According to the following scheme, electron transfer, intersystem crossing and energy transfer can all compete with fluorescence in deactivating an exciplex '(DA)* formed from the molecules A and D.
In polar solvents, polar exciplexes (contact ion pairs) dissociate into non- fluorescent radical ions (loose ion pairs or free ions) due to the stabilization of the separated ions by solvation. It has been observed that exciplex emis- sion decreases with increasing polarity of the solvent and that at the same
284 5 PHOTOPHYSICAL PROCESSES 5.4 BIMOLECULAR UI~.AC'I'IVA'I'ION I'KOCESSES
time the free-radical ions DO and A@ can be identified by flash spectroscopy (Mataga, 1984).
Assuming the existence of a quasi-stationary state the rate constant of an exothermic electron-transfer reaction can be written as
kdiR, k,, k-dirr, and k-, are the rate constants for diffusion, forward electron transfer from D to A, for the dissociation of the encounter complex to A and D, and for the back electron transfer from A o to DO, respectively. The terms with k - , have been neglected since k-, e k, can be assumed for exothermic reactions. According to the Marcus theory (1964) a relationship of the form exists for adiabatic outer-sphere electron-transfer reactions* between the free enthalpy of activation AGt and the free enthalpy of reaction AG. A in Equation (5.25) is the reorganization energy essentially due to changes in bond distances and solvation. As a consequence of this relation, the rate constant
should first increase with increasing exothermicity until the value AG = - A is reached and then decrease again. The dependence of log kc on AG ob- tained in this way is shown in Figure 5.26 by the dashed curve; the region of decreasing rate for strongly exergonic electron-transfer reactions (AG <
A) is referred to as the Marcus inverted region.
The temperature dependence of electron-transfer rate constants is inter- esting. In the normal region, it shows an activation energy as predicted from simple Marcus theory. In the inverted region, the activation energy is very small or zero. This agrees with the quantum mechanical version of the the- ory (Kestner et al., 1974; Fischer and Van Duyne, 1977), which makes it clear that the transition from the upper to the lower surface behaves just like ordinary internal conversion.
Studies of the fluorescence quenching in acetonitrile have shown that the electron-transfer reaction
* Redox processes between metal complexes are divided into outer-sphere processes and inner-sphere processes that involve a ligand common to both coordination spheres. The distinction is fundamentally between reactions in which electron transfer takes place from one primary bond system to another (outer-sphere mechanism) and those in which elec- tron transfer takes place within a primary bond system (inner-sphere mechanism) (Taube, 1970).
Figure 5.26. Dependence of the rate constant log k for electron-transfer processes on the free reaction enthalpy AG, Rehm-Weller plot (-) and Marcus plot (---) for I = 10 kcal/mol (adapted from Eberson, 1982).
leading to a radical ion pair is diffusion controlled if the free enthalpy of this reaction is AG I - 10 kcal/mol, and that in contrast to the Marcus theory it remains diffusion-controlled even for very negative values of AG. Therefore, Rehm and Weller (1970b) proposed the empirical relationship
AGt = AGl2 + [(AG/2)' + (A/4)2]"2 (5.27) which adequately describes the experimentally observed data, as can be seen from the solid curve in Figure 5.26. The free enthalpy of electron trans- fer AG can be estimated according to Weller ( 1982a) from the equation where E;il(D) and E.sd(A) are the half-wave potentials of the donor and ac- ceptor, AE,,,(A) is the (singlet or triplet) excitation energy of the acceptor, and AEcoUl is the Coulombic energy of the separated charges in the solvent in question. The authors suggested that the disagreement with the Marcus theory is due to fast electron transfer occurring via exciplex formation (Weller, 1982b), as shown in the following reaction scheme:
Encounter complex Exciplex
(d = 700 pm) (d -300 pm)
k I I * ks
'A* + 'D .--- ( A + ID) - '(A*D)
5 /'ti( I'OIJHYSICAL PROCESSES Experimental values of k,E,:; indicate that dissociation of weakly solvated dipolar exciplexes into a strongly solvated radical ion pair requires charge separation against the Coulomb attraction as well as diffusion of solvent molecules during resolvation (Weller, 1982b).
