Concise Physical Chemistry

c19 JWBS043-Rogers September 13, 2010 11:29 Printer Name: Yet to Come

308 CLASSICAL MOLECULAR MODELING

C C C C

C

C

FIGURE 19.3 Structurally distinct alkane conformers resulting from the tetrahedral sym-

metry of carbon.

of tetrahedral symmetry about all C atoms, we soon find that our models include

numerousconformersof the higher members of the alkane series.

We have the force constantskf of the C H bond from spectroscopic studies

(Sections 18.1 and 18.2). Using these force constants, we can relieve the arbitrary

nature of the C H bond lengths in CH 4 by starting at some reasonable value for the

bond lengthrand calculating the energy of the CH 4 molecule. The result will be, no

doubt, very high. Making systematic small changes inr(Problem 18.4) and repeating

the process, perhaps many times, the calculated energy can be brought to a minimum

value. At the optimum bond length, each H atom is as close as it can get to the bottom

of its Hooke’s law potential well while still respecting its neighbors. In optimizingE,

we have also optimizedr. This is the best value of the C H bond length in methane

we can get from the Hooke’s law force parameterkfwe have chosen.

This raises the question of the best force parameter we can choose. Will it be

exactly the spectroscopic constant? What if there is no spectroscopic constant? Ex-

perience has shown that all things considered, the best MM force parameters express

knowledge derived by fitting bond lengths and stretching energies to spectroscopy,

thermodynamics, X-ray crystallography, and that old favorite “chemical intuition.”^1

MMparametershave evolved away from spectroscopic forceconstants;thetwoare

not the same. MM parameters can be proposed, and then they can be revised in the

light of new experimental results. Spectroscopic force constants are determined by

a specific category of experiments. They can be made more accurate, but they do

not change.

We now have the tetrahedral bond angles and the bond lengths of CH 4 .Fromthis

we can express the structure of CH 4 in Cartesian coordinate locations of all of the

atoms in the molecule. There is nothing more we can know about the geometry of CH 4.

The method can be elaborated to determine the complete MM structure of any

molecule, provided that we have the force parameters for all of the structural forces

in the molecule.

There is the rub. It turns out that there are many subtle forces operative in molecules

larger than CH 4. It is the task of anyone who wishes to find the structure of a complex

molecule to seek out all of the forces within it and to determine the force parameters

of the stretch, bend, torsional deformations, van der Waals, or other interactions. One

is not advised to attempt this daunting task. Fortunately, N. L. Allinger and coworkers

(^1) “Chemical intuition” is not as silly as it sounds. Like the scriptures, it is the accumulated knowledge of
very many years of observation and experience.