Molecular pointgroups and symmetry in external magnetic fields.

Ansgar Pausch,Melanie Gebele,Wim Klopper

doi:10.1063/5.0069859

Ansgar Pausch, Melanie Gebele + Show 1 more

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https://doi.org/10.1063/5.0069859

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Abstract

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 pointgroup in an external magnetic field is constructed. For both pointgroups 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 pointgroups are discussed, and it is mathematically proven that they are all Abelian.

Highlights

If atoms are considered to be points, they belong to the threedimensional rotation group (Kh).17 Since molecules can be interpreted as a set of arbitrarily placed atoms in three-dimensional space, it must follow that all possible molecular point groups can be identified as Kh and its subgroups
Any valid symmetry operation of the system will act on the position vector of an atom (x) in such a way that
This implies that any improper rotation (σ, I, or Sn) maps the magnetic field onto its inverse, while proper rotations (Cn, E) map the magnetic field onto itself. This has a number of farreaching implications for molecular symmetry in external magnetic fields, as only those symmetry operations that map B onto itself according to Eq (2) can belong to the point group

Summary

Introduction

If atoms are considered to be points, they belong to the threedimensional rotation group (Kh).17 Since molecules can be interpreted as a set of arbitrarily placed atoms in three-dimensional space, it must follow that all possible molecular point groups can be identified as Kh and its subgroups. The molecular point group of a system can be identified by examining the symmetry operations (rotations, reflections, and combinations thereof), which map the molecule onto itself. The point group consisting of all possible combinations of these elements is C∞h, which is the point group of an atom in an external magnetic field.

Results

Conclusion