5940
J. Phys. Chem. 1993,97, 5940-5946
Pathways for Photoinduced Electron Transfer within a Mixed-Metal Bisporphyrin Anthony Harriman,**+Valerie Heitz,ti$ and Jean-Pierre Sauvage'vt Center for Fast Kinetics Research, The University of Texas at Austin, Austin, Texas 78712, and Facultk de Chimie, Universitk Louis Pasteur, 67000 Strasbourg, France Received: January 26, 1993; In Final Form: March 12, 1993
The photophysical properties of an oblique bisporphyrin, comprised of gold( 111) and zinc(I1) porphyrinic subunits separated by a 2,9-diphenyl- 1,lO-phenanthroline spacer moiety, have been studied. Upon selective excitation of either porphyrin, rapid electron transfer occurs from the zinc porphyrin to the appended gold porphyrin and the ground-state system is restored by relatively slow reverse electron transfer. The rates of the various electron transfer steps correlate with both reaction exergonicity and temperature but only poorly with the solvent polarity because of limited applicability of the dielectric continuum model to this system and solvent-induced changes in redox potentials. The magnitude of electronic coupling between the reactants shows a marked dependence on the energy gap between relevant orbitals on the porphyrin and the spacer group, consistent with through-bond interaction. It is concluded that reaction via the zinc porphyrin excited singlet and triplet states proceeds via electron transfer through the LUMO of the spacer, while the gold porphyrin triplet excited state reacts via hole transfer through the H O M O of the spacer moiety. Reverse electron transfer seems to show no preferred pathway and may involve through-space electron transfer.
The rates of intramolecularelectron transfer processes involving weakly-coupledreactants may be expressed in terms of the Fermi golden rule in which the rate constant (k)is related to the product of the electronic matrix coupling element squared (V)and the Franck-Condon weighted density of states (FCWD):'
Experimental Section
Butyronitrile (Aldrich) was fractionally distilled from KMn04 and CaC03 and all other solvents were spectroscopic grade materials stored over appropriate drying agents and fractionally distilled before use. Compounds were synthesized as before23 and the structures are shown in Figure 1. All experiments were k = (4r2/h)lq2(FCWD) (1) made with freshly prepared, dilute solutions of the compound in The matrix element V allows for the dependence of the rate of deoxygenated butyronitrile or the solvent under investigation. electron transfer on structural aspects (i.e., orientation, separation Singlet excited state lifetimes were measured by time-correlated, distance, and nature of the spacer moiety) and the Franck-Condon single-photon counting by using a mode-locked Nd-YAG laser factor provides for the dependenceonreaction exergonicity,solvent (Antares 76s) synchronously pumping a cavity-dumped reorganization energy, and nuclear vibrational frequency. For Rhodamine 6G dye laser (Spectra Physics 375B/244). A higha given geometry and spacer group, Vis expected to depend on radiance monochromator, together with glass cutoff filters, was the relative positioning of energy levels of relevant orbitals on the used to isolate fluorescence from scattered laser light. A reactants and spacer moiety,*J while the FCWD is expected to Hamamatsu microchannel plate was used to detect emitted depend on temperature and properties of both solvent and photons, for which the instrumental response function had an rea~tants.~.s The magnitudes of these various dependencieshave fwhm of 60 f 10 ps. Fluorescence decay profiles were collected been explored with a variety of model systems having donor and at six different wavelengths and analyzed according to global acceptor groups separated by a (semi)rigid spacer f ~ n c t i o n . ~ - ' ~ analysis methodology after computer deconvolution of the Particular attention has been given to photoinduced electron instrument respon~efunction.~~ Temperature-dependencestudies transfer between porphyrinic reactants because of the relevance were made with an optical Dewar, which was cooled or heated to bacterial photosynthetic reaction center For by a flowing stream of nitrogen. The temperature was measured one specific bisporphyrin (l),comprised of gold(II1) and zincby a thermocouple in contact with the solution and was accurate (11) porphyrinic subunits linked through a 2,9-diphenyl-1,loto i 1 OC. phenanthroline spacer, the various electron transfer pathways Flash photolysis studies were made with a frequency-doubled, have been elaborated in considerable detail and a full photon mode-locked Quantel YG402 Nd-YAG laser (pulse width 30 balance has been e s t a b l i ~ h e d . ~This 3 ~ ~ ~system is particularly ps). Laser intensities were attenuated with crossed polarizers attractive for mechanistic studies because, according to which and 300 laser shots were averaged for each measurement. porphyrin is excited, both singlet and triplet excited state processes Solutions were adjusted to possess absorbances of ca. 0.4 at 532 can be evaluated, together with the thermal reverse electron nm. Residual 1064-nm output from the laser was focused into transfer step. It has the additional attraction that the various 1/1 D3P04/D20 to produce a white light continuum for use as electron transfer steps lead to no overall change in electronic the analyzing beam. Variable delay times in the range 0-6 ns charge (Le., all steps involve charge shift not charge separation were selected in a random sequence and transient differential or recombination) such that attendant Coulombic energy terms absorption spectra were recorded with an Instruments SAUFSZOO are expected to be negligible.25 The present paper describes the spectrograph interfaced to a Tracor Northern 6200 MCA and rates of each electron transfer process as a function of reaction a microcomputer. Kinetic analyses were made by overlaying exergonicity,temperature, and solvent polarity in order to better about 40 individualspectra and fitting data at selected wavelengths by using computer nonlinear, least-squares iterative procedures. establish the reaction pathway. Additional studies are aimed at For these studies,the laser pulse was deconvoluted from the decay modulating the energy and geometry of the spacer moiety.26 profiles. For longer time scales, a conventional photomultiplier and monochromator system was used in place of the delay stage The University of Texas at Austin. * Universite Louis Pasteur. and the monitoring beam was a pulsed Xe arc lamp. +
0022-3654/93/2091-5940$04.00/0
0 1993 American Chemical Society
Photoinduced Electron Transfer
The Journal of Physical Chemistry, Vol. 97,No. 22, 1993 5941 Table I. The excited singlet-state energies of the fluorescent porphyrins were calculated at the intersection between excitation and fluorescence spectra recorded with narrow slitwidths. Values for the excited triplet state energies of the various porphyrins were calculated at the peak maximum for the highest energy peak recorded with the lowest possible slitwidths. The derived values are collected in Table I.
