《有机化学》课程教学资源（教材文献，英文版）CHAPTER 3 CONFORMATIONS OF ALKANES AND CYCLOALKANES

CHAPTER THREE Conformations of Alkanes and Cycloalkanes FIGURE 3.5 Distribution of molecular energies. (a) The r of molecules with temperature(T)) energy greater than Eact at area.( b)At some high temperature T2, the shape of the energy distribution emperature(T2) curve is different, and more molecules have energies in excess of eact. Energy 3.2 CONFORMATIONAL ANALYSIS OF BUTANE The next alkane that we examine is butane. In particular, we consider conforma- tions related by rotation about the bond between the middle two carbons (CH3CH2-CH2CH3) Unlike ethane, in which the staggered conformations are equiva lent, two different staggered conformations occur in butane, shown in Figure 3.6. The methyl groups are gauche to each other in one, anti in the other. Both conformations ar staggered, so are free of torsional strain, but two of the methyl hydrogens of the gauche conformation lie within 210 pm of each other. This distance is less than the sum of their an der Waals radii(240 pm), and there is a repulsive force between them. The desta- bilization of a molecule that results when two of its atoms are too close to each other is FIGURE 3. 6 The gauche and anti conforma and as Newman projections right). The gauche confor- mation is less stable than the anti because of the van de Waals strain between the methyl groups. Back Forward Main MenuToc Study Guide ToC Student o MHHE Website

3.2 CONFORMATIONAL ANALYSIS OF BUTANE The next alkane that we examine is butane. In particular, we consider conforma￾tions related by rotation about the bond between the middle two carbons (CH3CH2±CH2CH3). Unlike ethane, in which the staggered conformations are equiva￾lent, two different staggered conformations occur in butane, shown in Figure 3.6. The methyl groups are gauche to each other in one, anti in the other. Both conformations are staggered, so are free of torsional strain, but two of the methyl hydrogens of the gauche conformation lie within 210 pm of each other. This distance is less than the sum of their van der Waals radii (240 pm), and there is a repulsive force between them. The desta￾bilization of a molecule that results when two of its atoms are too close to each other is 94 CHAPTER THREE Conformations of Alkanes and Cycloalkanes Fraction of molecules having a particular energy Low temperature (T1) High temperature (T2) Eact Energy FIGURE 3.5 Distribution of molecular energies. (a) The number of molecules with energy greater than Eact at temperature T1 is shown as the darker-green shaded area. (b) At some higher temperature T2, the shape of the energy distribution curve is different, and more molecules have energies in excess of Eact. CH3 CH3 H H H H CH3 CH3 H H H H FIGURE 3.6 The gauche and anti conforma￾tions of butane shown as ball-and-spoke models (left) and as Newman projections (right). The gauche confor￾mation is less stable than the anti because of the van der Waals strain between the methyl groups. Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website

informational Analysis of Butane called van der Waals strain, or steric hindrance and contributes to the total steric strain. In the case of butane, van der Waals strain makes the gauche conformation approx- imately 3.2 kJ/mol(0. 8 kcal/mol) less stable than the anti. Figure 3. 7 illustrates the potential energy relationships among the various confor- mations of butane. The staggered conformations are more stable than the eclipsed. At any instant, almost all the molecules exist in staggered conformations, and more are present in the anti conformation than in the gauche. The point of maximum potential energy lies some 25 kJ/mol(6. 1 kcal/mol) above the anti conformation. The total strain in this structure is approximately equally divided between the torsional strain associated with three pairs of eclipsed bonds(12 kJ/mol: 2.9 kcal/mol) and the van der Waals strain between the methyl groups PROBLEM 3.3 Sketch a potential energy diagram for rotation around a car bon-carbon bond in propane. Clearly identify each potential energy maximum and minimum with a structural formula that shows the conformation of propane It that point. Does your diagram more closely resemble that of ethane or of butane? Would you expect the activation energy for bond rotation in propane to be more than or less than that of ethane? of butane? 大丈 15金 FIGURE 3.7 Potential energy diagram for rotation around the central carbon-carbon bond n butane Back Forward Main MenuToc Study Guide ToC Student o MHHE Website

