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 surfaceminima (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.

 

Ab initio MO methods