Non-radiative @E02256@ between two molecular entities separated by distances considerably exceeding the sum of their van der Waals radii. It describes the transfer in terms of the interaction between the @T06460@ of the entities in the very weak dipole-dipole @C01025@ limit. It is a Coulombic interaction frequently called a dipole-dipole @C01025@. The transfer @O04322@ from donor to acceptor, \(k_{\text{T}}\), is given by \[k_{\text{T}} = k_{\text{D}}\left ( \frac{R_{0}}{r} \right )^{6}=\frac{1}{\tau _{D}^{0}}\left ( \frac{R_{0}}{r}\right )^{6}\] where \(k_{\text{D}}\) and \(\tau_{\text{D}}^{0}\) are the @E02056@ @O04322@ and the @L03515@ of the excited donor in the absence of transfer, respectively, \(r\) is the distance between the donor and the acceptor and \(R_{0}\) is the @F02488@ or Förster radius, i.e., the distance at which transfer and spontaneous decay of the excited donor are equally probable (\(k_{\text{T}} = k_{\text{D}}\)) (see Note 3). \(R_{0}\) is given by \[R_{0} = Const.\left ( \frac{\kappa^{2}\mathit{\Phi}_{D}^{0}J }{n^{4}} \right )^{1/6}\] where \(\kappa\) is the orientation factor, \(\mathit{\Phi} _{D}^{0}\) is the @F02453@ @Q04991@ of the donor in the absence of transfer, \(n\) is the average @R05240@ of the medium in the @W06659@ range where @S05818@ is significant, \(J\) is the @S05818@ integral reflecting the degree of overlap of the donor @E02060@ with the acceptor @A00043@ and given by \[J = \int _{\lambda }I_{\lambda}^{D}(\lambda)\epsilon _{A}\left ( \lambda \right )\lambda^{4}\text{d}\lambda\] where \(I_{\lambda}^{D}(\lambda)\) is the normalized @S05827@ of the donor so that \(\int_{\lambda}I_{\lambda}^{D}(\lambda)\text{d}\lambda = 1\). \(\varepsilon_{\text{A}}({\lambda})\) is the @M03972@ of the acceptor. See Note 3 for the value of \(Const.\).
  1. The bandpass \(\Delta \lambda\) is a constant in spectrophotometers and spectrofluorometers using gratings. Thus, the scale is linear in @W06659@ and it is convenient to express and calculate the integrals in wavelengths instead of wavenumbers in order to avoid confusion.
  2. In practical terms, the integral \(\int_{\lambda}I_{\lambda}^{D}(\lambda)\text{d}\lambda\) is the area under the plot of the donor emission intensity versus the emission @W06659@.
  3. A practical expression for \(R_{0}\) is: \[\frac{R_{0}}{\text{nm}} = 2.108 \times 10^{-2}\left \{\kappa^{2}\mathit{\Phi}_{D}^{0}n^{-4}\int _{\lambda} I_{\lambda}^{D}(\lambda)\left [ \frac{\epsilon_{A}(\lambda)}{\text{dm}^{3}\ \text{mol}^{-1}\ \text{cm}^{-1}} \right ]\left ( \frac{\lambda}{\text{nm}} \right )^{4}\text{d}\lambda \right \}^{1/6}\] The orientation factor \(\kappa\) is given by \[\kappa  = \cos \theta_{\text{DA}} - 3\cos \theta_{\text{D}}\cos \theta_{\text{A}} = \sin \theta_{\text{D}}\sin \theta_{\text{A}}\varphi - 2\cos \theta_{\text{D}}\cos \theta_{\text{A}}\] where \(\theta_{\text{DA}}\) is the @A00346@ between the donor and acceptor moments, and \(\theta_{\text{D}}\) and \(\theta_{\text{A}}\) are the angles between these, respectively, and the separation vector; \(\varphi\) is the @A00346@ between the projections of the transition moments on a plane perpendicular to the line through the centres. \(\kappa^{2}\) can in principle take values from 0 (perpendicular transition moments) to 4 (collinear transition moments). When the transition moments are parallel and perpendicular to the separation vector, \(\kappa^{2} = 1\). When they are in line (i.e., their moments are strictly along the separation vector), \(\kappa^{2} = 4\). For randomly oriented @T06460@, e.g., in fluid solutions, \(\kappa^{2} = 2/3\).
  4. The transfer @Q04988@ is defined as \[\mathit{\Phi} _{\text{T}} = \frac{k_{\text{T}}}{k_{\text{D}}+k_{\text{T}}}\] and can be related to the ratio\(\frac{r}{R_{0}}\) as follows: \[\mathit{\Phi} _{\text{T}} = \frac{1}{1 + \left ( \frac{r}{R_{0}} \right )^{6}}\] or written in the following form:\[\mathit{\Phi} _{\text{T}} = 1 - \frac{\tau_{\text{D}} }{\tau_{\text{D}}^{0}}\] where \(\tau_{\text{D}}\) is the donor excited-state @L03515@ in the presence of acceptor, and \(\tau_{\text{D}}^{0}\) in the absence of acceptor.
  5. FRET is sometimes inappropriately called @F02453@-@R05333@ transfer. This is not correct because there is no fluorescence involved in FRET.
  6. Foerster is an alternative and acceptable spelling for Förster.
PAC, 2007, 79, 293. (Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)) on page 342 [Terms] [Paper]