Derivation of the AOM Parameterization from the Effective Hamiltonian for Complexed Transition Metal Ions with Application to Effectively Tetragonal Four-Coordinate Systems

The formalism of the angular overlap model for complexed transition metal ions is developed entirely from an effective Hamiltonian over five appropriate molecular orbitals. The five by five matrix algebra is spanned by a set of normalized irreducible tensorial matrices which transform under rotations according to the Wigner rotation matrices. Expansion of the effective Haimiltonian matrix in terms of this basis leads, with proper assumptions, to the AOM parameterization. The model is applied to four-coordinate effectively tetragonal systems to obtain a function of the spectroscopic parameters which is independent of the magnitudes of ligand-metal interactions but gives a value for a structural angle. Results are given for tetrabromo and tetrachloro Pd(II) and Pt(II) complexes