Development and implementation of theoretical methods for dealing with functions of the quantum-mechanical operator r in extended systems

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r for infinite, periodic systems is ill-defined. Nevertheless, it defines polarization and enters the Hamilton operator when dealing with external electric or magnetic fields. Although significant progress has been obtained during the last more than 10 years in treating this operator for extended systems, first recently the foundations for doing so has been put on a firm theoretical basis, and it has been shorn how the different suggestions are related and which ones are correct. It is the purpose of the present proposal to extent that work so that not only the polarization can be calculated but also electric and magnetic fields be included directly in an electronic-structure calculation. In order to identify the computationally most useful approach, first model studies with a Hückel-like model shall be performed, where the various approximations shall be tested. Subsequently, the methods that are found computationally most useful shall be implemented in an existing parameter-free, density-functional method for polymers and chain compounds. Studies on some realistic model compounds shall afterwards be performed. In parallel, more complicated functions of r→, e.g., r², shall be studied, too, from a more fundamental point of view.