Transitions parameterization scheme

We briefly summarize the parameterization schemes for f-electron energy levels, intraconfiguration transition probabilities, and the electron-phonon interaction, and review the current experimental situation for each area. We shall also speculate on potentially fertile areas of future investigation. 

A. Electron-Phonon Interaction Parameterization Scheme. In observing the fluorescence decay rate from a given J-manifold, it is generally found that the decay rate is independent of both the crystal-field level used to excite the system and the level used to monitor the fluorescence decay. This observation indicates that the crystal-field levels within a manifold attain thermal equilibrium within a time short compared to the fluorescence decay time. To obtain this equilibrium, the electronic states must interact with the host lattice which induces transitions between the various crystal-field levels. The interaction responsible for such transitions is the electron-phonon interaction. This interaction produces phonon-induced electric-dipole transitions, phonon side-band structure, and temperature-dependent line widths and fluorescence decay rates. It is also responsible for non-resonant, or more specifically, phonon-assisted energy transfer between both similar and different ions. Studies of these and other dynamic processes have been the focus of most of the spectroscopic studies of the transition metal and lanthanide ions over the past decade. An introduction to the lanthanide work is given by Hiifner (39). 

Co2(CO)q system, reveals that the reactions proceed through mononuclear transition states and intermediates, many of which have established precedents. The major pathway requires neither radical intermediates nor free formaldehyde. The observed rate laws, product distributions, kinetic isotope effects, solvent effects, and thermochemical parameters are accounted for by the proposed mechanistic scheme. Significant support of the proposed scheme at every crucial step is provided by a new type of semi-empirical molecular-orbital calculation which is parameterized via known bond-dissociation energies. The results may serve as a starting point for more detailed calculations. Generalization to other transition-metal catalyzed systems is not yet possible. 

The fundamental reasons for the difficulties faced by the MM methods when metal (both transition and nontransition) complexes are involved can be understood if one does not consider the MM as a purely empirical scheme (as it is frequently done), but think about them as of some reflection of specific features of molecular electronic structure, formalized by the form of the trial wave function of that class of compounds where such a parameterization might be possible. As shown in Chapter 3, organic compounds for which the MM methods are known to demonstrate significant successes can be described by the QC method, which directly leads to local and transferable two-center bonds. It is shown in Chapter 3 that the derivation of the MM method from the QC description is possible due to a common background of the MM and SLG description, which consists in the physical presence of two-center, two-electron bonds in organic molecules (in strict terms of Section 1.7 - numbers of electrons in each of the geminals weakly fluctuate). 

Various CNDO and INDO schemes have also been proposed for transition-metal clusters and for chemisorption on them. Although there have been some successes, it remains true that both the level of theory being used and the parameterization are both very much experimental. 

EHT, lEHT, MNDO, AMI, PM3, SINDOl, and INDO/S all predict the first few ionization potentials of non-metal containing systems within about 0.5 eV using Koopmans approximation. For higher energy ionization processes where orbital relaxation and correlation is required, the INDO/S scheme seems best. Only the EHT models yield ionization potentials from Koopmans approximation that are systematically useful. The INDO/S scheme has been parameterized for transition metals, but Koopmans approximation may not be used to estimate ionization potentials in most cases for the reasons discussed previously. A Cl on the ion is most useful, or a delta-SCF calculation can be used. 

---