Theoretical methods used in this thesis:
Optimization Methods

In this section we will describe the methods that optimize the potential energy as a function of the nuclear coordinates. That is, those methods that permit moving the nuclear coordinates of a molecular structure to find stationary points, mainly minima and saddle points, on the Potential Energy Surface. The stationary points may explain the chemistry of the molecule. It is expected that a minimum energy structures will be representative of a stable chemical species, as well as the energy and the structure of a saddle point will describe the mechanism and the kinetics of the considered reaction.

It is important to note that all the stationary points found by these methods are local, they are not absolute minima. Perhaps an important exception is the non-derivative algorithms, but their application is not usually addressed to reactivity. The theoretical prediction of a global minimum in a molecular system is still an unsolved problem [128]. A lot of work is devoted to this area, a particular example is the mechanism of protein folding [129].

The optimization methods explained here can be classified in several ways. We classify the methods depending on the need of first or second derivatives which is related with its efficiency and computational cost. It could be classified depending on the kind of stationary point we are looking for, that is, methods to locate minima and methods to locate saddle points. However, any of these classifications would not cover all the possibilities.