Page 188 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

168 attractive as the separation approaches the sum of their van der Waals radii, but then
becomes strongly repulsive as the separation becomes less than the sum of their van
CHAPTER 2
der Waal radii. The attractive interaction results from a mutual polarization of the
Stereochemistry, electrons of the atoms. Such attractive forces are called London forces or dispersion
Conformation,
and Stereoselectivity forces and are relatively weak interactions. London forces vary inversely with the
sixth power of internuclear distance and become negligible as internuclear separation
increases. At distances smaller than the sum of the van der Waals radii, the much
stronger electron-electron repulsive forces are dominant. Electrostatic forces must take
into account bond dipoles and their orientation. Bond dipoles also have a polarizing
effect on adjacent groups. 89
The separation of the total strain energy into component elements of bond length
strain, bond angle strain, torsional strain, and nonbonded interactions is useful for
analysis of structural and steric effects on equilibria and reactivity. Minimization of
the total strain energy of a molecule, expressed by a parameterized equation for each
of the force fields, can be accomplished by iterative computation. The quantitative
application of molecular mechanics for calculation of minimum energy geometries,
heats of formation, and strain energies has been developed to a high level of reliability.
The method has been refined to the point that geometries of saturated hydrocarbons

can be calculated to an accuracy of 0.005 Å in bond length and 1 in bond angle. 90
Similar accuracy can be obtained for unsaturated hydrocarbons 91 and molecules with
oxygen functional groups. 92 Molecular mechanics calculations can also be applied to
unstable reactive intermediates such as carbocations. 93
The molecular mechanics computations can be done using commercially available
programs. The parameters used in the programs determine the range of applicability
and reliability of the results. Several systems of parameters and equations for carrying
out the calculations have been developed. The most frequently used methods in organic
chemistry are those developed by N. L. Allinger and co-workers and is frequently
referred to as MM (molecular mechanics) calculations. 94 The most recent version is
called MM4. 95 The computations involve iterations to locate an energy minimum.
Precautions must be taken to establish that a true (“global”) minimum, as opposed
to a local minimum energy, has been achieved. This can be accomplished by using
a number of different initial geometries and comparing the structures and energies of
the minima that are located. In addition to comparing the relative energy of various
conformations of an individual molecule, MM computations can be used to calculate
total molecular energy (enthalpy of formation) to a high level of accuracy. Heats of
formation for most hydrocarbons are accurate to ±0 5kcal/mol. This application of
MM is discussed further in Section 3.1.2.4.

89 L. Dosen-Micovic, D. Jeremic, and N. L. Allinger, J. Am. Chem. Soc., 105, 1716, 1723 (1983);
B. Mannfors, K. Palmo, and S. Krimm, J. Mol. Struct., 556, 1 (2000).
90
N. L. Allinger, Y. H. Yuh, and J.-H. Lii, J. Am. Chem. Soc., 111, 8551 (1989); N. L. Allinger, K. Chen,
and J.-H. Lii, J. Comput. Chem., 17, 642 (1996).
91 N. Nevins, K. Chen, and N. L. Allinger, J. Comput. Chem., 17, 669 (1996); N. Nevins, J.-H. Lii, and
N. L. Allinger, J. Comput. Chem., 17, 695 (1996); N. Nevins and N. L. Allinger, J. Comput. Chem.,
17, 730 (1996).
92
C. H. Langley, J. H. Lii, and N. L. Allinger, J. Comput. Chem., 22, 1396, 1426, 1451 (2001).
93
B. Reindl, T. Clark, and P. v. R. Schleyer, J. Comput. Chem., 17, 1406 (1996); B. Reindl and
P. v. R. Schleyer, J. Comput. Chem., 18, 28 (1997); B. Reindl, T. Clark, and P. v. R. Schleyer, J. Comput.
Chem., 18, 533 (1997); B. Reindl, T. Clark, and P. v. R. Schleyer, J. Phys. Chem. A, 102, 8953 (1998).
94 N. L. Allinger, Y. H. Yuh and J.-H. Lii, J. Am. Chem. Soc., 111, 8551 (1989).
95
N. L. Allinger, K. S. Chen, and J. H. Lii, J. Comput. Chem., 17, 642 (1996).