called van der Waals strain, or steric hindrance and contributes to the total steric strain. In the case of butane, van der Waals strain makes the gauche conformation approx￾imately 3.2 kJ/mol (0.8 kcal/mol) less stable than the anti. Figure 3.7 illustrates the potential energy relationships among the various confor￾mations of butane. The staggered conformations are more stable than the eclipsed. At any instant, almost all the molecules exist in staggered conformations, and more are present in the anti conformation than in the gauche. The point of maximum potential energy lies some 25 kJ/mol (6.1 kcal/mol) above the anti conformation. The total strain in this structure is approximately equally divided between the torsional strain associated with three pairs of eclipsed bonds (12 kJ/mol; 2.9 kcal/mol) and the van der Waals strain between the methyl groups. PROBLEM 3.3 Sketch a potential energy diagram for rotation around a car￾bon–carbon bond in propane. Clearly identify each potential energy maximum and minimum with a structural formula that shows the conformation of propane at that point. Does your diagram more closely resemble that of ethane or of butane? Would you expect the activation energy for bond rotation in propane to be more than or less than that of ethane? Of butane? 3.2 Conformational Analysis of Butane 95 Potential energy, kcal/mol 3 kJ/mol 6 5 4 3 2 1 0 Potential energy, kJ/mol 25 20 15 10 5 0 0 60 120 180 240 300 360 Torsion angle,
14 kJ/mol FIGURE 3.7 Potential energy diagram for rotation around the central carbon–carbon bond in butane. Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website

CHAPTER THREE Conformations of Alkanes and Cycloalkanes MOLECULAR MECHANICS APPLIED TO ALKANES AND CYCLOALKANES f the numerous applications of computer Nonbonded interactions are the forces be technology to chemistry, one that has been tween atoms that aren't bonded to one another; enthusiastically embraced by organic chemists they may be either attractive or repulsive. It often examines molecular structure from a perspective sim- happens that the shape of a molecule may cause two ilar to that gained by manipulating molecular models atoms to be close in space even though they are sep- but with an additional quantitative dimension. Mo- arated from each other by many bonds. Induced- ecular mechanics is a computational method that dipole/induced-dipole interactions make van der allows us to assess the stability of a molecule by com- Waals forces in alkanes weakly attractive at most dis- paring selected features of its structure with those of tances, but when two atoms are closer to each other ideal "unstrained" standards. molecular mechanics than the sum of their van der waals radii makes no attempt to explain why the van der Waals nuclear-nuclear and electron-electron repulsive radius of hydrogen is 120 pm, why the bond angles in forces between them dominate the evan der waals term methane are 109.5, why the C-C bond distance in The resulting destabilization is called van der Waals ethane is 153 pm, or why the staggered conforma- strain tion of ethane is 12 k/mol more stable than the At its most basic level, separating the tota eclipsed, but instead uses these and other experi- strain of a structure into its components is a qualita nental observations as benchmarks to which the cor- tive exercise. For example, a computer-drawn model responding features of other substances are com- of the eclipsed conformation of butane using ideal bond angles and bond distances( Figure 3.8) reveals If we assume that there are certain"ideal"val- that two pairs of hydrogens are separated by ues for bond angles, bond distances, and so on, it fol- a distance of only 175 pm, a value considerably lows that deviations from these ideal values will smaller than the sum of their van der Waals radii destabilize a particular structure and increase its po-(2 120 pm 240 pm). Thus, this conformation is tential energy. this increase in potential energy is re- destabilized not only by the torsional strain associ- ferred to as the strain energy of the structure. other ated with its eclipsed bonds but also by van der terms include steric energy and steric strain Arith- Waals strain metically, the total strain energy(Es)of an alkane or At a higher level, molecular mechanics is ap. cycloalkane can be considered as plied quantitatively to strain energy calculations. Each component of strain is separately described by a Es= Bond stretching Eangle bending Torsional mathematical expression developed and refined so that it gives solutions that match experimental obser vations for reference molecules. These empirically d rived and tested expressions are then used to calcu- Bond stretching is the strain that results when C-c late the most stable structure of a substance. The and C-H bond distances are distorted from various structural features are interdependent; van their ideal values of 153 pm and 111 pm, re- der Waals strain, for example, might be decreased at the expense of introducing some angle strain, tor Anole bending is the strain that results from the ex- sional strain, or both. The computer program normal values of 109.5 for sp hybridized ces,torsion angles, and nonbonded interac carbon tions that gives the molecule the lowest total strain Torsional is the strain that results from deviation of This procedure is called strain energy minimization torsion angles from their stable staggered rela- and is based on the commonsense notion that the tionship most stable structure is the one that has the least straIn Evan der waals is the strain that results from"non- bonded interactions -Cont Back Forward Main MenuToc Study Guide ToC Student o MHHE Website

