## Projects

**These below are examples of projects our group can offer to Master and Bachelor students**

### Bachelor Projects

Several of the master projects listed above and described below can be adapted to be a bachelor project. Even more so, a solid background in math/physics/programming is required - please email your request to the relevant project proposer, mentioning your grades in all classes relevant.

### Master projects

The master projects that we offer require a solid background in maths, physics, and programming. Therefore, anyone interested should first follow the course on Quantum Simulations of Materials (MSE468, spring semester, taught either by Prof. Nicola Marzari or Dr. Giovanni Pizzi). If interested, please contact the responsible for the organisation of the projects Michele Simoncelli at least two weeks before the EPFL registration deadline, with a copy of your transcripts and a short description of your competences and interests. The projects listed below are also suitable for EPFL master students who will take the course “Research project in materials I” (10 credits). Be aware that all the master students are required to attend all the group meetings and recommended seminars, remote supervision is guaranteed in case of absence of places in the laboratory.

- Koopmans-compliant calculations on systems with analytical solutions
- Theoretical and computational study of cathode materials for eco-friendly rechargable batteries
- Develop an active-learning AiiDA lab application for the Materials Cloud
- Visualization plugins for the Materials Cloud platform
- Quantum dynamical effects in correlated materials
- Engineering defect centers for quantum computing
- First-principles quantum simulations of transition-metal compounds
- Predicting screening parameters for fast Koopmans-compliant calculations
- Machine Learning applied to the study of complex oxide materials
- Jupyter web applications for quantum simulations
- Development of and AiiDA lab application for the calculation of topological invariants
- Towards an improved description of molecular dissociation by using systematic approximations
- Developing an AiiDA workflow for the automated calculation of optical properties
- Electrostatic-based models of structural distortions in perovskites

##### Koopmans-compliant calculations on systems with analytical solutions

Density functional theory (DFT) is a go-to method for predicting the structural and spectroscopic properties of materials and molecules computationally. However, DFT is only approximate, and standard formulations of DFT exhibit some notable shortcomings. Our group has been developing Koopmans-compliant (KC) functionals [1], an extension to DFT that is far better at predicting quasiparticle-related quantities such as ionization potentials and electron affinities.

We have already shown, via numerical calculations on real molecules, that KC functionals work well [2]. However, we have never tested them on simple systems where analytical solutions exist. Such systems are a dream for physicists: their simplicity, and the fact that we know the exact solution from the start, makes it much easier to interpret what is going on and diagnose any problems. In this project, the student will test KC functionals on systems with analytical solutions. This will involve a mix of mathematical derivations and numerical calculations, all in an effort to assess what KC functionals do well, and what they do poorly. The student's conclusions will help inform the ongoing development of KC functionals.

**Requirements**: a strong mathematical background is essential. This project will involve running calculations with Quantum Espresso and Mathematica on Linux machines, so prior familiarity with Mathematica and Linux would be useful, as would completion of MSE-423 and MSE-468 or equivalent.

[1] G. Borghi et al., Koopmans-compliant functionals and their performance against reference molecular data, Phys. Rev. B 90, 075135 (2014).

[2] N. Colonna et al., Koopmans-compliant functionals and potentials and their application to the GW100 test set, J. Chem. Theory Comput. 15, 1905 (2019).

Contact: Edward Linscott

##### Theoretical and computational study of cathode materials for eco-friendly rechargeable batteries

**Requirements:** Prior to this project, the candidate must follow the two courses MSE-423 and MSE-468.

Description of the project:

Our society is currently making a big effort to undergo a transition to the climate-friendly ecosystem. Constant growing of the population is accompanied by needs in larger amounts of energy [1], which is currently being produced mainly by using oil, coal, natural gas, which are sources of huge CO2 emissions which lead to the global warming. This cannot be continued like that further because the consequences for our planet and for the humanity will be disastrous. In fact, many governments announced roadmaps for achieving carbon-free ecosystem by 2050 (Swiss Energy Strategy 2050, EU's Battery2030+ flagship). Therefore, all the traditional energy sources must be replaced by the renewable energy sources (solar, wind, hydro, etc.), but these are not stable, and hence we need efficient and eco-friendly ("green") battery technologies for storing large amounts of energy and use it later when there are large demands. This semester project is focused on the theoretical and computational investigation of batteries, more precisely of the positive electrodes ("cathodes") [2].

