Energy bond, spin-orbit reduction

The simplest crystal field theory deals with a purely atomic ion in a static electric field. This ionic model should, however, be regarded as an approximation to the real cases in which there can generally be certain amount of covalency in the bonding between the metal ions and the surrounding anions. The reduction of the Coulomb repulsion energy, expressed by the parameters B and C, and of the spin-orbit interaction constant A implies the wider spread of the orbital functions than the purely atomic d functions " > > (see also Table XXII of ref. 50). The most direct experimental evidence for this covalency is the hyperfine structure due to anion nuclei observed in the electron spin resonance spectra by the metal ions. This phenomenon will be discussed in detail in the next section. 

In addition to the conventional overlap energy term there is a second term that depends on the bond-order Pq and the repulsive integral between an electron in adsorbate orbital 0 and an electron in orbital I on the neighboring atom, is equal to /fjj, Ek).(2.282), and the second term in follows from the first term of (2.283a) when using definition Eq.(2.35c) for the bond-order Pi2 and the zero-differential overlap approximation Eq.(2.284). In section 2 Eq.(2.40b) related to Eq.(2.309) was derived. It was shown to lead to a reduction of the interaction energy of two electrons with different spins in the same orbital (see Eq.(2.42,II)). The result implies that Ucff is not independent of the bond-order. An improved expression for would be ... 

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