### Abstract

The GPAW electronic structure code, developed at the physics department at the Technical University of Denmark, is used today by researchers all over the world to model the structural, electronic, optical and chemical properties of materials. They address fundamental questions in material science and use their knowledge to design new materials for a vast range of applications. Todays hottest topics are, amongst many others, better materials for energy conversion (e.g. solar cells), energy storage (batteries) and catalysts for the removal of environmentally dangerous exhausts. The mentioned properties are to a large extent governed by the physics on the atomic scale,

that means pure quantum mechanics. For many decades, Density Functional Theory has been the computational method of choice, since it provides a fairly easy and yet accurate way of determining electronic structures and related properties. However, it has several drawbacks. A conceptual problem is the diculty of interpreting the calculated results with respect to experimentally measured quantities, resulting in, for example, the “band gap problem” in semiconductors. A practical issue is the necessity of adapting the method with respect to the system one wants to investigate by choosing a certain functional or by tuning parameters. A succesful alternative is the so-called GW approximation. It is mathematically precise and gives a physically well-founded description of the complicated electron interactions in terms of screening. It provides a direct link to experimental observables through the concept of quasiparticles. Furthermore, it is parameter-free and thereby equally applicable to dierent kinds of systems. Its downside lies in its immense computational costs that limit its use in practice. Often, only the G0W0 approach is considered, which can be regarded as the lowest level of the GW approximation. This thesis documents the implementation of the G0W0 approximation in GPAW. It serves two purposes: First, it can be read as a manual by anyone who is interested in doing GW calculations with GPAW. All features and requirements are explained in detail and many examples are given. This provides a full understanding of how the code works and how the outcome should be interpreted. Secondly, it gives an extensive discussion of calculated results for the electronic structure of 3-dimensional, 2-dimensional and finite systems and comparison with other implementations, methods and experiments. It shows that bandstructures, band gaps and ionization potentials can be obtained accurately with G0W0 for many dierent materials. But also exceptions are pointed out, where higher levels of the GW approximation might be necessary.

that means pure quantum mechanics. For many decades, Density Functional Theory has been the computational method of choice, since it provides a fairly easy and yet accurate way of determining electronic structures and related properties. However, it has several drawbacks. A conceptual problem is the diculty of interpreting the calculated results with respect to experimentally measured quantities, resulting in, for example, the “band gap problem” in semiconductors. A practical issue is the necessity of adapting the method with respect to the system one wants to investigate by choosing a certain functional or by tuning parameters. A succesful alternative is the so-called GW approximation. It is mathematically precise and gives a physically well-founded description of the complicated electron interactions in terms of screening. It provides a direct link to experimental observables through the concept of quasiparticles. Furthermore, it is parameter-free and thereby equally applicable to dierent kinds of systems. Its downside lies in its immense computational costs that limit its use in practice. Often, only the G0W0 approach is considered, which can be regarded as the lowest level of the GW approximation. This thesis documents the implementation of the G0W0 approximation in GPAW. It serves two purposes: First, it can be read as a manual by anyone who is interested in doing GW calculations with GPAW. All features and requirements are explained in detail and many examples are given. This provides a full understanding of how the code works and how the outcome should be interpreted. Secondly, it gives an extensive discussion of calculated results for the electronic structure of 3-dimensional, 2-dimensional and finite systems and comparison with other implementations, methods and experiments. It shows that bandstructures, band gaps and ionization potentials can be obtained accurately with G0W0 for many dierent materials. But also exceptions are pointed out, where higher levels of the GW approximation might be necessary.

Original language | English |
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Publisher | Department of Physics, Technical University of Denmark |
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Number of pages | 140 |

Publication status | Published - 2013 |

## Cite this

Hüser, F. (2013).

*Quasiparticle GW calculations within the GPAW electronic structure code*. Department of Physics, Technical University of Denmark.