J. Phys. Chem. 1991, 95, 192-193
192
Solvent Dependence of the Forward Electron Transfer Rate for the Porphyrln-Amidoquinone Molecule Orland W. Kolling Chemistry Department, Southwestern College, Winfield, Kansas 67156 (Receiued: April 9, 1990; I n Final Form: July 2, 1990)
An earlier major investigation of solvent effects upon the kinetics for the forward electron transfer by the porphyrinamidoquinone
molecule reported substantial changes in rate constants in going from aprotic dipolar to hydrogen bonding media. Such changes were interpreted previously in semiquantitative terms by using the Marcus theory for solvent reorganizational energy contributions to a Franck-Condon transition for the electron transfer. The original kinetics data have now been reexamined with respect to solvent type and an alternate solvation free energy model related to the Lay extension of the Marcus theory has been proposed.
Introduction Several covalently linked porphyrin quinones have served as model species for the investigation of environmental determinants upon electron-transfer kinetics within somewhat rigid porphyrin molecules. In recent experimental work with a zinc porphyrinquinone cage molecule, Delaney, Mauzerall, and Lindsey concluded that an observed minor solvent effect and temperature independence for the internal electron transfer are consistent with a nonadiabatic electron-tunneling description for the reaction.' By contrast, the rate of the forward electron transfer process in the porphyrin-amidoquinone molecule (PAQ) exhibits a substantial solvent dependence, which has been interpreted in terms of the solvent environmental influence upon the energy of the Franck-Condon charge-transfer state.2 For the latter, the kinetic rate constant data base is sizable and includes values in 22 solvents ranging in type from polar aprotic to hydrogen-bonding organic solvent^.^ However, because the validity of the model for the solvent effects upon the activation barrier of PAQ rests largely upon semiquantitative tests, it is important that alternate and more numerically precise descriptions of the solvent dependence for the electron-transfer process in PAQ be considered as well. One such quantitative model based on the Lay treatment3 of reorganizational influences by the solvent has been used with some success to resolve effects upon the back-electron transfer by the trans-stilbene-fumaronitrile ion pair.4 This approach is extended herein to the case of electron transfer within the porphyrin-amidoquinone molecule. The most common treatment of solvent influences upon electron-transfer reactions utilizes variations on the Marcus theory in which the solvent is viewed as a dielectric continuum. The solvent reorganizational energy (A,) in eq 1 is dependent upon A. = e2N(1/2al + 1/2a2 - l / r ) ( l / n 2 - l/e) (1)
the bulk solvent properties of index of refraction (n) and dielectric constant (e). Here, N is Avogadro's number, e the charge transferred, al and a2 the reactant radii, and r the path distance for the transferred e l e ~ t r o n . ~However, since the bulk solvent properties, e and n, correspond primarily to dipolarity and polarizability influences by the solvent, the additional role of hydrogen bonding by donor solvents has been incorporated by Lay' in the multiterm reorganizational energy function in eq 2. The A = (As)o
+ (A,)i + A, + AH + Xi,
(2)
separate A-terms in eq 2 refer to contributions from polarity (Ap), outer sphere (As)o, hydrogen bonding (A,,), intrinsic (Ain), and inner-sphere (AJi reorganizational energies. ( 1 ) Delaney, J.: Mauzerall,
957-963.
D.; Lindsey, J. J. Am. Chem. SOC.1990, 112,
(2) Schmid:, J.; Siemiarczuk, A.; Weedon, A.; Bolton, J. J . Am. Chem. SOC.1985, 107, 61 12-61 14. (3) Lay, P. A. J . Phys. Chem. 1986, 90, 818-885. (4) Kolling, 0. W. J. Phys. Chem. 1986, 90, 4664-4665. ( 5 ) Marcus, R. A. J. Phys. Chem. 1963, 67, 853-851.