More recent investigations of rigidly fixed donor-acceptor pairs, for ex-
I ample, of type 14 with different acceptors A (Closs et al., 19861, and also of
i free donor-acceptor systems (Gould et al., 1988) have shown, however, that rates of strongly exothermic electron-transfer reactions in fact decrease again, as is to be expected for the Marcus inverted region. The deviation of
I the original Weller-Rehm data from Marcus theory at very large exother- micities may well be due to the formation of excited states of one of the products, for which the exothermicity is correspondingly smaller, and to compensating changes in the distance of intermolecular approach at which the electron transfer rate is optimized.
Recently a number of covalently linked porphyrin-quinone systems such as 15 (Mataga et al., 1984) or 16 (Joran et al., 1984) have been synthesized in order to investigate the dependence of electron-transfer reactions on the separation and mutual orientation of donor and acceptor. These systems are also models of the electron transfer between chlorophyll a and a quinone molecule, which is the essential charge separation step in photosynthesis in green plants. (Cf. Section 7.6.1 .) Photoinduced electron transfer in supra- molecular systems for artificial photosynthesis has recently been summa- rized (Wasielewski, 1992).
Heavy-atom quenching occurs if the presence of' a heavy-atom-contain- I SC
ing species enhances the intersystem crossing '(MQ)* + '(MQ)* to such an extent that it becomes the most important deactivation process for the exciplex. Since the triplet exciplex is normally very weakly bound and dis- sociates into its components, what one actually observes in such systems is Luminescence quenching by oxygen appears to be a similar process with Q = ?02. The process is diffusion-controlled. and it may be thought of as
5.4 BIMOLECULAR DEACTIVATION PROCESSES 287
occurring via a highly excited triplet exciplex -'(MO,)** that undergoes in- ternal conversion to the lowest triplet exciplex '(MO,)* and decays into the components:
The net reaction consists of a catalyzed intersystem crossing which is spin allowed as opposed to the simple intersystem crossing (Birks, 1970). Triplet states may also be quenched by oxygen, but triplet-triplet annihilation (cf.
Section 5.4.5.5) seems to be the predominant mechanism.
5.4.5 Electronic Energy Transfer
If an excited donor molecule D* reverts to its ground state with the simul- taneous transfer of its electronic energy to an acceptor molecule A, the pro- cess is referred to as electronic. energy trunsfer:
The acceptor can itself be an excited state, as in triplet-triplet annihilation.
(Cf. Section 5.4.5.5.) The outcome of an energy-transfer process is the quenching of the emission or photochemical reaction associated with the donor D* and its replacement by the emission or photochemical reaction characteristic of A*. The processes resulting from A* generated in this man- ner are said to be sensitized.
Energy transfer can occur either radiatively through absorption of the emitted radiation or by a nonradiative pathway. The nonradiative energy transfer can also occur via two different mechanisms-the Coulomb or the exchange mechanism.
5.4.5.1 Radiative Energy Transfer
Radiative energy transfer is a two-step process and does not involve the direct interaction of donor and acceptor:
The efficiency of radiative energy transfer, frequently described as "trivial"
because of its conceptual simplicity (Forster, 1959). depends on a high quan- tum efficiency of emission by the donor in a region of the spectrum where the light-absorbing power of the acceptor is also high. I t may be the domi- nant energy transfer mechanism in dilute solutions, because its probability decreases with the donor-acceptor separation only relatively slowly as com- pared with other energy-transfer mechanisms. When donor and acceptor are identical and emission and absorption spectra overlap sufficiently, radiative
288 5 PHOTOPHYSICAL PROCESSES trapping may occur through repeated absorption and emission that increases the observed luminescence lifetime.
5.4.5.2 Nonradiative Energy Transfer The nonradiative energy transfer
is a single-step process that requires that the transitions D*+D and A-A*
be isoenergetic as well as coupled by a suitable donor-acceptor interaction.
If excited-state vibrational relaxation is faster than energy transfer, and if energy transfer is a vertical process as implied by the Franck-Condon prin- ciple, the spectral overlap defined by
is proportional to the number of resonant transitions in the emission spec- trum of the donor and the absorption spectrum of the acceptor. (Cf. Figure 5.27). The spectral distributions iD(s) and zA(fi) of donor emission and accep-
Emission Absorption
5.4 BIMOLECULAK L)CACI'IVAI'ION PROCESSES 289
tor absorption, respectively, are normalized to a unit area on the wave-num- ber scale, that is
This clearly reflects the fact that J is not connected to the oscillator strengths of the transitions involved.
