Analysis of reduced finite element schemes in parameter dependent elliptic problems

This thesis presents an analysis of modified finite element schemes applied to parameter dependent elliptic problems prone to locking. Two different problems of similar type are considered: the problem of anisotropic heat conduction and the thin shell problem.reviewe

Large-scale surface reconstruction energetics of Pt(100) and Au(100) by all-electron DFT

The low-index surfaces of Au and Pt all tend to reconstruct, a fact that is of key importance in many nanostructure, catalytic, and electrochemical applications. Remarkably, some significant questions regarding their structural energies remain even today, in particular for the large-scale quasihexagonal reconstructed (100) surfaces: Rather dissimilar reconstruction energies for Au and Pt in available experiments, and experiment and theory do not match for Pt. We here show by all-electron density-functional theory that only large enough "(5 x N)" approximant supercells capture the qualitative reconstruction energy trend between Au(100) and Pt(100), in contrast to what is often done in the theoretical literature. Their magnitudes are then in fact similar, and closer to the measured value for Pt(100); our calculations achieve excellent agreement with known geometric characteristics and provide direct evidence for the electronic reconstruction driving force.Comment: updated version - also includes EPAPS information as auxiliary file; related publications can be found at http://www.fhi-berlin.mpg.de/th/th.htm

Nonadiabatic Ehrenfest molecular dynamics within the projector augmented-wave method

We have derived equations for nonadiabatic Ehrenfest molecular dynamics which conserve the total energy in the case of time-dependent discretization for electrons. A discretization is time-dependent in all cases where it or part of it depends on the positions of the nuclei, for example, in atomic orbital basis sets, and in the projector augmented-wave (PAW) method, where the augmentation functions depend on the nuclear positions. We have derived, implemented, and analyzed the energy conserving equations and their most common approximations for a 1D test system where we can achieve numerical results converged to a high accuracy. Based on the observations in 1D, we implement and analyze the Ehrenfest molecular dynamics in 3D using the PAW method and the time-dependent density functional formalism. We demonstrate the applicability of our method by carrying out calculations for small and medium sized molecules in both the adiabatic and the nonadiabatic regime.Comment: 12 pages, 10 figure

All-electron density functional theory and time-dependent density functional theory with high-order finite elements

We present for static density functional theory and time-dependent density functional theory calculations an all-electron method which employs high-order hierarchical finite element bases. Our mesh generation scheme, in which structured atomic meshes are merged to an unstructured molecular mesh, allows a highly nonuniform discretization of the space. Thus it is possible to represent the core and valence states using the same discretization scheme, i.e., no pseudopotentials or similar treatments are required. The nonuniform discretization also allows the use of large simulation cells, and therefore avoids any boundary effects.Comment: 11 pages, 9 figures; final (=published) versio

All-electron time-dependent density functional theory with finite elements: Time-propagation approach

We present an all-electron method for time-dependent density functional theory which employs hierarchical nonuniform finite-element bases and the time-propagation approach. The method is capable of treating linear and nonlinear response of valence and core electrons to an external field. We also introduce (i) a preconditioner for the propagation equation, (ii) a stable way to implement absorbing boundary conditions, and (iii) a new kind of absorbing boundary condition inspired by perfectly matched layers.Peer reviewe

Protective Coating Interfaces for Perovskite Solar Cell Materials: A First-Principles Study

The protection of halide perovskites is important for the performance and stability of emergent perovskite-based optoelectronic technologies. In this work, we investigate the potential inorganic protective coating materials ZnO, SrZrO3, and ZrO2 for the CsPbI3 perovskite. The optimal interface registries are identified with Bayesian optimization. We then use semilocal density functional theory (DFT) to determine the atomic structure at the interfaces of each coating material with the clean CsI-terminated surface and three reconstructed surface models with added PbI2 and CsI complexes. For the final structures, we explore the level alignment at the interface with hybrid DFT calculations. Our analysis of the level alignment at the coating-substrate interfaces reveals no detrimental mid-gap states but rather substrate-dependent valence and conduction band offsets. While ZnO and SrZrO3 act as insulators on CsPbI3, ZrO2 might be suitable as an electron transport layer with the right interface engineering. © 2022 The Authors. Published by American Chemical Society.</p