Splitting of terms

Bethe H. (1929). Splitting of terms in crystals. Amer. Phys., 3 133-206. 

Crystal field theory has its origins in Hans Bethe s famous 1929 paper Splitting of terms in crystals. In that paper Bethe demonstrated what happens to the various states of an ion when it is placed in a crystalline environment of definite symmetry. Later, John Van Vleck showed that the results of that investigation would apply equally well to a transition-metal compound if it could be approximated as a metal ion surrounded by ligands which only interact electrostatically with the... 

One other point needs to be mentioned regarding the splitting of terms of the free ion in chemical environments, and this concerns the spin multiplicity. The chemical environment does not interact directly with the electron spins, and thus all of the states into which a particular term is split have the same spin multiplicity as the parent term. 

In order to illustrate the splitting of terms of a d" configuration, the states for a d2 ion in several point groups are shown below. The free-ion terms have been given on page 259. 

Figure 19 Zero-field splitting of terms S = 1 to S = 2Vi, assuming E= 0...

Bethe, H. (1929) Splitting of terms in crystals. (Termsaufspaltung in Kristallen.) Ann. Phys., 3, 133-206. [Transl. Consultants Bureau, New York.]... 

It has been shown in the last section, and will further appear in succeeding sections, that the hypothesis of the spinning electron has made it possible to understand the splitting of terms (multiplets), a phenomenon which the orbital picture by itself was quite incapable of explaining. The phenomenon in fact depends upon the possession of angular momentum by the electron itself this internal angular momentum, by the quantum rules, can be directed in different ways with respect to the direction of the orbital moment, or with respect to a direction marked out by external means. 

The splitting of terms into multiplets is associated with the conservation of the centre of gravity of the states... 

The actual S5nnmetry of the distorted MeFs units in most cases is lower than D4ft. But to describe the electronic spectra it will be sufficient to consider only the tetragonal field component, as minor structural differences disappear within the width of the absorption bands. The same holds for the splitting of terms through spin-orbit coupling which therefore can be neglected. 

Besides the splitting of terms observed in the electronic transitions of coordination compounds, other forms of experimental verification of the Jahn-Teller effect include the ESR spectra of coordination compounds. X-ray crystallographic data showing different M-L bond lengths, and thermodynamic data. As an example, consider the stepwise formation constants in Table 16.28 for [Cu(NH3)6] +, which... 

The total splitting of terms of maximum multiplicity due to the spin-orbit interaction can also be calculated through the use of formula (1.107). It is found to be equal to... 

The crystal field splitting of terms and for a d ion in an Oh field illustrating the nephelauxetic effect and the mixing of Tig terms is shown below. 

Two points should be noted. First, a detailed argument is required to relate the splitting of orbital energies to the splitting of term energies. 

The Pi- and Pi-branch and probably also the P2- and P2-branch exhibit a small doublet structure, which we interpret as a splitting of terms with weight 2. 

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