Aspects of frozen-phonon calculations: theory and application to high temperature superconductors

This thesis is concerned with two aspects of the frozen phonon technique - an ab-initio method to study the lattice dynamics of a crystal. In the first part of the work a complete formulation of the iterative linear-response (ILR) scheme for crystalline solids within the framework of the linearized augmented plane-wave (LAPW) method is presented. Analytical expressions are provided which are well suited for a direct implementation into existing all-electron LAPW band structure programs. The charge response of valence as well as core electrons is fully taken into account. Of particular importance is the development of efficient algorithms which reduce the complexity of specific aspects related to the calculation of the first-order Hamiltonian and overlap matrices. In the second part of this thesis first-principles frozen-phonon calculations of the 15 Raman-active modes in the high temperature superconductor YBa2Cu3O7 are presented. The determination of the respective dynamical matrices is based on the interpolation of atomic-force data. Two independent strategies are employed to minimize deviations between the experimentally determined phonon quantities (frequencies and eigenvectors) and the corresponding theoretical data. First, in the treatment of exchange and correlation effects the traditional LDA functional is replaced by a GGA functional. This improves the frequencies and eigenvectors of the Ba-Cu modes significantly. Second, the LDA functional is kept but the structural parameters (lattice constants, internal coordinates) are optimized prior to the frozen phonon calculation. This yields a theoretical framework in which an overall excellent agreement between theoretically and experimentally determined frequency values is obtainable. (author)