Featured Article pubs.acs.org/joc
Bimolecular Electron Transfers That Deviate from the Sandros− Boltzmann Dependence on Free Energy: Steric Effect Pu Luo, Joseph P. Dinnocenzo,* Paul B. Merkel,* Ralph H. Young,* and Samir Farid* Department of Chemistry, University of Rochester, Rochester, New York 14627, United States S Supporting Information *
ABSTRACT: As we reported recently, endergonic to mildly exergonic electron transfer between neutral aromatics (benzenes and biphenyls) and their radical cations in acetonitrile follows a Sandros−Boltzmann (SB) dependency on the reaction free energy (ΔG); i.e., the rate constant is proportional to 1/[1 + exp(ΔG/RT)]. We now report deviations from this dependency when one reactant is sterically crowded: 1,4-di-tert-butylbenzene (C1), 1,3,5-tritert-butylbenzene (C2), or hexaethylbenzene (C3). Obvious deviation from SB behavior is observed with C1. Stronger deviation is observed with the more crowded C2 and C3, where steric hindrance increases the interplanar separation at contact by ∼1 Å, significantly decreasing the π orbital overlap. Consequently, electron transfer (ket) within the contact pair becomes slower than diffusional separation (k−d), causing deviation from the SB dependency, especially near ΔG = 0. Fitting the data to a standard electron-transfer theory gives small matrix elements (∼5−7 meV) and reasonable reorganization energies. A small systematic difference between reactions of C3 with benzenes vs biphenyls is rationalized in terms of small differences in the electron-transfer parameters that are consistent with previous data. The influence of solvent viscosity on the competition between ket and k−d was investigated by comparing reactions in acetonitrile and propylene carbonate.
■
There, A•+/B and A/B•+ represent contact pairs with a proper orientation for electron transfer to occur, kd and k−d as well as k′d and k′−d are the rate constants for their formation and dissociation,4 while ket and k′et are rate constants for electron exchange between the contact pairs. Applying the steady-state approximation to the interconverting pairs A•+/B and A/B•+ results in eq 5 (for derivation see the Supporting Information).
INTRODUCTION Recently, we have described several types of bimolecular electron transfers in acetonitrile where the rate constants, k, followed a Sandros−Boltzmann (SB) dependence on the free energy changes (ΔG).1,2 One of these was a charge shift reaction involving electron exchange between aromatic compounds (benzenes and biphenyls) and their radical cations, eq 1.1 The rate constants followed the simple SB dependence of eq 2, where klim is the limiting rate constant in the exergonic region.3 The free energy change for the reaction is equal to the difference between the oxidation potentials of the two neutrals, eq 3.
k −d
(1)
k′
( ΔRTG )
(2)
ΔG = Eox (B) − Eox (A)
(3) 1
As we pointed out previously, the requisite reaction intermediates for electron transfer need to be considered to more fully understand the implications of eq 2. Endergonic or mildly exergonic electron transfer is expected to occur at contact according to the expanded kinetic scheme in eq 4. © 2012 American Chemical Society
k ′d
(4)
k −d ket
+
kd ΔG exp k ′d RT
( )
(5)
Because of the structural similarity of A and B in these reactions, the reasonable approximation was made that kd = k′d and k−d = k′−d. If, in addition, the term k−d/ket is small compared to 1 plus the exponential term, then eq 5 reduces to the simple SB form, eq 2, with klim = kd. Furthermore, while there is a difference in free energy between a contact pair and the corresponding free ions, that difference is the same for the reactants and the products if, as assumed, kd = k′d and k−d = k′−d.
klim 1 + exp
k ′et
kd
k= 1+
k A•+ + B ↽ ⇀ A + B•+
k=
kd ket k ′−d •+ A•+ + B ↽⎯ ⎯⇀ ⎯ ⎯ A•+/B ↽⎯ ⎯⇀ ⎯ ⎯ A/B•+ ↽ ⎯⎯⎯⇀ ⎯⎯⎯ A + B
Received: November 18, 2011 Published: January 30, 2012 1632
dx.doi.org/10.1021/jo202385f | J. Org. Chem. 2012, 77, 1632−1639
The Journal of Organic Chemistry
Featured Article
Then, the free energy of reaction within a contact pair is the same as that for the overall reaction, ΔG. Deviation from an SB dependence should be most obvious at the isoergic point (ΔG = 0). Within the accuracy of the measured rate constants and minor scatter attributable to structural differences among the reactants reported in our previous work,1 the ratio k−d/ket at ΔG = 0 was estimated to be ≤0.3. Larger values of this ratio, for example as a result of relatively small ket, should lead to perceptible deviations from the SB dependence. In our previous study, all the substituents on the benzene derivatives were methyl groups, presumably small enough to permit relatively strong π interactions and fast electron transfer at contact. We reasoned that sufficiently sterically crowded molecules would preclude such strong interactions, resulting in a smaller ket, a larger value of k−d/ket, and a measurable deviation from an SB dependence.
