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;
- The sum of all diatomic bond stretches (each expressed as
a simple Hookes law potential).
- The sum of all triatomic bond angle deformations (also a
simple Hookes law potential)
- The sum of all tetra-atomic bond torsions (a cosine
dependance)
- The sum of all non-bonded Van der Waals repulsions (using
a simple 6/12 potential).
- 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.