J. Phys. Chem. 1994,98, 1626-1633
1626
Intramolecular Photochemical Electron Transfer. 8. Decay of the Triplet State in a Porphyrin-Quinone Molecule' David D. Fraser and James R. Bolton' Photochemistry Unit, Department of Chemistry, The University of Western Ontario, London, Ontario, Canada N6A 5B7 Received: August 11, 1993; I n Final Form: November 18, 1993'
The rate constant for the quenching of the porphyrin triplet state in a covalently linked porphyrin-amidequinone molecule has been measured in several solvents and as a function of temperature in three solvents. A nanosecond laser flash photolysis apparatus permitted the observation of the porphyrin triplet state decay, with the quinone fully reduced or with it fully oxidized to allow enhanced quenching of the porphyrin triplet via electron transfer. A difference of rate constants in the two cases yielded the electron-transfer rate constant which ranged from 1.0 X lo4 s-] in acetonitrile to 2.8 X lo5 s-l in methylene chloride. It is shown that the available Gibbs energy and the electron-transfer rate constants, determined in various solvents over a 40 OC temperature range, do not exhibit the relationship put forth by Marcus electron-transfer theory. An alternative hypothesis of a fast equilibrium being established between the triplet porphyrin and a n intermediate state before the molecule reaches a radical-ion-pair state is supported by the observation of negative activation energies in benzonitrile and methylene chloride. Since neither the radical ion pair nor the intermediate was observed as a spectroscopic entity, it is not possible to identify conclusively the pathway of de-excitation of the porphyrin triplet.
Introduction
In photosynthetic bacteria293 the primary photochemical reaction is electron transfer from an excited bacteriochlorophyll-a dimer to a bacteriopheophytin-a, probably via a bacteriochlorophyll-a monomer, followed by the reduction of a ubiquinone. In green plants and algae (not as well studied), the primary photochemical reaction is similar, involving chlorophyll-a instead of bacteriochlorophyll-a as the pigment and plastoquinone (photosystem 11) or an iron-sulfur protein (photosystem I) instead of ubiquinone as the acceptor. In both thesesystems, the electrontransfer constituents are held together in a well-defined orientation by a protein matrix. It is to mimic this electron transfer that the molecule PAQ[5-(4-carboxyphenyl)-lO,l5,20-tri@-tolyl)por-
Q I
0
PAQ phine linked to methyl-p-benzoquinone via an amide group] was synthesized in this l a b o r a t ~ r yand ~ . ~ similar molecules by many others.6 The decay of the singlet state of PAQ has been well described by previous studies (using time-correlated single-photon counting) and shows excellent agreement with Marcus electron-transfer t he0ry.7-~ Abstract published in Aduance ACS Abstracts, January 1, 1994.
There have been several studies of photoinduced electron transfer from the triplet state. These are often in bimolecular systems, in which the determination of the electron-transfer rate constant can be complicated by the formation of triplet exciple~esl@ or~by ~ the diffusion limit.10J4J5 Electron transfer in polymethylene linked chromophores can depend on the chain dynamics.I6J7 Some systems have been studied at low temperatures so that intersystem crossing could compete effectively with electron transfer from the singlet state.I8J9 Even so, Levin et a1.20*21 reported the semiclassical bell-shaped curve for charge recombination with intersystem crossing to the ground state from triplet exciplexes. Avila et a1.,22and previously Vogelmann,23 found differing singlet and triplet reactivities in the bimolecular electron-transfer reactions which were attributed to possible differences in the inner-sphere reorganization energies of the singlet and triplet reactant states. Mauzerall et al.24 have constructed a molecule with four symmetrical linkages between a zinc porphyrin and a quinone, forming a cage. The electron-transfer rate constants from both the singlet and triplet states in this molecule in a variety of solvents have very small, even negative, activation energies, but there is no electron transfer from the free base porphyrin.24JS In a system similar to our own, but involving bimolecular quenching of triplet tetraphenylporphine (TPP) by benzoquinone, rate constants for electron transfer were found to be about 4 orders of magnitude smaller than the rate constant for the quenching of fluorescence; the result could not be explained using Marcus theory.14 This observation is similar to the decrease in quenching rateconstants seen in this study compared to quenching of fluorescence in the same molecule.* Preliminary experiments by Schmidt et aL7 in a variety of solvents also confirmed the slowness of quenching of triplets in PAQ. This paper describes experiments using laser flash photolysis to monitor the decay of the absorbance of the triplet state of PAQ in various solvents and over a 40 "C temperature range. The aims of this study were to determine if Marcus theory is applicable to electron transfer from the triplet state of PAQ and, if so, would it be simply an extension of the ranges of AGO already studied for the singlet state of PAQ.7,9 There is also the possibility that
0022-3654194120981626%04.50/0 0 1994 American Chemical Society
Intramolecular Photochemical Electron Transfer AGO/
2.0
standard Gibbs energy between the equilibrium states of the product and reactant. The reorganization energy A can be divided into two terms
eV
P*AQ
m
x = Xi" + h0",
(3) The inner reorganization energy Xi, arises from changes in the molecule's internal geometry and is solvent independent and small. In previous studies Xi, was taken to be 0.2 eV,6J77*8a value also used here in subsequent calculations of A. The outer reorganization energy A,,, arises from the reorganization of the molecule's external solvent environment. Imagining the donor and acceptor to occupy hollow spheres of radii rD and rA,respectively, in a dielectric continuum, with the distance between them rDA > rD + rA gives
1.5
1.o
0.5
0
The Journal of Physical Chemistry, Vol. 98, No. 6,1994 1627
PAQ
Figure 1. Gibbs energy diagram showing the energy levels and decay pathways of PAQ. The rate constants are as follows: kF, fluorescence; klc, internal conversion; k&, intersystem crossing from the singlet to the triplet state;k&, electron transfer from the singlet state; k n T ,electron transfer from the triplet state; L E T T , reverse electron transfer in the triplet state; kl3, k31,spin rephasing between the singlet and triplet radical ~ ,recombination from the singlet ion pairs; kp, phosphorescence;k ~charge radical ion pair.
