Potential Energy Calculation and Gradient Revolution

Recent advances in computational techniques enable an application of 

Quantum Chemistry . The theoretical methods are capable of supplying a wealth of information which complements experimental results. Systems and structures being inaccessible to experimental investigation may be studied by these methods. 

The widely used and ever-improving semi-empirical methods of quantum chemistry provided important results or, at least, prepared the way for a final theoretical treatment of chemical problems through the explicit formulation and modelling in connection with processing the experimental material. The spectrum of data spans from preliminary results to useful trend predictions to first approaches to sets of 

Moreover, we refer to these kinds of concepts as force field calculations (molecular mechanics) which approximate the potential field (Born-Oppenheimer approximation) by classical energy relations and adjustable parameters. These methods have successfully accompanied and completed the ab initio calculations until now. For the literature covering these methods and their results, we refer to other surveys. Because of the use of analytical potentials, the procedures are not as time-consuming as ab initio methods. However, their importance is placed behind the conceptually stronger ab initio methods, and they are not suited to localize structures between the minimizers on the PES as it is of primary importance for the kinetic characteristic of a chemical reaction. 

As discussed above, a fundamental problem in studying chemical reactivity is the quality of the calculated potential energy. Based on the ab initio SCF MO theory, the following quantities are decisive to obtain reliable potential energies  

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