Micro-iterative method

In the present section we study some of the possible strategies that can be adopted in the micro-iterative method.

A compromise between the need of using a second derivative method and the drawbacks when moving many degrees of freedom is the so-called micro-iterative method[108,160,65,84,81,161,95,120,162] described in section 1.3.7.4. In this case a Newton-like method[12] is used to locate a stationary point in a small core zone where the number of atoms to be moved is low enough to avoid computational problems. The rest of atoms of the system do belong to the environment zone which is minimized with an inexpensive method. Both processes alternate one each other until consistency. In our particular case, we make usage of Rational function optimization method implemented in the last section 3.1 as a second order method for the search in the core, while for the environment the L-BFGS method is applied. Although this scheme can be applied to locate any kind of stationary points, from here on we will refer only to saddle point structures.

In the micro-iterative scheme the core and environment zones do not have to match with the QM and MM regions respectively. The quantum region is selected in a QM/MM system as the set of atoms whose interactions need to be described by a QM potential, usually when bond breaking or charge transfer is involved. This selection will define a certain PES. Conversely, the selection of the core zone is just a strategy to locate stationary points and it can change when looking for different stationary points in a reaction mechanism.

The criterion to select this core zone is not based on the interaction energy but on geometrical criteria, that is, the core zone must include the atoms whose movement may play an important role when looking for the stationary point at the current chemical step. We will see that depending on the reaction type a big core (even bigger than the QM zone) must be chosen, while in some other cases a core with few atoms is enough to reach the stationary point easily.

This section is presented in two main parts. In section 3.2.1 the micro-iterative method as a possible solution to our problem is presented, and we discuss the different options that this method can offer. In section 3.2.2 we present the results as they have been obtained from Mandelate Racemase reaction. A discussion is done on the results obtained with the different options of the method. Finally, the conclusions are presented.