electron transfer from the triplet state of PAQ may be mediated by the existence of an intermediate state.
Theory The energies and de-excitation pathways for excited PAQ, based on previous studies, are shown in Figure 1. The triplet state of PAQ can be quenched via electron transfer, phosphorescence or nonradiative intersystem crossing, and collisions with ground-state molecules or with solution impurities. In addition to these first-order and pseudo-first-order processes, triplet-triplet annihilation may also be significant for long-lived triplets. By a full reduction of the quinone to hydroquinone, the electrontransfer pathway can be eliminated. This allows the calculation of the quenching rate constant due to electron transfer as the difference of the observed pseudo-first-order rate constants for PAQ and PAQH2. Marcus Theory. According to Marcus theory,Z6 the rate constant kET for endergonic or moderately exergonic electron transfer (the "normal" region) can be approximated by
where Ae is the charge transferred, topis the optical dielectric constant (= n2 where n is the index of refraction), and E, is the static dielectric constant of the solvent. For the triplet state of PAQ, the standard Gibbs energy of the reactant state is approximated by huo.0, the energy of the triplet state, which is estimated from the frequency of the maximum of the 0-0 phosphorescence band of TPP at low t e m p e r a t ~ r eThe .~~ Gibbs energy of the product state is calculated as the difference in standard reduction potentials of the P'+and Q'- components of PAQ plus a Coulombic work term for bringing P'+and Q'together. The standard Gibbs energy of the reaction is thus
where eo is the permittivity of free space. The energy of the porphyrin triplet state is assumed to be invariant with solvent.8 A second assumption is that the energies of the singlet and triplet radical ion pairs, calculated as the first two terms on the right-hand side of eq 5,need no further correction due to their multiplicity. The amide-methylene linkage in PAQ, although not completely rigid, restricts the center-to-center approach of the quinone to the porphyrin to greater than 12 A so that the spin-exchangeenergy is negligible.7~30Thus a singlettriplet splitting AC13' = 0 between the two radical-ion-pair states is used. The formula for kET (eq 1) may be linearized in the form
or
Yl = c,- x where
Yl = ln(k,,X'/2)
and
AG*=
AG* - (AGO-tX)' x=-kT 4XkT
+
(AGO X)' 4x
where Hrpis the electronic coupling term between the electronic wave functions of the reactant and product states, X is the Gibbs reorganization energy, k is the Boltzmann constant, AG* is the Marcus Gibbs activation energy, and AGO is the difference in the
If the system behaves according to Marcus theory, a plot of Y, vs X should yield a straight line with slope of -1 and intercept C1.
A further test of Marcus theory is to remove the explicit temperature term from the preexponential by combining it with
1628
The Journal of Physical Chemistry, Vol. 98, No. 6, I994
Fraser and Bolton
the left-hand side of the equation as
as
or
and the preexponential factor A by Y2 = c 2 - x
(7b)
where
k, = A exp( -
2)
So the activation energy for quenching due to the existence of the intermediate is
and
E,
+
AHQ* k T = AH,'
+ AHHETI + k T
(16) In eq 16 the enthalpy of the intermediate step L W I O may be sufficiently negative to make the overall activation energy negative.34.35
so that Hrpcan be determined from the intercept. Again the slope of Y2 vs X should be -1. The above expressions have been confirmed experimentally for electron transfer from the singlet state of PAQ.8v9
Kinetics Involving an Intermediate Step. Our observation of a negative activation energy in two solvents and a small positive value in a third solvent suggests a rapid equilibrium between the locally excited triplet state 3P*AQ and an intermediate state I prior to electron transfer as the rate-determining step.
