Pseudo-symmetry analysis of the d-block molecular orbitals in four-coordinate complexes

A rigorous definition of the concept of pseudo-symmetry, which is as important to chemistry as the concepts of symmetry implemented through group theory, should allow us to apply those group theoretical tools to molecules that are significantly distorted from those ideal symmetries best known and understood by the chemical community. In this paper, we consider four-coordinate transition-metal complexes with geometries along the interconversion path between the square and the tetrahedron and show how their molecular orbitals can be expressed in terms of either the tetrahedral or tetragonal symmetry groups. Furthermore, we analyze how the intensity of a d-d absorption band can be related to the degree of symmetry loss of the d-block molecular orbitals by means of their decomposition in terms of contributions from different pseudo-symmetry representations. As a final example, we also show how the substitution of a single ligand in a square planar complex affects the symmetry of the molecular orbitals and the absorption intensity associated to an electronic transition.