Cathode materials contain transition-metal compounds (TMCs) (see figure below, which is the crystal structure of LiFePO4 [3]), and from the theoretical point of view modelling of TMCs is very challenging due to the presence of strongly localized and partially filled d-type electrons. In this project the student will use Hubbard-corrected density-functional theory [4,5,6], which has proven to be successful for accurate modelling of TMCs. All calculations will be done using the Quantum ESPRESSO package, which is the most widely used open-source electronic-structure software for materials modelling at the atomistic scale [7,8]. For more information see this page.

[1] D. Larcher and J.-M. Tarascon, Nature Chem. 7, 19 (2014).

[2] L. Monconduit, L. Croguennec, R. Dedryvere, Book "Electrodes for Li-ion Batteries: Materials, Mechanics, and Performance", vol. 2, Wiley (2015).

[3] M. Cococcioni and N. Marzari, Phys. Rev. Materials 3, 033801 (2019).

[4] V.L. Campo Jr. and M. Cococcioni, J. Phys.: Condens. Matter 22, 055602 (2010).

[5] I. Timrov, N. Marzari and M. Cococcioni, Phys. Rev. B 98, 085127 (2018).

[6] I. Timrov, N. Marzari and M. Cococcioni, Phys. Rev. B 103, 045141 (2021).

[7] P. Giannozzi et al., J. Phys.: Condens. Matter 29, 465901 (2017).

[8] P. Giannozzi et al., J. Chem. Phys. 152, 154105 (2020).

This project requires the following skills:

- Good knowledge of quantum mechanics, density-functional theory
- Basic knowledge of Linux and bash scripting

Contact: Iurii Timrov, Francesco Aquilante

##### Develop an active-learning AiiDA lab application for the Materials Cloud

The Materials Cloud is a modern web platform built to support researchers in sharing data with other researchers as well as performing computational research directly on the platform. For example, researchers can use the platform to carry out structure optimization and band gap calculations and then publish their results to make it accessible for follow-up investigations.

In this project, the student will develop a new AiiDA lab application that enables researchers to use previously calculated results to determine which calculations/simulations to carry out next (active learning)[1-3]. The first stage of the project involves the identification of a suitable benchmark study and the research of pertinent machine learning algorithms. The student will then need to develop a design document for the application and start implementing a prototype implementation. The final stage is the implementation of a polished version of the app which will then be published on the Materials Cloud platform.

[1] Xue, Balachandran, Yuan, Hu, Qian, Dougherty, Lookman, PNAS, 113, 47 (2016).

[2] Balachandran, Prasanna, Young, Lookman, Rondinelli, Nat. Comm. 8, 1 (2017).

[3] Dai, Bruss, Glotzer, arXiv:1803.03296 [Cond-Mat, Physics:Physics], (March 2018).

The student should have a background in materials science and engineering, but is free in identifying the specific research focus suitable to their strengths and interests.

This project requires advanced software development experience with Python and basic experience with Jupyter notebooks.

Contact: Simon Adorf

##### Visualization plugins for the Materials Cloud platform

Our group has been developing AiiDA (www.aiida.net), a platform to automate simulation of materials, store results in a database, analyse the results and share them. Moreover, we develop Materials Cloud (www.materialscloud.org), a rich web interface to expose the AiiDA database and show research results, as well as to provide simulation tools to researchers. These projects require that the student is already expert with python, including its object-oriented programming features.

**Option 1**:
There is room for the students to choose a project to extend the functionalities to support researchers in the use of AiiDA via web interfaces, or to improve the web interface tools of Materials Cloud.

*These projects require experience with JavaScript, HTML, CSS.*

A non-exhaustive list of examples:

- New visualizer plugins of data in the database, or of specific physical properties: see e.g. http://materialscloud.org/tools/seekpath/ for crystal structures and Brillouin zones
- graph browsing, or Graphical Query Builder to look into the database
- advanced python tools to analyse calculation results

**Option 2**:

*These project requires experience with python and jupyter.*

Task: create interactive visualisations in python notebooks and/or as Materials Cloud tools (https://www.materialscloud.org/work/tools/options).

