Response of Periodic Systems to External Electric and Magnetic Fields

在过去的大约八年里，申请人与美国的一位同事一直致力于开发一种方法，用于研究准线性链化合物在外部静电场中的电子和结构响应，我们使用了模型哈密顿量。该方法已经实现到一个，并正在实现到另一个从头算程序包的聚合物。这个项目的重点是将该方法扩展到更高维度的基本方面，对磁场的处理，对离域基函数（如平面波）的处理，以及该方法的各种基本方面。正如我们以前的工作一样，所有的理论方法都应该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和处理不同类型的系统。对于电场和磁场，当研究无限周期系统时，r被涉及到对k的导数的算符所取代。最终，这意味着轨道的相位因子变得重要，并且对于暴露于电磁场中的无限周期系统，能带结构是非唯一的。此外，如何确定这类系统的激发能并不明显，部分原因是该方法是为带完全填充的系统制定的。这些方面也需要通过精心设计的模型系统进行研究。最后，目前使用的近似密度泛函在描述链系统对电场的响应时的问题也将通过考虑模型来研究

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