Solvent and temperature dependence of electron transfer in the

James H. Alstrum-Acevedo, M. Kyle Brennaman, and Thomas J. Meyer ... Michael Towrie, Jakub Šebera, Stanislav Záliš, and Antonín Vlček, Jr. .... J...
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J. Phys. Chem. 1993,97, 13126-13131

13126

Solvent and Temperature Dependence of Electron Transfer in the Inverted Region Pmgyun Cben, Sandra L. Mecklenburg, and Thomas J. Meyer' Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290 Received: August 3, 1993; In Final Form: September 30, 1993' The solvent and temperature dependences of the rate constant for the electron transfer reaction Rel(bpy*-PTZ'+)(CO)sCl- Re1(bpy-PTZ)(CO)3C1 (bpy-PTZ is 10-[4'-methyl-2,2'-bipyridin-4-yl]phenothiazine) have been studied by transient absorption measurements. This reaction, which w u r s in the inverted region, was induced following Re1 bpy excitation of ReI(bpy-PTZ)(CO)sCl and intramolecular -PTZ Re" electron transfer. On the basis of electrochemical measurements of A E l p [AE1/2 = E1/2(PTZo/+) - Elp(bpyO/-)] and dielectric continuum theory, the variation of In k in seven relatively polar solvents (k = 4.33 X 106 s-l in benzonitrile to 6.67 X lo6 s-l in propylene carbonate) can be accounted for quantitatively by the energy gap law. A linear correlation between In k and T for electron transfer in propylene carbonate over the range 223 K (k = 6.33 X lo6 s-l) to 303 K (k = 7.11 X lo6 s-l) is also consistent with the energy gap law. From temperature-dependent measurements of AElp, -dAE1p/aT AS = 12 cal mol-* K-l. From this value, the quantity Y / ~ U M = 3.4 eV-l obtained from an earlier free energy dependence study, and the variation of In k with T, a solvent reorganizational energy (X'o) of -0.4 eV can be calculated. This quantity also includes a contribution from low-frequency vibrations treated classically.

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Introduction Electron transfer in the inverted region has similarities with nonradiative decay of excited states.14 For either, -AGO > X (where AGO and A are the free energy change and reorganizational energy of the reaction), and the potential energy surface of the initial state is embedded within that of the final state. In the weak (vibrational) coupling limit where -AGO >> A, the rate constant (k) for both processes is predicted to decrease exponentially as -AGO increases by the energy gap law.14 This prediction has been verified for nonradiative decay of excited states including metal-to-ligandcharge transfer (MLCT) excited states of transition-metal complexes.3.5 Variations in the rate constant for nonradiative decay (k,) with solvent, temperature, and ionic strength can be accounted for quantitatively by the energy gap law.5 The pioneering work of Miller and C l o d based on organic donor-acceptor assemblies linked by rigid spacers was the first experimentalobservationof the inverted region effect for electron transfer. Since then it has been demonstrated in a number of other system^,^-^^ but data on solvent and temperature effects are limited.llJ2 We studied the free energy dependence of electron transfer in the inverted region based on the series fac-[ReI(4,4'-(X)*bpy)(CO)~(PY-PTZ)]+(X OCH3, CH3, H, C(O)NEt2, C02Et; pyPTZ is 10-(4-picolyl)phenothiazine) where variations in AGO were made by varying the substituent X.4

In these reactions the metal complex acts as a scaffold and photoinitiator for the study of an organic electron transfer. Rate constants for back electron transfer were obtained by transient absorption measurements following laser flash excitation, (k'in Scheme I). Free energy changes were estimated by electro*Abstract published in Aduonce ACS Abstracts, November 15, 1993.

0022-3654/93/2097-13 126$04.00/0

I

hv

[Re'(CO)3(bpy..-PTz*.)C11 ko

Experimental Section Materinls. Spectrogradeacetonitrile,acetone,methanol, DMF, DMSO, propylene carbonate, dichloroethane,dichloromethane, 0 1993 American Chemical Society