Results
1 M=Zn(ID 2 M=2HO
3 M=MgO 4 M = CIAl(lII) Figure 1. Structures of the bisporphyrins.
TABLE I: Redox Potentials for One-Electron Reduction of the Gold Porphyrin Subunit (&do) and Oxidation of the Excited Singlet (KF) Fluorescent Por byrin Subunit (&O), and Triplet (EtF! State Energy Levels for the Fluorescent Porphyrin Subunit, and the Triplet Energy of the Gold Porphyrin Subunit (Etc) for the Bisporphyrins 1-4s VusSCE
Eoxo; VusSCE
ESF:
compound
eV
eV
EtG," eV
1 2
-0.52 -0.54 -0.51 -0.51 -2.00
0.79 1.16 0.62 1.12 1.95
2.06 1.90 1.97 2.05
1.64 1.44 1.52 1.61
1.82 1.82 1.82 1.82
3 4 5
EtF,d
Redox potentials are given also for 2,9-diphenyl-1,lO-phenanthroline 5. 10.05 V. 10.02 eV. 10.05 eV.
*
Improved time resolution was achieved by using a frequencydoubled, mode-locked Antares 76s Nd-YAG laser to pump a Coherent 700 dual jet (Rhodamine 6G) dye laser operated at 76 MHz. A Quantel Model RGA67-10 regenerative amplifier, a Quantel Model PTA-60 dye laser, and a Continuum SPA1 autocorrelator were used to obtain 3-mJ pulses at 586 nm having a fwhm of ca. 500 fs. The spectrometer was run at a frequency of 10 Hz and data were acquired through a Princeton dual diode array spectrograph interfaced toa microcomputer. Thedetection setup and optical delay line were similar to those used for the 30-ps pulse width experiments; in both cases, the exciting and analyzing beams were almost collinear. Again, kinetic analyses were made by overlaying spectra collected at about 50 different delay times. Redox potentials for one-electron oxidation or reduction of the porphyrinic subunits were derived by cyclic voltammetry in deoxygenated butyronitrile containing tetra-n-butylammonium perchlorate (0.2 M). A glassy carbon working electrode was used in conjunction with a Pt counter electrode and an SCE reference electrode. The peaks were assigned to particular processes on the basis of measurements made with gold(III), zinc(II), free-base, magnesium(II), and chloroaluminum(II1) meso-tetrakis(3,5di-tert-butylphenyl)porphyrins.The redox potential for one-electron reduction of the gold(II1) porphyrinic subunit (Eredo)and redox potential for one-electron oxidation of the other porphyrinic subunit ( E , , O ) were measured for each compound and the results are collected in Table I. Redox potentials for one-electron reduction and oxidation, respectively, of 2,g-diphenyl-1,lO-phenanthroline(5) are also collectedin Table I. Excited-state energy levels were determined from luminescence spectra recorded in ethanol at 77 K and the values are given in
GeneralConsiderations. Thevarious processes that follow from selective excitation into either of the porphyrinic subunits in the bisporphyrin 1have been described in detai1;23*24 previous studies were made in N,N-dimethylformamide but the present work was done in butyronitrile because it was observed that 1 was more stable at elevated temperatures in this solvent. Briefly, upon excitation at 586 nm, where only the zinc porphyrin subunit absorbs, extremely weak fluorescence could be observed. The fluorescence spectrum corresponded to emission from a zinc porphyrin and the fluorescence decay profile, as recorded by timecorrelated, single-photoncounting techniques, could be analyzed satisfactorily in terms of a single-exponential process with a lifetime of 55 f 5 ps. This compares to a value of 2.3 f 0.1 ns observed for the corresponding model zinc porphyrin. Immediately after excitation of 1 with a 0.5-ps laser pulse at 586 nm, the characteristic differential absorption spectral features of the zinc porphyrin excited singlet state were observed. This state decayed with a lifetime of 55 f 5 ps to form a charge-transfer state, consisting of the zinc porphyrin *-radical cation and the gold(II1) porphyrin neutral radical, as formed by electron transfer from the excited singlet state of the zinc(I1) porphyrin to the appended gold(II1) porphyrin.
