Single-centre MO theory of transition metal complexes

• Published in: Journal of physics. B, Atomic, molecular, and optical physics Vol. 41; no. 3; pp. 035102 - 035102 (7)
• Main Authors: Lebernegg, S, Amthauer, G, Grodzicki, M
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 14.02.2008; Institute of Physics
• Subjects: Atomic and molecular physics; Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations); Density-functional theory; Electronic structure of atoms, molecules and their ions: theory; Exact sciences and technology; Physics; Transition elements Complexes; Electronic structure; Molecular orbital method; Hamiltonians; Pseudopotential; Ligand field theory; Theoretical study; Reliability; Electrostatic potential; Comparative study; Local density approximation
• ISSN: 0953-4075; 1361-6455
• DOI: 10.1088/0953-4075/41/3/035102

The full multi-centre molecular Hamiltonian in the local density approximation for a mononuclear transition metal complex is transformed into a single-centre Hamiltonian explicitly including overlap, covalency and ligand-field effects. The orbital interactions of the metal d-orbitals with the ligand orbitals appear as a repulsive pseudopotential yielding the dominant contribution to the ligand-field splitting. The reliability of this approach is examined by comparison with numerical electronic structure calculations in the local density approximation on three representative systems. Finally, the proof is given that the repulsive pseudopotential exhibits the same angular dependence as the electrostatic potential from the ligands entering the Hamiltonian of ligand-field theory. For this reason, ligand-field theory very often yields the correct splitting pattern of the d-orbitals whereas the radial part is considerably different from the simple expression of ligand-field theory. In particular, there is no general theoretical justification for an R-5-dependence of the ligand-field splitting even for complexes of cubic symmetry.