Electron Transfer in the Inverted Region

The Journal of Physical Chemistry, Vol. 97, No. 50, 1993 13127

and o-xylene were purchased from Burdick and Jackson Laboratories. n-Propionitrileand n-butyronitrilewere purchased from Aldrich and distilled from CaH2 before use. Ethanol was distilled from Mg turnings activated by 12. Benzonitrile (HPLC grade), toluene (spectrophotometricgrade), methanol-d (gold label), and n-methylformamide were purchased from Aldrich and used without further purification. 1.2-Dimethoxyethanewas obtained from Fisher Scientific. The supporting electrolyte [N(n-C4H&](PF6) was purchased from Aldrich and recrystallized twice from a HzO/ethanol (2:l v/v) mixture. heparation. The ligand bpy-PTZ was availablefrom previous studies.14 The complex [Re(bpy-PTZ)(CO)&l] was prepared by a procedure similar to that described previou~ly.~~ Stoichiometric amounts of Re(C0)sCl (362 mg, 0.1 mmol) and bpyPTZ (382 mg, 0.1 mmol) were mixed with 30 mL of toluene and heated at reflux for 1.5 h. After cooling, most of the toluene was removed by rotary evaporation and the concentrated solution was added to 60 mL of hexane with stirring. The bright yellow precipitate was collected by filtration and washed with hexane and diethyl ether to give 720 mg of the product. IR spectrum in CH3CN: v(C0) 2022, 1917, 1898 cm-1. Elemental Anal. Calcd: C, 47.19; H, 2.88; N, 6.11. Found: C, 47.23; H, 3.06; N, 6.18. Measurements. Electrochemical measurements were conducted by using a procedure described previously.138 The concentration of supporting electrolyte, [N(n-C4H9)4](PFa), was 0.005 M,andthesolutionswere -1WMin [Re(bpy-PTZ)(C0)3Cl]. AE1p values in each solvent were obtained as an average of at least three scans. The error was estimated to be -*7 mV. Temperature-dependent electrochemical measurements were conducted by using the same cell immersed in a water bath which provided a temperature variation from -10 to 50 OC ( f l "C). Transient absorption measurements were conducted by using a laser system that has been described previously.13~16 Laser excitation was provided by 420-nm, 4-11s pulses of energy 1.2 mJ/pulse. Solutions of [Re(bpy-PTZ)(CO)3C1] for solventdependent studies were deaerated by bubbling with high purity argon for 10-20 min. Samples for temperature-dependent measurements were further deaerated by three f r e e z e p u m p thaw cycles. Temperature control over the range -50 to +50 OC (f0.2 "C) was provided by an Oxford Cryostat Model DN1704 and Temperature Controller Model 3 120. Backelectron transfer rate constants wereobtained by monitoring the decay of the PTZ'+ transient absorption maximum at 5 10 nm.4913 The absorbancetime traces decayed with simple exponential kinetics.

TABLE I: Solvent Dependence of AEl/1 and k for Back Electron Transfer (ea 1) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

toluene o-xylene 1,2-dimethoxyethane dichloromethane 1,2-dichloroethane butyronitrile acetone ethanol benzonitrile propionitrile methanol methanol-d dimethylformamide acetonitrile dimethylsulfoxide propylene carbonate N-methylformamide

2.38 2.57 7.2 8.9 10.4 20.3 20.7 24.3 25.2 27.7 32.6 32.6 36.7 37.5 49.0 65.1 182

21.6 20.2 5.00 5.26 4.67 4.85 5.59 5.52 4.33 5.62 7.19 6.33 5.71 6.49 6.58 6.67 6.67

2.277 2.286 2.239 2.170 2.206 2.144 2.152

Static dielectric constant. k for back electron transfer monitored at 510 nm, h0.15 X 106. AE1p 7 mV measured as described in the Experimental Section.

*

16.00

A

7.0

=

x

6.0

15.50

5.0 15.25

I 2.25

2.20

AE,,,

2.30

(v)

1

I

k

Re'( bpy-PTZ) (CO),Cl

( 1)

A E l p values obtained from electrochemical measurements in seven relatively polar solvents with 0.005 M [N(n-C4H9)4](PF6) as supportingelectrolyte. A E l p is the potential differencebetween the [Re1(bpy-PTZ+/O)(CO)pCl] and [ReI(bpyO/--PTZ)(CO)3Cl] couples. Because the Ag wire used in the electrochemical

8.0

15.8 7.0 F.