ik,
~
k-l
PAQ where k1 is the rate constant for the formation of the intermediate from the locally excited triplet porphyrin, k-I is the rate constant forthereverseofthisstep, k e ~ i therateconstant s fortheformation of the triplet radical ion pair from the exciplex, and ko is the pseudo-first-order rate constant due to all processes other than electron transfer (i.e., those available to 3P*AQH2). Similar models have been put forward for some exciplexes31 and some systems involving triplet conformer^.^^ A steady-state analysis of the above scheme yields (9)
as the rate constant for quenching of 3P*AQ via intermediate formation and electron transfer in the rate expression
If, in addition, k-1
>> kET
then
This expression may also be derived using a kinetic analysis33 of the scheme shown in eq 8. Applying the expression k, = h k T exp( -
g)
for the first-order rate constant kl from transition-state theory to eq 11, one gets
The activation energy is defined from an Arrhenius analysis
%
Experimental Section All solvents were purified by distillation while being slowly bubbled with prepurified nitrogen. Benzonitrile (Aldrich HPLC) was distilled twice over phosphorus pentoxide.36 1,2-Dichloroethane (BDH Ominsolv) was distilled over phosphorus pentoxide. Methylene chloride (BDH Omnisolv) was distilled over phosphorus pentoxide, but this was found to give identical results to undistilledsolvent which was used thereafter. Acetonitrile (BDH Omnisolv) was distilled over calcium hydride. Acetone (BDH Omnisolv) was crystallized as NaI*3C&O and distilled. 1,1,1Trichloroethane (BDH Aristar) was used as supplied. A quantity of lead dioxide was washed several times in methylene chloride and dried under high vacuum for later use. Imidazole (Aldrich) was twice recrystallized from 3:l chloroform-hexane and added to the chlorinated hydrocarbon solvents to achieve a concentration of 2 X 10-4 M to prevent any acid buildup during p h o t o l y ~ i s . ~ ~ PAQH2 was synthesized by John Schmidt, a previous graduate student in this l a b o r a t ~ r y . ~TLC . ~ (on Machery-Nagel nonindicating silica gel) of PAQH2 eluted with methylene chloride and then 2% methanol-methylene chloride showed primarily PAQH2 and some PAQ. PAQ with the same elution showed the same spots, with that identified as PAQ being much stronger, plus a very weak spot attributed to photodegradation of PAQ.3a All samples were handled under reduced lighting because such porphyrin-quinone compounds can be photochemically untable.^^,^ PAQ samples were prepared by adding PAQH2 to methylene chloride (containing about 2 X 10-4 M imidazole), adding lead dioxide,4O shaking in a SuperMixer at maximum speed for 5 min, and filtering througha glass fiber filter (Millipore AP40) stuffed into a Pasteur pipette. An absorbance ratio of A246/&6 of about 2.0 indicated nearly complete quinone o~idation.~ For other solvents, some of the PAQ-methylene chloride solution was transferred to a cuvette and the methylene chloride evaporated under a stream of nitrogen. New solvent was then added to redissolve the PAQ. The PAQ or PAQHz solution was transferred to the freeze-pumpthaw cell and more solvent added to achieve an absorbance of 0.10 at the Q,(l,O) maximum (ca. 516 nm). With an extinction coefficient of about 2.0 X lo4M-I cm-I, this corresponds to 5 X 1 W M PAQ or PAQH2 in solution. Degassing by 4 or 5 freeze-pump-thaw cycles achieved a vacuum of less than 2 X 10-2 Pa for an estimated 0 2 concentration of less than 6 X M. Absorption spectra of the solutions were taken on a HP 8450A UV/vis diode array spectrophotometer. Apparatus. The experimental setup is shown in Figure 2. A PRA International LN 1000 N2 laser pumped a PRA LN 102 dye laser using 1.O X 1W2 M Coumarin 500 in ethanol ( - 5 16 nm). The dye laser beam was focused and directed through a hole in a mirror and then through a 1.6-mm hole in a polished aluminum
Intramolecular Photochemical Electron Transfer
The Journal of Physical Chemistry, Vol. 98, No. 6, 1994 1629 The Soret and Q-band extinction coefficients do not change significantly on oxidation of PAQHz to PAQ, since these bands arise solely from the porphyrin; only the quinone absorbance in the UV changes.39 Similarly, the triplet-triplet absorption spectrum is expected to arise only from the porphyrin.’ Thus, it is assumed that any change in absorbance at the monitoring wavelength of 444 nm arises from the ground-state porphyrins being excited to the triplet state. The rate law for decay of 3P*AQHz is4244
U
L,
D Mirror
BS
L1
Figure 2. Laser flash photolysis apparatus: PC = photoconductivity circuit; Amp = Comlinear CLC 100 amplifier; L1, L2,L3 = lenses; D = iris diaphragm; BS = beam splitter (microscope cover glass slide); F =
