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Pressure Tuning of Electron Attachment to Benzoquinones in Nonpolar Fluids: Continuous Adjustment of Free Energy Changes Richard Holroyd,* John R. Miller,* Andrew R. Cook,* and Masaru Nishikawa Chemistry Department, Brookhaven National Laboratory, Upton, New York 11973, United States ABSTRACT: Changing pressure from 1 to 2500 bar continuously tunes free energy changes for electron attachment to molecules in nonpolar liquids by nearly 0.3 eV. Rate constants for electron attachment to substituted benzoquinones were determined over an extended free energy range of nearly 1 eV by a combination of solute, pressure, temperature, and use of solvents with differing energies of the quasifree electron, V0: tetramethylsilane (TMS) and 2,2,4-trimethylpentane (TMP). The rates of attachment to both benzoquinone (BQ) and 2,5-dichlorobenzoquinone in TMS increase as the pressure increases to 2500 bar, while in TMP the rates are higher but change little with pressure; the rate of attachment to fluoranil in TMS is similarly high at 1 bar but decreases with increasing pressure. Together the observed rate constants can be qualitatively interpreted to yield a rate vs free energy relation having both normal and Marcus inverted region behavior. Because the electron attachment reactions yield excited states, quantitative interpretation of the free energy dependence requires knowledge of the excited state energies. The electron enters the second lowest π* orbital to form a π*−π* excited state, which quickly relaxes to the lower n−π* excited state. The rate of attachment to this excited state is low when the free energy of reaction, ΔG°, is positive and increases as ΔG° decreases until near −0.2 eV, after which the rate decreases. While excited state energies are uncertain, reasonable estimates are obtained from absorption, excitation, and fluorescence spectra of the product radical anions measured here. The results are modeled using Marcus theory with inclusion of a high frequency molecular vibration.

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INTRODUCTION The Marcus theory predicts an “inverted region” in which more driving free energy, −ΔG°, causes electron transfer rates to decrease. A spectacular example seems to occur in electron attachment to p-benzoquinone (BQ). This reaction with ΔG° = −2.42 eV is slower by a factor of 1000 than more moderately exoergic reactions.1,2 Previous studies2 have shown that electrons react by attaching to many organic compounds in nonpolar solvents. In tetramethylsilane (TMS) as solvent, the rate constant for attachment is high, of the order of 1013 M−1 s−1, for most compounds of positive electron affinity, i.e., for exoergic reactions. However, for benzoquinone1 and duroquinone, both very electronegative compounds, the rate of electron attachment in TMS at room temperature is unusually low. Also, in the gas phase, benzoquinone does not attach thermal electrons.3 The slow rate in TMS has been attributed in one study1 to electron attachment to an excited state from which detachment occurs in competition with deactivation. In another study,4 the fluorescence of the lower excited anion (BQ− *) was observed which indicated a long lifetime of this state, of the order of 50 ns at room temperature in 2,2,4trimethylpentane (TMP) as solvent. This study also concluded that electron attachment occurs first to form a higher excited state anion which rapidly converts by internal conversion to the fluorescing state. In both interpretations, attachment to form ground state anions is slow due to the Marcus inverted effect. The rates of electron attachment reactions depend on many parameters. First, the high rate of attachment can be attributed © 2014 American Chemical Society

to the high mobility of electrons in these solvents. Electron attachment can be considered as electron transfer from the solvent state to a solute. In this case, the rate should depend on the difference in energy between the electron in the solvent, designated ΔGs(e), and that of the anion, the free energy of reaction. An example showing this dependence is electron attachment to CO2. This reaction is reversible in nonpolar solvents, allowing the free energy of reaction to be measured. Those results show that the rate of attachment increases 3 orders of magnitude as the free energy change, ΔG°, decreases by 0.4 eV.2 Increasing pressure also causes the conduction band energy of the quasi-free electron in the liquid (V0)5 as well as ΔGs(e)6 to increase in nonpolar liquids, thus changing the energetics of the reaction. Measurements of electron attachment to other solutes as a function of pressure show that such reactions occur with a large decrease in volume, of the order of −200 cc/mol.7 These large volume changes include a contribution from electrostriction around the product anion. Therefore, a shift to the anion is favored by increasing pressure. The rate of electron attachment to CO2 is accelerated by pressure in both TMS and TMP.8 However, only a small fraction of the volume change occurs in the attachment step. Electron attachment to pyrimidine has been studied in these same solvents, and in contrast, the rate decreases slightly with increasing pressure.9 This is also an Received: December 10, 2013 Revised: January 31, 2014 Published: February 3, 2014 2164

dx.doi.org/10.1021/jp412090k | J. Phys. