Carlos Fiolhais

A Primer in Density Functional Theory

Density Functionals for Non-relativistic Coulomb Systems in the New Century.- Orbital-Dependent Functionals for the Exchange-Correlation Energy: A Third Generation of Density Functionals.- Relativistic Density Functional Theory.- Time-Dependent Density Functional Theory.- Density Functional Theories and Self-energy Approaches.- A Tutorial on Density Functional Theory.

Science learning in virtual environments: a descriptive study

Usually, students learn more if the method of instruction matches their learning style. Since Physics and Chemistry deal with three-dimensional (3-D) objects, the ability to visualize and mentally manipulate shapes is very helpful in their learning. In fact, much of what Physics and Chemistry students know takes the form of images. However, little attention has been given to the pedagogical effectiveness of visual stimuli in those disciplines. Computers are being increasingly used as teaching tools. The new approaches include simulations, multimedia presentations and, more recently, virtual environments. Computer-based worlds are useful to visualize physical and chemical processes allowing for better conceptual understanding. Since 3-D virtual environments need to be explored and evaluated in science education, we have created a virtual environment (Virtual Water) for studying phases of matter, phase transitions and atomic orbitals at the final year of high school and first year of university levels. Based on that work, we discuss the implications of visual learning in designing strategies to cater for differences in learning modes. Our study indicates that 3-D virtual environments may help students with high spatial aptitude to acquire better conceptual understandings. However, only some parameters (interactivity, navigation and 3-D perception) have shown to be relevant and only for some topics. On the other hand, stereoscopic visualizations do not seem to be relevant, with the exception of crystalline structures.

Ionization energy and electron affinity of a metal cluster in the stabilized jellium model: Size effect and charging limit

We report the first reliable theoretical calculation of the quantum size correction c which yields the asymptotic ionization energy I(R)=W+(12+c)/R+O(R−2) of a simple-metal cluster of radius R. Restricted-variational electronic density profiles are used to evaluate two sets of expressions for the bulk work function W and quantum size correction c: the Koopmans expressions, and the more accurate and profile-insensitive ΔSCF expressions. We find c≈−0.08 for stabilized (as for ordinary) jellium, and thus for real simple metals. We present parameters from which the density profiles may be reconstructed for a wide range of cluster sizes, including the planar surface. We also discuss how many excess electrons can be bound by a neutral cluster of given size. Within a continuum picture, the criterion for total-energy stability of a negatively charged cluster is less stringent than that for existence of a self-consistent solution.

Relativistic particle in a box

The problem of a relativistic spin 1/2 particle confined to a one-dimensional box is solved in a way that resembles closely the solution of the well known quantum-mechanical textbook problem of a non-relativistic particle in a box. The energy levels and probability density are computed and compared with the non-relativistic case. Resumo. O problema de uma particula de spin 1/2 confinada por uma caixa a uma dimensao e resolvido de uma maneira muito semelhante a da resolucao do problema de uma particula no-relativista numa caixa referido em muitos livros introdutorios de Mecânica Quntâica. Os niveis de energia e a densidade de probabilidade sao calculados e comparados com os valores nao-relativistas.

Física no computador: o computador como uma ferramenta no ensino e na aprendizagem das ciências físicas

The difficulties that many pupils show in understanding some physical processes are well known. Among various reasons for failure in Physics learning old or misguided education methods have been pointed out. The need to diversify methods to attack pedagogical failure led to the increasing use of the computer in Physics education. Currently this tool offers various possibilities to help solving problems in Physics education. We present an historical summary of the rise of computers in education. We relate computer applications to advances in learning theories. We review the main computer uses in science education, from simulations to virtual reality, including data acquisition and Internet. Although the balance of the use of the computers in education is clearly positive, many questions remain. In effect, in spite of its recognized potentialities, the computer did not become the magical key of educative success. We discuss some of the standing difficulties. The pedagogical potential of the computer could only be carried through if good educative software would become available and if this would be smoothly connected to syllabus and practice.

Toys in physics lectures and demonstrations—a brief review

The use of toys in physics teaching is common. This brief review of the physics of toys intends to show that they are not only very useful in lectures and demonstrations in order to motivate students but also very interesting from a scientific point of view. However, since their physics is sometimes too cumbersome, the effect can be the opposite. We call attention to some subtleties of toys used in physics or in general science teaching.

