Prof. Dr. rer. nat. Karsten Reuter

Lehrveranstaltungen und Termine

Ausgeschriebene Angebote für Abschlussarbeiten

Approximations of the many-electron wavefunction by a reduced density matrix approach

The electronic many-particle wave function is generally described by a linear combination of Slater determinants. Since the number of determinants is described by a combinatorial equation and grows exponentially with the number of single-particle functions, the full configuration interaction wave function where the complete Hilbert space of many-particle functions is taken into account are possible only for the simplest models. A more efficient representation of the correlated wave function which contains all relevant information about the electronic structure is provided by the 2-particle reduced density matrix. This object occurs already in Hartree-Fock theory as the direct product of the 1-particle density matrix and scales only with the fourth power in the number of basis functions. Hence efficient techniques to compute accurate 2-particle reduced density matrices are of great interest in electronic structure theory and the MSc project offers a chance to make a contribution to a fundamental problem of theoretical physics. In this project the mathematically inclined student will explore different approaches and algorithms to directly compute the 2-particle reduced density matrix of real molecular systems and possibly solids, using and extending existing programs and algorithms. This will include programming work on numerical algorithms as well as fundamental research on the underlying mathematical problem. The successful candidate should have a strong interest in numerical problems, programming skills in Python and ideally basic knowledge of a compiled programming language (C, Fortran).

geeignet als

• Masterarbeit Physik der kondensierten Materie
• Masterarbeit Kern-, Teilchen- und Astrophysik
• Masterarbeit Applied and Engineering Physics

Themensteller(in): Karsten Reuter

Development of a simulation protocol for ab initio molecular dynamics simulations of solid-water interfaces

Solid-water interfaces are of outstanding importance for electrochemistry and catalysis. With modern algorithms based on density functional theory the electronic structure of water and solids can be analyzed in great detail. A fundamental challenge is the description of the electrochemical double layer which effectively forms a capacitor subject to competing chemical and physical processes. Electrode water interfaces, for example, are often subject to faradaic and non-faradaic charge transfer processes which are difficult to separate in experiments. The goal of the MSc project is to develop a simulation protocol using ab initio molecular dynamics (MD) to model the behaviour of liquid water at transition metal interfaces, to identify structural and electronic properties at the interface and associated with the electric double layer. In the MSc project problems such as the construction of atomistic models of the liquid phase will be addressed along with a statistical description of the fluctuating behaviour of the fluid.  Electronic properties including work functions, electronic band structure, dipole effects, charge accumulation and capacitance effects due to interactions at the solid-liquid interface will be analyzed and compared to more  approximate models. Simulations will be carried out with ab initio MD simulation software such as CP2K and FHI-AIMS.

geeignet als

• Masterarbeit Physik der kondensierten Materie
• Masterarbeit Applied and Engineering Physics

Themensteller(in): Karsten Reuter

Tight-binding beyond the two-center LCAO approximation

Semiempirical electronic structure approaches like the density functional tight-binding (DFTB) method are popular due to their unrivaled computational efficiency. This often makes them the only option, e.g. for describing the electronic structure of nanoparticles, which may consist of tens of thousands of atoms. Their efficiency comes at the cost of limited accuracy and transferability, however. Currently, these shortcomings are compensated on a case-by-case basis by the introduction of empirical parameters. Unfortunately, even here the limitations of the underlying theory sometimes become evident.
The goal of this M.Sc. project is the development of a novel framework for a tight-binding-like theory that goes beyond the typical two-center approximation for the Hamiltonian. The candidate should be interested learning the fundamentals of electronic structure theory, implementing methods and performing numerical test of different approximations. The main focus of the work will be on programming. Experience with a scripting language (e.g. Python) is advantageous but not mandatory. Questions about the project can be directed to johannes.margraf@ch.tum.de.
     

geeignet als

• Masterarbeit Physik der kondensierten Materie
• Masterarbeit Applied and Engineering Physics

Themensteller(in): Karsten Reuter