Few historical remarks and overview of the methods

Theoretical chemistry was born in the context of theoretical physics, when physicists at the beginning of the XXth century tried to apply the newborn quantum mechanics to molecular systems. The understanding of the chemical bond, the electromagnetic spectra and the explanation of the stability of small molecular structures were some of the greatest achievements. A lot of effort has been done since then to improve the initial works made by Slater, Mulliken, Pauling, London and many others. This is why historically quantum chemistry has almost taken the whole task in theoretical chemistry [17].

After the second world war physicists were more interested in the sub-atom world, so the task to find an accurate description of molecular entities was left to a new class of scientists, the quantum chemists or theoretical chemists.

During the fifties and the sixties the appearance of computers made possible the first semi-empirical calculations and the stablishment of the basis in ab initio techniques. The application of quantum mechanics to molecular systems was so challenging and difficult that theoretical chemists have sometimes forgotten the real experimental results and have focused only on the numerical solution of the equations. The development, implementation and computation of the equations is such a hard and uncertain task that it must be contemplated as a computational experiment by itself.

At the same time, during the fifties the first computers permitted also the first computation of thermodynamic magnitudes using condensed phase simulations. Metropolis with the Monte Carlo method in 1953, Alder and Mainwright using molecular dynamics in 1957 to calculate the phase transition for a hard sphere system, and Rahman in 1964 with the first simulation of a Lennard-Jones liquid were the first attempts in the new area of simulation.

Both condensed phase simulations and quantum chemistry calculations have evolved separately until recently, when the computational power and some new theoretical developments have paved the way for a joint and complete overview of techniques. In this sense a theoretical chemist should contemplate his research task in a wider and interdisciplinary research. ^2.1Actually, recent text-books already contain a larger and interdisciplinary view of theoretical chemistry. For example, twenty years ago Levine's Quantum Chemistry [18] and Allen-Tildesley's Liquids simulation book [15] covered very different areas. On the contrary, nowadays Leach's [13], Cramer's [19] or Jensen's book [11] include the molecular orbital theory along with some simulation techniques.

Figure 1.1: General scheme for a theoretical study of a chemical reaction

My particular unified view of a theoretical study of a chemical reaction can be drawn in figure 1.1. The scheme is not intended to be exhaustive, there are many fields in theoretical chemistry that fall out of this classification (spectroscopy, structural chemistry, structure-activity relationships etc). But in my opinion every study of a chemical reaction should be contemplated by the different stages displayed in the figure. Every stage in figure 1.1 will be a section of this chapter. An important exception is the initial stage of knowing the structure and composition of the system. This question is not a problem in small sized systems, but in condensed phase systems the problem remains. The solvation of a macromolecule, protein folding or ligand binding are addressed to solve this problem in biopolymers, and the modeling of defects and impurities in solid state is also far from being solved.

In general optimization techniques and the exploration of phase space are usually applied to small sized systems and condensed phase systems respectively. Their common objective is the knowledge of the shape of the potential energy surface. However, one of the main arguments in this thesis is that optimization techniques can also be applied to condensed phase systems even when the exploration of phase space is feasible. We will see how both techniques can be applied to Mandelate Racemase reaction and how they complement each other.