96 CHAPTER THREE Conformations of Alkanes and Cycloalkanes MOLECULAR MECHANICS APPLIED TO ALKANES AND CYCLOALKANES Of the numerous applications of computer technology to chemistry, one that has been enthusiastically embraced by organic chemists examines molecular structure from a perspective sim￾ilar to that gained by manipulating molecular models but with an additional quantitative dimension. Mo￾lecular mechanics is a computational method that allows us to assess the stability of a molecule by com￾paring selected features of its structure with those of ideal “unstrained” standards. Molecular mechanics makes no attempt to explain why the van der Waals radius of hydrogen is 120 pm, why the bond angles in methane are 109.5°, why the C±C bond distance in ethane is 153 pm, or why the staggered conforma￾tion of ethane is 12 kJ/mol more stable than the eclipsed, but instead uses these and other experi￾mental observations as benchmarks to which the cor￾responding features of other substances are com￾pared. If we assume that there are certain “ideal” val￾ues for bond angles, bond distances, and so on, it fol￾lows that deviations from these ideal values will destabilize a particular structure and increase its po￾tential energy. This increase in potential energy is re￾ferred to as the strain energy of the structure. Other terms include steric energy and steric strain. Arith￾metically, the total strain energy (Es) of an alkane or cycloalkane can be considered as Es Ebond stretching  Eangle bending  Etorsional  Evan der Waals where Ebond stretching is the strain that results when C±C and C±H bond distances are distorted from their ideal values of 153 pm and 111 pm, re￾spectively. Eangle bending is the strain that results from the ex￾pansion or contraction of bond angles from the normal values of 109.5° for sp3 hybridized carbon. Etorsional is the strain that results from deviation of torsion angles from their stable staggered rela￾tionship. Evan der Waals is the strain that results from “non￾bonded interactions.” Nonbonded interactions are the forces be￾tween atoms that aren’t bonded to one another; they may be either attractive or repulsive. It often happens that the shape of a molecule may cause two atoms to be close in space even though they are sep￾arated from each other by many bonds. Induced￾dipole/induced-dipole interactions make van der Waals forces in alkanes weakly attractive at most dis￾tances, but when two atoms are closer to each other than the sum of their van der Waals radii, nuclear–nuclear and electron–electron repulsive forces between them dominate the Evan der Waals term. The resulting destabilization is called van der Waals strain. At its most basic level, separating the total strain of a structure into its components is a qualita￾tive exercise. For example, a computer-drawn model of the eclipsed conformation of butane using ideal bond angles and bond distances (Figure 3.8) reveals that two pairs of hydrogens are separated by a distance of only 175 pm, a value considerably smaller than the sum of their van der Waals radii (2  120 pm 240 pm). Thus, this conformation is destabilized not only by the torsional strain associ￾ated with its eclipsed bonds, but also by van der Waals strain. At a higher level, molecular mechanics is ap￾plied quantitatively to strain energy calculations. Each component of strain is separately described by a mathematical expression developed and refined so that it gives solutions that match experimental obser￾vations for reference molecules. These empirically de￾rived and tested expressions are then used to calcu￾late the most stable structure of a substance. The various structural features are interdependent; van der Waals strain, for example, might be decreased at the expense of introducing some angle strain, tor￾sional strain, or both. The computer program searches for the combination of bond angles, dis￾tances, torsion angles, and nonbonded interac￾tions that gives the molecule the lowest total strain. This procedure is called strain energy minimization and is based on the commonsense notion that the most stable structure is the one that has the least strain. —Cont. Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website

3.3 Conformations of Higher Alkanes The first widely used molecular mechanics pro- that molecular mechanics is no longer considered a gram was developed by Professor N L Allinger of the novelty but rather as one more tool to be used by the University of Georgia and was known in its various practicing organic chemist. They have been joined by versions as MM2, MM3, and so on. they have been re- programs that calculate the energies of conforma- fined to the extent that many structural features can tions by molecular orbital methods. The Learning by be calculated more easily and more accurately than Modeling CD that accompanies this text contains hey can be measured experimentally molecular mechanics software that lets you seek out Once requiring minicomputers and worksta. the most stable conformation of the structures you tions, many molecular mechanics programs are avail- assemble. It also contains the most stable conforma- strain energy calculations can provide is so helpful orbital calculations les as determined by molecular FIGURE 3.8 Ball-and-spoke and space-filling models of methyl-methyl eclipsed conformation of butane. 3.3 CONFORMATIONS OF HIGHER ALKANES Higher alkanes having unbranched carbon chains are like butane most stable in their all-anti conformations. The energy difference between gauche and anti conformations is similar to that of butane, and appreciable quantities of the gauche conformation are present in liquid alkanes at 25C. In depicting the conformations of higher alkanes it is often more helpful to look at them from the side rather than end-on as in a Newman projection. Viewed from this perspective, the most stable conformations of pentane and hexane have their carbon ""backbones"arranged in a zigzag fashion, as shown in Figure 3.9. All the bonds are staggered, and the chains are characterized by anti arrangements 68 Hexane FIGURE 3.9 Ball-and-spoke models of pentane and hexane in their all-anti (zigzag)con- Back Forward Main MenuToc Study Guide ToC Student o MHHE Website