Table 1. Methyl-Substituted Benzenes and Their Oxidation Potentials in Acetonitrilea B1 B2 B3 B4 B5 B6 B7 B8 B9
compound
Eox (V vs SCE)
benzene toluene m-xylene p-xylene 1,2,4-trimethylbenzene 1,2,3,4-tetramethylbenzene durene pentamethylbenzene hexamethylbenzene
2.48b 2.26b 2.098c 2.01b 1.905d 1.825b 1.753d 1.69e 1.580e
a
Data from equilibration of radical cations with neutral donors, using the last entry (B9, measured as a reversible potential by ultrafast cyclic voltammetry) as a reference point. bReference 5. cThis work. d Reference 6. eReference 8.
■
Table 2. Biphenyls and Their Oxidation Potentials in Acetonitrile
RESULTS AND DISCUSSION To assess whether steric hindrance could decrease k et sufficiently to cause deviation from the SB behavior, three crowded molecules were tested: 1,4-di-tert-butylbenzene (C1), 1,3,5-tri-tert-butylbenzene (C2), and hexaethylbenzene (C3). The oxidation potentials (Eox) of these compounds were determined with mV precision from equilibration experiments in acetonitrile using flash photolysis as described previously.5,6 The experimental error in ΔEox between equilibrating pairs was
BP1 BP2 BP3 BP4 BP5 BP6 BP7
substituents
Eoxa (V vs SCE)
4-COOMe none 3,3′-dimethyl 4-methyl 4,4′-dimethyl 3,4,4′-trimethyl 3,3′,4,4′-tetramethyl
2.102(6)b 1.953(6)c 1.844(4)c 1.798(5)b 1.670(2)c 1.621(4)b 1.581(1)b
a
The standard deviation in the last significant digit is given in parentheses. In general, the errors in the absolute Eox values are larger than in the ΔEox values (≤3 mV).7 bThis work. cReference 6.
generally ±0.003 V (examples are shown in the Supporting Information).7 The rate constants for electron exchange between radical cations and neutral reactants, k and k′, eq 1, involving these crowded molecules and nonhindered benzene and biphenyl derivatives (Tables 1 and 2) were measured by laser flash photolysis as described previously.1 1. Electron Transfer Reactions of tert-Butyl-substituted Benzenes (C1 and C2). Shown in Figure 1 and listed in Table 3 are the rate constants for radical ion equilibration reactions of the sterically crowded benzenes C1 and C2 with the biphenyl derivatives listed in Table 2. The data for both crowded compounds clearly deviate from the SB behavior observed for nonhindered analogues (black curve in Figure 1), particularly with respect to the extended transition region between the endergonic rise and the exergonic plateau. As discussed in section 4, this deviation from an SB dependency on ΔG is the result of a decreased rate constant for electron transfer within the contact pair (ket) relative to that for the reactions between two nonhindered reactants. Although the substituents in C1 and C2 are all tert-butyl groups, the deviation from SB behavior is clearly greater in C2. For example, at ΔG = 0, k is ∼4 times smaller for the reactions of C2 than of C1 (Figure 1). Most likely, the 1,3,5trisubstitution in C2 hinders π overlap in the contact pair
Figure 1. Equilibration rate constants (k and k′, eq 1) vs free energy change for reactions of tert-butyl-substituted benzenes (C1 and C2) with biphenyl derivatives in acetonitrile (Table 3). The data deviate markedly from those involving two nonhindered reactants, which were found1 to follow a Sandros−Boltzmann dependence on free energy (eq 2) with klim = 9 × 109 M−1 s−1 (black curve). The data for pairs of nonhindered reactants are shown in Figure 3. The colored curves are discussed in sections 4 and 5.
