Transition monopole approximation

It should be pointed out that the Forster calculations are based on the point dipole assumption which may be inaccurate when the separation distance is similar to the molecular size, as is the case for LHCII. In this situation the transition monopole approximation should also be considered. For chla Chang [172] has estimated that this leads to a Forster correction factor of 0.6-2.0 depending on orientation. 

Figure 7.5 shows the values of //2i(eo calculated for a pair of fran -butadiene molecules by the point-dipole (Eq. 7.18) and transition-monopole (Eq. 7.15) expressions. In panel A, the orientations of both molecules are held fixed while the center-to-center distance is varied in B the second molecule is rotated at a fixed distance. As a rule of thumb, the point-dipole approximation is reasonably satisfactory if the intermolecular distance is more than 4 or 5 times the length of the chromophores, although the relative error can still be substantial in some situations. 

Solute-solvent interactions always include London dispersion forces. Since HZ and X scarcely differ in molecular size, we expect approximate cancellation of the effect of dispersion forces in log m(yx- / hx)-Dispersion forces are equivalent to the interaction between virtual electronic oscillators. As much as a tenfold enhancement in interaction occurs if the oscillator of the solute particle is delocalised. The effect of delocalisation is equivalent to an increase in the distance between the two monopoles of the oscillator so that induced dipole-induced dipole interactions verge towards charge-dipole interactions. Because delocalised oscillators are also associated with a transition in the optical spectrum, a conjugate pair HZ, Z" for which one species is... 

The method of monopole interaction can be used for all transitions whether electrically or magnetically forbidden. In general, it will be more accurate than the electric dipole approximation, but it will also be more difficult to calculate. Moffitt (1956b) compromised by using the monopole interaction for nearest neighbors and the dipole interaction for the remainder. 

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