A Theory of Electronic Energy Transfer in Complex Molecular Systems

The Förster theory for energy transfer is critically reviewed in the context of the present-day theory of nonradiative transitions, and the fundamental tenets of the Förster theory are shown to be erroneous. A new theory of electronic energy transfer is constructed taking into account the electronic transition theory. The intermolecular interaction between donor and acceptor molecules is assumed to perturb electron states of isolated molecules before the donor-molecule excitation. A distinguishing characteristic of the intermolecular interaction is spatial delocalization of the wave functions of electron states of the interacting molecules. It is this fact that has made it possible to realize ordinary photophysical processes between electron states of various molecules in a bimolecular system. In the experiments under study, the result of the intermolecular nonradiative photoprocess is given as evidence of electronic energy transfer from the donor molecule to the acceptor molecule.     

Nonradiative and radiative Förster energy transfer between quantum dots

We theoretically study nonradiative and radiative energy transfer between two localized quantum emitters, a donor (initially excited) and an acceptor (receiving the excitation). The rates of nonradiative and radiative processes are calculated depending on the spatial and spectral separation between the donor and acceptor states and for different donor and acceptor lifetimes for typical parameters of semiconductor quantum dots. We find that the donor lifetime can be significantly modified only due to the nonradiative Förster energy transfer process at donor–acceptor separations of approximately 10 nm (depending on the acceptor radiative lifetime) and for the energy detuning not larger than 1–2 meV. The efficiency of the nonradiative Förster energy transfer process under these conditions is close to unity and decreases rapidly with an increase in the donor–acceptor distance or energy detuning. At large donor–acceptor separations greater than 40 nm, the radiative corrections to the donor lifetime are comparable with nonradiative ones but are relatively weak.     

Nature of the Electron Excited States and Energy Transfer in Bichromophore Coumarin Molecules

Results of experimental and theoretical research for three bichromophore molecules, trans-stilbene-CH₂-coumarin 120 (I), 4-methylumbelliferone-CH₂-UC 17, and 4-(3-fluoro)-methylumbelliferone-CH₂-UC 17 (II, III), are presented. Schemes of photophysical processes in the bichromophore molecules based on quantum chemical calculations by the INDO method and theory of radiationless transitions in polyatomic organic molecules are suggested. After optical excitation to the strong donor absorption band, the fast internal conversion processes develop there. As a result, the molecule is found in the S ₁ ^* -state localized on the acceptor moiety. It is shown that a mechanism of intramolecular transfer energy in bichromophores different from that proposed by Förster may be realized. Excitation energy, initially located on D, will be transferred from the donor moiety to the acceptor chromophore in convenience of the internal conversion process. The intramolecular electronic energy transfer from energy donor to energy acceptor may be interpreted as the internal conversion process. The rate constants of internal conversion are calculated.     

Photoinduced energy transfer in blend films of hole and electron transport materials

The photoluminescence properties of the blend films consisting of the hole transport and electron transport materials, PVK and Alq₃, are studied by steady-state and time-resolved photoluminescence (PL) spectroscopy. Both the relative intensity and the photoluminescence lifetime are intensively dependent of the weight ratios of PVK and Alq₃. The detailed analysis of experiment data provides clear evidence for a Förster energy transfer from excited PVK, as donor, to Alq₃, as acceptor, based on nonradiative resonant transfer mechanism, and allows the determination of Förster radius and the concentration dependent energy transfer efficiency.     

Effect of distance between acceptor and donor on optical properties of composite semiconducting polymer films

The excitation energy transfer from poly(N-vinylcarbazole) (PVK) to tris(8-hydroxyquinoline) aluminum (Alq₃) in composite films was investigated by adding an inert polymer, poly(methyl methacrylate) (PMMA). The energy transfer efficiency calculated from the photoluminescence (PL) excitation spectra is consistent with that from the time-resolved PL decay data of the composite films. We have found a linear relationship between the two kinds of the distances, which are calculated according to volume density and the Förster theory. Experimental results and analyses provide a facile method to infer the energy transfer efficiency and the distance between the donor and the acceptor molecules in the composite films.     

Determination of the Efficiency and Energy Transfer Rate in the Fluorescence of a Single Donor–Acceptor Pair Attached to a Biomolecule

Resonance energy transfer from a single donor molecule to a single acceptor molecule (Förster resonance energy transfer) is currently used to determine the microscopic parameters describing interconformational changes in a protein molecule to which this single donor–acceptor pair is attached. A recently developed method makes it possible to intricately search for such parameters using a formula for the efficiency of Förster resonance energy transfer, which is the sum of several Gaussians. Another simpler method for the determination of the desired parameters of interconformational transitions has been proposed in this work on the basis of statistical processing of fluctuating tracks of fluorescence of a single donor–acceptor pair attached to a protein molecule.     