more effectively than the 1,4-disubstitution in C1. As described below, the data for C2 are indistinguishable from those of hexaethylbenzene (C3), which has a comparable steric hindrance to π overlap. 2. Electron-Transfer Reactions of Hexaethylbenzene (C3). Hexaethylbenzene (C3) proved to be particularly well suited for this study because of its relatively low Eox and an absorption band of C3•+ with a maximum at 500 nm, where 1633
dx.doi.org/10.1021/jo202385f | J. Org. Chem. 2012, 77, 1632−1639
The Journal of Organic Chemistry
Featured Article
Table 3. Rate Constants for Equilibration between Radical Cations of tert-Butyl-Substituted Benzenes (C1 and C2) and Biphenyl Derivatives (Table 2) in Acetonitrile at Room Temperature and the Corresponding Reaction Free Energy Changea A BP1 C1 C1 C1 BP1 C2 C2 C2 a
B
ΔG (eV)
k (M−1 s−1)
k′ (M−1 s−1)
C1 BP2 BP4 BP5 C2 BP2 BP4 BP5
−0.031 −0.118 −0.273 −0.401 −0.055 −0.094 −0.249 −0.377
× × × × × × × ×
5.3 × 108 4.5 × 107
1.8 4.8 6.7 8.5 7.1 2.2 4.1 5.0
9
10 109 109 109 108 109 109 109
8.1 × 107 5.4 × 107
Figure 2. Equilibration rate constants (eq 1, Table 4) vs free energy change for reactions of hexaethylbenzene (C3) with methylsubstituted benzenes (blue circles) and with biphenyl derivatives (red circles) in acetonitrile. Also included are rate constants for C2 (unfilled squares) with biphenyl derivatives (Table 3 and Figure 1), whose dependence on ΔG is very similar to that for C3 with substituted biphenyls. The gray line at ΔG = −0.4 eV marks the approximate free energy beyond which electron transfer over longer (noncontact) distance starts to dominate (see footnote b, Table 4). The black curve represents the SB behavior of nonhindered reactant pairs, and the colored curves are discussed in sections 4 and 5.
Compounds arranged so that Eox(A) > Eox(B).
most of the radical cations of the benzene and biphenyl derivatives have weak or no absorption (see the Supporting Information). These factors made it possible to acquire sufficient data points to evaluate the kinetic parameters responsible for the observed deviation from the SB dependency. Data for the radical cation equilibration reactions (eq 1) between C3 and nonhindered benzene and biphenyl derivatives are given in Table 4 and in Figure 2 (filled blue and red circles,
A possible origin of the difference is discussed below. It is worth noting that this subtle difference is possible to detect only because of the high accuracy to which the differences in oxidation potentials (ΔG) and electron-transfer rate constants can be determined by the flash photolysis methods. At ΔG = 0, where the deviation from an SB dependence is the greatest, the interpolated rate constant for radical cation equilibration (k) between a benzene derivative and C3 is ∼2.3 × 108 M−1 s−1 and between a biphenyl derivative and C3 is ∼2.9 × 108 M−1 s−1. Compared with reactions between nonhindered reactants, where the rate constant at ΔG = 0 is equal to ∼klim/2, or 4.5 × 109 M−1 s−1, these rate constants are ∼20 and ∼16 times smaller, respectively. 3. Effect of Solvent Viscosity. As shown above, decreasing ket using sterically hindered reactants tends to increase the k−d/ ket ratio and, according to eq 5, can explain the deviation from an SB dependence for these reactants. This deviation is also predicted to depend on the magnitude of k−d, which can be changed by varying the solvent viscosity. For example, increasing the solvent viscosity is expected to decrease k−d, which should favor a kinetic behavior closer to an SB dependence. The concurrent effect on ket is not clear but is likely to be less than on k−d. Experiments to investigate these effects and their combined influence on the kinetic behavior are described below. Propylene carbonate was chosen as a viscous solvent for the electron-transfer reactions because it is highly polar, like acetonitrile, and it is 7.8 times more viscous.11 Before studying electron-transfer reactions in propylene carbonate, however, it was first necessary to evaluate the free energy changes for electron transfer in this solvent vs in acetonitrile. This was done by measuring electron-transfer equilibrium constants in both solvents for high, intermediate, and low-Eox pairs of nonhindered reactants as well as for pairs including a sterically hindered reactant, C2 or C3 (see the Supporting Information). In all cases, the ΔEox values in the two solvents were indistinguishable (≤3 mV) within experimental error. Thus, for the reactants studied here, ΔEox values in acetonitrile (but
