Energy Transfers

Energy transfer can occur when the excited state energy of the quencher Q is lower than that of the metal complex M  

This transfer is frequently referred to as a photosensitization reaction, where the quencher Q is sensitized to emission by excitation from M. In certain cases where it is not possible to generate the excited state Q by direct absorption of a photon from an incident light source, it is possible to access Q by energy transfer from a sensitizer. Mercury atoms can in selected cases be used as the sensitizer M. Table 1.2 demonstrates the triplet energies of a series of compounds that are frequently 

Because the energy differences 8E between the sublevel states of each multiplet of mA and nB are very small, 8E C kT at ambient temperature and above, they are nearly equally populated under equilibrium conditions (Boltzmann s law, Equation 2.9) and the probability of the formation of any given encounter spin state will be equal to all the others as there are mn choices, it will be equal to the spin-statistical factor a = (mn)  

For example, the multiplicity of radicals with one unpaired electron, S = V2, is 2S + 1=2. Each of four spin states is then expected to form with equal probability upon encounter of two radicals 2A and 2B, a = 1/4. Three of these are sublevels of the encounter complex with triplet multiplicity, S = SA + SB = 1, 2S + 1 = 3, and the fourth is the singlet encounter pair, S = SA + SB — 1 = 0, 2S + 1 = 1. Only the latter can undergo radical recombination to form a singlet product P=A B without undergoing ISC. The above considerations therefore suggest that the rate constant for radical recombination will not exceed one-quarter of the rate constant of diffusion, because only every fourth encounter will lead to recombination. 

This section deals with processes by which the excitation energy of an excited molecule D, the energy donor, is transferred to a neighbouring molecule A, the energy acceptor (Equation 2.31). The multiplicity of D and A will be specified as we look at the different mechanisms of energy transfer. 

Energy transfer permits electronic excitation of molecules A that do not absorb the incident light. This is exploited, for example, for light harvesting in photosynthetic 

The probability p that a photon emitted by D will be absorbed by A is given by Equation 2.32  

Nonradiative energy transfer is very often used in practical applications, such as to enhance the efficiency of phosphors and lasers. A nice example is the commercial phosphor Cas(P04)3 (FCl), which is doubly activated by Sb + and Mn + ions. When the phosphor is singly activated by Mn + ions, it turns out to be very inefficient, due to the weak absorption bands of the divalent manganese ion. However, coactivation with Sb + ions produces a very intense emission from the Mn + ions, because the Sb + ions (the donor centers) efficiently absorb the ultraviolet emission (253.6 nm) of 

F ure 5.17 Sequential steps for a nonradiative energy transfer process (see the text). 

To allow energy transfer, some interaction mechanism between the excited donor D and the acceptor A is needed. In fact, the probability of energy transfer from the 

The interaction Hamiltonian that appears in Equation (5.37) can involve different types of interactions namely, multipolar (electric and/or magnetic) interactions and/or a quantum mechanical exchange interaction. The dominant interaction is strongly dependent on the separation between the donor and acceptor ions and on the nature of their wavefunctions. 

For electric multipolar interactions, the energy transfer mechanism can be classified into several types, according to the character of the involved transitions of the donor (D) and acceptor (A) centers. Electric dipole-dipole (d-d) interactions occur when the transitions in D and A are both of electric dipole character. These processes correspond, in general, to the longest range order and the transfer probability varies with l/R, where R is the separation between D and A. Other electric multipolar interactions are only relevant at shorter distances dipole-quadrupole (d-q) interaction varies as l/R, while quadrupole-quadrupole interaction varies as l/R °. 

If a kilogram of matter can possess energy, how can from one body to another  

One way to transfer energy from one body to another is to place two bodies at different temperatures in contact with each other. It is a universal experience that in such circumstances the internal jenergy of the hotter body will decrease and the internal energy of the colder body will increase. Therefore, energy must have flowed from one to tlJe other. The energy which flows directly between two bodies in contact because of a temperature difference we call heat. j 

Our definition of heat is different from the one commonly used. We say, Heat is energy in transit from one body to another because of a temperature difference. In common English, people use heat interchangeably with temperature, This leads to such common phrases as It s not the heat it s the humidity and Beat the heat with a brand Xi air conditioner. Clearly, these rest on the human experience that when the temperature of the air is high, energy will flow into our bodies, uncomfortably. While it is flowing, it is heat. I 

The second way in which two bodies can exchange energy is by doing work upon each other. Again we must distinguish between an engineer s idea 

Name of species at rest Potential difference causing species to flow Name of species flowing 

