Computational methods at the atomic scale based on machine learning have been a fruitful research field in the past decade by merging the advantages of classical and quantum mechanical approaches. While parts of the field are already reaching a mature state, limitations of the models arising due to intrinsic assumptions are being explored to reach the next level in predictive accuracy and width of predictable target properties. One important area in this endeavor is the incorporation of long range effects arising from electrostatic and dispersion interactions.
The goal of this thesis is to advance our understanding of these effects by a combination of theoretical approaches and their application to target material systems. As preliminary work, a preexisting model for the description of electrostatics has been implemented and extended to further interactions including dispersion. The models both in original and extended form have been examined analytically to study their theoretical capabilities and how to use them most effectively in applications.
Over the coming years, the algorithms and insights developed in the first year will be applied to study relevant materials in order to understand the true capabilities of the long range models. Furthermore, mathematical methods will be used to answer questions regarding the theoretical foundations of the field with the aim of obtaining a more complete picture for how important long range effects are and how to best incorporate them into a machine learning framework.