Response of Periodic Systems to External Electric and Magnetic Fields

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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