Exposure-induced energy transfer in a resist matrix occurs not only between different states of a given radiation-sensitive resist molecule or component, but can also occur between such molecules or components when they are in close proximity to each other. It is customary to designate the molecule that carries the excitation energy as the donor (D) and the molecule that accepts the energy as the acceptor (A). The governing reaction is represented by Reaction [8.1]  

By nature, the energy transfer between molecules in resists is an electronic process, which is essentially adiabatic. Such a transfer will occur with reasonable probability only if the excitation energy of D is equal to or greater than that 

At the point of transfer, donor and acceptor molecules are coupled and form a single quanmm mechanical entity. The two distinct coupling mechanisms that 

The role of the central bond torsion and of the double bond and phenyl-vinyl torsions in nonvertical triplet excitation transfer to stilbenes was stressed [83]. The 

The most versatile method of forming triplets is by triplet-triplet energy transfer. 

Transfer of singlet excitation has been known for some time and has been studied by observation of induced fluorescence.140,141 In principle, one can imagine three general mechanisms for such energy transfer  

The trivial radiative process in which light emitted by D is reabsorbed by A. This process is trivial only in the mechanistic sense and must be taken into account in measurements of emission intensities. 

Dipole-dipole coupling, in which the transition moments of donor and acceptor are strongly coupled.142 Such interactions can occur over large distances if both of the moments are large and the transition energies are matched so that the overall process is isoenergetic. 

Collisional transfer, in which donor and acceptor approach each other sufficiently closely to allow spatial overlap of the orbitals of the donor and acceptor. 

If the quencher molecule Q has an excited state Q lower than M the excitation energy can be transferred according to 

Radiative or non-radiative deactivation of Q to Q then completes the quenching process. There are two major energy transfer processes. 

The HOMO and LUMO of the quencher Q must fall between the HOMO and LUMO of the energy donor 

Although the overall spin quantum number of the system M /Q rnust be kept in electron exchange, quenching can take place between singlet and triplet states in any combination  

Deactivation of the excited molecule M creates an electric field T/r3 which promotes the excitation of Q through its transition dipole R 

Instead of the usual decay by a radiative or nonradiative process, an excited molecule may decay by another process, energy transfer. The excited molecule, which is called th donor, may transfer the excitation energy to another molecule, called the acceptor. The transfer is primarily a phenomenon of dipole-dipole interactions between the donor and the acceptor. The rate of energy transfer depends on several factors the overlap of the emission spectrum of the donor with the absorption spectrum of the acceptor (/), the orientation of the donor and the acceptor transition dipoles (k), and the distance between the donor and the acceptor (r). The overlap J is described by the integral 

The distance between the donor and the acceptor r is described by Forster s theory. Forster derived an equation for the rate of energy transfer from a specific donor to a spcific acceptro kj  

At Ro the efficiency of transfer is 50%. The donor fluorescence quantum yield in the absence of transfer j) j and the overlap integral J are both incorporated in the equation of Rq  

FIGURE 17.14 Energy transfer in ANS and BSA complex. [Source Weber and Young (1964). With permission from Dr. Webber and the American Society for Biochemistry and Molecular Biology.] 

Construction of BODIPY-based probes with different mechanisms (a) PET (photoinduced electron transfer), (b) ICT (intramolecular charge transfer) and (c) FRET (Forster resonance energy transfer) channels. 

More related to general photochemistry are the papers which have appeared on wholly or partly diffusion-controlled reactions. The effect of a very short lifetime of the donor on the calculation of fluorescence quantum yields and lifetimes has been analysed by Viriot et al. Andre et al. analyse the kinetics of energy transfer to an acceptor when there are two different excited states capable of acting as donors and when interaction between these states is possible. The exchange interaction contribution to energy transfer between ions in the rapid diffusion limit 

Since energy transfer is important in biochemical systems Dewey and Hammes have developed a general method for estimating fluorescence resource energy between distributions of donors and acceptors on surfaces. Models of interest for membrane biochemistry are (a) an infinite plane, (b) parallel infinite planes, (c) the surface of a sphere, (d) the surfaces of concentric spheres, and (e) the surfaces of two separated spheres. 

Miyazaki, I. Shigeta, and K. Fueki. Radial. Phys. Chcm.. 1980. 16. 107. 

Charge separation is a light-induced effect of great interest beeause of its deployment as a means for utilization in solar energy conversion. A micellar system has been reported in which this achieved by bringing about a retardation of 

Kawasaki. K. Kasataiii, Y. Kusumoto. and N. Nakashima. Chcm. Lcii.. 1980, 1529. 

FIGURE 10. Different pathways for the deactivation of the excited state. 

In presence of a molecule of a lower energy excited state (acceptor), the excited donor (D ) can be deactivated by a process known as energy transfer which can be represented by the following sequence of equations. 