Schmidt et have extended the Marcus theory in order to focus upon the solvent dependence of the activation energy barrier between the equilibrium state 1 and a Franck-Condon state (2) for the forward electron transfer within PAQ. Their eq 3 includes 2PlP2 AE = Eo2 - E o I - -[O(t) a3
PI2 - L(n2)] - -[(O(t)]
a3
-[O(t) a3
+
- OSL(n2)]
(3)
the cavity radius ( a ) and dipole moments (p). The symbols O(e) and L(n2) are the Onsager and Lorenz parameters, i.e. (e - ] ) / ( e 2) and (n2- l)/(n2 + 2), respectively. However, like the original Marcus theory, the solvent effect does not include the more specific solvation influences of hydrogen bonding and acceptor-donor complexation. Even though solvent dipolarity-polarizability may well be the dominant influences upon the rate of electron transfer in PAQ, the exclusion of other important specific solvent effects including hydrogen-bonding behavior would be expected to give rise to highly scattered correlations2 between the rate constants and AE values calculated from eq 3. It is unlikely that the high degree of uncertainty in such correlations can be assigned solely to variations in a and p values. The objective for this report is to attempt to more precisely specify the influence of the solvent upon the forward electron transfer in PAQ by directing attention to the multiple contributory factors originating with the solvent itself, using an approach paralleling that of Lay.3
+
Results and Discussion Initially, it is helpful to separate the solvents used as media for the electron transfer by PAQ into groups according to the Chastrette-Purcell-generalized classification scheme.6 Of the 22 solvents included in the PAQ data base,2 five distinct solvent classes are represented: aprotic dipolar (AD); electron pair donor (EPD); aromatic apolar (ARA); aromatic polar (ARP); and hydrogen bonding (HB). In addition to these classes it is informative to place the haloaromatics and haloalkanes into a separate group. Thus, PAQ electron-transfer rate constants ( k m ) have been reordered by solvent class in Table I. It will be noted here that there is no clear qualitative distinction between the In kCTvalues in AD and EPD solvents; however, a significant increase in In kCT is apparent for ARA and ARP solvents. Similarly, the acceleration of the forward electron-transfer reaction by PAQ in halo-AD, halo-ARP, and HB media is even more pronounced. In the original work of Schmidt et al., the rate data as In kcT were correlated with the barrier energy from eq 3 but with the assumption that AE for diethyl ether serve as the reference valueG2 If a linear least-squares correlation is constructed for In kCT vs (6) Chastrette, M.: Rajzmann, M.; Chanon, M.; Purcell, K. J. Am. Chem. SOC.1985, 107, 1-1 1 .
0022-3654/9 1/2095-0192%02.50/0 0 1991 American Chemical Society
Electron Transfer for the Porphyrin-Amidoquinone Molecule TABLE I: PAQ Electron-Transfer Rate Constants and Solvent Parameters solvent class member In kn" ~ * b ab simple A D and acetone 17.22 0.71 EPD acetonitrile 17.75 0.75 0.19 diethyl ether 16.46 0.27 1,2-dimethoxyethane 17.76 0.53 1,4-dioxane 17.40 0.55 ethyl acetate 16.86 0.55 methyltetrahydrofuran 16.81 0.5W propionitrile 17.77 0.71 ARA and ARP anisole 19.59 0.73 benzene 19.07 0.59 benzonitrile 19.78 0.90 dibenzyl ether 19.12 0.80 18.61 0.54 toluene halo-AD and chlorobenzene 20.48 0.71 halo-ARP 1-chloronaphthalene 20.47 0.68' I ,2-dibromoethane 20.99 0.75 1 ,I-dichloroethane 19.88 0.53 I ,2-dichloroethane 20.11 0.81 dichloromethane 20.52 0.82 1, I , 1-trichloroethane 20.03 0.49 HB I-butanol 19.30 0.47 0.79 chloroform 21.56 0.58 0.44
"Obtained from km values of Schmidt et aI.* bKamlet-Taft parameters from summary tables of Kamlet, Abboud, Abraham, and ' values based on phenol blue as the solvatcchromic Taft.8 'New 7 indicator.
