A continuous symmetry analysis of chemical bonding

The ability to quantify the symmetry content of a given molecular system is important both for the quantitative prediction of its physical and chemical properties, as well as for the establishment of powerful theoretical concepts that can be derived solely from symmetry considerations. The symmetry content of a complex object such as a molecule relies, however, on the level of structural description that is chosen. This may range form a simple geometrical picture in which only the position of the nuclei is indicated, to a more or less detailed description of the electronic structure given by the different quantum chemical methods. Recently, a paper was published describing a new general methodology for calculating the symmetry content of diverse mathematical objects, such as vectors, operators, matrices, functions and more. In the present work we apply that approach to explore the inversion symmetry for diatomic molecules. Although it is a very simple system, general physical conclusions on the phenomenon of chemical bonding can be easily obtained from the symmetry analysis at different levels of description.