15.6

X

6.0

A

C

vi

15.4

5.0

15.2

Re'( bpy*--PTZ'+)(CO),Cl-

-

4 4.0 2.15

4.0

ReSults

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r h

x

-

The sequence of reactions in Scheme I1 was established by emission and transient absorption measurements. Emission from the initiallyformed ReII(bpy+) state is nearly completelyquenched That compared to that from [Re(4,4'-(CH3)2bpy)(CO)3Cl].15 the quenching results from -PTZ Re" electron transfer is shown by the appearance of intense absorption features at 510 and 390 nm in the transient absorption spectrum obtained following 420-nm laser excitation. These observations provide direct evidence for the formation of the redox-separated state ReI(bpy*--PTZ*+)shown in Scheme II.kJ3b Rate constants for the electron transfer reaction in eq 1 in a series of solvents were obtained by transient absorption measurements and are listed in Table I. Also listed in Table I are

8.0

15.75

15.2 22.1

15.4

-

3.4(AE,,,)

15.6

+

l.Z(l/Ds

15.8

- l/Do,)

Figure 1. (A) Plot of In kvs A E l p for backelectron transfer in [Rel(bpy'FTz'+)(CO)$l in seven polar solvents at room temperature. The solvents are labeled according to the numbering scheme in Table I, and the linear correlationcorrespondstotheequationlnk= 21.1 -2SAElpwithAE1/2 in eV; r = 0.89. (B) Plot of In k(obsd) vs In k(ca1c) where In k(ca1c) = 22.5 - 3.4(AE1p) 1.2(l/Dop - l/DJ with A E l p in eV; r = 0.95.

+

measurements was only a pseudoreference, the individual Ell2 values shifted from scan to scan, but AE112 values remained constant within experimentalerror (f7 mV). Thequantity AE1p is a measure of AGO for back electron transfer (see below). A plot of In k vs M1/2in a series of solvents is shown in Figure 1, where the correlation is limited to solvents of relatively high dielectric constant (0,> 20) to avoid complications from ionpairing effects. In several solvents, including butyronitrile, propylene carbonate, acetonitrile, and propionitrile,it was shown that k was the same within experimentalerror in the pure solvents as in the presence of 0.005 M [N(n-C4H9)4](PF,j). These are the solvents that were used for electrochemical measurements. In Figure 2A is shown a plot of M1pvs 1/D,, where D, is the static

Chen et al.

13128 The Journal of Physical Chemistry, Vol. 97, No. 50, 1993

h

>

v

N =.

Y

2120 0.01

0.02

0.03

0.04

I

0.05

I

I

I

I

260

280

300

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T(K)

1/D,

15.85

16.00

I..,

15.80

Y

C

15.65

4.0

Yo

200

225

6.0 250

275

300

325

350

T(K)

Figure 2. (A) Plot of AE112 vs 1/D, for the seven polar organic solvents

where electrochemical data were available with the linear correlation 1U1y= 4.6(1/D,) + 2.07, r = 0.93. (b) Plot of In k vs l/Da (Da is the staticdielectricconstant) in the extended rangeof solventslisted in Table I with the linear correlation In k = 15.7 - 2.6(1/Ds), r = 0.74. The dashed line is the correlationIn k = 15.9 - 12.1(1/D8),r = 0.86, found for the seven polar solvents (tilled circles). The solvents are labeled according to the numbering scheme in Table I.

TABLE II: Temperature De ndence of AE1/2 and k for Back Electron Transfer (ea l K n Propylene Carbonate ~~~

50 40 30 24 20 10 0 -10 -20 -30 -42 -52 b

7.11 6.88 7.08 6.71 6.80 6.86 7.02 6.56 6.76 6.55 6.57 6.33

2.175 2.168 2.175 2.163 2.157 2.152 2.145

for back electron transfer monitored at 510 nm, *0.15 X lo6. AE1p 7 mV measured as described in the Experimental Section.

dielectric constant of the solvent. In Figure 2B are shown plots of In k vs l/Dsfor an extended range of solvents and for just the solvents in Figure 2A. Values of k and AEllz for back electron transfer in propylene carbonate at a series of temperatures are listed in Table 11. In Figure 3 are shown plots of AE112vs Tand of In kvs Tin propylene carbonate.

Discussion The neutral complex [Re1(bpy-PTZ)(CO)3C1] was chosen for this investigation to allow the study to be extended to solvents of relatively low dielectric constant without complications from ionpairing effects. Our earlier studies on [Re1(bpy)(CO)3(py-PTZ)](PF6) showed that ion pairing is nearly complete even in very

Figure 3. Plots of (A) AEll2 vs T with best fit linear correlation AE1p = 2015 0.5(T), r = 0.94; and (B) In k vs T with the best tit linear correlationIn k = 15.5 + 8.8 X 1v(T), r = 0.82, in propylene carbonate

+

for back electron transfer in [Re1(bpy*--PTZ'+)(CO)3Cl]; see text for details.

