# Opportunities for B.Sc., M.Sc. or Ph.D. theses

If you are interested in doing a Bachelor, Master or PhD thesis with us, please do not hesitate to inquire either via email to Prof. Karsten Reuter or by stopping by at the secretary of the Chair of Theoretical Chemistry. Topics for Bachelor and Master theses are in general not individually announced, but are continuously available in one of our research focus areas. Please consult our research pages for more information.

At present we specifically invite applications for the following projects (other projects can be assigned on personal interest and availability).

### M.Sc. projects

**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.

**Implicit solvation studies using the Multipole Expansion model.**

One of the major goals in present energy science is to relieve society from its strong dependancy on limited and unrenewable energy sources, such as coal or oil. In this context, sunlight is very promising since abundantly available and easily accessible. However, for most applications photoenergy needs to be converted into chemical energy that can be stored, e.g. in batteries, by chemical reduction of carbon dioxide, or by splitting water into hydrogen and oxygen. In our project we want to gain a mechanistical understanding of the latter reaction on a titanium dioxide surface which has been observed experimentally.Previous first principles studies commonly neglected effects of the surrounding water molecules to avoid costly ab-initio molecular dynamics simulations. Faced with possibly charged intermediate states that are readily stabilized by a polar solvent like water, this approximation seems questionable. The interested student will investigate solvation effects in suitable, simplified model reactions using an implicit solvation scheme based on the Multipole Expansion (MPE) method in the framework of Density Functional Theory (DFT). Existing knowledge on UNIX based operating systems and programming is desirable, but not required.

**Tackling complexity in multiscale kinetic simulations: Kinetic Monte Carlo software performance analysis****.**

The kinetic Monte Carlo (kMC) method is ideal for tackling problems that require atomic scale detail but whose extent is beyond capabilities of state of the art quantum chemistry methods. In particular, it is routinely used for problems in crystal growth, heterogeneous catalysis, and solid diffusion, among others. Currently, one the most pressing challenge for the advancement of the method resides in the need for a more efficient treatment of problems of high complexity. In our group we are currently working towards solving these problems in two main areas of research: reactions in surfaces (heterogeneous catalysis) and lithium-ion diffusion in LTO (battery materials). In both cases, complexity becomes an issue when the microscopic rates (of diffusion or other elementary reaction events) are dependent on the instantaneous state of the system (lateral interaction effects). For heterogeneous catalysis, this problem is (combinatorially) exacerbated when the number of reactants considered is high, like in technological reactions. In the case of battery materials, typical crystal structures allow for a wide variety of local configurations leading to strong effects on microscopic diffusion rates.

The main tool to be used for this project is the `kmos' kMC framework; an extensible, modular software package, actively developed and used in our group. Recently, an extension has been implemented to better deal with the class of problems mentioned above. The interested student will be expected to familiarize him or herself with the concept of kMC simulations and with the `kmos' package and to implement and run a collection of kMC models of varying levels of complexity. The models used will include some developed in the Reuter group and some obtained from the scientific literature. The performance data obtained will be used to identify bottlenecks and guide the further development of `kmos'. Basic knowledge of UNIX based operating systems and some experience with programming (and/or scripting) languages (preferably Python) is desirable.

**Surface morphology in complex reaction environments: 3D ab initio thermodynamics phase diagrams.**

Ab initio thermodynamics represent a solid theoretical foundation through which “T = 0K” results from electronic structure calculations can be used to determine the equilibrium phase diagram of surfaces in a wide range of pressures and temperatures. In the context of heterogeneous catalysis, this provides an extensive amount of valuable information for the subsequent analysis of reactivity in realistic (finite pressure and temperature) conditions. This project will focus on the study of the Pd(100) surface. Palladium is widely used for automotive catalytic converters and represents a cheaper alternative to more widespread platinum. The work here proposed will build upon previous studies, in which phase diagrams for this surface under two simplified gas mixtures have been constructed: either under mixtures of CO and O_{2} or mixtures of NO and O_{2}.