Table 4. Rate Constants for Equilibration between Radical Cations of Hexaethylbenzene (C3) and Methyl-Substituted Benzenes (Table 1) or Biphenyl Derivatives (Table 2) in Acetonitrile at Room Temperature and the Corresponding Reaction Free Energy Changea,b A B7 B5 B4 B3 B2 B1 C3 C3 BP4 BP2 BP1
B
ΔG (eV)
k (M−1 s−1)
k′ (M−1 s−1)
C3 C3 C3 C3 C3 C3 BP6 BP7 C3 C3 C3
−0.089 −0.241 −0.346 −0.434 −0.596 −0.816 −0.043 −0.083 −0.134 −0.289 −0.438
× × × × × × × × × × ×
2.6 × 107
8.8 2.2 3.5 4.2 6.8 1.2 7.3 1.3 1.6 4.5 8.0
8
10 109 109 109 109 1010 108 109 109 109 109
1.3 × 108 4.9 × 107 8.0 × 106
a Compounds arranged so that Eox(A) > Eox(B). bFor the most exergonic reactions (B1•+ and B2•+ with C3), electron transfer apparently occurs over a longer distance such that steric hindrance no longer matters, in agreement with the change in mechanism anticipated10 to begin around −0.4 eV (see the Supporting Information). The reactions of C3 (hindered) and B8 (nonhindered) with B1•+ have equal rate constants (1.2 × 1010 M−1 s−1) at nearly equal values of ΔG (−0.79 and −0.82 eV). Both are ∼30% higher than the klim value of 9 × 109 M−1 s−1 for reactions via a nonhindered contact pair.1
respectively). Superimposed in Figure 2 are data for C2 (unfilled squares), which show a deviation from an SB dependence very similar to that for C3. This is not surprising because the steric crowding in C3 is similar to that in C2, as three alternating methyl groups in C3 lie above the plane of the benzene ring and the other three below it.9 A closer examination of the data for C3 reveals that its reactions with benzenes and biphenyls are discernibly different. 1634
dx.doi.org/10.1021/jo202385f | J. Org. Chem. 2012, 77, 1632−1639
The Journal of Organic Chemistry
Featured Article
not necessarily the absolute oxidation potentials, Eox) provide accurate estimates for those in propylene carbonate. Electron transfer reactions between nonhindered reactants were first investigated. On the basis of the discussion above, it seemed likely that, as in acetonitrile, these reactions would follow an SB dependence, except with a lower klim value due to the smaller value of kd in propylene carbonate. This expectation was borne out in practice. Plotted in Figure 3 are data for
Figure 4. Equilibration rate constants vs free energy change in propylene carbonate for reactions of nonhindered benzene and biphenyl derivatives (Table 5, unfilled black squares); of hexaethylbenzene (C3) with methyl-substituted benzenes (blue circles, Table 6); and of C3 with biphenyl derivatives (red circles, Table 6). The black curve is according to eq 2 with klim = 1.9 × 109 M−1 s−1. The colored curves are discussed in sections 4 and 5.
Table 6. Rate Constants for Equilibration between Radical Cations of Hexaethylbenzene (C3) and Methyl-Substituted Benzenes (Table 1) or Biphenyl Derivatives (Table 2) in Propylene Carbonate at Room Temperature and the Corresponding Reaction Free Energy Changea
Figure 3. Equilibration rate constants vs free energy change in acetonitrile (circles, from ref 1) and in propylene carbonate (squares, Table 5) for reactions among nonhindered benzene and biphenyl derivatives. The curves are according to eq 2 with klim = 9 × 109 and 1.9 × 109 M−1 s−1, respectively.
A B7 B5 B4 B3 BP4 BP3 BP2
reactions of pairs of nonhindered reactants in propylene carbonate (Table 5), as well as data in acetonitrile for Table 5. Rate Constants for Equilibration between Radical Cations of Methyl-substituted Benzenes (Table 1) and Biphenyl Derivatives (Table 2) in Propylene Carbonate at Room Temperature and the Corresponding Reaction Free Energy Changea
a
A
B
ΔG (eV)
BP4 BP1 BP2 B2 BP2
B7 B4 B6 BP2 B9
−0.045 −0.092 −0.128 −0.307 −0.373
−1 −1
k′ (M s )
× × × × ×
2.5 × 108 5.3 × 107 1.1 × 107
109 109 109 109 109
ΔG (eV)
k (M−1 s−1)
k′ (M−1 s−1)
C3 C3 C3 C3 C3 C3 C3
−0.089 −0.241 −0.346 −0.434 −0.134 −0.180 −0.289
× × × × × × ×
8.3 × 106
2.8 8.8 1.2 1.7 6.0 9.3 1.3
8
10 108 109 109 108 108 109
3.0 × 106
Compounds arranged so that Eox(A) > Eox(B).
