Response of Periodic Systems to External Electric and Magnetic Fields

在过去的大约八年中，申请人与美国的一位同事一直致力于开发一种方法来研究外部静电场中准线性链状化合物的电子和结构响应，其中我们使用了哈密顿模型。该方法已在一种方法中实现，并正在另一种聚合物从头算程序包中实现。这个项目的重点是将该方法扩展到更高维度的基本方面，磁场的处理，离域基函数(如平面波)，以及该方法的各种基本方面。与我们以前的工作一样，所有的理论方法都将通过模型计算来分析，既适用于大型有限系统，也适用于无限周期系统。模型的使用允许详细研究收敛行为并处理不同类型的系统。对于电场和磁场，当研究无限大的周期系统时，r都被涉及关于k的导数的算子所代替。最终，这意味着轨道的相位因子变得重要，并且对于暴露在电磁场中的无限周期系统，能带结构不是唯一的。此外，如何识别这类系统的激发能并不明显，部分原因是这种方法是针对完全充满带的系统而制定的。此外，还应通过精心设计的模型系统来研究这些方面。最后，还应通过考虑模型来研究目前使用的描述链系统对电场的响应的近似密度泛函的问题

During the last roughly eight years the applicant together with a colleague in the US has been working on developing a method for studying the electronic and structural responses of quasi-linear chain compounds in external electrostatic fields where we have used a model Hamiltonian. The approach has been implemented into one and is being implemented into another ab initio program packages for polymers. This project is focusing on fundamental aspects of extending the approach to higher dimensions, to the treatment of magnetic fields, to delocalized basis functions (like plane waves), and to various fundamental aspects of the approach. As in our previous work, all theoretical approaches shall be analyzed through model calculations both for large, finite systems and for infinite, periodic systems. The use of models allows for studying in detail convergence behavior and for treating different types of systems. Both for electric and for magnetic fields, r is replaced by operators involving the derivatives with respect to k when studying infinite, periodic systems. Ultimately, this means that phase factors of the orbitals become important and that the band structures are non-unique for infinite periodic systems exposed to electromagnetic fields. Furthermore, it is not obvious how to identify excitation energies for such systems, partly because the approach is formulated for systems with completely filled bands. Also these aspects shall be studied through carefully designed model systems. Finally, the problems of presently used approximate density-functionals in describing the response of chain systems to electric fields shall be studied, too, by considering models