Calculating potential energy surfaces
·
It is generally difficult to calculate chemical
properties to ‘within chemical accuracy’ (~ 4kJ/mol) for most systems,
particularly for reactions (can get good agreement with experiment for the H +H2
reaction!)
·
However, comparing similar systems can provide
useful results, e.g. comparing relative
calculated energy barriers, instead of absolute values
·
Comparison with experimental results is important
to test and validate theoretical predictions
·
Theory plays an important part in the
development of chemical concepts. An
example is the idea of a transition state for a reaction. This arose from considering potential
energy surfaces for chemical systems.
· To construct a
potential energy surface, we need to be able to calculate the energy of the
molecule at a particular geometry.
· Remember that we
can treat the nuclei as fixed when we calculate the energy of the electrons,
because of the Born-Oppenheimer approximation.
· The potential
energy surface (curve) for a diatomic molecule is easy to visualize – it is a
function simply of the interatomic distance.
· For systems of
three or more atoms, however, the energy is a function of (3N-6) coordinates,
and it is not possible to draw the surface.
This is not a problem for a computer though, which can perform
calculations in many dimensions.
· We do not need to
know what the whole potential energy surface looks like. Particularly important are key points on
the surface – minima (stable structures) and (first-order) saddlepoints
(transition structures).
· To optimize
molecular geometries (to find minima and transition states), or to simulate the
dynamics of a molecule, we need a technique capable of calculating the energy
of a molecular structure, and the first (and preferably second) derivatives of
the energy with respect to the coordinates of the molecule. Methods for calculating molecular potential
energy surfaces are described below.