hindered reactants in the same solvent (9.5 × 108 M−1 s−1). These reductions are ∼70−80% of those observed for the corresponding reactions in acetonitrile (∼20 and ∼16, respectively), indicating that k−d decreases slightly more than ket on going from acetonitrile to propylene carbonate. 4. Evaluating Deviations from an SB Dependence. According to eq 5, there are two possible sources of deviation from the simple SB dependence in eq 2: the ratios kd/k′d and k−d/ket. A deviation of kd/k′d from unity would simply shift the SB curve horizontally by the amount RT ln(kd/k′d) but not change its shape.1 Therefore, the extended transition between the endergonic and the exergonic regions observed with the crowded molecules can be explained only if k−d/ket is larger than for the nonhindered reactants. In principle, this could result from an exceptionally large value of k−d. For C2 and C3, however, the data deviate from an SB curve by at least a factor of ∼10 at ΔG = 0, implying that k−d/ket ∼18 or more. In contrast, k−d/ket is ≤0.3 for the nonhindered reactants.1 Unrealistically large values of k−d would be required to explain more than a minor part of this difference, especially considering that its complement, kd, appears to have similar values for C2, C3, and the nonhindered reactants (Figures 2 and 4). Thus, the main cause of the extended transition region must be a significantly decreased rate constant for electron transfer within the contact pair, ket, relative to that for the nonhindered reactants.
−1 −1
k (M s ) 1.5 2.0 1.8 2.2 1.9
a
B
Compounds arranged so that Eox(A) > Eox(B).
comparison. As anticipated, the reactions in the more viscous solvent still follow an SB dependence, but with a klim that is 4.7 times lower than the corresponding value in acetonitrile (1.9 × 109 vs 9 × 109 M−1 s−1). Analogous data for electron-transfer reactions involving the sterically crowded hexaethylbenzene (C3) with benzene and biphenyl derivatives in propylene carbonate are shown in Figure 4 (Table 6). Shown for comparison are data for the pairs of nonhindered reactants in propylene carbonate. The reactions of C3 show major deviations from an SB dependence. The transition from the endergonic to the exergonic regions is, as in acetonitrile, much broader for the reactions of C3. The interpolated rate constants (see section 4) for these reactions at ΔG = 0 of ∼5.9 × 107 M−1 s−1 and ∼8.3 × 107 M−1 s−1, for the benzenes and biphenyls, respectively, are ∼16 and ∼11 times smaller than the corresponding rate constant of the non1635
dx.doi.org/10.1021/jo202385f | J. Org. Chem. 2012, 77, 1632−1639
The Journal of Organic Chemistry
Featured Article
the dependence of k on ΔG. Therefore, rather than k−d and V, only k−d /V 2 was used as an independent parameter. Accordingly, the adjustable parameters were kd, k−d/V2, and λs. Good fits (the red and blue curves in Figures 1, 2, and 4) were obtained using the values listed in Table 7.
In the endergonic and mildly exergonic regions of interest in this work, electron transfer occurs at contact, eq 4. From molecular modeling, the bulky substituents in both C2 and C3 extend the molecular van der Waals surfaces further from the benzene plane by ∼1 Å relative to the nonhindered molecules.12 Because the sterically crowded reactants cannot achieve as strong a π overlap, the electron transfer rate constant, ket, should be smaller than for the nonhindered molecules, consistent with the above conclusions. The parameters responsible for the observed ΔG dependence of the rate constants in acetonitrile (Figure 2) and in propylene carbonate (Figure 4) were estimated by fitting the data to eq 5 together with a conventional Marcus expression13 for nonadiabatic electron transfer, ket. The parameters in this expression are the well-known electronic coupling matrix element (V), solvent and vibrational reorganization energies λs and λv, and an average vibrational frequency νv (see section 5 for a more detailed description). The data for C2 are very similar to the corresponding data for C3, consistent with the equal expansion of the van der Waals surfaces, and the two data sets were combined for the fitting. As evident from Figures 2 and 4, the data for benzenes and the biphenyls require somewhat different fitting parameters. The value of kd for the crowded molecules cannot be determined accurately from the exergonic data because the plateau may not have been reached before the onset of longerrange (noncontact) electron transfer at ca. −0.4 eV (Figures 2 and 4). Nevertheless, kd is clearly somewhat less than the limiting rate constant, klim, observed for the nonhindered reactants (9 × 109 M−1 s−1 in acetonitrile and 1.9 × 109 M−1 s−1 in propylene carbonate). Estimates of each kd were obtained from the fitting of the complete set of data in each solvent. The fitting procedure yielded larger values of kd for the biphenyls than those for the benzenes. This difference in kd may have its origin in the structure of the complexes along the path to electron transfer. In a contact pair involving a biphenyl, only one of its aromatic rings might overlap the aromatic ring of the other reactant. This hypothesis