Corning glass filter; thedottedlineabouttheN, laser indicates the Faraday cage. cone. That part of the laser beam passing through the cone and then into the sample cuvette constituted the excitation beam. The monitoring beam from a PTI Model LPS-220 150-W Xe arc lamp operated near 120 W was passed through a Bausch & Lomb 0.25-m monochromator and focused onto the opposite face of the cuvette. The monitoring beam, colinear with the laser beam, exited from the hole in the cone and diverged enough by the time it impinged upon the mirror with the hole that most of it was reflected and then focused onto the entrance slit of a Model 8241 5 Jarrell-Ash 0.25-m monochromator.41 The light exiting from the Jarrell-Ash monochromator was intercepted by a Hammamatsu R928 photomultiplier whose signal was amplified by two Comlinear CLC 100 amplifiers (DC to 500 MHz) before reaching a LeCroy Model TR8828D 200-MHz transient digitizer. After the excitation beam passed through the sample cell, part of it was reflected from a microscope cover glass slide to a Clairex CL 705HL CdS photoconductivity cell in series with a 5 0 4 load resistor and a 1.5-V battery. The leading edge of this signal was faster than the digitizer resolution and was used as a stop trigger. The stop trigger threshold was then set to accept only laser pulses within 5% of the maximum pulse energy, about 30 pJ. To reduce the electromagnetic interference from the laser’s spark gaps, the laser was enclosed in a Faraday case with a power line isolator and a beryllium-copper sawtooth gasket (Instrument Specialties, Inc.) on the case door and the power line from the isolator was plugged into a surge suppressor that is separate from the one powering the measuring devices. Still, there was a decaying ripple that lasted up to 500 ps. Fortunately, most of this was reproducible in both the transient and light-off signals and was subtracted out in the calculation of the transient absorbance.” The cuvette holder was an aluminum block with a copper tube wrapped around it to act as a heat exchanger. The entire block was covered with foam rubber for insulation (except holes for the light beams and the cuvette top). A 1:l ethylene glyco1:water mixture was pumped through the copper tubevia insulated plastic tubing to a heat-exchange coil in a thick-walled plastic dewar or plastic pail. Dewar temperatures lower than room temperature were maintained with ice water or cold tap water, while higher temperatures were maintained by an immersion heater in the plastic pail. The temperature of the outside of the cell was monitored by an unshielded YSI 44202 thermistor probe attached to a digital readout. This matched the temperature of the inside of the cell within 0.5 OC. The experiments were done in order of both increasing and decreasing temperature to ensure that there was no sample deterioration due to the higher temperatures. The signals were acquired on a computer under the control of a LeCroy program, Waveform Catalyst 3.03, and then analyzed using programs written in GAUSS 2.0 (Aptech Systems, Inc.: Maple Valley, WA).33
where the Mi are any quenching impurities, CT is the triplet concentration, and CG is the ground-state concentration so that the total porphyrin concentration co = CT + CG. This yields the integrated form
where AAo is the value of AA at t = 0, k,’ = k,
+ k3c0+ x k , , M i
(19)
i
and
The 3P*AQ transient decay fits best to the sum of two firstorder decays U ( t ) = a, exp(-k+)
+ a, exp(-k,t)
(21) where the fast component is attributed to the decay of 3P*AQ and the slow one to the decay of unoxidized 3P*AQH2.7 kET can be evaluated as the difference of the fast rate constant from the PAQ decay kfand the first-order rate constant from the 3P*AQH2 decay kl’.
k,
= k, - k1’
(22)
To test whether treatment with lead dioxide added any extra quenching impurities, a comparison was made of tetratolylporphyrin (TTP) plus imidazole in methylene chloride without and with lead dioxide treatment. The latter did not show any significant change in the decay rate.
Results and Discussion Marcus Analysis of the Kinetic Results. Solvent Dependence. Previous studies in this series examined electron transfer from the excited singlet state to the singlet radical-ion-pair state.7-9 Because both those studies and this work considered reactions involving no change in spin, the hypothesis to be tested is that the triplet-state reactions should differ from the singlet-state reactions only according to the change in AGO for the respective electron transfers, that is, that Hrpand X should be the same in any given solvent. This also implies that there is no significant change in molecular geometry between the singlet and triplet states. The reorganization energies are calculated as before* using r~ = 7 A, r A = 4 A, and IDA = 14 A and Xi, = 0.2 e v . Laser flash photolysis experiments on solutionsof PAQHl and PAQ were first carried out at r w m temperature to see if the resulting values of Y1 (eq 6c) follow the predictions of Marcus electron-transfer theory (Tables 1 and 2 and Figure 3). The expected Y1 values for acetonitrile and methylene chloride were calculated from eq 6a using experimentalvaluesof Hv9 Although the temperature dependence of kET for lP*AQ in benzonitrile is unknown, a value of Hrp = 3.7 X 10-4 eV can be estimated by