-
"(ZnP)-S-(AuP') ("ZnP)-S-(AuP') (2) The charge-transfer state decayed on a relatively slow time scale (T = 600 ps) to reform the ground-state system. ("ZnP) -S-(AuP')
(ZnP) -S(AuP')
(3) Excitation of 1 with a 30-ps laser pulse at 532 nm, where the gold(II1) porphyrin subunit absorbsabout 90%of the total incident photons, resulted in formation of the gold(II1) porphyrin triplet excited state. This species decayed with a lifetime of 120 f 10 ps, compared to a value of 1.4 f 0.2 ns recorded for the corresponding model gold(II1) porphyrin. On the basis of laser flash photolysis studies, decay of the triplet state was attributed to a combination of electron transfer to form the charge-transfer state
-
(ZnP)-S-(AuP')" ("ZnP)-S-(AuP') (4) and energy transfer to form the corresponding triplet excited state of the appended zinc porphyrin.
-
(ZnP)-S-(AuP+)*' "(ZnP)-S-(AuP') (5) After decay of the charge-transfer state (T = 600 ps), the lifetime of the zinc porphyrin excited triplet state could be measured by laser flash photolysis methods and was found to be 12 f 2 ns. This compares to a value of 820 f 50 ps measured for the corresponding monomeric zinc porphyrin under identical conditions. Quenching is attributed to electron transfer to the appended gold(II1) porphyrin, although the intermediate chargetransfer state could not be detected due to its short lifetime (T = 600 ps).
-
'*(ZnP)-S-(AuP') ("ZnP)-S-(AuP') (6) Rate constants were measured for each of the various steps by using time-correlated, single-photoncounting or picosecond laser flash photolysis techniques. The intermediate formation of the charge-transfer state was demonstrated unequivocally for reac-
5942 The Journal of Physical Chemistry, Vol. 97, No. 22, 1993
Harriman et al.
TABLE Ik Rate Constants and Reaction Exergonicities for the Various Electron-Transfer Steps in the Bisporphyrh in Butyronitrile at 25 OC compound
reaction‘
1
7 8 9
2
3
4
k/107,s-I 1800 650 170 7.8 4.2 0.62
10 7 8 9 10 7 8 9 10 7 8 9 10
0.0003 1900 610 230 8.1 78 0.7 0.02
AGO. eV ~
~
-0.75 -0.51 -1.31 -0.33 -0.22 -0.14 -1.68 +0.24 -0.83 -0.68 -1.14 -0.38 -0.41 -0.18 -1.64 +0.03
Refers to reaction number in the text.
tions 2 and 4, and its rate of decay was measured by picosecond laser flash photolysis methods, while population of the zinc porphyrin excited triplet state by reaction 5 was established by picosecond laser flash photolysis. These experiments have now been carried out under different experimental conditionsdeemed appropriate to study the effects of reaction exergonicity, temperature, and solvent polarity on the electron transfer rate constants. In all cases, the adopted methodology and the assignment of individual rate constants follows that explained pre~iously.23~2~ Effect of Reaction Exergonicity on the Rates of Photoinduced ElectronTramfer. Rateconstants for eachof theelectron transfer processes were derived for the seriesof mixed-metalbisporphyrins 1-4 in butyronitrile solution at 25 OC and are collected in Table 11, together with the respective reaction exergonicity (AGo).2g Rates of electron transfer following direct excitation into the fluorescent porphyrin subunit (k,) were derived by comparison of the excited singlet state lifetime with that of the corresponding model porphyrin, as measured by time-correlated, single-photon counting.
-
S * ( ~ ~ ) - ~ - ( ~ ~ (*+MP)-s-(AuP*) ~ + ) (7) Rates of electron transfer following selective excitation into the gold(II1) porphyrin subunit (ks) were measured by transient absorption spectroscopy following excitation with a 30-ps laser pulse at 532 nm. The lifetime of the initially produced gold(II1) porphyrin excited triplet state was compared with that of gold(111) meso-tetrakis(3,5-di-tert-butylphenyl)porphyrin and allowance was made for intramolecular triplet energy transfer.29
-
(MP)-s-(AUP+)*‘ (*+MP)-s-(AuP’) (8) Rates of reverse electron transfer (kg)were measured by transient absorption spectroscopy following excitation with a 0.5-ps laser pulse at 586 nm.
-
(*+MP)-s-(AuP’) (MP)-S-(AUP+) (9) Finally, rates of electron transfer from the excited triplet state of the fluorescent porphyrin subunit (klo) were measured by comparing the triplet lifetimewith that of the correspondingmodel porphyrin following excitation with a 30-ps laser pulse at 532 nm.
-
T
‘*(MP)-s-(AuP+) (‘+MP)-s-(AuP*) (io) It can be seen from the data collected in Table I1 that there is a progressive increase in the rate of photoinduced electron transfer with increasing reaction exergonicity, as expected for a nonadiabatic electron transfer process occurring within the “normal” regi0n.l Indeed, the rate of photoinduced electron transfer,
4.0 1.7
0.3
-0.1
-0.5
-0.9
-1.3
AGO (ev)
Figure 2. Correlation between the rate of photoinduced (singlet and triplet) electron transfer and the reaction exergonicityfor the bisporphyrins 1-4 in butyronitrile. The solid curve drawn through the data points is the best computed fit to eq 1 by using the parameters given in the text. The data points refer to reaction from ( 0 )excited singlet state of the fluorescentporphyrin, (X)excited triplet state of the fluorescentporphyrin, and (0)excited triplet state of the gold porphyrin and the number adjacent to each point refers to that particular bisporphyrin.
including both triplet and singlet excited state processes, could be satisfactorily explained in terms of eq 1 with the FCWD factor evaluated according to1 m
FCWD = [ ~ . X , ~ , T ~ - ’ / ~ C ( ~ ~ S ~exp{-[(X, /W!)
