Fitting PES Results to Analytic Equations

Once a PES has been computed, it is often fitted to an analytic function. This is done because there are many ways to analyze analytic functions that require much less computation time than working directly with ab initio calculations. For example, the reaction can be modeled as a molecular dynamics simulation showing the vibrational motion and reaction trajectories as described in Chapter 19. Another technique is to fit ab initio results to a semiempirical model designed for the purpose of describing PES s. 

Of course, the analytic surface must be fairly close to the shape of the true potential in order to obtain physically relevant results. The criteria on fitting PES resvJts to analytic equations have been broken down into a list of 10 specific items, all of which have been discussed by a number of authors. Below is the list as given by Schatz  

The analytic fimction should accurately characterize the asymptotic reactant and product molecules. 

It should have the correct symmetry properties of the system. 

It should represent the true potential accurately in the interaction regions for which experimental or nonempirical theoretical data are available. 

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