| All the thermodynamical properties of a given system can be obtained from the knowledge of the free energy of such system and its derivatives. Thus, a study of different methods to evaluate free energies is of considerable importance for physical, chemical and biological systems. However, free energy calculations are not straightforward in practice. For chemical systems for example, the complication is mainly due to the difficulty of calculating the entropy of the system. In order to overcome this difficulty, special methodologies have been introduced to provide some tools in the estimation of relative free energies for molecular systems via computer simulations. Another example where free energy calculations are challenging is the physics of phase transitions, i.e. the boiling of a liquid, the transition from paramagnetic to ferromagnetic behavior of a metal, etc.;This thesis is divided in two parts. In the first part, the evaluation of free energy differences in chemical reactions is investigated through a novel method developed by Laio et al called Metadynamics (1). This method not only allows for the evaluation of free energy differences but also accelerates the reactions, driving the system through high free energy barriers and sampling regions of low probability. As an application, two important carboxylic acids, malonic and formic acid, were studied and their structure, energetics, intramolecular reactions and solvent interactions were determined. The deprotonation of the formic acid in presence of water was also fully investigated. In the second part, phase transition phenomena are considered, using the phenomenological Laundau-Ginsburg-Wilson Free Energy Functional. We investigated self-assembled domain patterns of modulated systems. They appear as a result of competing short-range attractive and long-range repulsive interactions found in diverse physical and chemical systems. From an application point of view, there is considerable interest in this domain patterns, as they form templates suitable for the fabrication of nanostructures. We have generated a variety of new and exotic patterns, which represent either metastable or glassy states. These patterns arise as a compromise between the required equilibrium modulation period and the strain resulting from topologically constrained trajectories in phase space that effectively preclude the equilibrium configuration. |
