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 Website96 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