1630 The Journal of Physical Chemistry, Vol. 98, No. 6, 1994
Fraser and Bolton
was calculated from eqs 3 and 4 using values of the index of refraction n and the static dielectric constant cs vs temperature interpolated from literature value^.^^*^^ The temperature dependence of AGO arises from the variation of the static dielectric BzCN 1.5494 25.40 0.879 1.45 -0.02 0.369(40) constant in eq 5 . -0.14 0.269(4) 1.40 MeCl 1.4288 9.05 0.883 The value of Yz (eq 7c) in both methylene chloride and -0.05 0.332(15) 1.41 MeCN 1.3496 36.30 1.139 1.51 0.03 1.3560 20.56 1.09 Acet benzonitrile increased with increasing X (eq 6e) while decreasing 1.33 -0.20 DCE 1.4421 10.37 0.89 with increasing X in acetonitrile (Tables 3-5 and Figure 4). All -0.10 1.46 TCE 1.4359 7.25 0.82 these trends are very weak; in any solvent ET increases by less than a factor of 2 for a 30 OC temperature change. This shows "Experiments carried out at 296 K. All errors are one standard deviation. Where indicated by parentheses, errors have the units of the that the high-temperature limit of Marcus electron-transfer theory least significant digit of the accompanying value, otherwise they are given definitely does not work in the cases of PAQ in methylenechloride below. b BzCN, benzonitrile; MeC1, methylene chloride; MeCN, aceor in benzonitrile, since for thevalues of X and AGO used it predicts topitrile; Acet, acetone; DCE, 1,2-dichloroethane; TCE, l,l,l-trichloa decrease in Y2 with increasing X. In acetonitrile, Y2 is much roethane. Index of refraction at 296 K j 5 Static dielectric constant at smaller than, and changes much less rapidly than, predicted. A 296 K.& e Reorganization energy. Calculated from eqs 3 and 4. f A E O summary of the results of the temperature dependence analyses = E'p/p+-EOQ-/Q;error = f0.04V.* 8 AGO for the triplet-stateelectron transfer from eq 5; error = 4Z0.04 eV. * Electronic coupling coefficient, is shown in Table 6. from ref 9 for MeCl and MeCN and calculated for B z C N . ~ ~ Model Involving an Intermediate. We do not believe the results can be interpreted in terms of a rapid charge-transfer equilibrium TABLE 2: Experimental and Theoretical Kinetics of between the spectroscopic triplet state 3P*AQ and the radicalTriplet-State Electron Transfer in PAQ in Various Solvents ion-pair state 3(P+AQ*-) prior to the eventual charge recomkf/ kl',b 3 k ~ ~ , C 'yl,d 3xc 'Y1/ ' k ~ ~ ' ~ ~ ,bination g to the ground state because this equilibrium would have solvent 104 s-I 104 s-1 104 s-I exutl theor lo4 s-l to be established much faster than the charge recombination. BzCN 7.62 0.090 7.53(41) 11.17 8.18 12.89 42 Spin rephasing between singlet and triplet radical-ion-pairs is MeCl 21.83 0.180 21.65(54) 12.22 6.07 14.52 210 expected to occur with a rate constant similar to that in 1.25(7) 9.50 10.14 10.56 3.6 MeCN 1.53 0.280 photosynthetic bacterial reaction centers, that is, ca. 5 X 107 Acet 2.50 0.106 2.39(39) 10.13 11.22 s-1.7,30Thus the PAQ singlet radical ion pair will decay to the DCE 3.23 0.140 3.09(29) 10.28 5.23 TCE 2.02 0.280 1.74(24) 9.67 6.20 ground state with a rate constant larger than 2 X 1O7 s-1, depending on solvent.8 As seen in Table 2, the theoretical values of the Fast rate constant of a two-exponential fit to the PAQ triplet decay forward electron-transfer rates are much too slow for such an kinetics. * Pseudo-first-order rate constant from competing first- and second-order fit to PAQH2 triplet decay kinetics. ET = kr- kl'. YpPtl equilibrium to be formed. Also, neither the Gibbs energy nor the = ln(kETh1/2/eVl/2 s-I) for the triplet state; error = kO.10. X = reorganization energy varies sufficiently with temperature to AG*/kT; error = 4Z0.4. f Ylthmr= Cl - X ; CIcalculated from singlet Hrp overcome its dominance in the denominator of the experimental values; see Table 1. 3kET'bcor/s-' = eVl/z/x1/2 exp(Ylfhwr). term in eq 1-see Tables 3-5. Exciplex Model. One possibility for the identity of the 15 intermediateis that it isa tripletexciplex. Onthe basisofextensive 14 experimental results, Weller47#48has developed a correlation \ between the excited complex energy and the redox properties of 13the two components. It is then possible to estimate the exciplex N \ enthalpy of reaction as -A+ 12MeCl
