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是病态的。然而，它定义了极化，并在处理外部电场或磁场时进入汉密尔顿算子。虽然在过去的10多年里已经取得了显着的进展，在治疗这个运营商的扩展系统，最近这样做的基础已经放在一个坚实的理论基础上，它已被shorn如何不同的建议是相关的，哪些是正确的。本建议的目的是扩大工作范围，以便不仅可以计算极化，而且电场和磁场可以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，应首先使用类似Hückel的模型进行模型研究，并对各种近似值进行测试。随后，发现计算上最有用的方法应在现有的无参数，密度泛函方法的聚合物和链化合物。随后将对一些实际模型化合物进行研究。并行地，r→的更复杂的函数，例如，r²，也应该从更基本的角度进行研究。

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.