The coupling of the transitions is given by the interaction integral
6 = <V@'l.\~r,> = J VffirVldt (5.30) where fit involves the electrostatic interactions of all electrons and nuclei of the donor with those of the acceptor, and Y, = AT,,*, and Yf = AVDVA.
are antisymmetrized product wave functions of the initial and the final state.
The total interaction B may be written as the sum of a Coulomb and an exchange term; thus in the two-electron case Y, = +!+,[t,(1)vA(2) -
~ D * ( 2 ) ~ A ( l ) l l f i and *It, = [VD( l)vA*(2) - vD(2)vA*( 1 )I/@, and
6 = (6' - 0") = L J V D * ( ~ ) V A ( ~ ) ~ ~ ' W D ( ~ ) ~ Y A * ( ~ ) ~ ~ I ~ ~ Z
- J%*( 1 ) ~ ~ ( 2 ) f i ' ~ D ( ~ ) V A * ( I )dt,dtzI (5.31) where the second integral. the exchange term. differs from the Coulomb term in that the variable I and 2 are interchanged on the right.*
The functions t#, are spin orbitals and contain a space factor @, and a spin factor a or B. (Cf. Section 1.2.2.)
The Coulomb term represents the classical interaction of the charge dis- tributions Q,( 1 ) = lei $,, ( I I@,,( I ) and Q,(2) = 1c.l @A(2)@A (2) and may be expanded into multipole terms: dipole-dipole, dipole-quadrupole. etc. With MD and MA denoting the transition moments of the two molecules, and at not too small distances RA,, between the donor and the acceptor, the dipole term, which dominates for allowed transitions, may be written as
p(dipole-dipole) - MdM,lRiD (5.32)
and is thus related to experimentally measurable quantities (Fdrster, 1951).
The exchange interaction, which is responsible for example for the sin- glet-triplet splitting, is a purely quantum mechanical phenomenon and does not depend on the oscillator strengths of the transitions involved. The ex- change integral
Figure 5.27. Schematic representation of the spectral overlap J and its relation t o the emission and absorption spectrum.
- -
I t should be noted that here vA. and yt,,. denote wave functions o f the excited states o f A and D. respectively, and not the complex conjugate of yr, and yf,,.
representing the interaction of the charge densities QYI) = lei @Iy(l)@A"(l) and 9 3 2 ) = [el @,,(2)@,(2) vanishes if the spin orbitals v, and 1/,, or VA-: and Vl, . respectively, contain different spin functions. Since the charge densities Q: and Q: depend on the spatial overlap of the orbitals of D and A. the exchange interaction decreases exponentially with increasing internuclear distances. similarly as the overlap.
For forbidden donor and acceptor transitions the Coulomb term vanishes and the exchange term will predominate. If both transitions are allowed and the distance is not too small, the dipoledipole interactions will prevail. The higher multipole terms are important only at very short distances, where, however, the essential contributions arise again from the exchange interac- tion, unless it vanishes due to the spin symmetry.
Time-dependent perturbation theory yields for the rate constant of non- radiative energy transfer
(Cf. the Fermi golden rule, Section 5.2.3.) The density of states eE (number of states per unit energy interval) is related to the spectral overlap J, and using the relations for (3 given above the expressions derived by Forster (195 1) and Dexter (1953) for the rate constant of energy transfer by the Cou- lomb and the exchange mechanism, respectively, may be written as
and
f, and f, are the oscillator strengths of the donor and acceptor transition, respectively, L is a constant related to an effective average orbital radius of the electronic donor and acceptor states involved, and J is the spectral over- lap.
