1
Rotamers: Sawhorse and Newman
R
2
R
R
R1 R
Sawhorse Diagram
R
1
1
2
R1 1
R R
R R
R 2
Newman Projection
• Representation 1 is called a sawhorse diagram. • Representation 2 is called a Newman projection. • Both 1 and 2 are used to show the spatial relationship of the R groups and the R1 group. • Both the sawhorse diagram and the Newman projection are used to represent the relative spatial positions of R and R1 when there is rotation about the bond. • Note that the arrangement of R groups in both 1 and 2 is meant to represent a tetrahedral array, since each carbon is tetrahedral.
Drawing
staggered
eclipsed
More Drawing
Pretty, but wrong
This would be wrong
Ugly, and wrong
This would also be wrong
Rotamers: Rotation About C-C Single Bonds 1
R
R R
60°
R
3 RR
R 240°
120° 180°
R R 6 R R
1 RR 5
eclipsed
R
R
R R1
R RR
• The rotation is about the C–C bond, but the motion is followed by monitoring the position of the R1 group relative to the R groups. Why 60°? • The positions of the three R groups on the rear carbon or the front carbon are arranged to the corners of a tetrahedron. • The apex of each tetrahedron is the C–C bond, and the angle between the three other bonds is 120°. Bond rotations of 120°, or half that amount (60°), conveniently show if groups are closer to or further away from each other.
90°
270°
R1
RR1
R R
0° - 360°
7 R R 300°
R
• If 2 is used as a starting point, the R1 group on the "front" carbon (in red) appears to rotate in a clockwise direction through 360°, 60° at a time.
staggered
R R 2
RR
R R1
R
4
R
4
• Beginning with 2, rotation by 60° will generate a different-looking structure (3) where all of the bonds to groups overlap. • Another 60° rotation gives a structure 4 that looks like 2, but the R1 group is in a different spatial position. • Rotation in this manner, 60° at a time, generates several structures, eventually giving back 2 after rotation through 360°. • The 60° rotations generate structure where the R groups are as close together or as far apart as they can be.
Rotamers: Rotation About C-C Single Bonds 1
R
R R
R R 2
RR
R R1
R
0° - 360° 60°
7 R R 300°
R1
R
3 RR
90°
270°
R
RR1
R R
R 240°
120° 180°
R R 6 R R
R
R
R1
R RR
1 RR 5
R
R
4
5
• Although there are an infinite number of possible rotations, it is only necessary to focus on a few key structures. • Using the R1 group as a marker, it is close to a green R group (the bonds eclipse) in 3, 5 or 7. • Alternatively the R1 group is "in between" two green R groups (the bonds are staggered) in 2, 4 or 6. • If the R and R1 groups eclipse, they compete for the same space and repel one another. • This repulsion of groups that are close together in space is called steric hindrance. hindrance. • As rotation continues around the bond, more energy is required to bring those groups close together when they eclipse in order to force one past the other. • If the steric repulsion is too great, it constitutes a barrier that inhibits rotation. • This energy barrier is usually low enough that rotation continues, but it is hindered (slowed down) as the R and R1 groups sweep past each other. • The two cases, close together (eclipsed, 5) or far apart (staggered, 6), represent the maximum and minimum interactions for those groups.
Rotamers: Rotation About C-C Single Bonds 1
R
R R
R R 2
RR
R R1
R
0° - 360° 60°
7 R R 300°
R1
R
3 RR
90°
270°
R
RR1
R R
R 240°
120° 180°
R R 6 R R
R
R
R1
R RR
1 RR 5
R
R
4
6
• These structures show a "dynamic" rotation that occurs continuously, and each structure shown may be present for only a fleeting instant during the rotational vibration. • If each structure could be "frozen" at a particular rotation angle, slight differences in the spatial relationships of the atoms (their relative positions in three-dimensional space) can be examined. • Such imaginary "frozen" structures are called rotamers. • Rotation about carbon-carbon single bonds therefore generates many rotamers. • Looking at the entire molecule and selecting particular rotamers can define the relative positions of the constituent atoms in that structure. • A particular arrangement of all the atoms in space is known as a conformation for the molecule. • At normal temperatures, there is plenty of energy for rotation about carbon-carbon bonds, and organic molecules should be considered as dynamic species that have a large population of different rotamers.
Ethane: Sawhorse Diagrams H
H H
H H
H H
H
8
H
H
H
H
H H
0° - 360° 60°
300°
H
4
H H
90°
270°
H
• The simplest example of an organic molecule with one carbon-carbon bond is ethane (3), which is drawn as its sawhorse projection.
