Generalized selection rules for circular dichroism: a symmetry-adapted perturbation model for magnetic dipole allowed transitions

The independent systems approach for the circular dichroism (CD) of a magnetic dipole allowed transition of an achiral chromophore (A) in a chiral molecule leads to a perturbation expansion in terms of the electrostatic coupling operator V connecting the A states to those of the residual chiral framework C. The concomitant multipole expansion of V reduces the form of the CD to a power series in the inverse radial separation of A and C. Using the recently developed generalized selection rule procedure, the resultant expansion is analytically symmetry adapted to the point symmetries of the A and C chromophoric systems, with the explicit results presented for a wide range of symmetries. The results confirm that symmetry (particularly of A) is the principal determinant of the dominant CD mechanism, providing a rationale for the apparent inability of a unique mechanism to describe the CD activity of the wide range of A chromophore symmetries as found, for example, in transition metal complexes. Rigorous sector rules for the dominant mechanism for each A symmetry are derived. The general agreement with experimental behaviour consolidate the relevance of the independent systems approach.