dilute solutions in DCE in the absence of added supporting electr01yte.l~In addition, the backelectron transfer rateconstant for [Re1(bpy-PTZ)(CO)3Cl] is significantly smaller than that for [Re1(bpy)(CO)3(py-PTZ)](PF6) (Scheme I), which allowed for more accurate measurements of k with our nanosecond laser system. The dominant acceptor vibrations for nonradiative decay of MLCT excited states of polypyridyl complexes of RIP, 0d1,or Re1 are medium frequency ring stretching modes (by resonance Raman measurements).'' In these molecules, distortion, of these modes in the excited state is small and the excited-to-ground state energy gaps are relatively large.3.5 Under these conditions, the rate constant for nonradiative decay is governed by the energy gap law, which has been shown to account for solvent, temperature, ionic strength, and EO dependences.3-5 These results have also shed light on electron transfer in the inverted region, where there are clear similarities and some important differences compared to nonradiative decay.1" Previous studies have shown that the variation of k with AGO and ionic strength for electron transfer in the inverted region4J3 can be accounted for quantitatively by using the energy gap law (eq 2-4). The assumptions that were used in deriving these equations ln(k x 1s) = In(

F)+

ln[F(calc)]

(2)

The Journal of Physical Chemistry, Vol. 97, No. 50, 1993 13129

Electron Transfer in the Inverted Region

have been discussed previo~sly.~bt2J*~~ The quantity H a b is the electronic coupling matrix element between the two sites. Its magnitude depends on the extent of electronic orbital overlap. The quantity X'O is the sum of solvent reorganizational energy and the reorganizational energy contributed by low-frequency modes treated classically, X~,L(X'O = X, X~,L). The variation of the term Cwith solvent or temperature is expected to be relatively small compared to the other terms in eq 3. The quantities OM and SMare the quantum spacing and the electron-vibrational coupling constant of the acceptor 'mode" which are averaged quantities of contributions by a series of ring stretching modes. The electron-vibrationalcoupling constant is related to the change in equilibrium displacement (AQe)and reduced mass (M) by SM ='/~(MUM/~)(AQ For , ) the ~ . electron transfer in Scheme 11, vibrations at both the donor (bpy*-) and acceptor (PTZ'+) are involved as energy acceptors4 and

+

SM= Sw(PTZ*+)+ SM(bp)"-) In applying this result to electron transfer, AGO is related to AE1p by'',' AGO = -AE1,2

+ W,

(5) where w, for spherical ions of equal radii in a strong electrolytic solution is given byla w, =

e'

D,d( 1

+ j3d~"~)

(6)

This work term, w,, is an approximate correction for the electrostatic interaction between the anion bpy-and cation PTZ'+. The quantities D, and p are the static dielectric constant and ionic strength of the medium, e is the unit electronic charge, d is the distance of separation between the ions, and

0 = (8?rNAe2/1000D,kBT)"2 According to dielectric continuum theory, AGO is predicted to vary with l/D8,and the solvent reorganization energy, with both Dopand DVlaJ8 For spherical reactants of radii of (11 and a2 with a separation distance d, X,is given by1

These relationships provide a basis for accounting for solvent effects in the inverted region in the limit of applicability of dielectric continuum theory. A temperature dependence is also predicted from the energy gap law. From eqs 2 and 3, the temperature dependence arises from AG" (aAG"/aT -AS") and from the term containing X'O. In nonradiative decay of MLCT excited states, y[= In(&/ Shw) - 11 is relatively independent of temperature sincevariations in S parallel those in E0.3,s If it is assumed that X'O and y are temperature independent in the temperature range used in this study, the following relationship can be obtained

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For back electron transfer in eq 1, AHo C 0, AGO = AH" T A P , and alAG0l/aT = alAHo - TASol/aT ASo. Equation 8 then becomes

This analysis shows that both solvent and temperature effects are expected in the inverted region even though the presumption of a temperature independencehas been made in the literature." It is true, however, that compared to the case for typical, activated electron transfer in the normal region, temperature dependence in the inverted region is expected to be small.

