Molecular point groups and symmetry in external magnetic fields

As quantum-chemical calculations of molecules in static external magnetic fields are becoming increasingly popular, the description of molecular symmetry under such conditions is also becoming more and more relevant. Using group theory, a general scheme of identifying the molecular point group in an external magnetic field is constructed. For both point groups that are non-existent in the absence of a field (C$_{∞}$and C$_{∞h}$) and their double groups, the character tables are presented. General properties of all possible point groups are discussed, and it is mathematically proven that they are all Abelian.