3
H
240°
7
120°
H H
H
H
180°
H
H H
H H 6
5 H
H
H H
• Focus on the C-C bond, where each carbon atom is attached to three hydrogen atoms. Imagine holding the "left" or "back" carbon atom and rotate around the bond by twisting the "right" or "front" carbon atom clockwise by 360° in increments of 60°. • This process generates several rotamers, 3-8, and the rotation can be followed by focusing on the red hydrogen atom.
H H
7
H H
• The most notable feature of 3, 5, and 7 is the observation that the hydrogen atoms on the front carbon are "in between" the hydrogen atoms on the back carbon atom. • These three are referred to as staggered rotamers. • In 4, 6, and 8, the hydrogen atoms on the front carbon overlap (eclipse) those on the back carbon. • These are referred to as eclipsed rotamers.
Ethane: Newman Projections
staggered H
H
H
H
0° - 360°
14 HH
H
H
H
300°
60°
270°
90°
240°
120° 180°
H
H H
13
HH
H H
H9
HH
H H
H
10 HH
H
H
H H H
HH
H H
11 H
HH 12
eclipsed
8
• In the Newman projection (2), the bond of interest is viewed "head-on" so that one carbon atom is in front and the second is in the rear, as shown. • In order to "see" both carbons, the atom in front is represented as a "dot" and the one in the rear is represented as a "circle" as described above. • Since each carbon is tetrahedral, the bonds radiate from these two carbons, three to the front and three to the rear. • The rotamers for ethane are repeated as Newman projections in Figure 8.3 (see 9-14). • Clockwise rotation around the carboncarbon bond for ethane is shown, generating rotamers 10-14 with Newman projection 9 as the starting point. • For convenience, the red hydrogen is again used as a marker to follow this rotation.
Ethane: Newman Projections
Low energy H
H
H
H
0° - 360°
14 HH
H
H
H
300°
60°
270°
90°
240°
120° 180°
H
H H
13
HH
H H
H9
HH
H H
H
10 HH
H
H
H H H
HH
H H
11 H
HH 12
High energy
9
• In the eclipsed rotamer, atoms are close together in space. • The bonds connecting the C-H units in 10 are closer together than they are in 9. • It is reasonable to assume that when these electrons are close in space there will be electronic repulsion (like charges repel). • The electronic repulsion due to overlap of bonds is called torsional strain. • Since the hydrogen atoms and the bonds in 10 repel, they are pushed away from each other, and it “costs” energy to keep them together. • This repulsive energy is sometimes called torsional energy, but more commonly the term torsional strain is used to indicate this energy in combination with the steric strain from above. • When the hydrogen atoms are staggered (9), torsional strain is minimal. • This means that the eclipsed rotamers are higher in energy than the staggered rotamers. • Rotamer 10 is higher in energy than rotamer 9, where the hydrogen atoms are further apart and do not repel.
10
Torsion Strain and Rotamer Energy 3
4B
Energy (kcal/mole)
2.5 2 1.5 1 0.5
3B
0 0
50
100 150 200 250 300 Angular Rotation
350
• To go from one staggered-rotamer to the next during the rotation, the molecule must pass through an eclipsed rotamer. • Since the eclipsed rotamer is higher in energy, there is an energy barrier to rotation that is measured to be 2.9 kcal mol–1 (13.95 kJ mol–1). • If the staggered-rotamer 9 is taken as the standard, the energy of the eclipsed rotamer (10) will be 2.9 kcal mol–1 (13.95 kJ mol–1) higher in energy than 9. • Rotamers 9 and 10 define the upper and lower energy limits for rotation around the carboncarbon bond. 8 It is possible to plot angular rotation of the bond versus the relative energy of each rotamer generated by that rotation. The resulting energy curve (note the relative positions of the red hydrogen atom) is essentially a "map" that defines the energy barriers to rotation and the magnitude of those barriers. It is clear that complete rotation around the carbon-carbon bond in ethane must generate three eclipsedrotamers, each with an energy barrier of 2.9 kcal mol–1 (13.95 kJ mol–1). • Rotation "slows down" when these eclipsed-rotamers are encountered, since each presents a barrier to rotation. • Rotation in ethane is therefore said to be "hindered" rather than "free."
