Quantum mechanics
A quantum-mechanical calculation commences with the Schrodinger wave equation:| ⇒ Equation [44.1] | HΨ = εΨ |
where H is called the Hamiltonian operator (it describes the kinetic energies of the nuclei and electrons and the electrostatic interactions felt between individual particles), ε is the energy of the system, and Ψ is called a wavefunction - Ψ2 describes the probability of finding an electron at a particular set of co-ordinates.
The equation is used to describe the behaviour of an atom or molecule in terms of its wave-like (or quantum) nature. By trying to solve the equation the energy levels of the system are calculated. However, the complex nature of multielectron/nuclei systems is simplified using the Born-Oppenheimer approximation. Unfortunately it is not possible to obtain an exact solution of the Schrodinger wave equation except for the simplest case, i.e. hydrogen. Theoretical chemists have therefore established approaches to find approximate solutions to the wave equation. One such approach uses the Hartree- Fock self-consistent field method, although other approaches are possible. Two important classes of calculation are based on ab initio or semi-empirical methods. Ab initio literally means 'from the beginning'. The term is used in computational chemistry to describe computations which are not based upon any experimental data, but based purely on theoretical principles. This is not to say that this approach has no scientific basis - indeed the approach uses mathematical approximations to simplify, for example, a differential equation. In contrast, semi-empirical methods utilize some experimental data to simplify the calculations. As a consequence semi-empirical methods are more rapid than ab initio.
Molecular mechanics
Most molecular modelling packages allow the use of empirical methods which only consider the nuclei. These are called molecular mechanical methods and are faster than the quantum-mechanical methods. They are based on classical mechanics and therefore allow treatment of larger molecules. However, as electrons are not included in the calculation, this approach does not provide information on bond breaking or formation, or any details of orbitals involved in any interactions.
The computational laboratory
Like all laboratory classes it is important to go prepared so that you will get the most out of your time in the laboratory. This might include background reading, making an outline of the experimental procedure, a sketch (or photocopy) of the chemical structure of all molecules to be worked on, and a plan of how you will draw each molecule - obviously the more complex molecules may require more thought than a simple molecule. Once there, it is important to:
- Get a comfortable chair - you may be sitting in it for quite a while. Make yourself feel at ease and relax.
- Plan your work - a considerable amount of time in the laboratory will be spent constructing models, setting up calculations and evaluating results. It is therefore important to maximize your time on the computer by planning in advance.
- Follow all instructions carefully - remember that a computer carries out your instructions.
- Examine all results carefully - do not accept everything the computer prints out/displays. Question the results yourself - do they make sense? If not recheck your initial data entry.
- Save all your results for rechecking by yourself at a later date or for assessment by your tutor.
A typical software package used to perform computational chemistry should be able to:
- Build and display molecules.
- Optimize the structure of molecules.
- Investigate the reactivity of molecules.
- Generate and view orbitals and electronic plots.
- Evaluate chemical pathways and mechanisms.
- Study the dynamic behaviour of molecules.
Support our developers
