Formula recoupling

From Eq. (15) we observe that the intermolecular potential is completely specified by the coefficients v rPP ). These expansion coefficients can be obtained in various ways. If the intermolecular potential is given in terms of atom-atom potentials, it is possible to obtain explicit expressions for these coefficients (see Section II,C). If the long-range part of the potential is known from perturbation theory calculations in the multipole expansion, the expansion coefficients, after some angular momentum recoupling, can also be obtained from explicit formulas (see van der Avoird et al., 1980). If the (short- and intermediate-range) potential is known... 

Since only one possibility exists for the intermediate states Sas = SA+s and SCs = Sc + s, a single term arises in the recoupling formula. For electron delocalisation 5 = +1/2 whereas for the case of hole delocalisation s = —1/2 can be applied. 

Let us recapitulate the approach applied for trinuclear systems where each ket is constructed by means of its own coupling scheme depending on the localisation of the extra electron (hole). Any pair of kets is related through a recoupling formula which, for the four spins, contains the 9/-symbol, e.g. 

A detailed study of 0(4) transformation properties leads to an exact formula which is not explicitly shown. However, the important points are that (1) in the exact formula, the recoupling coefficient is written as... 

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