seems reasonable given that biphenyl and biphenyl radical cation have nonplanar structures.14 Because it has two rings, formation of such a complex would be statistically more favored for a biphenyl than for a benzene. Although minor scatter in the data might arise from differences between kd and k′d (eqs 4 and 5), there is no indication that the rate constants of the exergonic reactions of C2•+ and C3•+ and those of benzene or biphenyl radical cations (B•+ or BP•+) approach different plateaus. Accordingly, the ratio kd/k′d is unlikely to be very different from 1; therefore, kd and k′d were assumed to be equal in the fitting process to decrease the number of variables. To help in evaluating the remainder of the fitting parameters, we referred to earlier studies of radical ion pair reactions involving the same nonhindered reactants.15 There, ∼30% larger V and ∼10% larger λs were required for the benzenes than for the biphenyls. For consistency and to decrease the number of variables, we kept the respective ratios (1.3 and 1.1) constant when estimating the values of V and λs for the present reactions in acetonitrile and in propylene carbonate. In the previous studies,15 the same values of λv and νv were used for both types of reactants, and they were used here as well. As discussed above, the degree of deviation from SB behavior is determined by k−d/ket. For nonadiabatic electron transfer, ket is proportional to V2; so only the ratio k−d/V2 actually affects
Table 7. Parameters Used To Fit the Data in Figures 2 and 4 and the Derived Rate Constants of eq 5 at the Isoergic Pointa solvent acetonitrile
propylene carbonate
parameters
BP
B
BP
B
k−d/V2 (1015 s−1 eV−2) λs (eV) kd and k′d (109 M−1 s−1) k at ΔG = 0 (108 M−1s−1) ket at ΔG = 0 (109 s−1)
2.3 0.41 6.5 2.9 3.0
1.3 0.45 4.5 2.2 3.3
0.46 0.55 1.7 0.83 0.65
0.27 0.60 1.2 0.59 0.66
a
Based on the equations in section 5 with fixed electron-transfer parameters λv = 0.25 eV, hνv = 0.174 eV (1400 cm−1).
The magnitude of V can be determined from an estimate of k−d. As discussed elsewhere, the solvent stabilization of the radical ion should increase when the contact pair dissociates.1 Taking this factor into account leads to a rather large estimate of k−d in acetonitrile, ∼6 × 1010 s−1 (see the Supporting Information for details). In propylene carbonate, where kd for nonhindered compounds is ∼5 times smaller than in acetonitrile, k−d was assumed to decrease proportionally (∼1.2 × 1010 s−1). From these estimates and the values of k−d/V2 in Table 7, estimates of V of ∼5 and ∼7 meV are obtained for the reactions with biphenyls and benzenes, respectively. These values of V are much smaller than typical values for nonhindered electron donors and acceptors in contact (∼100 meV).10 This large difference indicates that the increased interplanar separation significantly reduces the strength of the interaction between the π systems overall. The values of λs are ∼30% greater in propylene carbonate than in acetonitrile. In macroscopic theories, λs is determined by the familiar factor (1/n2 − 1/ε),16 which has similar values in the two solvents (0.479 for propylene carbonate and 0.526 for acetonitrile).17 The different values of λs in the present fits may reflect molecular-level differences in the organization of solvent molecules around a contact pair. The smaller V for the two-ring compounds is attributed to smaller π orbital overlap compared to the one-ring compounds and is consistent, for example, with the prediction that more complex nodal structures for molecular orbitals of larger aromatic systems result in smaller matrix elements.15 A smaller λs for the two-ring vs one-ring compounds is supported by the fact that exciplex spectra of biphenyls are less sensitive to solvent polarity than those of benzenes (0.35 vs 0.49 eV shifts of the emission maxima upon going from cyclohexane to acetonitrile).15a Both differences are attributable to a lesser solvation for a biphenyl radical cation than for a benzene radical cation in a contact pair or exciplex, consistent with a larger charge delocalization over two aromatic rings. The values of λv and λs listed in Table 7 fall in the ranges reported for related electron-transfer reactions,10,15 but they do not represent a unique set of parameters. For example, variations in λv of ±0.04 eV together with ∓0.02 eV changes in λs gave similarly good fits. Alternatively, varying λv by the 1636
dx.doi.org/10.1021/jo202385f | J. Org. Chem. 2012, 77, 1632−1639
The Journal of Organic Chemistry
Featured Article
thereof is Pm, eq 7b. Analogously, the products (A/B•+) may be left with several quanta, nhνv. For the m → n transition, the free energy change is ΔG + (n − m)hνv, giving rise to the Marcus exponential in eq 7c. The mode-specific electron-transfer integral is ⟨n|m⟩V, where ⟨n|m⟩ is the corresponding Franck− Condon (vibrational overlap) integral and V is the usual integral over electron coordinates. Vibrationally excited product states are needed for a realistic description at exergonicities exceeding ∼hνv, and vibrationally excited initial states are included for consistency.20 The remaining symbols have their usual meanings.
