## 3 Controlled Energy Transfer  
### Static-Field Induced EET  
It is somewhat surprising to observe that seemingly little attention has been given to the effect of local static electric fields on the process of electronic energy transfer. First, let us consider a static field whose strength, assumed to be uniform across the sample, is under direct experimental control. The most obvious evidence for the existence of any such effect, modifying the transfer efficiency, may be anticipated as a change in the relative intensities of fluorescence from the donor and acceptor [9]. For example, an enhanced rate of energy transfer, relative to donor emission, will lead to stronger fluorescence from the acceptor--unless the donor emission is itself modified to the same degree by the static field. In this respect, the surest guide to rate modification will be the specific effect of the static field on the acceptor. For a given donor-acceptor pair in the solution phase, for which there is a free molecular orientation with respect to any fixed-direction, an externally applied field may correctly be assumed to negate any consistent effect on the rate of energy transfer. Much the same conclusion can be drawn for any randomly oriented ensemble of donors and acceptors in a solid, heterogeneous medium. In any such system (provided that the rotational relaxation times exceed the emission timescales), one might only expect a marginally broadened distribution of donor and acceptor fluorescence intensities. However, the situation is very different in the case of a medium in which the static field can affect the orientational distribution. An obvious instance is a doped liquid crystal, though the molecules in any polar liquid will experience the same effect to some degree. Indeed, the structure of most molecules have a sufficiently low symmetry to support a permanent electric dipole--specifically, those that belong to one of the Schoenflies point groups C\({}_{\rm s}\), C\({}_{\rm n}\) or C\({}_{\rm nv}\). The most familiar manifestation of alignment in a static field, featuring in the Debye equation, is the dipolar contribution to electronic polarisation [39]. There are two distinct mechanisms through which the applied electric field may modify observations of energy transfer [40]. One is by direct engagement in one of the electronic transitions--either the donor decay or the acceptor excitation; the other is through an effect on the relative alignment of those two components. The first of these effects requires that the given transition is allowed by both single-quantum (electric dipole, E1) and two-quantum (E1\({}^{2}\)) selection rules. In fact, for polar molecules of every symmetry type, all of their conventional (i.e., E1-allowed) electronic transitions are also E1\({}^{2}\)-allowed, so this condition is automatically satisfied. Nonetheless, the contribution of the latter, static field-engaging channel, will generally be small since it arises from a higher order of perturbation theory. The second mechanism for a field-induced change in the energy transfer rates, i.e., that which occurs through an influence on molecular orientation, arises from the conventional average value of the orientation factor--the 2/3 in Equation (3)--being modified as a result of partial alignment, commonly signified by a Boltzmann-weighted distribution function. As [PERSON] showed in a comprehensive analysis of the orientation factor known as 'kappa squared' [41], optimal alignment can enhance the rate of transfer by a factor of up to six (the isotropic value 2/3 increasing to an upper limit of 4). Methods for estimating the value of the orientation factor are discussed in a useful review by [PERSON] [42]. The matrix element for EET is dominated by the input-field-independent term of Equation (2), but it also comprises correction terms that arise due to the presence of the static electric field. With respect to the first mechanism described above, the most significant process involves a linear coupling of the static field with either D or A.