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

对于无限的周期系统，R是不明确定义的。然而，它定义了极化，并在处理外部电场或磁场时进入哈密尔顿算符。尽管在过去10多年里，在处理扩展系统的这个操作员方面取得了重大进展，但首先，最近这样做的基础已经建立在坚实的理论基础上，并且没有考虑到不同的建议是如何联系在一起的，以及哪些建议是正确的。本建议的目的是扩大这项工作的范围，以便不仅可以计算极化，而且可以将电场和磁场直接包括在电子结构计算中。为了确定计算上最有用的方法，首先应使用类似于Hück el的模型进行模型研究，其中应测试各种近似。随后，被发现在计算上最有用的方法应在现有的聚合物和链状化合物的无参数、密度泛函方法中实施。之后，将对一些现实的模型化合物进行研究。同时，还应从更基本的角度研究r→的更复杂的功能，例如r？

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.