Solvent Dependence. From the data in Table I, there is a discerniblesolvent effect on back electron transfer in [Re*(bpy'-PTZ'+)(C0)3Cl] with kvaryingfrom 4.3 X 106s-1 in benzonitrile to 2.2 X lo7 s-l in toluene. In order to test the energy gap law results in eqs 2-3, A E 1 / 2 values were obtained by electrochemical measurements as an approximate measure of AGO (eq 5). Electrochemical measurements, and therefore the energy gap correlation, were limited to polar solvents. The linear correlation between AElp vs 1/D, in seven polar solvents in Figure 2A demonstrates that AE1/2varie~ as l/Ds as predicted by dielectric continuum theory.18 A plot of In k vs AElp in the same seven solvents of relatively high polarity (Os 1 20) is shown in Figure 1A. The linear relationship ( r = 0.89) reveals that the variation of k with solvent is largely due to the change in AGO as predicted by the energy gap law. According to the results in eqs 2,3, and 7, an additional solvent dependence in k arises from X,which is a function of (l/Dopl/Ds). A linear least-squares fit of thedata (In k, p E 1 1 2 ) in these seven solvents gave, as a best fit, In k = 22.5 - 3.4AE1/2 1.2(1/ Dop- l/D,) (Figure lB), with the coefficient for AE1/2 fixed at 3.4. This results in an improved correlation ( r = 0.95) and is consistent with the dielectric continuum result in eq 7. The coefficient for A E 1 / 2 was taken from a previous study on back electron transfer in [ (4,4'-(X)2(bpy*-)Re1(CO)3(py-PTZ'+).4This is a reasonable procedure, since from eq 3, the quantity, y/ ~ W M , should be the same for the two reactions because they involve essentially the same donor-acceptor pair. The correlation is consistent with dielectric continuum theory, but the coefficient for (l/Dop- l/Ds) is smaller than the calculated value.lg The solvent effect is relatively small, and in the range of polar solvents in Figure 1, k varies by -43% from 4.33 X 106 s-1 (benzonitrile) to 6.67 X lo6 s-l (propylene carbonate). Significantly larger solvent variations have been observed for inverted electron transfer in a series of organic donor-acceptor linked systems." The greater sensitivity to solvent in these reactions can be attributed, at least in part, to the greater bridge length (17.4 A vs 7.4 A) and smaller sizes. There is rotational flexibility in the -CH2- link to -PTZ, and a variety of inter-ring separation distances that range from 5 to 8 (f1) A (center-to-center) are possible.4b From theobservation of energy gap law behavior in this and the earlier study,4J3 it can beinferred that there may be nearly a constant separationdistance between the electron transfer donor and acceptor with Hab remaining relatively constant throughout. Electron transfer may occur predominantly with the donor-acceptor pair at or near close contact where electronic orbital overlap and electrostatic attraction are maximized. Rotational flexibility may be a contributing factor to the scatter in the correlations in Figure 1. An attempt was made to incorporate all of the data in the extended range of solvents in Table I into a single acceptable correlation, including solvents for which electrochemical data were not available. A plot of In k vs l/Ds in 14 solvents is shown in Figure 2B. The physical meaning of the correlation is not clear. A plot of the best fit correlation forjust the polar solvents of Figure 2A is shown as the dashed line in Figure 2B. Since dielectric continuum theory appears to apply to the polar solvents, it may not apply to the extended correlation. The In k values in toluene and o-xylene were excluded from the correlation in Figure 2B because they were much larger than expected from the energy gap law (entries 1 and 2, Table I). The rate enhancement may arise because of participation of decay channels involving other, close-lying states in addition to back electron transfer. The energy gap for electron transfer in these solvents is high (2.62.7 eV), based on the correlation between A E 1 / 2 and 1/D, in Figure 2A. This energy gap is sufficient to populate the phenothiazine triplet state at -2.64 eV,Zoor the initially formed MLCT state in Scheme 11, for example. The

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13130 The Journal of Physical Chemistry, Vol. 97, No. 50, 1993

