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| Home > Publications database > Density-Functional Perturbation Theory within the All-Electron Full-Potential Linearized Augmented Plane-Wave Method: Application to Phonons |
| Book/Dissertation / PhD Thesis | FZJ-2022-03456 |
2022
Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag
Jülich
ISBN: 978-3-95806-649-6
Please use a persistent id in citations: http://hdl.handle.net/2128/31894
Abstract: Solids consisting of periodic lattice structures exhibit vibrational modes of their atomic nuclei. In the context of a quantum-mechanical description, the excitations of the collective lattice vibrations are quantized and behave like particles. These quasiparticles are called phonons and essential for describing a diverse spectrum of central solid properties and phenomena. Density-Functional Theory (DFT) according to Kohn and Sham has established itself as a very successful, state-of-the-art, material-specific, theoretical, and computational framework. It enables us to calculate the phonon modes with very high predictive power from the first principles of quantum mechanics for describing electrons and ions. Two different approaches to obtaining phonon properties are employed: (i) the Finite Displacement (FD) ansatz, where the second-order derivatives of the total energy with respect to atomic displacements are approximated by difference quotients that involve the forces exerted on the atoms due to their finite displacement, and (ii) the Density-Functional Perturbation Theory (DFPT), a variational approach delivering the desired second-order derivatives from linear responses to an infinitesimal displacement wave. The ambition of this dissertation is to pursue a DFPT beyond the common frameworks with plane-wave basis functions. It is realized by means of the Full-Potential Linearized Augmented Plane-Wave (FLAPW) method, an all-electron electronic-structure method based on muffin-tin (MT) spheres circumscribing the atomic nuclei. The FLAPW method is known for providing the density-functional answer to arbitrary material systems, i.e., independent of which chemical element in the periodic table is chosen. I report on the implementation and validation of the DFPT approach within the FLAPW method in terms of the newly-developed computer program juPhon. Its algorithm describes the properties of phonons in harmonic approximation and is based on the input of the FLEUR code, which is a DFT implementation utilizing the aforementioned FLAPW ansatz. In detail, I elucidate the numerical challenges and show how they have been surmounted enabling us to reliably set up a dynamical matrix, the associated phonon energies of which are many orders of magnitude smaller than the ground-state energy of a crystal. This covers (i) implementing the self-consistent Sternheimer equation, which determines the first-order variations of the charge density as well as the effective potential due to the presence of the displacement wave, and (ii) accounting for the features of the LAPW basis-set. Owing to the displaced atoms, the latter entails considering both Pulay basis-set corrections and discontinuities at the MT-sphere surfaces in the section-wise defined LAPW basis and the potentials. While the Pulay terms compensate for the representation of the wave functions outside the Hilbert space spanned by the finite LAPW basis-set, the discontinuities require the introduction of surface integral contributions. Decisive has amongst others been a sustainable programming paradigm, making juPhon become a complex and sophisticated testing and application software. Within this thesis, I finally benchmark the juPhon phonon dispersions of bulk fcc Cu, Au, Al, Ne, and Ar as well as bcc Mo by comparing them with respective FD computations and experimental reference data. These results show a good agreement.
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