Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

energy change between initial and final states and k is the reorganizationenergy required to change from initial to final equilibrium nuclear coordinates.For charge transport between nanocrystals, the tunneling rate is slowcompared with typical vibrational frequencies and the system must, on average,sample the crossing point many times before transfer can occur. In thisnonadiabatic limit, the rate of electron transfer is given byk ¼2p jV 12 j 2 ðFCÞ ð1Þtwhere V 12 is the electronic coupling matrix element between initial and finalstates on resonance and FC is the Frank–Condon factor, given by the sum ofoverlap integrals of the vibrational wave functions of the initial and finalstates, weighted by the Boltzmann probability of occupation of the initialvibrational state.At high temperatures, when the vibrational frequencies are all smallcompared with kT/h, the vibrations may be treated classically and Eq. (1)reduces to [12]k ¼2p jV 12 j 2 ð4pkkTÞ 1=2 e DE*=kT ð2ÞtwhereðDE* ¼ DGB kÞ 2ð3Þ4kTo calculate the total reorganization energy k in Eq. (3), both internalvibrations in the molecules and changes in the configuration of the solventor dielectric surrounding the molecules must be taken into account. Denotingthe internal and dielectric contributions as k i and k o respectively, we havek ¼ k i þ k oð4ÞThe contribution from the dielectric can be estimated using a dielectriccontinuum model, where the slow (nonelectronic) part of the response is responsiblefor the reorganization barrier to electron transfer. For electrontransfer between two spheres, k o is given byk o ¼ 1e2 1þ 1 14pe 0 2r 1 2r 2 de op1e swhere r 1 and r 2 are the radii of the two spheres, d is their center-to-centerseparation, and e op and e s are respectively the optical and static dielectricconstants of the surrounding dielectric.ð5ÞCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.