On possible example is the realisation of a tool that, given the Hamilonian parameters as obtained from a Wannier-Function calculation, can compute the interpolated band structure on the fly, and when zooming recalculates the band structure on the selected region, giving the illusion of an infinite-zoom capability. This project would help students in better understanding band structures, dealing with the interpolation of them from DFT calculations on denser grids using Wannier functions, and to put this knowledge together in a useful and advanced web tool.

Contact: Elsa Passaro,Valeria Granata, Giovanni Pizzi

##### Machine Learning applied to the study of complex oxide materials

The use of density-functional theory (DFT) [1,2] to simulate properties of materials is an essential tool for research and development of modern technologies. The existing DFT implementations are based on traditional approximations to the full quantum mechanical treatment of the many-electron problem. Only very recently, the scientific community has recognized the possibility of an alternative class of approximations, this time based on machine learning algorithms that are trained in order to reproduce the full quantum mechanical accuracy by supervised learning from a large data set.

In this project, the student will be guided through the development of a simple, yet effective neural network that can augment the accuracy of existing DFT-based methods. The project will be tailored to the prediction from first principles of the properties of complex oxide materials interesting for their many technological applications.

Current use of Linux, as well as interest and skills in computer programming are requirements for this project. Prior knowledge of machine learning is strongly recommended. DFT calculations will be performed using the Quantum ESPRESSO package [3,4] which is the most widely used open-source electronic-structure software for materials modelling at the atomistic scale.

[1] P. Hohenberg and W. Kohn,Phys. Rev.136, B864 (1964)

[2] W. Kohn and L. Sham,Phys. Rev.140, A1133 (1965)

[3] P. Giannozzi et al., J. Phys.: Condens. Matter 29, 465901 (2017)

[4] P. Giannozzi et al., J. Chem. Phys. 152, 154105 (2020)

Contact: Francesco Aquilante, Iurii Timrov

##### Quantum dynamical effects in correlated materials

Electronic structure calculations are fundamental to understand several physical properties of materials. For many ground state quantities, like the density or the total energy, density functional theory (DFT) is the way to go. However, to reproduce spectra that are measured, e.g., in photoemission experiments, DFT shows its limits, and more advanced theories are needed.

In this project, the student will approach electronic structure calculations from a theoretical perspective and apply DFT to a prototypical material. In a second stage, the study of more refined properties will be pursued, with an emphasis on dynamical quantum effects.

The project involves the use of the open-source software Abinit on Linux machines. A prior basic knowledge of Linux and bash scripting is recommended, as well as the main concepts of quantum mechanics applied to computational solid state physics. For that, the two courses MSE-423 and MSE-468 are strongly recommended.

Contact: Marco Vanzini

##### Engineering defect centers for quantum computing

The advent of quantum computers would revolutionise the scientific world. Industrial giants like IBM, Microsoft and Google, and a bigger and bigger number of researchers, are involved in a race for developing the technology to build a big and fault tolerant quantum computer. Among the most promising qubit candidates, defect centers in semiconductors stand out for the extremely long coherence time at room temperature. Thanks to their optical properties, these systems can be used successfully also for quantum communication (encrypt messages thanks to the laws of quantum mechanics) and quantum sensing (measuring very small quantities due to the extreme sensitivity to perturbations).

In this project, the student will perform electronic structure calculations to discover new defect centres in semiconductors. The first step consists in investigating the stability of the defects and their capability of storing quantum information. In a second stage, the defects will be engineered in order to overcome the limitations emerged in the first analysis.

The project involves the use of the software Quantum ESPRESSO on Linux machines. A prior basic knowledge of Linux and bash scripting is recommended, as well as the main concepts of quantum mechanics applied to computational solid state physics. For that, the two courses MSE-423 and MSE-468 are strongly recommended. The knowledge of the theory of quantum information is NOT required.

