Chapter 6. Calculation of physical and chemical properties of nanomaterials. (2 hours).

1. Chapter 1. Introduction, perspectives, and aims. On the science of simulation and modelling. Modelling at bulk, meso, and nano scale. (2 hours). Chapter 2. Experimental Techniques in Nanotechnology. Theory and Experiment: “Two faces of the same coin” (2 hours). Chapter 3. Introduction to Methods of the Classic and Quantum Mechanics. Force Fields, Semiempirical, Plane-Wave pseudpotential calculations. (2 hours) Chapter 4. Intoduction to Methods and Techniques of Quantum Chemistry, Ab initio methods, and Methods based on Density Functional Theory (DFT). (4 hours) Chapter 5. Visualization codes, algorithms and programs. GAUSSIAN; CRYSTAL, and VASP. (6 hours). .

2. . Chapter 6. Calculation of physical and chemical properties of nanomaterials. (2 hours). Chapter 7. Calculation of optical properties. Photoluminescence. (3 hours). Chapter 8. Modelization of the growth mechanism of nanomaterials. Surface Energy and Wullf architecture (3 hours) Chapter 9. Heterostructures Modeling. Simple and complex metal oxides. (2 hours) Chapter 10. Modelization of chemical reaction at surfaces. Heterogeneous catalysis. Towards an undertanding of the Nanocatalysis. (4 hours)º

3. In the past years, theoretical and technological advancements have produced an impressive improvement of computational facilities providing a wide range of methodologies, economically and conceptually accessible for a huge number of researchers in different fields of molecular sciences. Electronic structure calculations represent nowadays one of the most commonly used approaches by the physical-chemical community, allowing highly accurate description of systems with a large number of atoms, i.e., systems with an order of atoms of 102-103 and more. Martin, R. Electronic Structure Basic Theory and Practical Methods; Cambridge University Press: Cambridge, UK, 2004. Hung, L.; Carter, E. A. Chem. Phys. Lett. 2009, 475, 163. .

4. However, there is still a lot of work to do. As a matter of fact, modeling at the electronic level of systems with high configurational complexity is still challenging. In this case, the main problem is either practical and conceptual as the different observables to be modeled depend on processes occurring at different length, energy, and time scales. Computational tools typically employed for systems of such dimensions are classical simulations which, however, produce reliable results as far as transitions in quantum degrees of freedom do not take place. On the other hand, when the observables of interest explicitly involve quantum degrees of freedom, e.g., chemical reactions or spectral transitions, their modeling should be derived from statistical averages of genuine quantum states interacting with fluctuating perturbing environments. .

5. Our ability to model physical and chemical processes at the atomic and sub-atomic levels has progressed rapidly over the last three decades, due to development of theoretical methods based on statistical mechanics and quantum mechanics, rapid increases in computer speed and memory, more efficient algorithms and a steady improvement in force field development. Among the most useful theoretical methods for surface science are ab initio and classical density functional theories and molecular simulation methods, that is the numerical solution of the equations of statistical mechanics using Monte Carlo or molecular dynamics techniques. .

6. Theory and simulation can provide fundamental understanding of observed phenomena, and can be used to make predictions for systems that are difficult or impossible to study experimentally, for example adsorption of toxic or biological agents, or behavior at very high temperature or pressure. In addition, theory and simulation can give detailed molecular level information that is difficult or impossible to determine from laboratory experiments. Examples are the molecular structure of adsorbed phases, detailed mapping of diffusion of guest molecules in highly disordered microporous materials, the pressure tensor in a pore and the wave function of the electrons. These methods also find important applications in determining the limits of well known macroscopic laws, which may break down for nano-scale systems. Examples are the concept of surface tension1 and Gibbs’ surface thermodynamics in general, related equations such as those of Kelvin,2 Young and Laplace,1 Fick’s Law of diffusion3–6 and the Second Law of Thermodynamics .

7. Theory and experiment each have different strengths and limitations, but these are complementary to a large extent and there is much to be gained by constructing research programs that combine the two. Significant difficulties in experimental studies of adsorption and confinement effects include identifying the nature and composition of the host adsorbate phase, longlived metastable states, and preferential adsorption of trace impurities on the pore walls, while in theoretical and simulation studies the main difficulties are uncertainties about the pore morphology and topology of the real materials (in the case of non-crystalline materials), and about the force fields involved. .

8. A further limitation for simulation at present is that current computers are not yet powerful enough to carry out molecular dynamics simulations for longer than about a microsecond of real time. While this is sufficient for studies of relatively small adsorbate molecules, the self-assembly of larger surfactant or protein molecules on solid surfaces and in pores requires longer times. Such studies are likely to become possible in the next decade, when more powerful machines are available. While metastability also occurs in theoretical calculations, free energy calculations enable this to be detected and the true equilibrium state determined; moreover, the nature and composition of the host phase is readily determined. .

10. Chapter 3. Introduction to Methods of the Classic and Quantum Mechanics. Force Fields, Semiempirical, Plane-Wave pseudpotential calculations. (2 hours) Juan Andrés y Lourdes Gracia Departamento de Química-Física y Analítica Universitat Jaume I Spain & CMDCM, Sao Carlos Brazil Sao Carlos, Novembro 2010

11. 1) Force Fields

15. 2) Semi-empirical

17. 3) Plane-Wave pseudopotential calculations In the Plane-Wave method, the single electron (pseudo-) wave function is explanded using a plane-wave basis set: