Förster Resonance Energy Transfer
1 Large Excitation Energy Transfer Dynamics in Nano-Hybrid Systems
by Dirk Ziemann, Thomas Plehn and Volkhard May Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, D-12489 Berlin, Germany, EU
2 Introduction
Electronic excitation energy transfer (EET) represents an ubiquitous phenomenon in physical chemistry, nanophotonics, plasmonics and other disciplines of nanoscience. It interrelates quantum system [math]1[/math] with ground state [math]|1g\rangle[/math] and excited state [math]|1e\rangle[/math] to quantum system [math]2[/math] with ground state [math]|\2\bar{g}\rangle[/math] and excited state [math]|\2\bar{e}\rangle[/math] via the energy exchange matrix element [math]V_{\rm EET}=\langle\2\bar{e}|\langle\1g|\hat{W}|\1e\rangle|\2\bar{g}\rangle[/math][11]. The complete Coulomb-interaction (electrostatic interaction) among the charges of system 1 and system 2 (electrons and nuclei) is denoted by [math]\hat{W}[/math]. The formula assumes vanishing wave function overlap between both systems. Thus charge (particle) exchange contributions do not appear. Besides a sufficiently large [math]V_{\rm EET}[/math] a further supposition for efficient EET is that the excitation energy [math]E_{1 e} - E_{1 g}[/math] of the one system is comparable with the excitation energy [math]E_{2 \bar e} - E_{2 \bar g}[/math] of the other system.We also emphasize that this type of EET can be understood as the short distance version of a general quantum electrodynamic photon exchange process (see, for example, [11]).
The variant of EET which refers to molecules is connected with the name of Förster. Respective rates display the famous [math]\frac{1}{R^{6}}}[/math]-dependence ([math]R[/math] denotes the intermolecular distance) since the coupling is dominated by molecular electronic transition point dipoles. If the charge distribution in the interacting species is more complex the [math]\frac{1}{R^{6}}}[/math]-dependence of the rate undergoes drastic changes. This can be demonstrated, for example, by combining nano-systems of varying composition and shape [13, 14]. The coupling of molecules to differently shaped semiconductor nano-crystals (NCs) was of particular interest in this respect (c.f., for example,[4] - [10]). In contrast to the extended experimental work, theoretical studies describing molecule-NC EET with an atomistic resolution found less interest. A dipyridyl porphyrin interacting with a Cd[math]_{33}[/math] Te[math]_{33}[/math] NC coated by a Zn[math]_{78}[/math]S[math]_{78}[/math] shell has been investigated in [7] using a DFT approach.