For this project, the interested student will construct an ab initio thermodynamics phase diagram for the Pd(100) surface under exposure to a mixture of O_{2}, CO and NO gases and evaluate the extent of thermodynamic stability of coadsorption phases containing the three adsorbates, as well as the conditions for oxide formation under such complex gas mixtures. This work will complement our recent theoretical prediction suggesting that it is not possible to infer kinetic behavior in complex gas mixture from the separate analysis of simplified gas mixtures. In this project, the student will learn how to perform total energy calculation using the modern density functional theory (DFT) code CASTEP. Existing knowledge of UNIX based operating systems and basic scripting is desirable, but not required.

**Higher alcohol synthesis from syngas on metal catalysts.**

Higher alcohols are attractive fuel additives since they can be blended directly into gasoline. At present, the sustainable production of ethanol from biomass occurs primarily via fermentation. The synthesis of higher alcohols from biomassderived syngas (mainly CO and H2) represents an interesting alternative, since it allows for the use of a wider range of biomass sources. Still, the lack of efficient catalysts limits the industrial use of this approach.

The focus of the present project is on the catalytic properties of extended metal surfaces for ethanol synthesis. Experimentally, Rh catalysts show some selectivity and activity towards higher alcohol synthesis, though often in modified forms. With the use of computational modeling we aim for an improved understanding of the reaction mechanism on this type of catalysts. In the proposed M.Sc. project, the student will use density functional theory (DFT) to investigate key reaction steps such as CC coupling steps on different metal surfaces and at different active sites. Also the effect of the local environment in terms of adsorbate-adsorbate interactions will be investigated. The obtained DFT calculations will be used to establish energetic trends in the form of scaling relations and in the end provide the input for microkinetic models such as meanfield and kinetic Monte Carlo simulations. Prior experience with UNIX based operating systems and a scripting language (e.g. Python) is advantageous, but not a prerequisite.

**Germanium Intercalation of Graphene on Silicon Carbide: Can We Understand the Interface?**

Germanium intercalated quasi-freestanding monolayer graphene (Ge-QFMLG) grown on SiC has recently been proven to be an ideal material to form ballistic graphene pn-junctions because the graphene layer doping level depends on the Ge layer thickness intercalated between the SiC substrate and the graphene sheet. The p-type doped interface contains double as many intercalated Ge atoms than the n-doped structure. So far all attempts to identify the interface structure were based on density-functional theory (DFT) using smaller approximated unit cells (3 SiC cells). However, for a reliable structure prediction of the two different interfaces the large (6sqrt3x6sqrt3)R30 unit cell (108 SiC and 169 graphene unit cells) is necessary. To correctly address the van der Waals (vdW) bonded graphene layer state-of-the-art dispersion corrections have to be included. A structure search on the bases of DFT for structure sizes with hundreds of atoms is currently computationally too demanding. A promising compromise between computational cost and accuracy is the Density Functional based Tight Binding (DFTB) method incorporating a state-of-the-art vdW correction scheme.

The proposed MSc thesis is part of a collaborative research project with the group of Prof. Dr. F. S. Tautz (Forschungszentrum Juelich). We will perform a multilevel structure search to address the challenges of predicting an interface structure for very large systems. First, under consideration of the substrate symmetry, we will generate trial interface structures. Then, for these structures, we will construct a surface phase diagram using the semi-empiric DFTB method including dispersion corrections to identify the most promising candiates. The search will then be refined by recalculating the lowest energy structure candidates in DFT. In the process, the MSc student will deepen his/her theoretical background in the interdisciplinary field of materials science and become familiar with state-of-the-art computational methods and modeling techniques. Existing knowledge on UNIX based operating systems and basic programming skills (preferably in Python) is desirable.

