Computational Chemistry

Etotal¼EstretchþEbendþEtorsion¼ 6 : 67 þ 0 þ 21 : 0 þ250 kJ mol$^1

¼277 kJ mol$^1

So the relative energies are calculated to be

Eðstructure 2Þ$Eðstructure 1Þ¼ 277 $344 kJ mol$^1 ¼$67 kJ mol$^1

This crude method predicts that stretching the central C/C bond of
2,2,3,3-tetramethylbutane from the approximately normalsp^3 –C–sp^3 –C length of
1.583 A ̊ (structure 1) to the quite “unnatural” length of 1.600 A ̊(structure 2) will
lower the potential energy by 67 kJ mol$^1 , and indicates that the drop in energy is
due very largely to the relief of nonbonded interactions. A calculation using
the accurate forcefield MM3 [ 12 ] gave an energy difference of 54 kJ mol$^1 between
a “standard” geometry approximately like structure 1, and afully optimized
geometry, which had a central C/C bond length of 1.576 A ̊. The surprisingly
good agreement is largely the result of a fortuitous cancellation of errors, but this
does not gainsay the fact that we have used our forcefield to calculate something
of chemical interest, namely the relative energy of two molecular geometries.
In principle, we could have found the minimum-energy geometry according
to this forcefield, i.e. we could have optimized the geometry (Chapter 2 ). Geometry
optimization is in fact the main use of MM, and modern programs employ analy-
tical first and second derivatives of the energy with respect to the geometric
coordinates for this (Chapter 2 ).

3.3 Examples of the Use of Molecular Mechanics

If we consider the applications of MM from the viewpoint of the goals of those who
use it, then the main applications have been:

1. To obtain reasonable input geometries for lengthier (ab initio, semiempirical or
   density functional) kinds of calculations.


2. To obtain good geometries (and perhaps energies) for small- to medium-sized
   molecules.


3. To calculate the geometries and energies of very large molecules, usually
   polymeric biomolecules (proteins and nucleic acids).


4. To generate the potential energy function under which molecules move, for
   molecular dynamics or Monte Carlo calculations.


5. As a (usually quick) guide to the feasibility of, or likely outcome of, reactions in
   organic synthesis.
   Examples of these five facets of the use of MM will be given.

60 3 Molecular Mechanics