point in methanol (entry 11, Table I) was also excluded from the correlation because of the quantum effect described below. From our results, a solvent dependence for electron transfer in the inverted region does exist, but is relatively small. The microscopic origin of the effect is not thermal activationof solvent dipole orientational modes (librations) in the usual sense.lszJ1 Rather, it comes from the librations acting as acceptors (b) and, more importantly, from the influenceof the solvent on the energy gap (AGO). The energy gap plays the major role. It dictates the magnitude of the vibrational overlap integrals for the v(bpy) and v(PTZ) ring stretching modes that dominateas energy acceptors. This effect can be accounted for by the energy gap law result in eqs 2 and 3 and the application of dielectric continuum theory to b. Solvent Quantum Effect. In previous studies on nonradiative decay of the MLCT excited states of [Ru1I(bpy)3I2+21 and a series of 2,2'-bpy complexes of OsI1,Sb a kinetic isotope effect of -2 was observed between H2O and DzO and of 1.5 between CHpOH and CHpOD. This is a quantum effect most likely from participation of high-frequency 0-H modes at -3400 cm-I as energy acceptors. Even though the electron-vibrationalcoupling constant and change in equilibrium displacement (AQA may be relatively small for these modes, ho is large, and they contribute in an experimentally significant way to nonradiative decay. There is also a kinetic isotope effect for electron transfer in the inverted region in ReI(bpy'--PTZ'+)(CO)$l. The ratio of rate constants between CH30H and CHpOD is kH/kD 1.14 (points 11 and 12 in Figure 2B). The appearance of this effect points to an additional, nonclassical role for hydroxylic solventsas energy acceptors. It is based on a coupling between v(0H) and the change in charge distribution between the electron transfer reactants and products. Temperature Dependence. According to eq 9, a temperature dependence is expected in k from two sources. One is from the term that contains the solvent reorganizational energy (Ad.It arises because as the temperature is increased, there is a broader distributionof solvent librations in the surrounding medium. This opens new vibrational overlapchannels for nonradiative decay by meeting the energy match requirement imposed by energy conservation. The second source of a temperature dependence is the energy gap. The temperature dependenceof the energy gap is a measure of the difference in entropic content between reactants and products, alAGoldT ASo.This quantity is nonzero if there are changes in quantum spacings in the solvent librational modes before and after electron transfer.22 From the data in Table I1 and Figure 3B, k does have a perceptible, if small, temperature dependence in propylene carbonate, varying from 6.29 X 106 s-I at221 Kto7.11 X 106s-l at323K. Theexpectedlinearvariation with T is observed (r = 0.82; although an equally acceptable correlation with 1 / T exists as well, r = 0.84). The slope of the correlation is 9 X 10-4 K-I. The entropic change can be calculated separately from the temperature-dependent electrochemical data since a(AE1p)aT ASo 5 X 10-4 eV K-' = 12 cal mol-' K-1-29 The positive entropicchangeisexpected given the nature of the electron transfer in eq 1. There is a loss of electrostatic charge in the reaction. This decreases interactions with solvent dipoles and, with it, the quantum spacings for the surrounding librational modes. The temperature dependencies of lAGol and k can be used to calculate 1'0.Taking - y / h w ~= 3.4 eV-1 and hw = 1350 cm-1 from back electron transfer in [(4,4'-(X)zbpy*-)Re*(CO)p(pyPTZ*+)],4ASo = 5 X 1 W eV K-1, In k / A T = 9 X 10-4 K, and eq 9 gives X'O 0.4 eV in propylene carbonate. In this treatment the (relatively small) variations in D, and Dopwith temperature were negle~ted.~'The quantity X'O includes contributions from solvent librations and low-frequency vibrational modes treated classically and gives a lower limit to the reorganizational energy.