Highest energy H H
Energy Diagram for Ethane
H H
H H
H H
3 H H
Energy (kcal/mole)
2.5
H H
H H
2 1.5 1
H
0.5 H
0 0 H
H
50
100 150 200 250 300 350 Angular Rotation
H
H
H
H
H
H
Lowest energy
12
Ethane: Molecular Models
staggered
3A
3B
4A
4B
eclipsed
3C
4C
Substituted Ethanes” Longer Chain Alkanes H X C H
H C 15
H H
H H H3C C C CH3 H 19 H
H X C H
H C
X
16 H
H H Cl C C H H 20 H
H Y C H
H C 17 H
H H Cl C C Cl H 21 H
X
H H H3 C C C H H 18 H H H Cl C C CH3 H 22 H
• Rotamers of substituted alkanes can be categorized into two fundamental types, X-C-C-H (15) and X-C-C-X (16) where rotation occurs about a single C-C bond, and X can be any substituent. • The interactions X and H or X and X are important, and it is assumed that the X-H interactions in the second case are much less. • If this analysis is extended slightly to include Y-C-C-X (17), then the Y-X steric interactions must be examined, assuming the X-H and Y-H interactions are much less. • This model means that ethane can be used as a standard for alkanes where the X-X interactions using 16 are H-H. • Other alkanes or compounds with substituents are treated as substituted ethane derivatives and the important interactions are X-X in 16 and X-Y in 17. • In propane (18), the Me-H interaction (X-Y) as well as the H-H interaction are important. In butane (19), the X-X interactions are Me-Me and H-H and the X-Y interaction is Me-H. • There are X-Y interactions in chloroethane (20), Cl-H,and in 1,2-dichloroethane (21) there are two X-X interactions (Cl-Cl and H-H) as well as a X-Y interaction (Cl-H). • In chloropropane (22) there are three X-Y interactions (Cl-Me, Cl-H and Me-H), as well as the X-X interaction (H-H). • As the number of atoms increases, the interactions increase.
13
Rotation in Longer Chain Alkanes: 23-26
H H
R
• A generic alkane is shown as its staggeredrotamer in Newman projection 23.
H
• Rotation of the indicated bond in 23 clockwise through 360°, 60° at a time, leads to a series of rotamers (follow the motion of the red R group relative to R1 in green) 23-28.
H R 23 1
RH
H H
HH
H R
0° - 360°
28 R1H
H
H
R
H
300°
60°
270°
90°
240°
120° 180°
H R1
27
H H
1 RH
R1R 26
24
• In 23 the R and R' groups are as far apart as possible, but rotation through 60ｰ gives an eclipsed rotamer (24) where R and R' do not eclipse each other, but R eclipses a H and R' eclipses a different hydrogen. • The eclipsing the bonds and atoms in 24 makes it higher in energy than 23.
H
H
H HH
14
H R
1
25 R
• Rotation by another 60° generates a staggered rotamer (25) that is different from 23 in that R and R' are closer together. • The steric and electronic repulsion that will make 25 higher in energy than 23. • There are no eclipsed bonds, so both 23 and 25 are lower in energy than 24. • The next 60° rotation generates an eclipsed rotamer (26) where R and R' completely eclipse each other and this is clearly the highest energy rotamer, higher than 25 and certainly higher than either staggered rotamer
Rotation in Longer Chain Alkanes: 26-23 H H
R
H
H R 23 1
HH
H R
0° - 360°
28 R1H
300°
270°
H
H
R
H
240° 180°
H R1
27
H H
HH R1R 26
15
• Rotamer 26 is an eclipsed rotamer, but it is higher in energy than eclipsed rotamers 24 and 28 since the R/R’ groups are eclipsed whereas in 24 and 28 R eclipses H and R’ eclipses H. • This higher energy eclipsed rotamer is known as the syn-rotamer, and it poses the highest energy RH H barrier to rotation in this molecule. H • When 26 is rotated by 60°, another staggered rotamer is obtained (27), which is the same 1 60° 24 energy as 25 when R and R’ are the same. RH • Another rotation by 60° generates another eclipsed rotamer (28), which also has a R-H and a R'-H interaction. 90° • A last 60° rotation completes the cycle to give 23 again. • Note that 23 is a staggered rotamer, but the H R/R’ groups are as far apart as possible. 120° H H • In staggered rotamers 25 and 27, the R/R’ groups are closer together in space than they are H R in 23. 1 • Therefore, 23 is the lowest energy staggered 25 R rotamer, and the groups are 180° apart. • For this reason, 23 is identified as the antirotamer. • To distinguish staggered rotamers 25 and 27 from 23, 25 and 27 are known as gauche rotamers.
Propane and Butane R H
H
H
H
60°
60°
15
H
H
H
R
H
60°
60°
R R
R1R
17
18
HH
H R
R
R1H
19
20
1
HH
H H
1
16 H
H
H R1H
R1
60°
H
RH
H H
R 60°
H
H
H
H 1
R
15
Lower energy
C1-C2