+ AGO +
w=o
w h c ~ ) ~ / 4 X ~ k ~(1Tl al ])
S = hv/hcv
(1 1b)
Here, AS and XV refer respectively to the solvent and nuclear reorganization energies, kB is the Boltzmann constant, c is the speed of light, and Y is a single average skeletal vibration. In attempting to fit the data to eq 1, we have arbitrarily assigned a “typical” value for Y of 1500 cm-I, but it should be noted that, since all the data points lie in the normal region, the quality of the fit is insensitive to the numerical value assigned to v. We have further assumed a value for the nuclear reorganizationenergy XV = 0.20 eV, which seems appropriate for porphyrinic species that do not undergo substantial geometry changes upon oneelectron oxidation or r e d u ~ t i o n . With ~ ~ these assumptions in mind, the best computed fit to eq 1 was obtained with AS = 1.28 eV and V = 37 cm-I (Figure 2). The derived value for Yseems rea~onable,~’ given the high rates of electron transfer and the 8.5 A edge-to-edge separation between porphyrinic subunits,32 but there is no valid reason to suppose that electron transfer steps proceeding from different excited states should exhibit the same value of V. Furthermore, since the data points do not straddle the maximum, the derived parameters must be regarded with caution and are probably not unique solutions. Consequently, independent estimates of Vand AS for each electron transfer step were sought by separate experiments using zinc(II)/gold(III) bisporphyrin 1. Rates of reverse electron transfer are also collected in Table 11, although electron-transfer products were observed only for 1 and 3. We presume that reverse electron transfer is faster than photoinduced electron transfer in bisporphyrins 2 and 4, due to the relative slowness of the forward reactions. Where measurements were possible, the derived rates of reverse electron transfer were found to be slow considering the high reaction exergonicities. This behavior is consistent with reverse electron transfer being within the Marcus inverted region,’ but including the rates of reverse electron transfer together with the rates of photoinduced electron transfer gave a poor global fit to eq 1. It appears, therefore, that forward and reverse electron transfer processes exhibit quite distinct rate us reaction exergonicity profiles” and/ or different electronic matrix coupling factors. Temperature Dependence for the Various Electron Transfer Processes in the Bisporphyrin 1. Equation 1 can be rewritten in
Photoinduced Electron Transfer
The Journal of Physical Chemistry, Vol. 97. No. 22, 1993 5943
TABLE In: Activation Enthalpies, Solvent Reorganization Energies, and Electronic Matrix Coupling Elements Derived from the Temperature Dependence Studies for 1 in Butyronitrile and the Slopes and Maximum Rate Constants Derived from the Solvent Dependence Studies for 1 in the Solvents Listed in Table III
18.0
reaction"
u*,b eV
2 3 4 6
0.090 0.003 0.130 0.180
--
-.-i5
d0
is
4:O
4:s
S:O
5:s
1/T x 1000 (K-l) Figure 3. Arrhenius-type plots for the effect of temperature on the rates of electron transfer occurring in 1 in butyronitrile; data points are shown for photoinduced electron transfer from the excited singlet ( 0 )and triplet (+) states of the zinc porphyrin and excited triplet state of the gold(II1) porphyrin (U) and for reverse electron transfer (A). The solid line drawn through each set of data points is the best fit to eq 12.
the form of an Arrhenius-type expression in which the rate of electron transfer can be related to In[kT'/2] = In A - ( W / R T )
A = { ( 4 ~ ~ V ~ / h ) [ 4 a X ~ kexpS J~/~]
(12a) (12b)
Here, AH* refers to the activation enthalpy, as defined by eq 11. In applying eq 12, we assume that the conformation of the bisporphyrin and the reaction exergonicity remain independent of temperature. With respect to the former assumption, we note that the conformation of the molecule is constrained by the bulky tert-butyl groups attached to both porphyrins and, although not rigid, there are few degrees of rotational freedom. In support of the latter assumption, we expect there to be only a small entropy change associated with the various electron transfer processes, since a charge shift between porphyrinic species destroys a solvation environment around one porphyrin but creates a similar one around the other porphyrin. It is also important to note that for butyronitrile the solvent reorganization energy (As) is insensitive to temperature and varies by less than 5% over the temperature range under investigation. Rate constants for each of the various electron transfer steps following from selective excitation into one of the porphyrinic subunits in 1were measured in butyronitrile over the temperature range -90 to 100 OC. Figure 3 shows Arrhenius-type plots for each of the electron-transfer process; namely, photoinduced electron transfer from the excited singlet (kz)and triplet (k6) states of the zinc porphyrin, photoinduced electron abstraction by the excited triplet state of the gold(II1) porphyrin (ks), and reverse electron transfer (k3). Linear plots to eq 12 were observed in each case, and values for the activation enthalpies, as derived from the slopes, are collected in Table 111. The solid line drawn through each set of data points represents the best fit to eq 11 and the derived values for the solvent reorganization energy (AS) are collected in Table 111. The average value for AS is 1.36 f 0.1 1 eV. By use of this latter value, the magnitude of the electronic coupling matrix element (V) was calculated for each process from the intercepts of Figure 3 and the derived values are compiled in Table 111. For the purpose of this latter calculation, the nuclear reorganization energy (XV) was assumed to be 0.20 eV.30 Solvent Dependence of the Rates of Electron Transfer for the Bisporphyrin 1. In an attempt to test the internal consistency of the parameters derived above, the rates of the various electron transfer steps were measured in a range of solvents at 25 O C . It is recognized that the solvent reorganization energy (hs)depends markedly on the nature of the solvent34and is often calculated on the basis of considering the reactants to be two spheres of
X,,b
eV
v,bcm-1
slopec
85 5 110 35
-0.81 -0.97 -0.83 -0.71
1.47 1.31 1.33 1.29
ko/1o9: s-I 160 1.7 555 42
Refers to the reaction number in the text. Derived from measurement of the rate of electron transfer as a function of temperature in butyronitrile. Derived from measurement of the rate of electron transfer in solvents of different polarity.