All-optical switching between quantum dot nanoarrays

An all-optical switching device is proposed, based on a sandwich structure comprising two-dimensional square-lattice nanoarrays of donor and acceptor quantum dots. The system operates on Förster energy transfer between the dark states of the individual nanoparticles, normally precluded by selection rules. On application of an off-resonant laser beam, a nonlinear mechanism activates transfer between spatially correlated quantum dots across an optically passive spacer layer, signifying an active switching action with parallel processing capability. In this report, electrodynamic theory is employed to analyse the system and to evaluate its energy transfer fidelity. The results of model calculations are presented in graphical form.     

Energy migration and transfer between chromophores embedded in Gaussian space

We have used a Monte Carlo method to investigate energy migration and transfer between chromophores embedded in Gaussian space. In using this method we have obtained fluorescence quantum yields, fluorescence depolarization, and the respective decay profiles of donor fluorescence. It was shown that all photophysical observables are dependent upon the number of donor and acceptor chromophores and upon the Förster radii ratio. The latter feature is particularly interesting, and it indicates the existence of correlations between donor and acceptor chromophores. It was shown that the excitation of the donor chromophore at the origin leads to different values of observables, in comparison with an excitation of a randomly selected donor chromophore. The results presented show the importance of the averaging procedures needed to be developed while dealing with specific distribution functions, as, for example, in the case of energy migration and trapping in aromatic polymers and copolymers.     

Electronic excitation energy transfer between two single molecules embedded in a polymer host

Unidirectional electronic excitation energy transfer from a photoexcited donor chromophore to a ground state acceptor chromophore - both linked by a rigid bridge - has been investigated by low temperature high-resolution single molecule spectroscopy. Our approach allows for accurately accessing static disorder in the donor and acceptor electronic transitions and to calculate the spectral overlap for each couple. By plotting the experimentally determined transfer rates against the spectral overlap, we can distinguish and quantify F?rster- and non-F?rster-type contributions to the energy transfer.     

Isotope effect,energy gap law and temperature effect in resonance energy transfer

The purpose of this paper is to derive an expression for the energy transfer probability that differs from that of Förster and Dexter in that it can be used explicitly for discussing the effects of deuteration and temperature on the rate of energy transfer, and the relation between the energy gap of the donor and acceptor molecules and the rate of energy transfer. It is found that, as in radiationless transitions, the temperature dependence of the rate of energy transfer can be expressed as

and effects of isotope substitution, and the energy gap between the excited donor and unexcited acceptor molecules on the energy transfer probability, are determined mainly by the Franck-Condon factor.     

Förster resonant energy transfer in quantum dot layers

Förster resonant energy transfer (FRET) in quantum dot (QD) layer structures has been analyzed. Small and large colloidal CdTe QDs were used as donors and acceptors, respectively. A FRET theory for random donor/acceptor distributions in two dimensions, taking into account exclusion zones around the donors, was applied to characterize FRET in a mixed monolayer. The exclusion zones provide a possibility to include the QD size in the FRET analysis and to determine its impact on the FRET efficiency. The acceptor concentration dependence of the FRET efficiency can also be described within this theory. In a separate donor/acceptor layer structure the distance dependence of the FRET efficiency as well as the acceptor enhancement was investigated. Both were found to agree well with the model of FRET between donor and acceptor layers.     

Influence of conducting nanocylinder on resonance energy transfer in donor-acceptor pair of molecules

We propose a mathematical model of nonradiative electronic excitation energy transfer between donor and acceptor molecules near the surface of an infinitely long conducting nanocylinder by means of surface plasmons. We reveal that, under resonance conditions, the rate of transfer increases compared to the case of the absence of the conducting cylindrical surface. The dependence of the energy transfer rate on configurational parameters system is found.     

