The use of plastic or metal molecular models is an indispensable tool in attempting to understand the many subtle three dimensional effects in chemical reactivity. Such model are particularly useful in studying properties such as molecular strain, steric effects, stereoselectivity, conformation etc in a relatively qualitative manner. Frequently however, one encounters more quantitative questions. Which of two molecules is the more strained? Which face of a molecule is the more hindered? What is the most stable molecular conformation? What is the distance between two atoms or the dihedral angle between two vicinal hydrogens in a molecule? Plastic models can only provide very limited answers to such questions, and a more quantitative treatment has to be used. In theory, one such treatment might be to solve the Schroedinger wave equation for the molecule in question to the desired level of accuracy. Unfortunately, the "desired accuracy" for many of the phenomena noted above is of the order of 4 - 20 kJ/mol, and even for quite simple molecules this can be prohibitive in terms of computer time.

It has been frequently noted however that several molecular properties can be accurately expressed in terms of a summation of individual bond properties, without the need to explicitly solve any wave equations. Studying such molecular properties in terms of non-quantum mechanical models has become known as the Molecular Mechanics approach (MM). Briefly, MM assumes that the energy of a molecular system comprises essentially five additive, and non-interacting, terms. These are;

  1. The sum of all diatomic bond stretches (each expressed as a simple Hookes law potential).
  2. The sum of all triatomic bond angle deformations (also a simple Hookes law potential)
  3. The sum of all tetra-atomic bond torsions (a cosine dependance)
  4. The sum of all non-bonded Van der Waals repulsions (using a simple 6/12 potential).
  5. The sum of all electrostatic attractions of individual bond dipoles.
Each of these functions are mathematically extremely simple and computationally fast to evaluate, provided one has access to simple parameters such as stretching force constants, bond dipole moments, etc. The total energy is simply summed over all these terms. Clearly, terms 1-3 will account for any strain present in the system, term 4 expresses steric repulsion and term 5 covers hydrogen bonding etc. For a specified molecular system, the MM model strives to minimise this total energy, by adjusting all the bond lengths, angles, and torsion angles (which together allow for all the possible 3N-6 degrees of freedom in the molecule). This process is the mathematical equivalent of actually bending bits of plastic etc together in order to construct your model.

The types of information that this model is capable of giving you include the optimised molecular geometry of a particular conformation, the final total energy (in kJ/mol) and an analysis of this energy in terms of strain, steric effects etc. Such information is capable of providing answers to the questions posed at the start of this introduction. However, if the "bonds" in a molecule cannot be simply related to much simpler diatomic species, ie as in non-classical species such as norbornyl cation, diborane, even aromatic systems, then all the above additivity no longer applies. For this reason, molecular mechanics works best for simple hydrocarbons bearing possibly just a few substituents. Clearly it is also inapplicable for studying reactions, when the breaking of bonds is involved. In this event one has to resort to solving the full wavefunction for the molecular system, although the method can be used for modelling the transition state of the reaction. In this experiment, you will be using the most popular implementation of the MM model, due to Allinger and known as MM2.