TABLE I V Solvent Reorganization Energies and Rate Constants for Electron Transfer for 1 in a Series of Solvents at 25 *C solvent X,,eeV log k2 log k3 log kq log k6 CH3OH C2HsOH CH3CN DMF" PCb acetone BCNC CH2C12
DMSOd CHC13 CH2CICH2Cl
1.53 1.43 1.51 1.33 1.38 1.42 1.36 1.09 1.26 0.76 1.10
9.76 9.93 9.90 10.26 10.22 9.94 10.26 10.67 10.50 11.31 10.92
9.06 9.23 9.11 9.21 9.23 9.19 9.23 9.10 9.27 9.13
9.17 9.31 9.25 9.55 9.39 9.67 9.81 10.76 9.77 11.18 10.82
7.50 7.76 7.47 7.94 7.84 7.79 7.89 8.74 8.30 8.76
*
N,N-Dimethylformamide. Propylene carbonate. Butyronitrile. Dimethyl sulfoxide. e Calculated from eq 14. a
radius r in a dielectric continuum:35
As = {[e2/4~fo1[(l/r) - (1/"/eoJ
- (l/es)ll
(13)
Here, D refers to the center-to-center separation distance (D= 13.5 A)32and topand es refer respectively to the optical and static dielectric constants of the surrounding medium. Because of the oblique geometry of the bisporphyrin 1 it is unlikely that we can treat the reactants as spheres and, therefore, we have difficulty to calculate Xs from eq 13. However, from the above determination of Xs = 1.36 f 0.1 1 eV in butyronitrile, we can formulate the solvent dependence of Xs by the following expres~ion:3~ Xs = 2.88[(1/~,,)
- ( l / ~ s ) ]= 2.88f
(14) The calculated values for AS in the series of solvents under investigationare collected inTable IV. Unfortunately, thevalues lie within a fairly narrow range, since the choice of solvent is limited by the solubility of 1. Equation 1 can be rewritten in the following form, which highlights the solvent dependence of the rate of electron transfer: 83
In [k(Xs)'/2] = In B - (AG*/kBT)
(154
B = { ( 4 ~ ~ V ~ / h ) [ 4 ~ k ~exp-' T ] - ~ / ~ ] (15b) Although individual redox potentials for porphyrinic species are dependent on the nature of the solvent," the difference between oxidation and reduction processes remain reasonably insensitive to changes in solvent. Thus, for this special case of a charge-shift reaction between porphyrinic species, AGO is essentially independent of solvent and, consequently,any significantsolvent effect on AG*can be attributed to modulation of AS according to eq 14. Rate constants for each of the electron transfer steps were measured for 1 in the series of solvents at 25 OC and the results are collected in Table IV. The data are also plotted in Figure 4 in the form of eq 15. Although there is considerable scatter
Harriman et al.
5944 The Journal of Physical Chemistry, Vol. 97,No. 22, 1993
6 A G * ~ ~ T
21.0
0.0
0.2
0.4
AG'lkgT
210g
Figure 4. Effect of solvent on the rates of electron transfer for 1 at 25 OC; data points are shown for photoinduced electron transfer from the excited (a) singlet and (b) triplet states of the zinc porphyrin and (c) excited triplet stateof thegold(II1) porphyrin and (d) for reverseelectron transfer. The solid line drawn through each set of data points is the best fit from least-squares analysis.
v
Figure 5. Correlation between the derived rate constant for electron transfer at zero activation free energy change and the squareof thederived electronic matrix coupling element .for the various electron-transfer processes occurring in 1.
tance (d) according to among the data points, each plot was linear with a slope in the region of -1 -0, as expected from eq 15. The slopes, as calculated by linear least-squares analysis of the data, are provided in Table 111. For reverse electron transfer the slope is close to the required value of -1.0, but this may be quite fortuitous since the rates hardly change with solvent polarity. This might be expected since the rate of reverse electron transfer is expected to lie close to the plateau of a Marcus-type plot, since -AGO = A, where the rate might be relatively insensitive to changes in AG*. Significantly smaller slopes were obtained for the photoinduced electron transfer steps, although these reactions are expected to lie within the normal region. The poor correlation is not caused by the numerical value used for AS, since attempts to refine this parameter did not improve the fit, but arises from the scatter in the data points. [It should be noted that the rate of triplet energy transfer from gold(II1) porphyrin to the appended zinc porphyrin (i.e., reaction 5) was independent of the nature of the solvent.] The intercepts also provide valuable information in that they refer to the rateconstant for electron transfer at zero activationfree energy change (k,,). Essentially, this is the maximum value for that particular rate of electron transfer and the derived values are also provided in Table 111.