Self-compression of metallic clusters under surface tension

Abstract The stabilized jellium model is used to explore the physics of self-compression for spherical clusters of simple-metal atoms. Within the continuum or liquid drop model, strong compression of the interior ionic density of a small cluster (with respect to the bulk density) results from cooperation between surface tension and surface suppression of the elastic stiffness. The latter effect is due to the large negative value of σ″, the second derivative of surface tension with respect to uniform strain. Self-compression also renormalizes the effective curvature-energy coefficient, and contributes to the asymptotic (large-radius) size effect on the ionization energy. A quantum-mechanical calculation of interior density as a function of electron number displays small shell-structure oscillations around the average behavior predicted by the liquid drop model. Numerical results are presented for clusters of Al, Na, and Cs. For compact 6-atom clusters of these metals, predicted bond lengths are smaller than their bulk values by 10%, 6%, and 4%, respectively.

Transferability of a local pseudopotential based on solid-state electron density

Local electron - ion pseudopotentials fitted to dominant density parameters of the solid state (valence, equilibrium average electron density and interstitial electron density) have been constructed and tested for sixteen simple metals. Calculated solid-state properties present little evidence of the need for pseudopotential non-locality, but this need is increasingly evident as the pseudopotentials are transferred further from their solid-state origins. Transferability is high for Na, useful for ten other simple metals (K, Rb, Cs, Mg, Al, Ga, In, Tl, Sn, and Pb), and poor for Li, Be, Ca, Sr and Ba. In the bulk solid, we define a predictor of transferability and check the convergence of second-order pseudopotential perturbation theory for bcc Na. For six-atom octahedral clusters, we find that the pseudopotential correctly predicts self-compressions or self-expansions of bond length with respect to the bulk for Li, Na, Mg, and Al, in comparison with all-electron results; dimers of these elements are also considered. For the free atom, we examine the bulk cohesive energy (which straddles the atomic and solid-state limits), the atomic excitation energies and the atomic density. For the cohesive energy, we also present the results of the simpler stabilized jellium and universal-binding-energy-curve models. The needed non-locality or angular-momentum dependence of the pseudopotential has the conventional character, and is most strongly evident in the excitation energies.

Mean-field theories with mixed states and associated boson expansions

Abstract A variational derivation of the Liouville-von Neumann equation of quantum-statistical mechanics is presented, in order to formulate mean-field approximations appropriate to mixed states. The Hartree-Fock and the RPA at finite temperatures are particular cases of the general formalism. A thermal boson expansion is defined, which allows us to describe anharmonic motion around a thermal excited state. In a numerical application on the basis of the Lipkin model, temperature-dependent phase transitions are observed.

Density functional theory study of the oxoperoxo vanadium(V) complexes of glycolic acid. Structural correlations with NMR chemical shifts

The DFT B3LYP/SBKJC method has been used to calculate the gas-phase optimized geometries of the glycolate oxoperoxo vanadium(V) complexes [V(2)O(2)(OO)(2)(gly)(2)](2-), [V(2)O(3)(OO)(gly)(2)](2-) and [VO(OO)(gly)(H(2)O)](-). The (51)V, (17)O, (13)C and (1)H chemical shifts have been calculated for the theoretical geometries in all-electron DFT calculations at the UDFT-IGLO-PW91 level and have been subsequently compared with the experimental chemical shifts in solution. In spite of being applied to the isolated molecules, the calculations allowed satisfactory reproduction of the multinuclear NMR solution chemical shifts of the complexes, suggesting that the theoretical structures are probably close to those in solution. The effects of structural changes on the (51)V and (17)O NMR chemical shifts have been analysed using the referred computational methodologies for one of the glycolate complexes and for several small molecules taken as models. These calculations showed that structural modifications far from the metal nucleus do not significantly affect the metal chemical shift. This finding explains why it is possible to establish reference scales that correlate the type of complex (type of metal centre associated with a certain type of ligand) with its typical region of metal chemical shifts. It has also been found that the V[double bond, length as m-dash]O bond length is the dominant geometrical parameter determining both delta(51)V and the oxo delta(17)O in this kind of complex.