TABLE 1: Energetics of Triplet-State Electron Transfer in PAQ in Various Solvents* solventb e,d X,CeV AE'/V A3Go,geV HW,hmeV
A
d
G 11-
2
-E
10-
DCE
A
TCE
9-
A Acet 0
MeCN
1
AHEX'
AH,O(Ex) - hvo.0
where AHfo(Ex) is the exciplex enthalpy of formation. For charge-transfer exciplexes MH,o(Ex) = e(ED+/Do -EA/,-') + ('dmt-
ust&)
-
+
AHEx" 0.32 eV (24) U h t is a destabilization energy of the exciplex due to interaction of the ground states of the two components and is usually nonzero only in complexes that are bound in the ground state. Ushb is an energy of stabilization of the exciplex due to interaction of the excited donor-acceptor molecule and the charge-transfer state. A H E ~is~ the ' enthaIpy of solvation of the exciplex. In triplet exciplexes, is estimated as48
assuming that the value in benzonitrile falls on the same line of ln(kETX1/2Hrp-2)vs AG*f k T for IP*AQ in other solvent^.^^^^ Figure 3 indicates that the experimental values do not show a uniform trend among the solvents and that the value of Yl in most solvents is well below the values predicted in polar solvents. The value of kET for 3P*AQ in benzonitrile a t room temperature obtained by Schmidt et aL,7 4.6 (*0.2) X lo4 s-1, is even lower than that determined in this work, 7.5 (*0.4) X IO4 s-1. Temperature Dependence. To determine if (analogous t o the case of singlet electron-transfer rate constants9) the values of Hrp vary between solvents or may be different from the singlet values, the temperature dependence of the triplet decays was studied. X
where E'CT is the energy of the unperturbed (i.e., gas phase) charge-transfer state
ECT" = e(ED+,Do-EA,,+')
+ 0.32 eV
(26) and j3 is the Hamiltonian matrix element of the interaction between the triplet and charge-transfer states. In eqs 24 and 26 the value 0.32 eV has been determined from a plot of measured singlet exciplex formation enthalpies vs the difference in redox energies of the charge-transfer components. Weller uses the Kirkwood-Onsager dielectric continuum model
Intramolecular Photochemical Electron Transfer
TABLE 3 temp: K 277.6 286.1 296.0 306.5 316.9
The Journal of Physical Chemistry, Vol. 98, No. 6, 1994 1631
Triplet-State Electron Transfer in PAQ in Benzonitrile at Various Temperatures. ne €2 eV A3Go,feV 3X,geV kf,lo4 s-I k~',lo4 s-l 1.5584 1.5543 1.5494 1.5543 1.5392
27.14 26.30 25.40 24.53 23.74
0.8748 0.8767 0.8789 0.8814 0.8840
-0,0171 -0.0183 6.0197 -0.021 1 -0.0225
8.79 8.52 8.23 7.95 7.69
9.76 8.49 7.62 6.81 5.96
k ~ ~ 104 , h s-l
0.06 0.08 0.09 0.10 0.12
9.70 8.41 7.53 6.71 5.84
Y2{ 9.549 9.423 9.330 9.233 9.114
The symbols in Tables 3-5 all have the same definition. Error f0.5 K. Index of refraction, interpolated from the literature values.45 Static dielectric constant, interpolated from the literature values.& a Reorganization energy, calculated from eqs 3 and 4. f AGO for the triplet-state electrontransfer reaction, calculated from eq 5. EX = AG*/kT; error = f0.17%. kET = kf- kl'; error = f0.91 X 104 s-l for benzonitrile, k1.1 X 104 s-l for methylene chloride, f0.07 X 104 s-l for acetonitrile. Y2 = ln(kET(XkT)'/2/eV s-'); error = 10.12 for benzonitrile, f0.054 for methylene chloride, f0.07 1 for acetonitrile.
Triplet-State Kinetics in PAQ in Methylene Chloride at Various Temperatures. temp: K nc €2 X,L eV A3G0,f eV 2 8 eV kf,104
TABLE 4
277.9 286.0 295.4 306.3
1.4387 1.4342 1.4290 1.4230
9.85 9.52 9.07 8.46
0.8869 0.8860 0.8830 0.8760
278.0 287.9 295.7 304.2 3 12.0
1.4386 1.4332 1.4288 1.4242 1.4199
9.84 9.44 9.05 8.58 8.10
0.8869 0.8856 0.8828 0.8777 0.8705
Increasing Temperature -0.1291 6.76 -0.1328 6.50 -0.1381 6.17 -0.1463 5.76 Decreasing Temperature -0.1292 6.76 -0.1337 6.43 -0.1383 6.16 -0,1446 5.84 -0.1517 5.52
ke~,hJio4 s-l
'Yz'
28.0 23.2 21.8 15.7
27.8 23.0 21.6 15.5
10.610 10.434 10.387 10.066
27.3 22.0 17.9 15.2 15.2
27.2 21.8 17.7 15.1 15.0
10.586 10.383 10.189 10.036 10.042
The symbols in Tables 3-5 all have the same definition. Error f0.5 K. Index of refraction, interpolated from the literature valucs.45 Static dielectric constant, interpolated from the literature values.& Reorganization energy, calculated from eqs 3 and 4. f AGO for the triplet-state electrontransfer reaction, calculated from eq 5. 8 X = AG*/kT; error = 10.17%. kET = kf- k~';error = f0.91 X lo4 s-' for benzonitrile, k1.1 X 104 s-] for methylene chloride, f0.07 X lo4 s-l for acetonitrile. Y2 = h(kET(XkT)'/2/eV SI); error = f0.12 for benzonitrile, f0.054 for methylene chloride, f0.071 for acetonitrile. The decay of 'P*AQH2 in methylene chloride did not show a temperature dependence. kl' = 1800 s-I.
TABLE 5
Triplet-State Kinetics in PAQ in Acetonitrile At Various Temperatures.