**Projector functions for the DFT+U occupation matrix.**

DFT is, in principle, an exact theory. However, in practise this only holds if the exact exchange correlation-functional (xc-functional) is known. Unfortunately, the exact expression is unknown and for the practical use of DFT, approximations are needed. Nowadays, most of the used xc-functionals contain an expansion around the homogeneous electron gas limit, in their formulation. In such functionals, the electron-electron interaction is modelled by the classical coulomb interaction and the approximated exchange-correlation potential. Due to the approximations in the exchange-correlation potential, it is not possible to capture entirely the correct electron-electron interactions and thus, the correct description of the quantum mechanical many-body problem still remains a challenge. Especially the local spin-density approximation (LSDA) and spin-polarized generalized gradient approximation ( σ -GGA) often fail in describing the ground-state properties of systems whose electrons are more localized, like in transition metal oxides (TMO) and rare-earth compounds.

One of the most important errors introduced by the approximation of the xc-functional is the so called self-interaction error (SIE), which in general leads to an over-delocalization of the electron density. However, many other qualitative and quantitative failures in DFT, such as the above described failing in a correct description of strongly correlated systems, can be attributed to that failure. In recent years, an approach to cure the SIE has become quite popular, the DFT+U methodology. DFT+U, also known as LDA/GGA+U, introduces a corrective Hamiltonian, inspired by the generalized Hubbard model, which is added to the usual LDA or GGA Hamiltonian. A central aspect of this methods are the so called hubbard projectors, introduced for counting the numbers of electrons on a certain atom. Based on the idempotence error of the DFT+U occupation matrix, the goal is to define a strategy to define optimized hubbard projectors for transition metal oxides. As a first step the approach will be tested using the common test system for the use of DFT+U, NiO. In a second step the stretegy will be also applied to more complex transition metal oxides (like TiO2). The goal here is, to find a projector function which is described by a linear combination of Ti basis functions and O basis functions.

The student will work with the quantum chemistry code FHI-aims and with the inspyred package. The later is a framework for creating bio-inspired computational intelligence algorithms in Python.

**Development of Design Principles for Conductive Metal-Organic Framework Synthesis.**

Metal-Organic Frameworks (MOFs) are artificial, self-assembled, networks of metal centres connected by organic linker molecules. In general, these compounds are porous electric insulators. However, trace gas sensing applications utilising the porosity of the framework are in need of semi-conducting MOFs. Only recently, synthetic development lead to the discovery of potential candidate compounds which show promising features.

Taking the position of an synthetically working chemist dealing with these materials, one has very often no definite clue where to start to systematically improve the electrical conductivity of these materials. In order to save manpower, time, and chemicals it would then be appreciable to have at hand a set of rules of thumb which can help to efficiently steer the synthetic workflow. Potentially, such principles can be deduced from charge transport theory. When dealing with the electrical conductivity of a material two principal factors come into play: its mobility and the available number of charge carriers.

Working closely together with the group of professor Fischer here at TUM, the interested student will apply models for the mobility and charge carrier density to MOFs. Evaluating the observable trends will ideally lead to a set of qualitative principles. These will in turn help synthetically working chemists with systematic studies on the electrical conductivity of MOFs.

**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.

**Approximations of the many-electron wavefunction by a reduced density matrix approac**h

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).

### B.Sc. projects

**I) Photo-catalytic CO2 reduction**

Among other things humanity is facing two problems in the not too far future, global warming due to an overabundance of greenhouse gasses such as CO2 in the atmosphere and the need to transition away from finite fossil fuels to renewable energies. A way to tackle both these problems presents itself in the form of photochemical carbon dioxide reduction, where sunlight is harnessed to convert CO2 to higher energy products such as methanol. Unfortunately, currently available CO2 photo-reduction catalysts all suffer from very low turnover rates and are therefore not suitable for large scale industrial application. In the proposed Bachelor's project, candidates will employ state of the art computational---such as embedded density functional theory/classical mechanics simulations---and theoretical methods developed in the Reuter group to identify efficiency limiting steps and search for more effective photo-catalysts. Existing knowledge of UNIX based operating systems and programming is desirable, but not a necessity.