k, = (2 x 1 0 ' ~ )exp[-crd]
(16) where the attenuation factor a has a value of 1.2 A-I. For the bisporphyrin 1 (d = 8.5 A),32we might expect to observe k, = 8 X 108 s-I for through-space electron transfer. This value is close to that derived for reverse electron transfer (k, = 1.7 X lo9 s-I) but is very much lower than the values observed for photoinduced electron transfer. In these latter cases, therefore, it is probable that electron transfer proceeds by way of orbitals locatedon the 2,9-diphenyl-1,IO-phenanthrolinespacer moiety.39 Thederivedvalues of V, which are expected to be more reliable than the corresponding k, values, range from 5 to 110 cm-I and are less than k ~ T ( = 2 1 0cm-I). Our values are in the same range as those reported for related photoinduced and thermal electrontransfer processes across comparable separation distances.lq4,31 The magnitude of Vis related to the orbital overlap integral, decreasing exponentially with increasing separation distance, and dependson the stereochemistry and chemical nature of the spacer moiety.' For through-bond electron or hole transfer via superexchange interaction between the reactants and spacer, V is expected to depend upon the inverse of the energy gap between the initial state and the spacer (6EAe) according to4
Discussion The rates of the various electron transfer steps in the oblique bisporphyrin appear to correlate well with nonadiabatic electron transfer theory.' In particular, the effectsof reaction exergonicity and temperature on the rate constants can be explained satisfactorilyin terms of eq 1with the Franck-Condon factor asdefined in eq 11. The structure of the oblique bisporphyrin, however, does not facilitate meaningful application of the simple dielectric continuum model to calculate the appropriate value for the solvent reorganization energy (eq 13). Instead, we have quantified this parameter by comparing observed and calculated activation enthalpies and found a relatively high value (AS = 1.36 f 0.1 1 eV) for butyronitrile. Solvent polarity affects the magnitude of As, although the actual correlation is quite poor, and there may be additional solvent effects. The size of the electronic coupling matrix element (V) and the rate constant for electron transfer at zero activation free energy change (k,), as listed in Table 111, depend markedly on the nature of the reacting species and can be utilized to elicit the reaction pathway. The derived values for k, exhibit a clear dependence on VL (Figure 5 ) , as predicted by eq 1, and vary from 5.5 X 10" s-l (for reaction via the excited triplet state of the gold(II1) porphyrinic subunit) to 1.7 X 109 s-1 (for reverse electron transfer). On the basis of pulse radiolytic charge shift reactions, Miller and cow o r k e r ~have ~ ~ concluded that the rate of through-space electron transfer decreases with increasing edge-to-edge separation dis-
Here, BABand BBCrefer respectively to the electronic coupling terms between initial and spacer states and between spacer and final states. In principle, V can be calculated from molecular orbital (MO) theory and, for simple systems, such calculations have been quite ~uccessful.~~ A qualitative description of the through-bond interaction for the bisporphyrin 1within the frontier MO framework is depicted in Figure 6, where the energies of donatingand accepting orbitals on the zinc(I1) and gold(II1) porphyrins are compared to the energies of the LUMO and HOMO on the 2,9-diphenyl-l,10phenanthroline spacer moiety.42 For reaction to proceed by way of electron transfer through the LUMO of the spacer moiety, it is important to minimize the energy gap (B- = ~ B A Bbetween ) the donating orbital and the LUMO of the spacer. Similarly, for reaction via hole transfer through the HOMO of the spacer, it is important to minimize the energy gap (B+ = ~ E A Bbetween ) the accepting orbital and the HOMO of the spacer. The relevant energy gaps have been calculated for each of the electron transfer processes43and are collected in Table V. It can be seen that reaction from the first excited singlet and triplet states of the zinc porphyrin is likely to proceed by way of electron transfer through the LUMO of the spacer since B- is considerable smaller than B+. However, the gold(II1) porphyrin excited triplet state is expected to react by way of hole transfer through the HOMO of the spacer since, in this case, B+ is much less than B-. There
The Journal of Physical Chemistry, Vol. 97, No. 22, 1993 5945
Photoinduced Electron Transfer
b
LUMO
t
1-
I - L L
wz c W
LU MO
-I
d
LUMO I
Figure 6. MO diagrams illustrating the energy gaps for through-bond electron and hole transfer in 1. The systems refer to electron transfer occurring via (a) the excited singlet and (b) the excited triplet states of the zinc porphyrin, (c) the triplet excited state of thegold(II1) porphyrin, and (d) reverse electron transfer. Values for the energy gaps are collected in Table V.
