Ground term

In 1927 Hund formulated two empirieal mles that enable us to determine whieh of the terms arising from equivalent eleetrons lies lowest in energy. This means that for a ground eonfiguration with only equivalent eleetrons in partly filled orbitals we ean determine the lowest energy, or ground, term. These mles are ... 

There are two further rules for ground terms which tell us whether a multiplet arising from equivalent electrons is normal or inverted. 

T2g ground term and so reduces the temperature dependence of the magnetic moment. 

All d" configurations with T ground terms give rise to magnetic moments which are lower for second- and third-row than for first-row transition elements and are temperature dependent, but in no case so dramatically as for low-spin d". ... 

In tetrahedral fields the splitting of the free ion ground term is the reverse of that in octahedral fields so that, for d ions in tetrahedral fields A2g(F) lies lowest but three spin-allowed bands are still anticipated.In fact, the observed spectra usually consist of a broad, intense band in the visible region (responsible for the colour and often about 10 times as intense as in octahedral compounds) with a weaker one in the infrared. The only satisfactory interpretation is to assign these, respectively, as, wj = 7 i (P)-i A2(F) and ut = i(F)- A2(F) in which case U = ) should be... 

In a cubic field three spin-allowed transitions are expected because of the splitting of the free-ion, ground term and the presence of the term. In an octahedral field the splitting is the same as for the octahedral d ion and the same energy level diagram (p. 1029) can be used to interpret the spectra as was used for octahedral Cr Spectra of octahedral Ni usually do consist of three bands which are accordingly assigned as ... 

For d ions in tetrahedral fields the splitting of the free-ion ground term is the inverse of its splitting in an octahedral field, so that ig(F) lies lowest. In this ca.se three relatively intense bands are to be expected, arising from the transitions ... 

The T ground term of the tetrahedral ion is expected to lead to a temperature-dependent orbital contribution to the magnetic moment, whereas the A ground term of the octahedral ion is not, though mixing of the excited T2g(F) term into the AigiF) ground term is expected to raise its moment to ... 

Electronic absorption spectra are produced when electromagnetic radiation promotes the ions from their ground state to excited states. For the lanthanides the most common of such transitions involve excited states which are either components of the ground term or else belong to excited terms which arise from the same 4f" configuration as the ground term. In either case the transitions therefore involve only a redistribution of electrons within the 4f orbitals (i.e. f—>f transitions) and so are orbitally forbidden just like d—>d transitions. In the case of the latter the rule is partially relaxed by a mechanism which depends on the effect of the crystal field in distorting the symmetry of the metal ion. However, it has already been pointed out that crystal field effects are very much smaller in the case of ions and they... 

The effect of axial ligands on ground state properties of complexes with orbitally degenerate ground terms. G. A. Webb, Coord. Chem. Rev., 1969, 4,107-145 (151). 

On the right side of Fig. 3-9 are represented the relative energies of the two Tig terms, the and 2g. The ground term is the from the 2g configuration. Spin-allowed electronic transitions (those between terms of the same spin angular momentum - but see also Sections 3.6, 3.7 and Chapter 4) now take place upon excitation from -> A2g, The d-d spectra of octahedrally... 

All this is summarized in Fig. 3-12. The energy ordering of the free-ion terms is not determined by consideration of angular momentum properties alone and in general yields only to detailed numerical computation. The ground term - and only the ground term - may be deduced, however, from some simple rules due to Hund. 

Hund s first rule The ground term will be one of maximum spin-multiplicity (maximum S)... 

Hund s second rule If ambiguity remains, the maximum-spin ground term will then be one with maximum L... 

The ground term of the cP configuration is F. That of is also F. Those of and d are " F. We shall discuss these patterns in Section 3.10. For the moment, we only note the common occurrence of F terms and ask how they split in an octahedral crystal field. As for the case of the D term above, which splits like the d orbitals because the angular parts of their electron distributions are related, an F term splits up like a set of / orbital electron densities. A set of real / orbitals is shown in Fig. 3-13. Note how they comprise three subsets. One set of three orbitals has major lobes directed along the cartesian x or y or z axes. Another set comprises three orbitals, each formed by a pair of clover-leaf shapes, concentrated about two of the three cartesian planes. The third set comprises just one member, with lobes directed equally to all eight corners of an inscribing cube. In the free ion, of course, all seven / orbitals are degenerate. In an octahedral crystal field, however, the... 

An S term, like an s orbital, is non-degenerate. Therefore, while the effect of a crystal field (of any symmetry) will be to shift its energy, there can be no question of its splitting. The ground term for the configuration is S. In an octahedral crystal field, this is relabelled Aig, in tetrahedral symmetry, lacking a centre of inversion, it is labelled M]. 

Much useful understanding of the processes of crystal-field theory, however, can be had from a study of just the free-ion ground terms. Application of the simple process in Section 3.7 identifies the ground terms for d free ions as D, D,... 

Ignoring spin, the ground term for d is the same as for [Pg.52]

The effects of an octahedral crystal field upon each of the ground terms is shown in Fig. 3-20. This diagram was constructed as follows. From our previous discussions, + Eg, F Tig + Tig + Aig (with Ti, always in the middle), and... 

Figure 3-20. The symmetrical pattern of ground term splittings in octahedral symmetry.

The information in Section 3.9 and Section 3.10, referring to the crystal-field splittings of ground terms and all terms of the same spin multiplicity, can be very neatly encapsulated within two famous diagrams due to Orgel. Somewhat analogous. 

In octahedral symmetry, the F term splits into Aig + T2g + Tig crystal-field terms. Suppose we take the case for an octahedral nickel(ii) complex. The ground term is 2g. The total degeneracy of this term is 3 from the spin-multiplicity. Since an A term is orbitally (spatially) non-degenerate, we can assign a fictitious Leff value for this of 0 because 2Leff+l = 1. We might employ Van Vleck s formula now in the form... 

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