3.3 Conformations of Higher Alkanes 97 The first widely used molecular mechanics pro￾gram was developed by Professor N. L. Allinger of the University of Georgia and was known in its various versions as MM2, MM3, and so on. They have been re- fined to the extent that many structural features can be calculated more easily and more accurately than they can be measured experimentally. Once requiring minicomputers and worksta￾tions, many molecular mechanics programs are avail￾able for personal computers. The information that strain energy calculations can provide is so helpful that molecular mechanics is no longer considered a novelty but rather as one more tool to be used by the practicing organic chemist. They have been joined by programs that calculate the energies of conforma￾tions by molecular orbital methods. The Learning By Modeling CD that accompanies this text contains molecular mechanics software that lets you seek out the most stable conformation of the structures you assemble. It also contains the most stable conforma￾tions of some molecules as determined by molecular orbital calculations. 3.3 CONFORMATIONS OF HIGHER ALKANES Higher alkanes having unbranched carbon chains are, like butane, most stable in their all-anti conformations. The energy difference between gauche and anti conformations is similar to that of butane, and appreciable quantities of the gauche conformation are present in liquid alkanes at 25°C. In depicting the conformations of higher alkanes it is often more helpful to look at them from the side rather than end-on as in a Newman projection. Viewed from this perspective, the most stable conformations of pentane and hexane have their carbon “backbones” arranged in a zigzag fashion, as shown in Figure 3.9. All the bonds are staggered, and the chains are characterized by anti arrangements of C±C±C±C units. Pentane Hexane FIGURE 3.8 Ball-and-spoke and space-filling models of methyl-methyl eclipsed conformation of butane. FIGURE 3.9 Ball-and-spoke models of pentane and hexane in their all-anti (zigzag) con￾formations. Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website

CHAPTER THREE Conformations of Alkanes and Cycloalkanes 3. 4 THE SHAPES OF CYCLOALKANES: PLANAR OR NONPLANAR? During the nineteenth century it was widely believed--incorrectly, as we'lI soon see- that cycloalkane rings are planar. A leading advocate of this view was the German chemist Adolf von Baeyer. He noted that compounds containing rings other than those based on cyclopentane and cyclohexane were rarely encountered naturally and were dif- ficult to synthesize. Baeyer connected both observations with cycloalkane stability, which he suggested was related to how closely the angles of planar rings match the tetrahedral value of 109.5. For example, the 60 bond angle of cyclopropane and the 90 bond angles of a planar cyclobutane ring are much smaller than the tetrahedral angle of 109.5 Baeyer suggested that three- and four-membered rings suffer from what we now call angle strain. Angle strain is the strain a molecule has because one or more of its bond angles deviate from the ideal value; in the case of alkanes the ideal value is 109.5 Although better known now According to Baeyer, cyclopentane should be the most stable of all the cycloal rrect theory that kanes because the ring angles of a planar pentagon, 1080, are closer to the tetrahedra e plan Baeyer was responsible for angle than those of any other cycloalkane. A prediction of the Baeyer strain theory notable advances in the that the cycloalkanes beyond cyclopentane should become increasingly strained and cor respondingly less stable. The angles of a regular hexagon are 1200, and the angles of larger polygons deviate more and more from the ideal tetrahedral angle warded the 1905 Nobel Prize in chemistry for his Some of the inconsistencies in the Baeyer strain theory will become evident as ork in that area use heats of combustion (Table 3. 1)to probe the relative energies of cycloalkanes most important column in the table is the heat of combustion per methylene(CH2) group Since all of the cycloalkanes have molecular formulas of the type CnH2n. dividing the heat of combustion by n allows direct comparison of ring size and potential energy Cyclopropane has the highest heat of combustion per methylene group, which is con- sistent with the idea that its potential energy is raised by angle strain. Cyclobutane has less angle strain at each of its carbon atoms and a lower heat of combustion per meth- ylene group. Cyclopentane, as expected, has a lower value still Notice, however, that ontrary to the prediction of the Baeyer strain theory, cyclohexane has a smaller heat of combustion per methylene group than cyclopentane. If bond angle distortion were greater in cyclohexane than in cyclopentane, the opposite would have been observed TABLE 3.1 Heats of Combustion(-AHo)of Cycloalkanes Heat of combustion Heat of combustion per CH2 group Number of Cycloalkane CH2 groups kJ/mol (kcal/mol) kJ/mol (kcal/mol) Cyclo (499.8) 697 (166.6) Cyclobutane (650.3) 681 1627) Cyclopentane 3.291 (786.6 658 (157.3) Cyclohexane 3.920 (936.8) 653 (156.0 Cycloheptane 3456789 599(1099.2) 657 (157.0) Cyclooctane 5,26712588) 658 (157.3) Cyclononane 5933(14180) 659 (157.5) Cyclodecane 659 (157.5) Cycloundecane 7,237(17298 658 (157.3) Cyclododecane 7,845(1875.1) 654 (156.3) Cyclotetradecane 9139(2184.2) 653 (156.0) Cyclohexadecane 10.46 (2501.4) 654 (156.3) Back Forward Main MenuToc Study Guide ToC Student o MHHE Website