5.4.5.3 The Coulomb Mechanism o f Nonradiative Enetgy Transfer
Energy transfer according to the Coulomb mechanism, which is also referred to as the Forster mechanism, is based on classical dipoledipole interac- tions. From Equation (5.32) the interaction energy is seen to be proportional to Rid, with RAD being the donor-acceptor separation, and is significant at distances up to the order of 10 nm, which is large but less than the range of radiative energy transfer. Introduction of reasonable numerical values into the Forster equation for the rate constant [Equation (5.34)] leads to the ex- pectation that k,, can be much larger than the diffusion rate constant kdiw
5.4 BIMOLECULAR DEACTIVATION PROCESSES 291
From Equation (5.3 1) it is seen that spin integration yields a nonvanishing Coulomb interaction only if there is no change in spin in either component.
Thus
ID* + 'A +- 'D + 'A*
and
are fully allowed.
However, triplet-triplet energy transfer )D* + 'A +- 'D + 3A*
is forbidden. Nevertheless, it is sometimes observed, because the spin-se- lection rule, which strongly reduces the magnitude of kET, also prolongs the lifetime of 3D* to such an extent that the probability of energy transfer can still be high compared with the probability of deactivation of 3D* (Wilkinson,
1964).
5.4.5.4 The Erchange Mechanism o f Nonradiatiue Enetgy Transfer
According to Equation (5.39, energy transfer by the exchange mechanism is a short-range phenomenon since the exchange term decreases exponen- tially with the donor-acceptor separation RAD. Since it requires the interven- tion of an encounter complex (D* e - e A) it is also called the overlap or collision mechanism. The Wigner-Witmer spin-selection rules (Section 5.4.1) apply, and the spin-allowed processes
ID* + 'A -* ID + 'A*
and
are referred to as singlet-singlet and triplet-triplet energy transfer, respec- tively. The singlet-singlet energy transfer is also allowed under the Coulomb mechanism, which, as a long-range process, in general predominates. Col- lisional singlet-singlet energy transfer is therefore likely to be rare and ob- servable only under special conditions-for example, with biacetyl as a quencher, since this shows only a very weak absorption in the UVIVIS re- gion (Dubois and Van Hemert, 1%4), and when it is intramolecular (Has- soon et al., 1984).
Triplet-triplet energy transfer, on the other hand, is a very important type of energy transfer observed with solutions of sufficient concentration. It has been established as occurring over distances of 1-1.5 nm, comparable with coilisional diameters. Steric effects were shown to be significant; for in-
stance, the introduction of gem-dimethyl groups into the diene used as a quencher reduces the rate constant of fluorescence quenching of diazabicy- clooctene (17) by a factor of 3 4 . Apparently, it is important which regions of the molecules touch in the encounter complex (Day and Wright, 1969).
Intramolecular triplet-triplet energy transfer in compounds of the type D-Sp-A, where Sp is an appropriate spacer, such as trans-decalin or cy- clohexane, has also been studied and a relation between charge transfer and energy transfer has been shown to exist. As depicted in Figure 5.28, electron transfer can be symbolized as electron exchange between the LUMOs of donor and acceptor, hole transfer as electron exchange between the HOMOs, and triplet-triplet energy transfer as a double electron exchange involving both the HOMOs and the LUMOs. This simplified view suggests that the probability of triplet-triplet transfer should be proportional to the product of the probabilities of hole transfer and electron transfer. Indeed, a remarkably good proportionality between rate constants k,, of triplet-triplet energy transfer and the product k,k, of rate constants of electron transfer and hole transfer has been observed experimentally (Closs et al., 1989). This proportionality has also been found in ab initio calculations indicating that the observed distance dependence of electron transfer, hole transfer, and triplet-triplet energy transfer is determined not only by the number of inter- vening CC bonds but also by an angular dependence of the through-bond coupling (Koga et al., 1993).
Triplet-triplet energy transfer is most important in photochemical reac- tions. It is utilized to specifically excite the triplet state of the reactant. This process is referred to as photosensitization and the donor 'D* is called a triplet sensitizer jSens*. For efficient triplet sensitization the sensitizer must absorb substantially in the region of interest, its intersystem crossing effi-
Figure 5.29. Three possible situations for luminescence quenching: a) only triplet excitation can be transferred from the sensitizer Sens to the molecule M (triplet quenching), b) singlet as well as triplet transfer is possible, and c) M can capture singlet excitation from Sens and transfer triplet excitation back to Sens.
So
Figur* 5.30. Triplet-triplet energy transfer from biacetyl in benzene to various ac- ceptors. Rate constant k, as a function of the triplet energy ET of the acceptor (by permission from Lamola, 1968).
