In recent years, data-driven methods have become increasingly appealing to predict and accelerate chemical property prediction and molecular dynamics. Leveraging graph representations, graph neural networks have become the method of choice for this task. Initially, these models aimed to incorporate invariance to permutations and translations to align with the laws of physics. Nevertheless, subsequent work demonstrated that it is crucial to not only account for invariances but also to address rotational equivariance of molecular structures. Most commonly, performance benchmarking of machine learning models in this space occurs on the QM9 and MD17 datasets. However, most recently, it was shown that electron densities inherently contain more information than energy and other common properties of these benchmarks. Hence, this work emphasizes predicting a molecule’s electron density from its 3-dimensional atomistic representation via a data-driven approach. To predict densities, this study provides an extension to the QM9 dataset by computing density target values, i.e., densities coefficients, via density functional theory. Moreover, this work extends two algorithmic methodologies, a message passing and an attention-based methodology, to maintain rotational equivariance while including an arbitrary number of type-l features per irreducible representation, which is a prerequisite to predict and compute the electron density. Initial benchmarking revealed that the message passing model performs considerably better than the attention-based model. In fact, the message passing model, benchmarked on common public datasets, performs on par with state-of- the-art methodologies. Likewise, the electron density predictions achieve excellent results with mean absolute errors of 0.30%. Even when training on a small subset of data, decent errors of 1.37% on the test dataset are achievable. In summary, two different methodologies of equivariant machine learning models are introduced and benchmarked on common datasets. In addition, the scope of available properties within the QM9 dataset is extended to allow the prediction of information-rich electron densities.

As part of a Seminar at during my M.Sc. at TUM, I experimented with the implementation of Quantum Support Vector Machines and Classical Suport Vector Machines.