3.4 THE SHAPES OF CYCLOALKANES: PLANAR OR NONPLANAR? During the nineteenth century it was widely believed—incorrectly, as we’ll soon see— that cycloalkane rings are planar. A leading advocate of this view was the German chemist Adolf von Baeyer. He noted that compounds containing rings other than those based on cyclopentane and cyclohexane were rarely encountered naturally and were dif- ficult to synthesize. Baeyer connected both observations with cycloalkane stability, which he suggested was related to how closely the angles of planar rings match the tetrahedral value of 109.5°. For example, the 60° bond angle of cyclopropane and the 90° bond angles of a planar cyclobutane ring are much smaller than the tetrahedral angle of 109.5°. Baeyer suggested that three- and four-membered rings suffer from what we now call angle strain. Angle strain is the strain a molecule has because one or more of its bond angles deviate from the ideal value; in the case of alkanes the ideal value is 109.5°. According to Baeyer, cyclopentane should be the most stable of all the cycloal￾kanes because the ring angles of a planar pentagon, 108°, are closer to the tetrahedral angle than those of any other cycloalkane. A prediction of the Baeyer strain theory is that the cycloalkanes beyond cyclopentane should become increasingly strained and cor￾respondingly less stable. The angles of a regular hexagon are 120°, and the angles of larger polygons deviate more and more from the ideal tetrahedral angle. Some of the inconsistencies in the Baeyer strain theory will become evident as we use heats of combustion (Table 3.1) to probe the relative energies of cycloalkanes. The most important column in the table is the heat of combustion per methylene (CH2) group. Since all of the cycloalkanes have molecular formulas of the type CnH2n, dividing the heat of combustion by n allows direct comparison of ring size and potential energy. Cyclopropane has the highest heat of combustion per methylene group, which is con￾sistent with the idea that its potential energy is raised by angle strain. Cyclobutane has less angle strain at each of its carbon atoms and a lower heat of combustion per meth￾ylene group. Cyclopentane, as expected, has a lower value still. Notice, however, that contrary to the prediction of the Baeyer strain theory, cyclohexane has a smaller heat of combustion per methylene group than cyclopentane. If bond angle distortion were greater in cyclohexane than in cyclopentane, the opposite would have been observed. 98 CHAPTER THREE Conformations of Alkanes and Cycloalkanes TABLE 3.1 Heats of Combustion (H°) of Cycloalkanes Heat of combustion per CH2 group Cycloalkane Cyclopropane Cyclobutane Cyclopentane Cyclohexane Cycloheptane Cyclooctane Cyclononane Cyclodecane Cycloundecane Cyclododecane Cyclotetradecane Cyclohexadecane Number of CH2 groups 3 4 5 6 7 8 9 10 11 12 14 16 Heat of combustion kJ/mol 2,091 2,721 3,291 3,920 4,599 5,267 5,933 6,587 7,237 7,845 9,139 10,466 (kcal/mol) (499.8) (650.3) (786.6) (936.8) (1099.2) (1258.8) (1418.0) (1574.3) (1729.8) (1875.1) (2184.2) (2501.4) kJ/mol 697 681 658 653 657 658 659 659 658 654 653 654 (kcal/mol) (166.6) (162.7) (157.3) (156.0) (157.0) (157.3) (157.5) (157.5) (157.3) (156.3) (156.0) (156.3) Although better known now for his incorrect theory that cycloalkanes were planar, Baeyer was responsible for notable advances in the chemistry of organic dyes such as indigo and was awarded the 1905 Nobel Prize in chemistry for his work in that area. Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website