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

For the specific case of charge transfer between two nanocrystals, wewill now attempt to identify the main contributions to k i and k o . This problemhas been studied by Brus [13], who applied the Marcus theory of electrontransfer to silicon nanocrystals surrounded by solvent. To calculate the internalreorganization energy, we must consider how the lattice in the nanocrystalresponds to the addition (or removal) of an electron. In general, changingthe charge state of the nanocrystal changes the equilibrium nuclear configurationand we denote the energy associated with the change from the unchargedconfiguration to the charged configuration on a single nanocrystalas k s . Because reorganization is necessary in both nanocrystals for electrontransfer to occur, the total value of k l in Eq. (4) is given by the sum of thedeformation energies k s on both nanocrystals.To understand the origin of k s in more detail, we must consider thevibrational modes which transform between the charged and uncharged configurations.These modes are the phonon modes of the nanocrystal, whichmay be either acoustic or optical. The strength of coupling of phonon modesto the electronic state of the nanocrystal is dependent on the chemicalcomposition of the semiconductor and on the nanocrystal size. In a nonpolarmaterial such as silicon, the relevant coupling is with acoustic phonons.Acoustic phonons couple to the energy of the system through the deformationpotential (a change in the electronic energy due to strain in the lattice). Innanocrystals, the contribution to k s from coupling to acoustic phononsthrough the deformation potential is expected to scale approximately asr 3 , where r is the nanocrystal radius [14]. Brus estimated a value of k s = 12meV in silicon nanocrystals of diameter 2 nm [13].In polar nanocrystals such as CdSe, the situation is more complicatedbecause optical phonons may also couple to the electronic state through theFro¨hlich interaction. This interaction involves a polarization of the crystallattice in response to an internal electric field. The Fro¨hlich interaction isresponsible for the vibrational structure seen in emission spectra of CdSenanocrystals, although, in that case, the scaling of coupling strength withnanocrystal size is complicated because both an electron and hole are presentin the nanocrystal and partially compensate each other’s charge [15]. Thesimpler case of coupling of optical phonons to a change in the overall chargestate of the nanocrystal (polaron formation) has been modeled in CdSe byOshiro et al. [16], who find that the relaxation energy associated with polaronformation increases rapidly as the nanocrystal size becomes less than theexciton Bohr radius, reaching a value of k s c 30 meV for a diameter of 2 nm.We are not able to make an accurate estimate of the additional reorganizationenergy due to deformation potential coupling in CdSe nanocrystals; howeverwe expect the contribution from Fro¨hlich interaction to dominate. Becausethe longitudinal optical (LO) phonon energy in CdSe (26.5 meV) is compa-Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.