277.3 286.4 296.3 306.0 316.8 326.8
1.3580 1.3538 1.3494 1.3450 1.3402 1.3357
39.39 37.83 36.25 34.77 33.23 31.90
1.1304 1.1345 1.1389 1.1432 1.1480 1.1525
277.9 287.3 295.9 306.7 316.6 326.3
1.3577 1.3535 1.3496 1.3447 1.3403 1.3359
39.28 37.69 36.30 34.66 33.25 31.96
1.1307 1.1349 1.1387 1.1435 1.1479 1.1523
Increasing temperature -0.0475 10.85 -0.0486 10.52 -0.0498 10.20 -0.0510 9.89 -0.0523 9.58 -0.0536 9.30 Decreasing Temperature -0.0476 10.83 -0.0487 10.50 -0.0497 10.21 -0.051 1 9.87 -0.0523 9.58 -0.0536 9.32
1.21 1.37 1.53 1.67 1.72 1.77
0.93 1.09 1.25 1.39 1.44 1.49
7.332 7.511 7.666 7.786 7.843 7.893
1.09 1.22 1.36 1.47 1.43 1.so
0.81 0.94 1.08 1.19 1.15 1.22
7.198 7.366 7.520 7.631 7.619 7.694
a The symbols in Tables 3-5 all have the same definition. Error f 0 . 5 K. Index of refraction, interpolated from the literature valucsj5 Static dielectric constant, interpolated from the literature values.& Reorganization energy, calculated from eqs 3 and 4 . 1 AGO for the triplet-state electrontransfer reaction, calculated from eq 5. 8 X = AGo/kT; error = fO.l7%. ET = kr - kl'; error = f0.91 X lo* s-l for benzonitrile, f 1 . 1 X 104 s-l for methylene chloride, f0.07 X lo4s-I for acetonitrile. Y2 = ln(keT(XkT)L/Z/eVs-l); error = 10.12 for benzonitrile, f0.054 for methylene chloride, f0.071 for acetonitrile. The decay of 3P*AQH2 in acetonitrile did not show a temperature dependence. kl' = 2800 s-l.
to calculate the exciplex solvation enthalpy
where 1.1 is the dipole moment of the exciplex, p is the equivalent sphere radius, and L is the static dielectric constant. That the calculated activation energies Ea for quenching in benzonitrile and in methylene chloride (Figure 5 and Table 7) are negative indicates that a fast equilibrium between triplet porphyrin and a triplet exciplex might precede ion pair formation. The observation of a negative activation energy requires a state with enthalpy sufficiently low that the enthalpy of the transition state to the ion pair is less than that of the initial triplet. In a review of several studies, Kapinus" states that triplet exciplexes of porphyrins seem to be almost entirely locally excited triplet porphyrin in character, with a weak binding energy, but stabilized greatly by a large positive entropy of formation from the triplet
state. Using a suggestion of Schmidt et a1.4 of a 2-Ddipole moment for the excited singlet state of PAQ and assuming that a triplet exciplex has a dipole moment of similar magnitude, then AH& has a value of only 3 meV. With a negligible interaction Hamiltonian 0 (= Hq), compared O- hqO, = -AHhmI. This is clearly insufficient to account for the -0.120 and -0.166 eV activation energiesseen in benzonitrile and methylene chloride, respectively. ConformerModel. There may be one or more triplet conformers which establish an equilibrium with the initially formed triplet more rapidly than the rate at which one of them transfers an electron to form the triplet radical-ion-pair state, the other conformers not undergoing electron transfer. Rotations about the methylene single bonds would certainly allow such a fast equilibrium. other Possibiities. A molecular system similar to those studied by Avila et a1.22and Vogelmannz3in which there is a difference
1632 The Journal of Physical Chemistry, Vol. 98, No. 6, 1994
121 11c
10MeCl
9-
I
MeCN
6
'5
8
7
9
10
1'1
A 3G*/kT Figure 4. Marcus analysis of the temperature dependence of km using methylenechloride eq7: 0,methylenechlorideincreasing temperature; 0, decreasing temperature, A, benzonitrile; 0, acetonitrile increasing temperature; 0,acetonitrile decreasing temperature. The error bar on the line for benzonitrile represents one standard deviation and is larger than the errors in the other two solvents. The unmarked solid lines show the expected dependence using Hrp= 3.3 X l e eV for benzonitrile33 and values from singlet data for methylene chloride and acetonitrile!
TABLE 6 Marcus Analysis of the Temperature Dependence of km of JP*AQ in Three Solvents. solventb BzCN MeCl(inc) MeCl(dec) MeCN(inc) MeCN(dec)
SlOpeC
intercept
rd
0.38(2) 0.51(9) 0.47(8) -0.36(4) -0.32(5)
6.20(1) 7.17(7) 7.39(8) 11.30(5) 10.68(6)
0.998 0.97 1 0.956 -0.977 -0.954
a Results are from the plots of Figure 4. inc or dec refer to increasing or decreasing temperature experiments, respectively. Expected slope is -1. d Correlation coefficient.