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- -

-

It is the same magnitude as the reorganizationalenergy estimated for back electron transfer in acetonitrile in Scheme I.4b This comparison provides an additionalcheck showing the applicability of the energy gap law. Contrary to previous expectations in the literature, our results show that a temperature dependence does exist for electron transfer in the inverted region. It is partitioned microscopically between an entropic effect and a broadened distribution of solvent librations. Our results verify that this temperature dependence exists and that it can be dealt with quantitatively by the energy gap law. Acknowledgement is made to the National Science Foundation for financial support under Grant No. CHE-8806664 and to the National Institutes of Health for postdoctoral support for S.L. Mecklenburg under Grant No. GM 145 11. We would also like to thank Professor E. F. Hilinski at Florida State University for suggesting the existence of another decay channel in nonpolar solvents and Dr. L. Della Ciana for a sample of bpy-PTZ. References and Notes (1). (a) Sutin, N. Prog. Inorg. Chem. 1983,30,441. (b) Brunschwig, B. S.; Sutin, N. Commenfs Inorg. Chem. 1987, 6, 209. (c) Siders, P.; Marcus, R. A. J. Am. Chem. Soc. 1981,103,748. (d) Marcus, R. A. J. Phys. Chem. 1989,93,3078. (e) Marcus, R. A.; Sutin, N. Eiochim. Eiophys. Acto 1985, 81 I , 265. (2) (a) Kestner, N. R.; Logan, J.; Jortner. J. J. Phys. Chem. 1974, 78, 2148. (b) Efrima, S.; Bixon, M. Chem. Phys. 1976, 13, 447. Ulstrup, J.; Jortner, J. J. Chem. Phys. 1975,63,4358. (d) Englman, R.; Jortner, J. Mol. Phys. 1970,18,145. (e) Bixon, M.; Jortner, J.J. Chem. Phys. 1968,48,715. (f) Freed, K. M.; Jortner, J. ibid. 1970,52,6272. (g) Islampour, R.; Alden, R. G.; Wu, G. Y. C.; Lin, S. H. J. Phys. Chem. 1993,97, 6793. (3) Kobcr, E. M.; Caspar, J. V.; Lumpkin, R. S.; Meyer, T. J. J . Phys. Chem. 1986, 90, 3722. (4) (a) Chen, P.; Duesing, R.; Tapolsky, G.; Meyer, T. J. J. Am. Chem. Soc. 1989,111, 8305. (b) Chen, P.; Duesing, R.; Graff, D. K.;Meyer, T. J. J . Phys. Chem. 1991,95,5850. (c) Chen, P.; Westmoreland,T. D.; Danielson, E.; Schanze, K.; Anthon, D.; Neveux, P. E., Jr.; Meyer, T. J. Inorg. Chem. 1987, 26, 1116. ( 5 ) (a) Caspar, J. V.; Meyer, T. J. J . Phys. Chem. 1983,87, 952. (b) Caspar, J. V.; Sullivan, B. P.; Kobcr, E. M.; Meyer, T. J. Chem. Phys.Leff. 1982,91,91. (c) Vining, W. J.; Caspar, J. V.; Meyer, T. J. J. Phys. Chem. 1985,89,1095. (d) Caspar, J. V.; Meyer, T. J. J. Am. Chem.Soc. 1983,105, 5583. (e) Lumpkin, R. S.; Meyer, T. J. J. Phys. Chem. 1986,90,5307. (f) Kim, H.; Kitamura, N.; Tazuke, S . J . Phys. Chem. 1990, 94, 1414; 7401. (6) (a) Miller, J. R.; Calcaterra, L. T.; Closs, G. L. J. Am. Chem. Soc. 1984,106,3047. (b) Closs, G. L.; Calcaterra, L. T.; Green, N. J.; Penfield, K.W.; Miller, J. V. J. Phys. Chem. 1986,90,3673. (c) Closs, G. L.; Miller, J. R. Science 1988,240,440. (7) (a) Ohno, T.; Yoshimura, A.; Mataga, N. J . Phys. Chem. 1986,90, 3295. (b) Asahi, T.; Mataga, N. ibid. 1989, 93, 6575. (c) Zou,C.; Miers, J. B.; Ballew, R. M.; Dlott, D. D.; Schuster, G. B. J . Am. Chem. Soc. 1991, 113,7823. (d) Gould, I. R.; Ege, D.; Mattes, S. L.; Farid, S. J. Am. Chem. Soc. 1987,109,3794. (e) Gould, I. R.; Moser, J. E.; Armitage, B.; Farid, S . ibid. 1989,111,1917. (f) Gould, I. R.; Moody, R.; Farid, S . ibid. 1988,110, 7242. ( 8 ) (a) Imine, M. D.; Harrison, R. J.; Bcddard, G. S.; Leighton, P.; Sanders, J. K. M. Chem.Phys. 1986,104,315. (b) Archer, M. P.; Gadzekpo, V. P. Y.;Bolton, J. R.; Schmidt, J. A,;W d o n , A. C. J. Chem.Soc., Furaduy Trans. 2 1986,82,2305. (c) Wasielewski, M. R.; Niewczyk, M. P.; Svcc, W. A,; Pewitt, E. B. J. Am. Chem. Soc. 1985, 107, 1080. (d) McLendon, G.; Miller, J. R. J. Am. Chem. Soc. 1985, 107, 7781. ( e ) McLendon, G. Ace. Chem. Res. 1988, 21, 160. (9) (a) McClcskey, T. M.; Winkler, J. R.; Gray, H. B. J. Am. Chem.Soc. 1992, 114, 6935. (b) Fox, L. S.;Kozik, M.; Winkler, J. R.; Gray, H.B. Science 1990, 247, 1069. (10) (a) Maqueen, D. B.;Schanze, K. S . J . Am. Chem.Soc. 1991,113, 7470. (b) MacQueen, D. B.; Eyler, J. R.; Schanze, K. S . J. Am. Chem. Soc. 1992, 114, 1897. (11) (a) Liang, N.; Miller, J. R.; Closs, G. L. J. Am. Chem. Soc. 1990, 112, 5353. (b) Kroon, J.; Oevering, H.; Verhoven, J. W.; Warman, J. M.; Oliver, A. M.; Paddon-Raw, M. N. J. Phys. Chem. 1993,97,5065. (c) Smit, K. J.; Warman, J. M.;de Haas, M. P.; Paddon-Raw, M. N. Chem. Phys. h i t . 1988. 152, 177. (12) (a) Thompson, P. A.; Simon, J. D. J. Am. Chem. Soc. 1993, 115, 5657. (b) Mussell, R. D.; Nocera, D. G. J . Phys. Chem. 1991,95,6919. (13) (a) Chen, P.; Mecldenburg, S. L.; Duesing, R.; Meyer, T. J. J. Phys. Chem. 1993, 97, 6811. (b) Deusing, R. Ph.D. Dissertation, University of North Carolina at Chapel Hill, 1989. (14) Della Ciana, L., Hamachi, I., Meyer, T. J. J . Org. Chem. 1989,54, 1731.

