The choice of atomic coordinate systems and the transformation between different representations has been a matter of debate since the first molecular potential energy surfaces were explored. Many of these representations are based on our own, however biased, way of thinking about molecules in terms of atoms and bonds. Internal coordinates span the potential hypersurface on the basis of bond distances, angles and dihedrals, but for a non-redundant description there is no unique set available. The coupling between different coordinates strongly depends on the criteria applied in their construction as well as the specific point in chemical space being described. This matter is particularly complicated when following the course of a chemical reaction, whereby the number or type of bonds will necessarily change. Defining a set of coordinates for start, end points and everything in between is difficult and will usually require user input. In this work, we focus on the use of what is commonly refered to as Z-matrices, a set of non-redundant internal coordinates with an explicit ordering of the atoms in the system. It should be noted that while (non-)redundant internal coordinates are regularly applied in molecular simulations, also as intermediate representations, Z-matrices are less common and almost solely used for user interactions and as input format for quantum chemical packages.