Contact: Francesco Libbi

##### First-principles quantum simulations of transition-metal compounds

**Requirements:** Prior to this project, the candidate must follow the two courses MSE-423 and MSE-468.

Description of the project:

Transition-metal compounds (TMCs) have many technological applications, e.g. they are used to fabricate cathodes in Li-ion batteries, thermoelectric devices, photocatalysts, to name a few. From the theoretical point of view, modelling of TMCs is very challenging due to the presence of strongly localized and partially filled d-type electrons. DFT+U and DFT+U+V are simple and at the same time powerful tools to model TMCs [1], however, the Hubbard U (on-site) and V (inter-site) parameters are often treated semi-empirically, which is a somewhat unsatisfactory approach. Recently, a new efficient linear-response approach was developed for the first-principles calculation of U and V based on density-functional perturbation theory [2, 3]. In this project, the student will learn how to compute U and V parameters, and how to perform DFT+U and DFT+U+V calculations for TMCs to investigate their structural, electronic, and magnetic [4]. All calculations will be done using the Quantum ESPRESSO package, which is the most widely used open-source electronic-structure software for materials modelling at the atomistic scale [5, 6]. For more information see this page.

[1] V.I. Anisimov, J. Zaanen, O.K. Andersen, Phys. Rev. B 44, 943 (1991).

[2] I. Timrov, N. Marzari and M. Cococcioni, Phys. Rev. B 98, 085127 (2018).

[3] I. Timrov, N. Marzari and M. Cococcioni, Phys. Rev. B 103, 045141 (2021).

[4] C. Ricca, I. Timrov, M. Cococcioni, N. Marzari, and U. Aschauer, Phys. Rev. Research 2, 023313 (2020).

[5] P. Giannozzi et al., J. Phys.: Condens. Matter 29, 465901 (2017).

[6] P. Giannozzi et al., J. Chem. Phys. 152, 154105 (2020).

This project requires:

- Knowledge of quantum mechanics in condensed matter and solid-state physics
- Basic knowledge of Linux and bash scripting

Contact: Iurii Timrov

##### Predicting screening parameters for fast Koopmans-compliant calculations

Density functional theory (DFT) is a go-to method for predicting the structural and spectroscopic properties of materials and molecules computationally. However, standard formulations of DFT exhibit some notable shortcomings, including the fact that they do not comply with Koopmans theorem.

Our group has been developing Koopmans-compliant functionals [1], an extension to DFT that complies with Koopmans theorem, making it far better at predicting quasiparticle-related quantities such as ionization potentials and electron affinities [2]. However, these calculations are relatively complicated, especially because we must first calculate a lot of screening parameters.

In this project, the student will investigate how we can streamline these complicated calculations. Specifically, they will investigate (a) if screening parameters can be accurately predicted from other system properties that are easier to calculate and (b) if these screening parameter estimates give sufficiently accurate ionization potentials and electron affinities.

This project will involve running calculations with Quantum Espresso on Linux machines. For this reason, prior familiarity with Linux is essential, as is completion of MSE-423 and MSE-468 or equivalent. Familiarity with python is also strongly recommended.

[1] G. Borghi et al., Koopmans-compliant functionals and their performance against reference molecular data, Phys. Rev. B 90, 075135 (2014).

[2] N. Colonna et al., Koopmans-compliant functionals and potentials and their application to the GW100 test set, J. Chem. Theory Comput. 15, 1905 (2019).

Contact: Edward Linscott

##### Prediction of shear and layer-breathing modes for layered materials

When atoms oscillate in a layered material, composed by 2D layers, the low-energy part of the vibrational spectrum is characterised by two fundamental sets of normal-mode vibrations, where the layers oscillate as rigid units. These oscillations can be either parallel (shear modes) or perpendicular (layer-breathing modes) to each other.

We have already performed a study that, given the symmetry of the layered material, can predict these modes, typically plotted as a function of the number of layers in the multilayer, in what is called a "fan diagram". This method has also been implemented in an online tool on the Materials Cloud. Below you can find a screenshot for molybdenum disulphide.

The goal of this project is to:

- create a database of computed interlayer force-constant parameters for the known 2D materials, e.g. for all materials of our 2D database. This part will involve running simulations with Quantum ESPRESSO, using the AiiDA code to manage the simulation workflows;
- extend the online tool so that, for known materials, the force constants are taken from our computed database (rather than using random initial values)
- extending its applicability also to heterostructure formed by different layers, that are now routinely realised experimentally (now, the tool is able to predict frequencies only for multilayers composed of identical layers). This includes computing force constants for multiple pairs of layers, and for different angles between them.

