Electronic structure theory meets precision measurements

Electronic structure theory and precision measurements go hand in hand. Reliable predictions of atomic and molecular properties are often very useful and sometimes strictly necessary in order to design the best possible experimental setups and to interpret the measured results. This thesis is motivated by the search for new physics with molecules, where symmetry breaking molecular enhancement factors are crucial for the interpretation of measurements. Such enhancement factors should be provided by theoretical methods and the main question of this thesis is: How accurate can electronic structure methods be and how to quantify this accuracy?

To answer this question, the performance of the state-of-the-art relativistic coupled-cluster method for predicting molecular properties was thoroughly examined. In addition, a scheme for estimating the uncertainty of the obtained results from first principles was investigated. This scheme was benchmarked using both ground and excited state hyperfine structure (HFS) constants. Comparison between the calculated and experimental HFS constants showed excellent agreement within the estimated uncertainty, demonstrating the reliability of the relativistic coupled-cluster method and, more importantly, the scheme for estimating the uncertainty for predicting core-like properties.

The relativistic coupled-cluster method could consequently be used to determine the more exotic symmetry breaking molecular enhancement factors, where no experiment is available. Accurate values of these properties and, equally important, reliable uncertainty estimates will be crucial in the interpretation of the, yet to come, first measurements of symmetry breaking effects in molecules. Such measurements will have a large impact on the development of new physics theories.