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A wide variety of schemes to compute short-range and long-range correlations is discussed. The emphasis lies on an overview and on the interrelations between the various schemes, rather than on a detailed presentation. The need for effective interactions, and their proper handling is outlined at the end.

Dense hydrogen is studied in the framework of wave packet molecular dynamics. In this semiquantal many-body simulation method the electrons are represented by wave packets which are suitably parametrized. The equilibrium properties and time evolution of the system are obtained with the help of a variational principle. At room temperature the results for the isotherms are in good agreement with anvil experiments. At higher densities beyond the range of the experimental data a transition from a molecular to a metallic state is predicted. The wave packets become delocalized and the electrical conductivity increases sharply. The phase diagram is calculated in a wide range of the pressure-density-temperature space. The observed transition from the molecular to metallic state is accompanied by an increase in density in agreement with recent reverberating shock wave experiments.

We present the ionic geometries of Na + 9 and Na + 55 clusters obtained in the "cylindrically averaged pseudopotential scheme". Our structures are tested by calculating photoabsorption spectra and comparing them to the experimentally measured ones. We employ a local pseudopotential that has been constructed to reproduce atomic and bulk properties of sodium. Comparing the results using different pseudopotentials, we find that the position of the dipole resonance is greatly influenced by details of the pseudopotentials, showing that these must be used consistently both in the geometry optimization and the calculation of the optic response. PACS. 36.40.-c Atomic and molecular clusters -31.15.-p Calculations and mathematical techniques in atomic and molecular physics -71.15.-m Methods of electronic structure calculations

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