Influence of energy transfer on the intensity pattern of vibronic excitation studied by reduced density-matrix theory

Intensity pattern of the vibronic transitions of a molecular dimer consisting of two molecules interacting through the Coulombic coupling is theoretically studied using a reduced density-matrix approach. The monomeric molecules are assumed to be electronic two-state systems. A single vibration mode with a high frequency and a continuous distribution of low-frequency phonons represented by the Ohmic spectral density are coupled to the electronic transition of the respective molecules. The spin-Boson model is employed to include the effect of electron-vibration and electron-phonon couplings. The intermolecular Coulombic coupling is assumed to be weak (inducing the Förster type of energy transfer process). It is found that, in addition to the well-known excitonic shifts, the intensity of the vibronic side bands reduces with the intermolecular coupling strength in the J-aggregate type of dimer while it increases in the H-aggregate type. When the vibronic bands are blurred by the broadening resulting from the coupling of the electrons to the continuous distribution of the phonons, the absorption line shape shows a wide range of variation depending on the strength of the intermolecular coupling.     

Study of energy transfer in a solution of coumarin 460 and rhodamine 6G by time-resolved laser-induced fluorescence spectroscopy

A multi-photon fast analog technique has been used to study nonradiative energy transfer from coumarin 460 to rhodamine 6G molecules. At low acceptor concentrations (<10^-2 mol/1) the fluorescence decay from coumarin deviates markedly from monoexponential behavior. The complex decay of the donor fluorescence reflects the time-dependent population of donor-acceptor pairs. Various energy transfer kinetics were investigated. The donor decay was found to be consistent with Förster kinetics and the critical energy transfer radius was found to be (5.46±0.10) nm.     

Using single donor–acceptor pairs to study the conformational dynamics of macromolecules

It is shown that in the presence of triplet levels of donor and acceptor molecules, the formula for function E(R) describing the dependence of efficiency E of Förster energy transfer on donor–acceptor distance R differs considerably from the one commonly used in experimental works.     

Radiationless transitions in complexes

A theoretical study is presented for the possible changes in radiationless transition probability from the first excited states to the ground state when a molecule enters a complex. An expression is derived that incorporates the contribution from the totally symmetric intermolecular vibration of the donor relative to the acceptor. The bond-length change has been calculated for a molecule entering a complex and on excitation of the latter in the chargetransfer band and also in states localized in the donor. It is found that there should not be large changes in probability for transitions localized in the donor.     

Nonradiative energy transfer in carbocyanine dye compositions inside surfactant micelles

Utilizing forced concentration of carbocyanine dye molecules DiI and DiD within a surfactant micelle, we have detected nonradiative transfer of electronic excitation energy for low initial dye concentrations in the aqueous micellar solution. Luminescence and fluorescence anisotropy decay studies allowed us to establish that in the micelles, the hydrophilic head of the dye is in contact with the water while the C18H37 groups are located in the hydrocarbon core of the micelle. We show that due to the structural features of the DiD acceptor molecule, rotational diffusion of the acceptor in the micelle is more free than for the donor DiI, the motion of which is constrained in the micelle. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 2, pp. 152–157, March–April, 2006.     

On the luminescence of luminol in DMSO in the presence of potassium superoxide-18-crown-6-ether and fluorescein

Luminol solution in DMSO in the presence of [18C6…K]⁺ O₂⁻ supramolecular complex (achieved from KO₂ and 18-Crown-6 (18C6)-ether) is chemiluminescent, and its intensity depends on the complex concentration. Using fluorescein (Fl) as an energy acceptor in this system, the luminescence energy transfer process from chemically excited species, aminophtalate dianion, to Fl could be evidenced. On the basis of Förster theory, the critical energy transfer distance, for both fluorescence and chemiluminescence, has been determined. The values are comparable: 22.41 Å (for chemiluminescence) and 20.88 Å (for fluorescence).     

7-Hydroxy-4-methyl-8-(4′-methylpiperazine-1′-yl)methyl coumarin: An efficient probe for fluorescence resonance energy transfer to a bioactive indoloquinolizine system

Solvatochromic effects on the fluorescence behavior of 7-hydroxy-4-methyl-8-(4′-methyl-piperazine-1′ yl)methylcoumarin (HMMC) was studied in different solvents. The fluorescence of HMMC was found to be highly sensitive to both the polarity and the protic character of the solvent. Exploiting the polarity-sensitive fluorescence property of HMMC, its excited-state dipole moment has been determined. Fluorescence (Förster) resonance energy transfer (FRET) process from HMMC to a potent bioactive molecule 3-acetyl-4-oxo-6,7-dihydro-12 H indolo-[2,3-a] quinolizine (AODIQ) was studied. From the determined K_SV and R₀ values, it is argued that a long-range dipole-dipole interaction is operating for the energy transfer mechanism. The energy transfer efficiency (E) and the distance between the acceptor and the donor (r₀) have been determined.