For energy transfer to occur, the energy level of the excited state of D has to be higher than that for A and the time scale of the energy transfer process must be faster than the lifetime of D. Two possible types of energy transfers are known—namely, radiative and nonradiative (radiationless) energy transfer. 

Radiative transfer occurs when the extra energy of D is emitted in form of luminescence and this radiation is absorbed by the acceptor (A). 

For this to be effective, the wavelengths where the D emits need to overlap with those where A absorbs. This type of interaction operates even when the distance between the donor and acceptor is large (100 A). However this radiative process is inefficient because luminescence is a three-dimensional process in which only a small fraction of the emitted light can be captured by the acceptor. 

While most of the materials used in studies of this type are non-polymeric in nature, the potential of various aromatic moieties as electron donors in polymers of structures (4), (40) and (41) has been explored [19, 72], and in future it may be possible to incorporate donor, acceptor and other sensitizing functions together into a single polymeric material. 

The rate constants for the vibrational relaxation of N2H by He, Ar, and Kr were estimated in a selected-ion flow tube study to be less than 1x10 molecule -s (Ar, Kr) [2]. 

Rate constants for the AJ=+1 (J = 1 -0 and J = 2 -1) and AJ = 4-2 (J = 2 0) rotational excitations of N2H by electron impact were calculated using a semiclassical, first-order perturbation theory that treats only the electron-dipole term of the interaction potential. 

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Much use has been made of micellar systems in the study of photophysical processes, such as in excited-state quenching by energy transfer or electron transfer (see Refs. 214-218 for examples). In the latter case, ions are involved, and their selective exclusion from the Stem and electrical double layer of charged micelles (see Ref. 219) can have dramatic effects, and ones of potential imfKntance in solar energy conversion systems. 

Chemical properties of deposited monolayers have been studied in various ways. The degree of ionization of a substituted coumarin film deposited on quartz was determined as a function of the pH of a solution in contact with the film, from which comparison with Gouy-Chapman theory (see Section V-2) could be made [151]. Several studies have been made of the UV-induced polymerization of monolayers (as well as of multilayers) of diacetylene amphiphiles (see Refs. 168, 169). Excitation energy transfer has been observed in a mixed monolayer of donor and acceptor molecules in stearic acid [170]. Electrical properties have been of interest, particularly the possibility that a suitably asymmetric film might be a unidirectional conductor, that is, a rectifier (see Refs. 171, 172). Optical properties of interest include the ability to make planar optical waveguides of thick LB films [173, 174]. 

Translational -> internal energy transfer Surface excitation (phonon, electron)... 

In coimection with the energy transfer modes, an important question, to which we now turn, is the significance of classical chaos in the long-time energy flow process, in particnlar the relative importance of chaotic classical dynamics, versus classically forbidden processes involving dynamical tuimelling . 

It should be emphasized that the existence of energy transfer modes hypotliesized earlier with the polyad breakdown is completely consistent with the energy transfer being due to non-classical, dynamical tiumelling processes. This is evident from the observation above that the disorder in the FI2O spechnm is attributable to non-classical effects which nonetheless are accompaniments of cte.s/c CT/bifiircations. 

Davis M J 1995 Trees from spectra generation, analysis, and energy transfer information Molecular Dynamics and Spectroscopy by Stimulated Emission Pumping ed H-L Dai and R W Field (Singapore World Scientific)... 

Aziz R A 1984 Interatomic potentials for rare-gases pure and mixed interactions Inert Gases Potentials, Dynamics and Energy Transfer in Doped Crystals ed M L Klein (Berlin Springer) oh 2, pp 5-86... 

Note that in this special case, the heat absorbed directly measures a state fiinction. One still has to consider how this constant-volume heat is measured, perhaps by an electric heater , but then is this not really work Conventionally, however, if work is restricted to pressure-volume work, any remaining contribution to the energy transfers can be called heat . 

Quack M and Troe J 1977 Unimoiecuiar reactions and energy transfer of highiy excited moiecuies Gas Kinetios and Energy Transfervo 2 (London The Chemicai Society)... 

This is no longer the case when (iii) motion along the reaction patir occurs on a time scale comparable to other relaxation times of the solute or the solvent, i.e. the system is partially non-relaxed. In this situation dynamic effects have to be taken into account explicitly, such as solvent-assisted intramolecular vibrational energy redistribution (IVR) in the solute, solvent-induced electronic surface hopping, dephasing, solute-solvent energy transfer, dynamic caging, rotational relaxation, or solvent dielectric and momentum relaxation. 

Kajimoto O 1999 Soivation in supercriticai fluids its effects on energy transfer and chemicai reactions Chem. Rev. 99 355-89... 

