclipsed conformations can describe the feature of its conformational analysis; in the case of butane, however, two conformations are not enough to describe the feature of the curve. Of the eclipsed form, 5, the one with φ = 0o is called cis form, and of the staggered form, 6, the one with φ = 60o is called gauche form and the other, 8, with φ = 180o is referred to trans or anti form.

▶go to S2.3 Gauche and Anti Forms

　Because of the proximity of two methyl groups, 5 is associated with larger energy than 7, and 6 is associated with larger energy than 8. Cases where this treatment is not applicable because of more complicated structures are involved will be discussed later.

　One can write many Newman projection for one particular molecule. For an ethane derivative ABCC-CDEF, projection can be done either from ABC side(16) or from DEF side(15). In addition, there are many rotational isomers(rotamers) in relation to the rotation about C-C bond. Much the same is true for perspective drawings(11)-(14).

▶(Back to Q2.4 as necessary)

2.4 Relative abundance of conformers

　Ethane has two conformers; eclipsed and staggered. Does then ethane consist in two equal amount of two conformers? By any means not. The two conformers have different steric energy, and hence the relative population of two conformers may be different.

　This situation can be visualized if we assume that the tortion angle-energy plot is a kind of reaction coordinate, which exhibit the energy change associated with the progress of the reaction. The vertical coordinate, the reaction coordinate corresponds to tortion angle. The eclipsed form is equivalent to the activate complex of a chemical reaction. Such a high energy species will have a very short lifetime, and is impossible to isolate. In addition to the case of ethane, for propane and butane, the eclipsed form is an intermediate of a reaction which has a very short lifetime.

　One can assume that ethane exists most of the time as the most stable staggered form. In the case of butane there are two staggered form, and hence it exists as a mixture of these two conformers. In such a case the relative amount of two conformers will depend on the difference of Gibbs free energy ΔG. Generally speaking, for an equilibrium A ・ B, ΔG is expressed by the following equation

ΔG = -2.303 RT log K

where K is the equilibrium constant(K = [B]/[A]), R is the gas constant(=1.98 cal deg-1 mol-1) and T is the absolute temperature.

▶go to S2.4

▶(Back to Q2.6 as necessary)

If x is the molar fraction of the gauche form, (1 - x )/x = 4.95; ∴x = 0.168. i.e., anti form 83% and gauche form 17%. This does not, however, mean that one can separate butane into the anti and gauche forms. In order to separate two rapidly exchanging species. e. g., 6 and 8 at room temperature, the energy of barrier of the exchange--in the case of butane, the energy difference between 6 and 8 or 5 and 7, should be at least as large as 100 kJ mol-1. As is indicated in the Fig. 2.4, the energy difference is ca. 15-20 kJ mol-1, indicating that at room temperature the exchange is very rapid.

▶(Back to Q2.7 as necessary)

2.5 Stereochemical nomenclature of ethane derivatives

　We have already learned several terms, such as gauche, anti, staggered or eclipsed, to name the conformers based on the Newman projection. These are, however, insufficient when a more complex molecule is involved. For instance, there are three staggered forms for 2,3-dimethylbutane as shown below. It is impossible to define these as gauche or anti as long as we use the relations of methyl groups as the standard.

　A systematic nomenclature was proposed which could be applicable to such complex cases. For a four-atom system A-C1-C2-B, a tortion angle q (23) is defined. Atoms C1 and C2 may be other types of atoms, but for simplicity we take these two as carbon atoms.

The definition of tortion angle is as follows.

  • 1) We look the molecule from C1-C2 axis as shown in 23
  • 2) Rotate A-C1bond so that A overlaps B.
  • 3) The tortion angle is defined as the necessary angle of rotation to overlap A with B.
  • 4) The tortion angle is positive if the required rotation is clockwise, and negative if the rotation is anticlockwise.

　It is important to notice that the tortion angle has a sign while dihedral angle is not. We shall use tortion angle as far as possible in this textbook.

Ligands A and B are chosen from the ligands bonded to C1and C2, respectively

  • 1) If all three ligands are different, the priority is determined by the sequence rule.
  • 2) If two ligands are identical, the rest is chosen regardless of the priority based on the sequence rule.
  • 3) If three ligands are identical, the one associated with the smallest tortion angle is chosen.

　In practice, the tortion angle of ethane derivatives is not necessarily a multiple of 60o. Hence, the value of tortion angle itself is not included in the stereochemical names. A circle (tortion angle = 360o) is divided into several sections as is shown in 24-26, and each section is given a name. By combining these names, a system of nomenclature of ethane derivatives is formed. The upper half of the circle is syn region, and the lower half is anti region (cf. 25). The p of 26 stands for periplanar region, and c for clinal region. By combining these regions, you can obtain 27. The essence of this nomenclature will be summarized in ▶S2.5.

▶Back to Q2.8 as necessary

▶go to S2.5 The stereochemical nomenclature based on the rotation about a single bond