Contact: Giovanni Pizzi

##### Jupyter web applications for quantum simulations

In this project, we plan to develop Jupyter notebooks with educational content for computational materials science and condensed-matter physics classes, addressing a number of existing ones at EPFL focused on quantum-mechanical simulations, as its first goal, but with direct applicability to courses in other universities worldwide.

Importantly, we do not just plan to provide Jupyter notebooks: by preparing these using custom widgets and converting them into fully-interactive web apps, we will make them directly accessible from web platforms (such as our own https://www.materialscloud.org) in full open-access mode. Thanks to this design, students can focus at first on the educational content and challenges, rather than on the underlying technology to create web apps. However, thanks to the possibility to check and modify the app's source code, this approach also encourages active learning and computational thinking.

We will mainly depend on our OSSCAR technologies for this project. Below shows one OSSCAR web application for the numerical solution of the time-dependent Schrödinger equation.

**Requirements:** Good python programming skills and knowledge in quantum mechanics and simulations. The candidate should complete course MSE-468.

Contact: Dou Du and Giovanni Pizzi

##### Development of and AiiDA lab application for the calculation of topological invariants.

In the past decade, the ability to classify material with a given topological class has been one of the main interests within the field of condensed matter physics[1]. To this end, one or more topological invariants need to be evaluated. They can be used to determine to which topological class a material belongs and can also be shown to be directly tied to the manifestation of interesting properties, such as the Anomalous Quantum Hall Effect (AQHE) and Quantum Spin Hall Effect (QSHE)[2,3]. To this end, several methodologies and corresponding tools have been developed, such as Z2pack[4], which tracks the evolution of the Hybrid Wannier Charge Centers (HWCCs) within a given surface.

In this project, the student will develop a new AiiDA lab application that enables researchers to easily calculate several topological invariants of a material, given only its structure. The idea is to provide a turn-key solution which will remove the barriers that such a problem could present, such as knowledge of DFT calculations and python and bash scripting languages.

[1] Yan, B., & Zhang, S. C. (2012). Topological materials. Reports on Progress in Physics, 75(9), 096501. [2] Kane, C. L., & Mele, E. J. (2005). Z 2 topological order and the quantum spin Hall effect. Physical review letters, 95(14), 146802 [3] Haldane, F. D. M. (1988). Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the" parity anomaly". Physical review letters, 61(18), 2015. [4] Gresch, D., Autes, G., Yazyev, O. V., Troyer, M., Vanderbilt, D., Bernevig, B. A., & Soluyanov, A. A. (2017). Z2Pack: Numerical implementation of hybrid Wannier centers for identifying topological materials. Physical Review B, 95(7), 075146.

The student should have a background in physics oriented towards materials science.

This project requires advanced software development experience with Python and basic experience with Jupyter notebooks.

Contact: Davide Grassano

##### Towards an improved description of molecular dissociation by using systematic approximations

The proposed project belongs to the field of electronic structure theory, an ever-growing research area, where physics, chemistry and material science meet in a fascinating way. Bond breaking and bond formation are examples of ubiquitous processes in chemistry. Despite this fact, their description from a theoretical point of view is still a very challenging one. At present many theoretical approaches either provide unsatisfactory results, or they are accurate but not widely applicable, mainly due to their high computational cost.

In recent years the framework of the adiabatic connection fluctuation dissipation (ACFD) theorem [1] has become a promising alternative to ground state density-functional theory (DFT). The approach has been applied to tackle the problem of bond breaking and calculation of the correlation energy of atoms, molecules and solids, with very encouraging results [2, 3, 4, 5]. Further progress in this research area has been hindered by the lack of systematic approximations beyond the two simplest ones, that is to say the so-called random phase approximation (RPA) and the RPA plus exact-exchange (RPAx) one.

The aim of the proposed project is to i) build systematic approximations beyond RPA and RPAx, and ii) test their performance on an exactly solvable model system, which is a simplified but still representative version of real ones.

On the long term the project has the potential to also involve implementation of the newly developed approximations in an electronic structure theory code, such as Quantum Espresso, to carry out calculations of the dissociation curve of small molecules.

