Theory of Nonradiative Energy Transfer between Two Optical Ions Using Proper Adiabatic Approximation

Abstract

Using the adiabatic approximation of polyatomic molecules and methods of molecular quantum electrodynamics, we have derived the Förster-Dexter theory of energy transfer between two optical ions. Although we have assumed a single configurational coordinate, the theory can be easily formulated for a multiple normal coordinate system. This approach leads smoothly to the energy transfer rates originally derived by Dexter1 for electric dipole-electric dipole interaction without any additional assumptions regarding the normalization of the wavefunctions in the energy space. Using the transfer rates thus derived, and the band shape functions, W p , a new function F(T) has been proposed to study the temperature dependence of energy transfer rates due to the overlap of the emission and absorption lineshapes of the donor and acceptor ions, respectively. This function has been studied for various scenarios of the relative alignment of the zero phonon lines of these ions in order to understand the participation of phonons in the energy transfer process. We have also compared this quantum mechanically derived F(T) function with that derived using semiclassical theory. The agreements are very good at high temperatures.