## Wikipedia - Förster-Radius (de) Wikipedia - Förster-Resonanzenergietransfer (de) Wikipedia - Talk:Förster resonance energy transfer (en) Wikipedia - Trasferimento di energia per risonanza (it) Wikipedia - نقل الطاقة برنين فورستر (ar) Wikipedia - 蛍光共鳴エネルギー移動 (ja) Förster-resonance-energy transfer (FRET)

Also contains definition of: dipole–dipole excitation transfer
https://doi.org/10.1351/goldbook.FT07381
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 $$Const.$$.
Notes:
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.
Source:
PAC, 2007, 79, 293. (Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)) on page 342 [Terms] [Paper]