Racah interelectronic repulsion energy

Table 13 Racah Interelectronic Repulsion Energies for Free Metal Cations, Weak- /Strong-Field Crossover Energies, d-Electron Configurations and LFSEs for Pseudo-Octahedral d" Complexes"...

There are two principle methods for determining Dq spectroscopically —the method used depending upon the metal ion in question. With some ions the lowest energy, spin-allowed transition corresponds exactly with lODg, at least to a first order approximation. In these circumstances, lODq is simply the energy of this absorption band and is obtained without recourse to calculation. All other spin-allowed transitions in cubic molecules will be functions of lODq and also of the Racah interelectronic repulsion parameters B and/or C (2) (or alternatively the Slater-Condon Fk parameters UO))- Where lODq cannot be directly estimated from an absorption band energy, two or more observed transition energies must be used to solve the appropriate secular equations. 

The energy level diagram for Ti3+ in fig. 3.4 shows the manner by which the 2D spectroscopic term is resolved into two different levels, or crystal field states, when the cation is situated in an octahedral crystal field produced by surrounding ligands. In a similar manner the spectroscopic terms for each 3d" configuration become separated into one or more crystal field states when the transition metal ion is located in a coordination site in a crystal structure. The extent to which each spectroscopic term is split into crystal field states can be obtained by semi-empirical calculations based on the interelectronic repulsion Racah B and C parameters derived from atomic spectra (Lever, 1984, p. 126). 

State. In order to obtain knowledge about the potential energy curves for the alternative spin states and hence about the respective non-adiabatic energy difference between the two minimum positions, help by reliable calculations was needed. DFT was our method of choice here [2,12], our experience is, that one may confidently use DFT results, if only Franck-Condon transitions from the ground state to lower excited states and polyhedron structures at or near to those for the ground state are utilised - and also, that the calculations are performed in the presence of a charge-compensating solvent medium. One has further to note, that the Racah parameters of interelectronic repulsion cannot be reproduced by DFT sufficiently well - they usually come out too small in comparison to the experimental values. 

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