Boiton K and Nordhoim S 1996 A ciassicai moiecuiar dynamics study of the intramoiecuiar energy transfer of modei trans-stiibene Chem. Phys. 203 101-26... 

Straub J E and Berne B J 1986 Energy diffusion in many-dimensionai Markovian systems the oonsequenoes of oompetition between inter- and intramoieouiar vibrationai energy transfer J. Chem. Phys. 85 2999-3006... 

Straub J E and Berne B J 1986 Energy diffusion in many dimensional Markovian systems the consequences of the competition between inter- and intra-molecular vibrational energy transfer J. Chem. Phys. 85 2999 Straub J E, Borkovec M and Berne B J 1987 Numerical simulation of rate constants for a two degree of freedom system in the weak collision limit J. Chem. Phys. 86 4296... 

Gershinsky G and Berne B J 1999 The rate constant for activated barrier crossing the competition between IVR and energy transfer to the bath J. Chem. Phys. 110 1053... 

For example, energy transfer in molecule-surface collisions is best studied in nom-eactive systems, such as the scattering and trapping of rare-gas atoms or simple molecules at metal surfaces. We follow a similar approach below, discussing the dynamics of the different elementary processes separately. The surface must also be simplified compared to technologically relevant systems. To develop a detailed understanding, we must know exactly what the surface looks like and of what it is composed. This requires the use of surface science tools (section B 1.19-26) to prepare very well-characterized, atomically clean and ordered substrates on which reactions can be studied under ultrahigh vacuum conditions. The most accurate and specific experiments also employ molecular beam teclmiques, discussed in section B2.3. 

Harris J 1991 Mechanicai energy transfer in particie-surface coiiisions Dynamics of Gas-Surface Interactions ed C T Rettner and M N R Ashfoid (London Royai Society of Chemistry) p 1... 

Hodgson A, Meryl J, Traversaro P and Zhao H 1992 Energy transfer and vibrational effeets in the dissoeiation and seattering of D2 from Cu(111) Nature 356 501... 

Wang Z S, Darling G R and Holloway S 2000 Translation-to-rotational energy transfer in seattering of H2 moleeules from Cu(111) surfaees Surf. Sc/. 458 63... 

The first classical trajectory study of iinimoleciilar decomposition and intramolecular motion for realistic anhannonic molecular Hamiltonians was perfonned by Bunker [12,13], Both intrinsic RRKM and non-RRKM dynamics was observed in these studies. Since this pioneering work, there have been numerous additional studies [9,k7,30,M,M, ai d from which two distinct types of intramolecular motion, chaotic and quasiperiodic [14], have been identified. Both are depicted in figure A3,12,7. Chaotic vibrational motion is not regular as predicted by tire nonnal-mode model and, instead, there is energy transfer between the modes. If all the modes of the molecule participate in the chaotic motion and energy flow is sufficiently rapid, an initial microcanonical ensemble is maintained as the molecule dissociates and RRKM behaviour is observed [9], For non-random excitation initial apparent non-RRKM behaviour is observed, but at longer times a microcanonical ensemble of states is fonned and the probability of decomposition becomes that of RRKM theory. 

Uzer T 1991 Theories of intramolecular vibrational energy transfer Rhys. Rep. 199 73-146... 

Lin Y N and Rabinovitch B S 1970 A simple quasi-accommodation model of vibrational energy transfer J. Rhys. Chem. 74 3151-9... 

Brickmann J, Pfeiffer R and Schmidt P C 1984 The transition between regular and chaotic dynamics and its influence on the vibrational energy transfer in molecules after local preparation Ber. Bunsenges. Phys. Chem. 88 382-97... 

Sibert E L III, Reinhardt W P and Hynes J T 1982 Classical dynamics of energy transfer between bonds in ABA triatomics JCP77 3583-94... 

In this chapter we shall first outline the basic concepts of the various mechanisms for energy redistribution, followed by a very brief overview of collisional intennoleciilar energy transfer in chemical reaction systems. The main part of this chapter deals with true intramolecular energy transfer in polyatomic molecules, which is a topic of particular current importance. Stress is placed on basic ideas and concepts. It is not the aim of this chapter to review in detail the vast literature on this topic we refer to some of the key reviews and books [U, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, and 32] and the literature cited therein. These cover a variety of aspects of tire topic and fiirther, more detailed references will be given tliroiighoiit this review. We should mention here the energy transfer processes, which are of fiindamental importance but are beyond the scope of this review, such as electronic energy transfer by mechanisms of the Forster type [33, 34] and related processes. 

A 3.13.2 BASIC CONCEPTS FOR INTER- AND INTRAMOLECULAR ENERGY TRANSFER... 

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