The Journal of Physical Chemistry, Vol. 95, No. 1, 1991
be stated as composite outer sphere reorganizational free energy contributions that are only partially represented by theflt,n2) of Schmidt et al. in eq 3. It has been demonstrated by Brady and Cam7 that such f(t,n2) quantities correspond to dipolar and inductive contributions only and the singlefln2) component quantifies the inductive dependence of the activation barrier upon the solvent reaction field. Since the various h terms in eq 2 are difficult to evaluate with a precision comparable to the experimental rate constants and activation energies, exact and direct empirical tests of the Lay model in its initial form cannot be made at present. However, as was noted by Lay,3 the relative magnitudes and signs of the interactive solvent terms in relationships like eq 4 can be established by using an empirical free energy function of the form developed by Kamlet and Tafte8 The reduced form for the Kamlet-Taft linear solvation energy relationship, which parallels the AGet statement above, is given in eq 5 . In this free energy XYZ = XYZo s(x* d6) aa bo (5) equation in the variable XYZ the S(T* + d6) term corresponds to the (AGp AG,) sum, aa to AGH for hydrogen-bond donor solvents, bo for HB acceptor basicity to AGis, and XYZo is equivalent to AGin. For the solvents used to investigate the medium dependence of the forward electron transfer by PAQ, the HB basicity (bj3) is not a significant variable and is actually zero for most cases in Table I. The values for the other Kamlet-Taft parameters, x* and a are listed in Table I, and for the d6 term as the polarizability (inductive) contribution, the 6 values are 0.5 for aromatics (ARA and ARP) and 1.0 for all haloalkanes and haloaromatics. The final linear solvation energy function that is given as eq 6 was established by standard multiple regression procedures applied to the data in Table I. In kCT= 2.75(x* 1.056) 2.94a 15.72 (6) slope-intercept uncertainties fO.O1; In kcT(calcd) f0.03 SD; n = 22; r = 0.947 As noted before, the intercept (equivalent to AGin) is the value of In kcr in the absence of a solvent and as expected is significantly less than the value in diethyl ether used to determine A ( M ) from eq 3. The function in eq 6 more adequately delineates the relative magnitudes of the separate reorganizational energy contributions as well. It is clear that solvent dipolarity and solvent hydrogenbonding acidity have comparable effects upon the forward electron-transfer process (i.e. s / a ratio of nearly unity). Likewise, the pronounced acceleration evident in the Table I data for the haloalkanes and haloaromatics can now be specified as an inductive solvent contribution having an effect equal to that of solvent dipolarity, again inferred from the coefficient ratio s/sd of approximately unity. Obviously, the multiterm models for the solvent reorganizational energy and solvation free energy given by eqs 2 and 4 are incapable of providing exact structural interpretations of the solvent role in the internal electron transfer by the PAQ m o l e ~ u l e . ~For example, it is unclear why the solvent inductive effect in the forward electron transfer by PAQ is relatively large (s N sd) while that for the back electron transfer by the stilbene-fumaronitrile ion pair is small and more typical for electron transfer (s > 4.' The large d6 contribution is consistent with the dependence of the rate constant upon the Lorenz (n2) term noted by Schmidt et aL2 in eq 3 and may possibly be associated with the larger dipole moment for the charge-separated state for PAQ. However, the linear free energy models proposed herein can yield important information about both general and specific solvent effects upon the electron-transfer process. When coupled with measured reaction entropies for electron-transfer reactions in mixed solvents, other specific solvent effects that contribute to and are associated with selective solvation can be identified as well.lo
+
a a
0
I O
0
/
I
Figure 1. Distribution of residuals (R)in In kCT as a function of -A(AE). R is computed with respect to the calculated In km from an assumed least-squarcs linear relationship for In kCTvs A(AE). Symbols are (0) halo-AD and halo-ARP, 0 A R A and ARP, (A)HB, and ( 0 )AD and EPD solvcnts.
A(AE) where A ( M ) = Md - ME,@, a plot of the corresponding residuals with respect to In kcr can be. examined for trends in the basic data. Such a graph is shown in Figure 1. Again, the solvent class distinctions are striking and indicate that a multiple variable description of solvent characteristics is required. In eq 3 just as in the original Marcus model (eq I), the functions flt.n2) are appropriate measures of only the solvent polaritypolarizability influences' upon the electron-transfer processes. As an alternative approach, the solvent reorganizational free energy contributions to the solvent dependence of the activation barrier can be resolved into a linear sum paralleling the Lay statement in eq 2. For eq 4, the linear sum includes separate outer sphere and inner sphere components (os and is) as well as polarity and hyrogen-bonding dependencies. (The intrinsic component AGh refers to the reorganizational free energy in the absence of an interacting solvent.) In reality the first three terms in eq 4 can (7) Brady, J.; Carr, P. J . Phys. Chem. 1985,89, 5759-5766.
+
+ +
+
itGI I
193
+
+
+
(8) Kamlet, M.; Abboud, J.; Abraham, M.; Taft, R.J . Org. Chem. 1983, 48, 2877-2887. (9) Brady, J.; Carr, P. J . Phys. Chem. 1984,88, 5796-5799. (10) Blackbourn, R.; Hupp, J. Inorg. Chem. 1989, 28, 3786-3790.
