20.7A: Spectral Features

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Crystal Field Theory copes reasonably well for d¹ (d⁹) systems but not for multi-electron systems, which are the more common. To deal with these systems we need to introduce a new concept, that of the electronic state. Electronic configurations refer to the way in which the electrons occupy the d orbitals, so for Ti(III) we write an electronic configuration of [Ar] 3d¹ and in an octahedral crystal field the lowest energy configuration would be written as t_2g¹ e_g⁰.

The electronic state refers to energy levels available to a group of electrons. This is much more complex than the single electron case since not only is it necessary to consider the crystal field effects of the repulsion of the metal electrons by the ligand electrons, but it is necessary to include the interactions between the electrons themselves.
When describing electronic configurations, lower case letters are used, thus t_2g¹ etc.

For electronic states, upper case (CAPITAL) letters are used and by analogy, a T state is triply degenerate. Subscripts 1 and 2 are used to distinguish states of like degeneracy and g and u subscripts indicate the presence of a center of symmetry eg. T_1g, T_2g, T_1u and T_2u.

These symbols are further modified to show the spin multiplicity of the electronic state using the Russell-Saunders Notation.
If we consider the Ti(III) case, the electronic configuration is d¹. In an octahedral crystal field this would give rise to a t_2g¹ arrangement and the excitation of the low lying electron to the higher level would then give an e_g¹ arrangement.

Only one d-d transition is expected and this roughly corresponds to what is observed for Ti(III) complexes, although it is somewhat more complicated due to Jahn-Teller considerations. At the high energy end of the spectrum, the presence of a charge transfer band should be noted as well. The origin of this will not be covered in detail in this course.

One approach taken when we consider the Russell-Saunders scheme with the various electronic states makes use of what are called Orgel diagrams. The relevant Orgel diagram for the D ground state is given below:

oct 4,9 tet 1,6 <-------------------------------------------> oct 1,6 tet 4,9

For a Fe(II) high spin octahedral complex we would write the free ion electronic configuration as d⁶ and in the octahedral crystal field it would be described as t_2g⁴ e_g².

The Russell-Saunders scheme that takes into account the electron-electron interactions would be described by a free ion ground state of ⁵D. In octahedral and tetrahedral crystal fields, this D state is split into E_(g) and T_2(g) terms. To decide which side of the D Orgel diagram should be applied to the interpretation can be quickly determined by looking at the electronic configuration and noting that the ground state is triply degenerate and the excited state is doubly degenerate (i.e. we must use the right-hand-side).
It is expected then that there should be 1 absorption band found in the electronic spectrum and that the energy of the transition corresponds directly to Δ. The transition is written in a notation that is read from right to left, which in this case is 5E_g ← 5T_2g.

Contributors and Attributions

Prof. Robert J. Lancashire (The Department of Chemistry, University of the West Indies)