Figure 5.28. Frontier orbital representation of electron exchange in a) electron transfer, b) hole transfer, and c) triplet-triplet energy transfer (adapted from Closs et a]., 1989).
, - - - - - - - - . - - - - - - - - -. - - - - - - - . - - - - - - - - - - -
Sens M Se ns M Sens M
so So So so so
1 294 5 1'1 I( ) l UI'HYSICAL PROCESSES
ciency must be high, and its triplet energy must be higher than that of the acceptor.
The desired relationship of the energy levels of the sensitizer Sens and the acceptor molecule M is depicted in Figure 5.29a. If the energy levels are disposed as shown in Figure 5.29b, singlet-singlet and triplet-triplet energy
I transfer are both possible. The situation shown in Figure 5.29c, however, would allow singlet-singlet energy transfer from the sensitizer to the mole- cule M and subsequent triplet-triplet energy transfer back to the sensitizer.
When the triplet energy E., of the acceptor is about 3.5 kcallmol or more , below that of the donor, triplet-triplet energy transfer is generally diffusion controlled, that is, kET = kdiW When both triplet energies are the same, then only the 0-0 bands overlap and kET is smaller by a factor of lo2; it decreases even further with increasing E,. This is evident from the results of Lamola (1968) shown in Figure 5.30, where the rate constant kET of the triplet-triplet energy transfer of biacetyl is plotted against the triplet energy ET of various acceptors.
Example 5.10:
Terenin and Ermolaev (1956) were the first to observe triplet-triplet energy transfer by measuring the benzophenone-sensitized phosphorescence of naph- thalene in a rigid glassy solution at 77 K. The relative energies of the lowest singlet and triplet states of these molecules are shown in Figure 5.31. Excita- tion of the I(n,n*) state and subsequent intersystem crossing produce the TI state of benzophenone, which may transfer the excitation energy to the T I state
-_--_---_-_ -- -- -- -- - -
Filter
E I TI
Figure 5.31. Relative energies of the lowest singlet and triplet states of benzophenone and naphthalene, and triplet sensitization of naphthalene; direct excitation of the higher-lying naphthalene S, state is prevented by a filter.
5.4 BIMOLECULAR DEACTIVATION PROCESSES 295
of naphthalene. The use of a filter prevented direct population of the TI state of naphthalene via excitation of its S, state followed by intersystem crossing.
5.4.5.5 Triplet-Triplet Annihilation
Energy transfer can also occur between two molecules in their excited states; this phenomenon is most common for two triplet states due to their relatively long lifetimes. According to the Wigner-Witmer spin-selection rules the following triplet-triplet annihilation processes are allowed by the exchange mechanism:
where the double asterisk is used to denote higher excited states. The first process is most important and for most organic molecules the combined trip- let energy is sufficient to excite one of them into an excited singlet state.
The donor and the acceptor molecules are identical in many cases, and, as shown for the (Hz + H,) system in Section 4.4, the acceptor molecule will undergo internal conversion and finally reach the lowest excited singlet state, so triplet-triplet annihilation may be summarized by the equation If 'M* is fluorescent, triplet-triplet annihilation produces delayed fluores- cence, reflecting the long lifetime of 3M* (Parker, 1964). This phenomenon was first studied for pyrene, and was therefore dubbed "P-type delayed flu- orescence" in contrast to the "E-type delayed fluorescence" discussed in Section 5.1.1.
Example 5.11:
Triplet-triplet annihilation (TTA) between different molecules A and X (hetero- TTA) may produce the excited singlet state of either A or X. This reaction is utilized in a general and synthetically useful method of generating singlet ox- ygen according to
sen^ + hv - 'Sens* -, 'Sens*
'Sens* + IO, -+ Sens + 10,
Strongly absorbing dyes such as Rose Bengal or methylene blue are usually used as photosensitizers. (Cf. Section 7.6.3.)
Singlet oxygen generation is used in photodynamic tumor therapy-for in- stance, with porphyrins as photosensitizers. (Cf. Dougherty. 1W2.) The dis- advantage of natural porphyrins such as hematoporphyrin is that they are of low chemical stability and have an absorption spectrum similar to that of