Crystal field theory splitting energy

Eor transition metals the splitting of the d orbitals in a ligand field is most readily done using EHT. In all other semi-empirical methods, the orbital energies depend on the electron occupation. HyperChem s molecular orbital calculations give orbital energy spacings that differ from simple crystal field theory predictions. The total molecular wavefunction is an antisymmetrized product of the occupied molecular orbitals. The virtual set of orbitals are the residue of SCE calculations, in that they are deemed least suitable to describe the molecular wavefunction. 

Figure 5.6 Energy level diagram of the splitting of the J-orbitals of a transition metal ion as a result of (a) octahedral co-ordination and (b) tetrahedral coordination, according to the crystal field theory. (From Cotton and Wilkinson, 1976 Figure 23-4. Copyright 1976 John Wiley Sons, Inc. Reprinted by permission of the publisher.)...

The analogy between the two theories is only formal. Crystal field theory is a purely electrostatic approach that does not take into consideration the formation of MOs and the nature of the bond. According to crystal field theory, optical and magnetic properties are ascribed to crystal field splitting between two AOs, whereas in ligand field theory energy splitting occurs between AOs, and... 

Thus, for a transition metal ion in a simple cubic lattice, crystal field theory predicts that the (/-orbitals are split into two types, one consisting of two members, henceforth referred to as the eg set, of higher energy than the remaining three, which are also degenerate and referred to as the t2g set. The labels eg and t2g are given because of their transformation properties in the group Of, which describes the site symmetry of an ion in a simple cubic lattice.19... 

A prediction of crystal field theory as outlined in the preceding subsections is that the crystal field splitting parameter, A, should be rather critically dependent upon the details of the crystal lattice in which the transition metal ion is found, and that the splittings of the /-orbital energies should become larger and quite complicated in lattices of symmetry lower than cubic. The theory could not be expected to apply, for example, to the spectra of transition metal ions in solution. 

The theoretical energy values for 3H4, JG4, JD2 are shown in tables 10-12 together with the observed values and the values obtained by semiempirical calculations based on crystal field theory (Faucher and Moune, 1997). T s are the irreducible representations in S4 symmetry. The possible irreducible representations are l i. r2, r3, r4 for a two-electron system where r3 and F4 are degenerate. The theory overestimates Stark splittings of the 3H4 level, compared to the experimental values. One reason for this is the neglect of lattice relaxation... 

However, in sulphides and related minerals, the effects of covalent bonding predominate and orbital overlap must be taken into account. Thus, concepts of molecular orbital theory are described in chapter 11 and applied to aspects of the sulfide mineralogy of transition elements. Examples of computed energy diagrams for molecular clusters are also presented in chapter 11. There, it is noted that the fundamental 3d orbital energy splitting parameter of crystal field theory, A, receives a similar interpretation in the molecular orbital theory. 

Crystal-field (or d-d) transitions. Splitting of the J-orbital energy levels of a transition-metal ion by the crystal (or ligand) field of the surrounding anions gives rise to the possibility of electronic transitions between these levels. Such d-d transitions are responsible for the colors of many transition-metal-bearing minerals and are best treated within the formalism of crystal-field theory. 

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