INTRODUCTION

There is no substitute for practical laboratory experience, but computer modelling methods play an important role both as an aid in interpreting experimental results and as a means of explaining these results. Molecular modelling is now used not just in chemistry but in a wide range of subjects such as pharmacology and mineralogy. Figure 1.1, for example, shows a computer model of the protein haemoglobin.

One example of the computer modelling approach is to provide a reasonably accurate first guess at a structure which can then be used in methods such as X-ray diffraction of powders which, unlike the X-ray diffraction of single crystals, do not provide enough information to determine the total structure from scratch.

In the field of drug design, computer methods have been used to screen for potentially active compounds or suggest modifications of known compounds that would be more active. Testing of inactive compounds can be avoided.

Zeolites and other structures with cages or channels will accommodate some molecules at the expense of others. Modelling of these structures has enabled planned synthesis of required molecules by predicting the cavity needed to produce the molecule.

There are areas of chemistry where it is difficult or impossible to obtain experimental results. A good example of this is the determination of the nature of reaction intermediates in chemical kinetics. In favourable cases, reaction intermediates can be studied spectroscopically using specialized techniques that allow observations on a very short time-scale of the order 10-9; 10-15 seconds.

However, in the majority of cases, the path of a reaction is inferred from the stereochemistry or distribution of products and the effect of changing reaction conditions such as the polarity of the solvent. Modern computational techniques allow us to follow a reaction path. In solids very simple techniques can be used to find the most favourable path for diffusion of ions. At the other extreme, very sophisticated and accurate molecular orbital techniques can calculate the energy along the entire reaction path from reactant(s) to productls) for gas phase reactions of small molecules. More often modelling is used to calculate the relative stabilities of proposed intermediates.

It is possible to model molecules or structures that only exist at high temperatures and/or high pressures or are too dangerous to handle. Theoretical methods have been used, for example, to predict that at the temperatures and pressures in the interior of the planet Jupiter (Figure 1.2), hydrogen can exist as a liquid metal. Conditions under which such a form of hydrogen would occur were not achieved experimentally on Earth until 1996.

You are going to look in this Book at some of the methods used to model molecules and at the principles behind them. On the CD-ROM, you will study some examples.

We start by looking at a simple, but surprisingly effective, model that is based on a picture of molecules as charged spheres linked by springs.

MOLECULAR MECHANICS

Molecular mechanics has proved particularly useful for studying large molecules and crystalline solids where more accurate methods are very demanding of computer resources.

We shall look at the principles behind this method by considering some examples. First we consider a simple ionic solid, then move to an example where some allowance for covalency is required. Finally we consider the modelling of organic molecules.

2.1 Ionic solids

The starting point for the application of molecular mechanics to ionic solids is similar to the starting point for lattice energy calculations. Indeed the method can be used to calculate lattice energies, but it is also used to study the effect of defects, the nature of crystal surfaces and properties of crystals.

As for lattice energies, we start by placing the ions of the crystal on their lattice sites.

* What is the force holding ions together in a crystal?

* Electrostatic attraction between the positively- and negatively-charged ions.

The ions are assumed to be on their lattice sites with their formal charges, so that in NaCl, for example, we have an array of Na+ and Cl- ions. The net interaction can be obtained by summing the interactions over all the pairs of ions, including not only the attraction between Na+ and Cl- but also the repulsion between ions of the same sign. The net interaction decreases with distance but slowly so that it is difficult to obtain an accurate value.

To calculate lattice energies, this summation can be achieved for simple lattice structures by introducing the Madelung constant. However, for layer structures with low symmetry this approach is not feasible, as a single Madelung constant will not suffice. Since the computer programs in use are set up to be of general application, they employ methods that give a good approximation to the sum over an infinite lattice for any unit cell.

However, electrostatic interaction is not all that has to be considered. We know, for example, that ions are not just point charges but have a size; the shell of electrons around each nucleus prevents too close an approach by other ions. We therefore include a term to allow for the interaction between shells on the different ions. It would be possible to give each ion a fixed size and insist that the ions cannot be closer than their combined radii. However, most programs use a different approach by including terms representing intermolecular forces.

The intermolecular forces act between cations, and between cations and anions, as well as between anions. For oxides in particular, however, the cation–cation term is often ignored.

Salts such as magnesium oxide can be thought of as close-packed arrays of anions with cations occupying the octahedral holes.

* Do the cations come into contact with each other in such a structure?

* No, not if the anions have the larger ionic radius.

Because the cations are held apart by the anions, the cation–cation interaction is unimportant.

The final thing we need to take into account is the polarizability of the ions. This is a measure of how easily the ions are deformed from their normal spherical shape. In a perfect crystal, the ions are in very symmetrical environments and can be thought of as spherical. If one ion moves to an interstitial site, leaving its original position vacant, then the environment may not be so symmetrical and it may be deformed by the...