Extinction Coefficients and Transition Moments

During a transition, an electron initially in one orbital suddenly finds itself in another. Intuitively, one can see that such a process should be unfavorable unless the electron is initially in a reasonable part of the first orbital (j)i, i.e., one where the probability of finding it is significant, and ends in correspondingly reasonable part of the second orbital 02 the transition to occur easily, the two orbitals must therefore overlap in space, i.e., there must be regions where their product 0i / 2 does not vanish. 

The total overlap between two AOs of an atom, say the Is and 2p AOs of the hydrogen atom, vanishes because although the two AOs do overlap in space, the regions where the product (ls)(2pj is positive are balanced by those where it is negative (Fig. 6.8a). This is because the yz plane is a node for the 2p AO, which is positive to the right of it and negative to the left of it, whereas the Is AO has the same sign all over. Now the variable X has the same nodal properties as the 2p AO (Fig. 6.8a). It follows that the product 2pJ X is positive everywhere, as is the Is AO. The triple product s)(2p )x is therefore also positive everywhere. There is therefore a finite transition moment for the transition Is 2p, which should be allowed.  

Note that molecules in solution have random orientations, so that the plane of polarization of incident light is effectively random. Thus while the transition Is - 2p could not be brought about by light polarized along the y axis (Fig. 6.8c), nor the transition Is 2py by light polarized along the X axis, there are always photons around with all possible polarizations so it is only necessary that one of the transition moments differ from zero. 

Similar arguments apply to transitions in molecules. For example, a 7T - 7T transition will be possible only if the incident light is polarized parallel to the n MOs and if one of the MOs has an additional node perpendicular to the plane of polarization. Thus a transition between the bonding and antibonding MOs of ethylene is possible if, and only if, the light is polarized along the C—C bond (Fig. 6.9a). In the case of such a tc 7T transition, the product il/iil/2 will usually be large because the n MOs will 

FIGURE 6.8. (a) The total overlap between the AOs Is and 2p of H vanishes (b) the transition moment along the x axis does not, but (c) that along the y axis does. 

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