TABLE V Energy Gaps, Electronic Coupling Terms, and Maximum Rate Constants for 1 reactiona B_,beV B+,C eV BABBBC,~ eV2 ko/109,' S-' 2 3 4 6
0.73 1.48 2.79 1.15
2.47 1.16 0.65 2.47
0.0080 0.0007 0.0085 0.0060
160 1.7 555 42
Refers to the reaction number given in the text. Calculated as B= -[EredS- ED], where ErdSis the one-electron reduction potential for 2,9-diphenyl-l,lO-phenanthroline (Ered5= -2.00 V us SCE) and E D is the redox potential of the donating orbital: ED(eq 2) = [0.79 - 2.061 -1.27 V US S C E ED (eq 3) = -0.52 V US SCE; ED(eq 4) = 0.79 V us SCE; E D (eq 6) = [0.79 - 1.641 = -0.85 V us SCE. Calculated as B+ = [EoxS- E A ] , where Eox5is the one-electron oxidation potential for 2,9-diphenyl-l,lO-phenanthroline(,Fox5 = 1.95 V us SCE) and EA is the redox potential of the accepting orbital: E A (eq 2) = -0.52 V us SCE; E A (eq 3) = 0.79 V us SCE; E A (eq 4) = [-0.52 + 1-82] = 1.30 V us S c E E ~ ( e q 6=-0.52VusSCE. ) dCalculatedfromeq17. eExtrapolated from the solvent dependence of the rate of electron transfer.
are relatively large energy gaps for both electron and hole transfer for reverse electron transfer and, based on the 6 E ~ values, e there is a slight preference for hole transfer. However, as mentioned above the rateof reverse electron transfer is close to that expected for a through-space process such that this reaction might not involve significant through-bond interaction. For the photoinduced electron transfer processes there is a rough correlation between k, and ~ E A Bas, indicated by the data given in Table V. The product of the electronic coupling terms for a spacer-mediated superexchange process (@AB&), as calculated from eq 17, remains fairly constant for the three processes (Table V). Thus, coupling between the LUMO and/ or HOMO of the spacer moiety and orbitals on the excited-state species is both efficient and relatively insensitive to the nature of the excited state. From the derived values, it appears that the triplet excited state of the zinc porphyrin is less well coupled to the LUMO of the spacer than is the corresponding excited singlet state. However, the charge-transfer state is very weakly coupled to orbitals located on the spacer moiety. It is this poor coupling that gives rise to the slow rate of reverse electron transfer, not the large ~ E A B Clearly, . the bridging 2,9-diphenyl-1,lO-phenanthroline spacer does not promote strong coupling between the redox products and there is no need to invoke a superexchange interaction to explain the rate for reverse electron transfer. A
detailed understanding for the weak coupling in the chargetransfer state must await the results of MO calculations. A through-bond superexchange mechanism also explains the poor correlation observed for the solvent effect on the rate of electron transfer. Although AGO remains relatively insensitive to solvent, individual redox potentials change by as much as 140 mV as the solvent is varied. This will affect the energies of donating and accepting orbitals on the porphyrinic subunits. Furthermore, it is likely that similar solvent effects will modulate the energies of the LUMO and/or HOMO on the spacer moiety. The solvent may influencethe rate of electron transfer, therefore, by modifying ~ E A B in,additionto affecting AG*. Current studies are aimed at refining our mode of modulating ~ E A without B affecting AG*.
Acknowledgment. Support for this work was provided by the C.N.R.S., the National Science Foundation (CHE 9102657), and NATO (920916). The CFKR is supported jointly by the Division of Research Resources of the N.I.H. (RR00886) and by The University of Texas at Austin. We thank the US. Department of Energy for the award of a grant enabling construction of the femtosecond laser flash spectrometer. References and Notes (1) Closs, G. L.; Miller, J. R. Science 1988, 240, 440. (2) Beratan, D. N. J. Am. Chem. SOC.1986, 108, 4321. (3) Plato, M.; Mobius, K.; Michel-Beyerle, M. E.; Bixon, M.; Jortner, J. J. Am. Chem. SOC.1988, 110, 7279. (4) Miller, J. R. Nouu.J . Chim. 1987, 11, 83. (5) Krmn, J.; Verhoeven, J. W.; Paddon-Row, M. N.; Oliver, A. M. Angew. Chem., Int. Ed. Engl. 1991, 30, 1358. (6) (a) Liang, N.; Miller, J. R.; Closs, G. L. J . Am. Chem. SOC.1989, 111,8740. (b) Liang, N.; Miller, J. R.; Closs, G. L. J . Am. Chem. SOC.1990, 112,5353. (7) Heitele, H.; Michel-Beyerle, M. E. J . Am. Chem. SOC.1985, 107, 8286. (b) Heitele, H.; Michel-Beyerle, M. E.; Finckh, P. Chem. Phys. Lett. 1987, 134, 273. (c) Finckh, P.; Heitele, H.; Volk, M.; Michel-Beye.de, M. E. J . Phys. Chem. 1988, 92, 6584. (8) Liu, J.