i
12
-21 10
=-9
9.0
311
312
313
3:4
3:5
3:6
3!7
103 K I T Figure 5. Arrhenius analysis of kQ from eq 14. The symbols are the same as those used in Figure 4.
TABLE 7: Arrhenius Analysis of the Intermediate Model solvent" A,b s-* E,,ceV AHo'mo,deV r+ BzCN -0.998 1827(24) -0.0948(32) -0.120 MeCI( inc) 756( 57) -0).142(26) -0.167 -0.967 -0.977 MeCl(dec) 772(48) -0.140(18) -0.165 MeCN(inc) 2.17(11) X lo5 0.074(10) 0.970 0.048 0.932 MeCN(dec) 1.19(7) X lo5 0.063(12) 0.037 a Increasing or decreasing temperature experiments. Arrhenius preexponential factor defined by eq 15. Arrhenius activation energy calculated from eq 14. Activation enthalpy, defined by eq 16. Correlation coefficient.
in the reorganization energy between singlet and triplet reactions still would have a positive definite Gibbs activation energy49 forestalling the observation of a negative Arrhenius activation energy.
Fraser and Bolton The zinc porphyrin quinone cage molecule of Mauzerall et al.24,25has both extended and compact conformers with an interconversion much slower than the triplet lifetimes. Electron transfer occurs from the singlet and triplet states of both conformers with the respective rates only weakly dependent on solvent and temperature. This dielectric saturation is assumed to occur because the molecule is sufficiently complex to maintain most of its environment regardless of solvent. The weak temperature dependence is then primarily due to changes in the Franck-Condon factor from shifts in vibrational frequencies between the reactant and product states.50 In contrast, the singlet electron-transfer rateconstants for PAQ depend very much on s0lvent,8~~ and we do not expect this to change for the triplet state. Conclusions In a porphyrinquinone molecule, covalently linked by an amide bridge, the triplet state of the porphyrin is quenched by the presence of the quinone relative to the corresponding rates with a hydroquinone component. Considering the energy levels of the two constituents, it is presumed that the quenching is due to electron transfer from the porphyrin to thequinone. There appears to be an intermediate state between the triplet porphyrin and the triplet radical-ion-pair state. A fast equilibrium between the triplet porphyrin and the intermediate is then established before electron transfer to the ion pair state occurs. Subsequently, the electron may return to form the ground-state porphyrin. The existence of such an intermediate is indicated, but by no means conclusively, by the observation of negative or small positive activation energies for the quenching of 3PSAQ. Thus, it cannot be determined if Marcus electron-transfer theory applies to each elementary step, since the Gibbs energy of the postulated intermediate and the reorganization energies between this and the adjacent states are not known. If such an intermediate does not exist, then the relation between the quenching rates and the available Gibbs energy in a variety of solvents shows that Marcus electron-transfer theory does not describe the system studied, in contrast to its experimental confirmation in the case of singlet states in the same molecule. Given that neither the radical ion pair nor the intermediate was observed as a spectroscopic entity, it is not possible to identify conclusively the pathway of de-excitation of the porphyrin triplet state. Acknowledgment. We thank Profs. W. R. Ware and A. C. Weedon for the use of their freeze-pumpthaw apparatus. This research was supported by an Operating Grant from the Natural Sciences and Engineering Research Council of Canada. D.D.F. acknowledges the support of an Ontario Graduate Scholarship from the Ontario Ministry of Colleges and Universities. References and Notes (1) Contribution No. 498, Photochemistry Unit, Department of Chemistry, The University of Western Ontario. (2) Deiscnhofer, J.; Michel, H. EMBO J. 1989, 8, 2149. (3) Chang, C.-H.;Tiede, D.; Tang, J.; Smith, U.; Norris, J.;Schiffer, M. FEES Lett. 1986, 205, 82. (4) Paper 3: Schmidt, J. A.; Siemiarczuk, A.; Weedon, A. C.; Bolton, J. R. J. Am. Chem.Soc. 1985, 107,6112. ( 5 ) Schmidt, J. A. Ph.D. Thesis: Intramolecular Photochemical Electron Transfer in Porphyrin-Quinone Molecules; University of Western Ontario: London, Ontario, 1986. (6) Connolly, J. S.;Bolton, J. R. In Photoinduced Electron Transfer. Part D. Photoinduced Electron Transfer Reactions: Inorganic Substrates ; Amsterdam, 1988; and Applications; Fox,M. A., Chanon, M., Us.Elsevicr: p 303. (7) Paper 4: Schmidt, J. A.; McIntosh, A. R.; Weedon, A. C.; Bolton, J. R.; Connolly, J. S.;Hurley, J. K.; Wasielewski, M . R. J . Am. Chem. Soc. 1988, 110, 1733. (8) Paper 5: Schmidt, J. A.; Liu, J.-Y.; Bolton, J. R.; Archer, M. D.; Gadzekpo, V. P. Y . J. Chem. SOC.,Faraday Trans. I 1989,85, 1027. (9) Paper 7: Liu, J.-Y.; Bolton, J. R. J. Phys. Chem. 1992, 96, 1718. (10) Whitten, D. G. Rev. Chem. Inrermed. 1978, 2, 107.
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