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Light, Life, and Measurement
Published in Thomas M. Nordlund, Peter M. Hoffmann, Quantitative Understanding of Biosystems, 2019
Thomas M. Nordlund, Peter M. Hoffmann
As we have seen, the radiative rate is directly proportional to the (integrated) absorption coefficient, which turns out to be proportional to the magnitude of the transition dipole moment squared. The distance dependence of the interaction, 1/r6, dies off quickly with distance, but typical values of the constant R0 make the transfer rate significant in the 1–10 nm region. See Table 9.4. A bit of thought about distance will reveal the primary assumption behind the transfer theory of Equations 9.32 and 9.33: the distance between donor and acceptor dipole moments can only be defined when r is significantly larger than the diameters of the molecular groups responsible for the dipole moments. Such groups might be tryptophan, heme, dansyl, Alexa fluor, etc., indicating that the Förster approximation commonly breaks down below about 1 nm.
Quantitative Molecular Electro‐Optics: Macromolecular Structures and Their Dynamics in Solution
Published in Stoyl P. Stoylov, Maria V. Stoimenova, Molecular and Colloidal Electro-Optics, 2016
Dietmar Porschke, Jan M. Antosiewicz
It is remarkable that in the early days of quantum mechanics, it was not generally accepted that absorption of light by chromophores is anisotropic. W. Kuhn reported [34] that Max Born, one of the founders of quantum mechanics, believed in isotropic absorption of light by chromophores. In order to get experimental evidence against this view, W. Kuhn performed a new type of experiments and measured for the first time the electric dichroism of some simple chromophores. Now there is no doubt anymore that absorption of light is anisotropic. Electromagnetic radiation may induce the transition of molecules to excited states; this transition is determined by the transition dipole moment of the molecules, which describes the plane of polarization of the electromagnetic radiation required for the interaction with the molecule. The probability of light absorption in the absorption band of any molecule is maximal, when this light is polarized parallel to the transition dipole moment; the probability is zero for perpendicular polarization. In general, the absorption of light is proportional to the square of the scalar product between the electric field vector of the light and the transition dipole vector. The absorption of light by a chromophore is described quantitatively by an extinction tensor ϵ^=(000000003ε)
Holographic Spectral Hole Burning: From Data Storage to Information Processing
Published in Günter Mahler, Volkhard May, Michael Schreiber, Molecular Electronics, 2020
Cosimo De Caro, Stefan Bernet, Alois Renn, Urs P. Wild
According to classical electromagnetism, the energy of a dipole in a static electric field is linearly proportional to the applied field. Therefore the Stark shift of an S1 ← S0 transition is proportional to the static electric field and the dipole moment difference between the first excited state S1 and the ground state S0. The electric dipole moment is a specific property of each molecule. Its value and direction give information about the charge distribution of the system studied. Not every molecule has a permanent dipole moment: in molecules with inversion symmetry the dipole moment is zero. On the other side, the dipole moment of a molecule embedded in a crystal or an amorphous system can be composed of a permanent contribution and an additional induced term that arises from an electrostatic interaction between the molecule and its microenvironment (local effective field) (20–23). Thus, Linear Stark effect can even be observed on molecules without a permanent dipole moment if these molecules are embedded in a host material (12,21,24). In amorphous systems, the absolute values of the induced contributions are described by a Gaussian distribution (12,23,21,25), and the orientations of the total dipole moments are isotropic. The analysis of the line shape and line width of a spectral hole under the influence of an external electric field requires that all parameters determined by the molecular and experimental arrangement geometries be considered (12,21,26). In particular, the orientation of the applied electric field with respect to laser light polarization plays an important role. Depending on the angle between these two vectors, different line shapes have been observed in organic-dye-doped polymers (20,21,24). Meixner et al. (12,20,21) have analyzed this problem and studied the influence of an electric field on spectral holes in chlorin/PVB samples, a well-known system used in Stark effect measurements (20,21,27–30). They found that the effect of photose-lection by excitation with linear polarized light has to be taken into account. Maximum absorption of the exciting light is achieved only when the transition dipole moment orientation is parallel to the exciting light polarization. On the other hand, the Stark effect of these molecules depends on the direction of the external field with respect to the dipole moment difference. Thus, the Stark effect and the molecule selection during burning are influenced by different geometrical angles, which are connected by the fixed intramolecular angle between the dipole moment difference and the transition dipole moment. A theoretical analysis of the line shapes therefore includes a rather complicated geometric averaging over the absorption and the Stark effect properties of all molecules in the isotropic system.
Interaction between the end groups and the main chain of conjugated polymers by time-resolved EPR and fluorescence spectroscopy
Published in Molecular Physics, 2019
Motoko S. Asano, Sho Hashimoto, Takuya Shinozuka, Yasutaka Fushimi, Kotohiro Nomura
The radiative rate constant is proportional to the square of the transition dipole moment. Thus the enhancement of the radiative rate constant in ZnPFV implies that the ZnPor part has a larger transition moment in the polymer. As described before, the molar extinction coefficient of the FV unit is significantly greater than that of the ZnPor part in the lowest singlet excited state [38]. Mixing between the π-electron systems in the end-group and main chain allows the excited singlet state of the ZnPor to ‘borrow’ transition intensity from PFV. In the excited singlet state, a structural change toward coplanar geometry between the end ZnPor group and the neighbouring FV units leads to partial delocalisation of π-electrons. It is highly likely that such partial delocalisation of π-electrons yields the observed significant enhancement of the radiative rate constant as well as the broad emission feature of the ZnPor part.