Electron Transfer in the Inverted Region

The Journal of Physical Chemistry, Vol. 97, No. 50, 1993 13131

(15) (a) Worl, L. A.; Duesing, R.; Chen, P.;Ciana, L. D.; Meyer, T. J. J . Chem.Soc.,Dalron Trans.1991,849. (b) Luong, J. C. Ph.D. Dissertation, Massachusetts Institute of Technology, 1981. (16) (a) Duesing, R.;Tapolsky, G.; Meyer, T. J. J. Am. ChrmSoc. 1990, 95, 5850. (b) Danielson, E. In preparation. (17) (a) Dallinger, R. F.;Woodruff, W. H. J. Am. Chem.Soc. 1979,101, 4391. (b) Bradley, P. G.; Kress, N.; Homberger, B. A.; Dallinger, R. F.; Woodruff, W. H. J. Am. Chem. Soc. 1981,103,7441. (c) Mabrouk, P.A.; Wrighton, M.S.Inorg. Chem. 1986,25,526. (d) Mallick, P.K.;Strommen, D. P.;Kincaid, J. R. J. Am. Chem. Soc. 1990, 112, 1686. (18) (a) Brunschwig, B. S.;Ehrenson, S.;Sutin, N.J . Phys. Chem. 1987, 91,4714. (b) . . Kirkwood, J. G.; Westheimer, F. H. J. Chrm. Phys. 1938,6,

sob.

(19) The coefficient for ( I / D o p- 1/D,) in the energy gap law correlation is given by

where all the terms are defined in the text. With Y / ~ W M= 3.4 eV-’, ~ W = 1350 cm-1, y = 0.57, the radii of PTZ and [Re(bpy)(CO),CI] equal to 2.5 and 5 A’” (Sullivan, B. P.J . Phys. Chem. 1989,93,24), respectively, and

M

d=7.5A, thecoefficientfor(l/D -1/D,)is-7. Thismodeloverestimates the solvent dipole reorganization3 energy because electron transfer occur8 between PT2+ and bpy-, and the actual distance between them is smaller (5-8 A). If the close contact distance is used ( 5 A), the coefficient is -3. Thcradius~stdforbpy~in thecalculationis theaverageradiusofthecomplex. The use of a smaller radius for bpy- (2-2.5 A) is not correct because a large volume around bpy’ is shielded from solvent molecules by the complex (see text). (20) (a) Moroi, Y.; Braun, A. M.; Gratzel, M. J. Am. Chem. Soc. 1979, 101,567. (b) Maestri, M.; Gratzel, M. Ber. Bunseng-Ges. PhysChcm. 1977, 81, 504. (21) Van Houten, J.; Watts, R. J. J. Am. Chem. Soc. 1975, 97, 3843. (22) Hupp, J.; Neyhart, G.; Meyer, T. J.; Kober, E. K . J. Phys. Chem. 1992, 96, 10820. (23) The work term correction in propylenecarbonate is small, w, = 0.037 eV. It is expected to be relatively temperature independent becaw variations in D, are expected to be small within the temperature range used in this study, which are above its freezing point and well below its boiling point. The temperaturecoefficient of the refractiveindex (Dop= n2) of propylenecarbonate is dn/dT = O.OO0 375 K-I (Riddick, J. A.; Bunger, W. B.; Sakano, T. K. Orgunic Solvents; John Wiley & Sons: New York, 1986; p 434).