**II) Battery materials: LTO for LIBs**

Rechargeable lithium-ion batteries (LIBs) are key components of today's technology that power a range of devices from mobile phones to electric vehicles. During the discharge/charge cycles the electrode materials of a LIB take up or release Li ions and electrons, thereby undergoing changes in chemical composition, structure and electronic structure. In case of lithium-transition metal-oxides, which represent an important class of LIB electrode materials, reversible (de)intercalation of lithium ions in their structures can take place, and the redox-reaction involves a change in the oxidation state of the transition metal atoms. The focus of our project is on lithium-titanium-oxide materials, especially on Li4Ti5O12 (LTO), which can be used as an anode material for LIBs. The computational studies aim to contribute to a better atomic scale understanding of materials properties, such as Li ion mobility and electronic conductivity. Key issues to be dealt with include structural disorder and the occurrence of different oxidation states of the titanium atoms as the Li content is varied. In the BSc project you will use density functional theory techniques to study relations between the chemical composition, structural features and the electronic structure of Li-Ti-O materials. Prior experience with Linux and a scripting language is advantageous but not a prerequisite.

**III) Bistability in NO oxidation reactions in Pd(100)**

Palladium is a very interesting material for automotive catalytic converters and their properties have been extensively studied. However, the actual composition of the surface during operation, whether it is the pristine metal termination, a monolayer surface oxide or a bulk oxide layer, is still unknown. Recently, theoretical and experimental analysis on conditions of CO oxidation have suggested that actually two distinct terminations (pristine metal and surface oxide) might be present simultaneously, i.e. the surface is bistable. Recently, we have developed first-principles kinetic Monte Carlo models to analyze the NO oxidation properties of Pd(100), a reaction of interest for catalytic converters for lean-burn and diesel engines. In this project, the student will use these models to analyze the (relative) kinetic stability of the monolayer surface oxide and the pristine metal surface for different conditions of NO and O_{2} partial pressures, with the aim of determining whether a bistability region analogous to the one observed for CO oxidation exists also for NO oxidation.

**IV) A chemical puzzle: How the structure of a molecule influences the polarizability**

Despite the rapid advancement in computing power and methods, the calculation of large chemical systems remains a challenge for modern ab initio electronic structure theory. To investigate and understand processes in proteins, polymers or covalent organic frameworks, empirical force field methods have been used with some success. A main shortcoming of existing force fields is the ability to describe the polarization of the electron density with respect to changes in the environment. To overcome this problem, a new method to describe the polarizability is developed in our group (titled 'enhanced ACKS2'). One of the remaining obstacles is a property called 'response matrix', which depends in an unknown way on the geometry of the molecule, making it necessary to perform expensive computations that countermand the efficiency of the force field approach. In the proposed Bachelor's project the candidate will employ state of the art computational methods to perform a systematic investigation of the response matrix for a wide range of chemically diverse molecules and molecular fragments. This data is then analyzed to shed light on the structure-property relationship and to predict response matrices for different molecules, eventually employing machine learning methods. Existing knowledge of UNIX based operating systems and programming (Python) is highly desirable, but not a necessity.

**V) Synthesis of graphene on Cu surfaces: Identification of precursor molecules**

Two-dimensional materials (2DMs) such as graphene, hexagonal boron nitride, silicene and others, are currently amongst the most intensively studied classes of materials that hold great promise for future applications in many technological areas. However, the main hurdle against practical utilization of 2DMs is the lack of effective mass production techniques to satisfy the growing qualitative and quantitative demands for scientific and technological applications. The proposed BSc project aims to gain an atomic-scale understanding of the growth of graphene on Cu surfaces. The structures, energies and vibrational frequencies of possible precursor molecules formed during the growth process will be investigated using density functional theory. The calculated frequencies of the identified stable precursor molecules can be directly compared to data from experimental collaborators performing Raman spectroscopy. The obtained insight will be useful for guiding future experiments aimed at optimizing the growth conditions. Existing knowledge of UNIX based operating systems and programming (Python) is highly desirable, but not a necessity