Ligand Influence upon Radial Wave Functions

The influence of the ligand field upon the radial distribution function for the 3d orbitals of a transition metal complex ion has been investigated. A simple one-electron approximation was used for the metal ion and a point-charge model was employed for the ligands. Exact numerical solutions of the resulting radial equations were obtained and compared with one-parameter variation functions. For reasonable ligand charges and distances, the displacements in orbital energies and transition frequencies are found to be smaller than the errors in current theories. However, the differential expansions and contractions in the orbitals are sufficiently large to produce significant changes in certain radial integrals.