[1] D. Langreth and J.P. Perdew. Solid State Commun., 17, 1425, (1975).

[2] M. Fuchs and X. Gonze. Phys. Rev. B, 65, 235109, (2002).

[3] M. Hellgren and U. von Barth. Phys. Rev. B, 78, 11510, (2008).

[4] J. Toulouse, I.C Gerber, G. Jansen, A. Savin, and J.G. Ángyán. Phys. Rev. Lett., 102, 096404, (2009).

[5] N. Colonna, M. Hellgren, and S. de Gironcoli. Phys. Rev. B, 93, 195108, (2016).

**Requirements:**
The student taking up this project should have a solid knowledge of quantum mechanics and condensed matter theory. Since the work will involve analytical calculations and the use of technical computing software such as Mathematica a strong mathematical background is highly desirable.

Contact: Giovanna Lani

##### Developing an AiiDA workflow for the automated calculation of optical properties

The optical properties of materials play an important role in many applications, ranging from solar cells to plasmonic nanoparticles. Finding the optimal materials for these applications is challenging, both due to the size of the design space and the costs involved in synthesizing and investigating each material. Here, computer simulations using electronic structure methods can provide an initial screening of large numbers of materials by predicting the relevant properties in an automated fashion.

In this project, the student will develop a workflow for determining the dielectric tensor of a bulk material with AiiDA [1], a powerful materials’ infrastructure for high-throughput calculations. The workflow will subsequently be applied to a class of materials relevant to the application that most piques the student’s interests. Time permitting, these results can then be used to for example derive the Spectroscopic limited maximum efficiency (SLME) [2, 3], a screening metric for single-junction photovoltaic cells, or calculate the extinction spectra of nanoparticles [4] with different morphologies using tools such as DDSCAT [5].

[1] S. P. Huber et al., AiiDA 1.0, a scalable computational infrastructure for automated reproducible workflows and data provenance, Sci. Data 7, 300 (2020). [2] L. Yu and A. Zunger, Identification of Potential Photovoltaic Absorbers Based on First-Principles Spectroscopic Screening of Materials, Phys. Rev. Lett. 108, 068701 (2012). [3] K. Choudhary, M. Bercx et al., Accelerated Discovery of Efficient Solar Cell Materials Using Quantum and Machine-Learning Methods, Chem. Mater. 2019, 31, 15, 5900–5908 (2019). [4] T. Willhammar, et al., Structure and vacancy distribution in copper telluride nanoparticles influence plasmonic activity in the near-infrared, Nat. Commun. 8, 14925 (2017). [5] B. T. Draine and P.J. Flatau Discrete-Dipole Approximation For Scattering Calculations. J. Opt. Soc. Am. A 11, 1491 (1994).

**Requirements**: Moderate experience with the Python programming language and a good understanding of condensed matter theory. Prior experience with electronic structure methods - density functional theory in particular - is a plus.

Contact: Marnik Bercx

##### Electrostatic-based models of structural distortions in perovskites

Perovskites, which the chemical formula ABO3, are a highly versatile and chemically diverse class of materials hosting properties from superconductivity to piezoelectricity. Many high-temperature phases adopt a cubic paraelectric phase, one with no spontaneous polarization, and, at lower temperatures transition to a more stable polar or antipolar phase. The paraelectric phases can host local atomic displacements leading to local dipoles that are, on the whole, disordered. This has, for example, been observed in barium titanate (BaTiO3). We have already identified phases of cubic BaTiO3, with no net polarization, that possess such local dipoles. At a given temperature, the stability of a phase is largely dictated by long range electrostatic effects.

In this project, focusing on cubic BaTiO3, the student will build an electrostatic-based model to calculate the effect of these local dipole orderings on the energetics of the phase using well-establish methods for calculating periodic electrostatic quantities in crystalline systems. Depending on the student’s interest, the summation techniques can be extended and optimized and/or parameterized using results of their own density functional theory calculations using Quantum Espresso. Time permitting, this model can be extended to other phases of BaTiO3.

**Requirements:**
The student should have a solid analytical skills, knowledge of quantum mechanics and condensed matter. Prior experience with first-principles calculations (for example from MSE 468) and basic programming knowledge is a plus.

Contact: Michele Kotiuga