-Y.; Bolton, J. R. J. Phys. Chem. 1992, 96, 1718. (9) Oevering, H.; Paddon-Row, M.N.; Heppener, M.; Oliver, A. M.; Cotsari, E.; Verhoeven, J. W.; Hush, N. S. J . Am. Chem. SOC.1987, 109, 3260. (10) (a) Joran, A. D.; Leland, B. A.; Geller, G.G.; Hopfield, J. J.; Zewail, A. H.; Dervan, P. D. J. Am. Chem. SOC.1984,106,6090. (b) Joran, A. D.; Leland, B. A,; Geller, G. G.; Hopfield, J. J.; Zewail, A. H.; Dervan, P. D. J . Phys. Chem. 1985,89, 5571. (1 1) Wasielewski, M. R.; Niemczyk, M. P.; Johnson, D. G.; Svec, W. A.; Minsk, D. W. Tetrahedron 1989, 45, 4785. (12) Heitele, H.; Michel-Beye.de, M. E.; Finckh, P. Chem. Phys. Lett. 1987, 138, 237. (13) (a) Irvine, M. P.; Harrison, R. J.; Beddard, G.S.;Leighton,P.;Sanders, J. K. M. Chem. Phys. 1986,104,315. (b) Harrison,R. J.;Pearce,B.; Beddard, G. S.; Cowan, J. A,; Sanders, J. K. M. Chem. Phys. 1987, 116, 429. (14) (a) Calcaterra, L. T.; Closs, G. L.; Miller, J. R. J. Am. Chem. SOC. 1983,105,670. (b) Miller, J. R.; Calcaterra, L. T.; Closs, G. L. J.Am. Chem. SOC.1984,106,3047. (c) Johnson, M. D.; Miller, J. R.; Green, N. S.; Closs, G. L. J . Phys. Chem. 1989, 93, 1173. (15) (a) Wasielewski, M. R.; Niemczyk, M.P.; Svec, W. A.; Pewitt, E. B. J. Am. Chem. SOC.1985,107,1080. (b) Wasielewski, M. R.; Johnson, D. G.;Svec, W. A.; Kersey, K. M.; Minsk, D. W. J . Am. Chem. SOC.1988,110, 17219. (c) Wasielewski, M.R.; Johnson, D. G.; Niemczyk, M. P.; Gaines, G. L. 111; ONeil, M. P.; Svec, W. A. J . Am. Chem. SOC.1990, 112, 6482. (16) Gust, D.; Moore, T. A. Science 1989, 244, 35. (17) (a) Sessler, J. L.; Johnson, M. R.; Liu, T.; Creager, S. E. J . Am. Chem. SOC.1988, 110, 3659. (b) Rodriguez, J.; Kirmaier, C.; Johnson, M. R.; Friesner, R.;Holten, D.;Sessler, J. L. J . Am. Chem.Soc. 1991,113, 1652. (18) Delaney, J. K.; Mauzerall, D. C.; Lindsey, J. L. J. Am. Chem. SOC. 1990, 112, 957. (19) Gaines, G. L., 111; ONeil, M. P.; Svec, W. A.; Niemczyk, M. P.; Wasielewski, M. R. J . Am. Chem. SOC.1991, 113. 719. (20) (a) Heiler, D.; McLendon, G.;Rogalskyj J. Am. Chem. SOC.1987, 109,604. (b) Helms, A,; Heiler, D.; McLendon, G. J . Am. Chem. SOC.1992, 114,6227. (21) Osuka, A.; Maruyama, H.; Mataga, N.; Asahi, T.; Yamazaki, I.; Tamai, H. J . Am. Chem. SOC.1990, 112,4858. (22) (a) Johnson, D. G.;Svec, W. A.; Wasielewski, M.R. Isr. J . Chem. 1988, 28, 193. (b) Zaleski, J. M.; Chang, C. K.; Leroi, G.E.; Cukier, R. I.; Nocera, D. G. J. Am. Chem. SOC.1992, 114, 3564. (23) Brun, A. M.; Harriman, A.; Heitz, V.; Sauvage, J.-P. J. Am. Chem. SOC.1991, 113, 8657. (24) Brun,A. M.;Atherton,S. J.;Harriman,A.; Heitz, V.;Sauvage, J.-P. J . Am. Chem. SOC.1992, 114,4632.
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501. (28)Calculated according to AGO = -F[EaA eo^ + Es] where E o Aand Eo 1) refer to the redox potentials for respectively one-electron reduction of the gold(II1) porphyrin and one-electron oxidation of the fluorescent porphyrin and ES is the excitation energy. (29) In each case, the rate constant for triplet energy transfer from gold(111) porphyrin to the appended fluorescent porphyrin ( k ~ was ) measured by recording the yieldofthelatter s p i e s o n longer timescales. Therateconstant for electron transfer was calculated as k4 = ( I / T ) - ki - kd where T refers to the lifetime of gold(II1) porphyrin subunit in the bisporphyrin and kd is the lifetime of the model gold(II1) porphyrin measured under identicalconditions. (30) We have used a low value for the nuclear reorganization energy since it is well-knownthat metalloporphyrins undergo only slight structural changes upon electron transfer. Indeed,X-ray data indicate minimal geometry changes between a zinc porphyrin and the corresponding r-radical cation. See: Huppert, D.; Kanety, H.; Kosower, E. M. Faraday Discuss. Chem. SOC.1982, 74, 161. (31)Gainesetal.?oreportedV = 33cm I forphotoinducedelectrontransfer across 1 1 A for a series of triptycene-linked porphyrinquinones, while Finckh et al.'.' observed Vvalues ranging from 9 to 65 cm-l for photoinduced electron transfer from pyrene to N,N-dimethylaniline across various aromatic spacer moieties. (32) Chardon-Noblat, S.; Guilhem, J.; Mathis, P.; Pascard, C.; Sauvage, J.-P. In Photoconversion Processes for Energy and Chemicals; Hall, D. O., Grassi, G., Eds.; Elsevier: London, 1989;p 90.
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