same amounts (±16%), coupled with ca. ±10% changes in V, gave similar fits. Thus, based on plausible values for k−d and reorganization energies, the matrix elements V are probably accurate to ca. ±1 meV. In addition to the adjustable parameters, Table 7 includes the resulting values of the overall rate constant, k, and the rate constant for electron transfer within the contact pair, ket, at ΔG = 0. Whereas kd for the nonhindered reactants is 4.7 times smaller in propylene carbonate than in acetonitrile (1.9 × 109 vs 9 × 109 M−1 s−1), the corresponding reduction for the reactions of C3 is somewhat smaller, ∼3.8 (Table 7).18 It is interesting to note that these decreases are smaller than the ratio of solvent viscosities, 7.8.11 A possible explanation is that kd is not determined solely by translational diffusion,4 but also by partial desolvation and reorientation to form a properly oriented contact pair, A•+/B. In either solvent, the predominant reason for the deviation from an SB dependency for the electron-transfer reactions is a decrease in the electron-transfer rate constant ket, undoubtedly due to the larger separation distance between the π systems caused by the steric crowding in C2 and C3. For example, in acetonitrile the estimated value of ket at ΔG = 0 for the crowded reactants is ∼3 × 109 s−1 (Table 7), whereas a lower limit for the corresponding value for the nonhindered reactants is ∼2 × 1011 s−1. As mentioned in the Introduction, the latter value is based on the quality of fit to an SB plot,1 which required that k−d/ket ≤ 0.3, and on an estimate of k−d of ∼6 × 1010 s−1. It should be noted that the estimated difference in ket at ΔG = 0 between these two types of reactions, a factor of ≥50, is based on the assumption that k−d is approximately the same in the two cases, but that estimate is otherwise independent of the actual value of k−d. The greater interplanar separation of the hindered reactants results in a much smaller matrix element (V) and much slower electron transfer. A value of V of ∼5−7 meV for the crowded reactants is consistent with the values of ∼1.0 and 1.4 meV reported for electron transfer in solvent separated radical ion pairs (SSRIP).10 The separation, r, between radical ions in an SSRIP is estimated to be ∼7 Å,10 whereas r for contact between the present crowded reactants is expected to be ∼4.5 Å (i.e., 1 Å greater than for unhindered reactants). The dependence of V on r is conventionally assumed to obey eq 6. A 5−6 fold increase in V for a ∼2.5 Å decrease in separation distance yields a β of ∼1.3 Å−1, which is consistent with literature values.19 It is worth noting that the much larger V for nonhindered radical ions in contact (∼100 meV) would require a much larger value of β.10 More likely, however, eq 6 is inapplicable to π systems in intimate contact, where the detailed nodal properties of the orbitals are a critical factor.
V ∝ exp( −βr /2)
∞
k=
∑ m=0
∞
Pm(
∑ km → n) n=0
⎛ mhvv ⎞ ⎡ ⎛ hv ⎞⎤ ⎟ /⎢1 − exp⎜ − v ⎟⎥ Pm = exp⎜ − ⎝ RT ⎠ ⎣ ⎝ RT ⎠⎦
km → n
⎛ 4π3 ⎞1/2 ⎟⎟ |⟨n|m⟩V |2 = ⎜⎜ 2 ⎝ h λ sRT ⎠ ⎛ [ΔG + (n − m)hv + λ ]2 ⎞ v s ⎟ × exp⎜⎜ − ⎟ 4λ sRT ⎝ ⎠
(7a)
(7b)
(7c)
Equation 7 applies to nonadiabatic electron-transfer processes with small values of V. If the geometry of the contact pair is independent of the solvent, V should be too. The data for the crowded reactants are consistent with small V (Table 7), and with the same values in acetonitrile and in propylene carbonate, supporting the analysis based on eq 7. While the dielectric relaxation time of the solvent, τL, is ∼10 times longer in propylene carbonate than in acetonitrile,21 it plays no role in nonadiabatic electron transfer, because the small V limits the rate instead. The internal and external consistency of the present analysis is strong evidence in its favor. However, it is not possible to rule out the alternative that V is considerably larger than the ∼5 meV estimated here, that the electron-transfer process is adiabatic or intermediate between adiabatic and nonadiabatic, and that the slower electron transfer in propylene carbonate is then a result of the slower dielectric relaxation in that solvent.22
6. CONCLUDING REMARKS Charge shift reactions between nonhindered neutral and radical cation reactants in both acetonitrile and propylene carbonate follow a Sandros−Boltzmann dependency on the reaction free energy. This dependence indicates that electron transfer is not rate-limiting; therefore, the only information that can be learned about the kinetics of electron transfer within the contact pairs (A•+/B ⇌ A/B•+) is that the transfer in the exergonic direction must be appreciably faster than the competing diffusional separation. For the exergonic reactions, the limiting rate constant is ∼5 times smaller in propylene carbonate, reflecting the smaller rate constants for encounter in the more viscous solvent. For the sterically crowded reactants 1,3,5-tri-tert-butylbenzene (C2) and hexaethylbenzene (C3), the separation distance in a face-to-face contact pair with a nonhindered partner is ∼1 Å larger than for two nonhindered reactants. As a result, π overlap is reduced and electron transfer becomes much slower than diffusional separation, leading to a strong deviation from
(6)
5. Electron-Transfer Theory. The colored curves in Figures 2 and 4 were used to interpolate the data for comparisons at equal values of ΔG and, in particular, at ΔG = 0. As outlined above, they were obtained by fitting the data to eq 5 together with a well-known expression for ket, eq 7.13 Here, reorganization of the solvent and displacements of lowfrequency molecular vibrational coordinates are described by a low-frequency reorganization energy, λs. Reorganization of high-frequency vibrational coordinates is described by a representative frequency νv and a high-frequency reorganization energy λv. The reactants in the contact pair (A•+/B) may have several quanta of vibrational energy, mhνv; the probability 1637
dx.doi.org/10.1021/jo202385f | J. Org. Chem. 2012, 77, 1632−1639
The Journal of Organic Chemistry
Featured Article
the SB dependency in both solvents.23 In both acetonitrile and propylene carbonate, the reactions with the benzenes are slightly, but consistently slower than with the biphenyls. Fitting the data to a conventional electron transfer theory yielded information about the parameters controlling electron transfer involving these sterically crowded molecules. The electronic coupling matrix elements (V) and reorganization energies (λs and λv) are consistent with those for electron transfer reactions in radical ion pairs.10,15 Furthermore, differences between benzenes and biphenyls can be explained by differences in the fitting parameters V and λs that are similar to differences observed in radical ion pair reactions of these reactants.15 These consistencies provide additional support to the fitting procedure. At ΔG = 0, the electron transfer rate constants in propylene carbonate are ∼4 times smaller than in acetonitrile. This difference can be explained in terms of larger values λs in propylene carbonate. Importantly, as demonstrated here, comparison with electron transfer models and evaluation of the controlling parameters for bimolecular electron transfer reactions is possible only when signif icant deviation f rom an SB dependency is observed. Of course, other factors besides steric effects should be able to reduce electron transfer rate constants sufficiently for observable non-SB behavior, e.g., large conformational changes upon electron transfer.24 Work along these lines, to define the scope and limitations of SB dependency in electron-transfer reactions, is under way.
■
Laser Flash Photolysis Measurements. Absorption spectra of radical cations and of mixtures thereof in equilibrium as well as decay kinetics were measured using a nanosecond laser flash photolysis apparatus. A Lambda Physik Lextra 50 XeCl excimer laser was used to pump a Lambda Physik 3002 dye laser, providing ∼7 ns, 2 mJ, 343 nm pulses. The laser dye was p-terphenyl. Transient absorptions were monitored at 90° to the laser excitation using pulsed xenon lamps and timing shutters. A monochromator and a photomultiplier tube were used for kinetic measurements, or a diode array detector for obtaining transient absorption spectra. For kinetic analyses the signal from the photomultiplier tube was directed into a Tektronix TDS 620 digitizing oscilloscope and then to a computer for viewing, storage, and analysis. To reduce second-order radical ion decay, the beam energies were attenuated, keeping the optical density below 0.04, and data were averaged over 30−80 pulses. All measurements were carried out at ambient temperature (∼293 K). Donor concentrations ranged from 0.5 to 50 mM. In addition, the solutions contained 1 mM N-methylquinolinium hexafluorophosphate (NMQ+), an electron-acceptor sensitizer, along with 0.5 M toluene (or benzene, in the cases of the highest Eox reactants) usually in dioxygensaturated acetonitrile. For the reactions in propylene carbonate, 0.3 M toluene was used to minimize the effect on the bulk viscosity. Toluene (or benzene) served as a codonor to rapidly and efficiently quench the excited NMQ+ singlet state (1NMQ+*), produced by laser excitation, to yield NMQ• radicals and codonor radical cations. Dioxygensaturation allows rapid (
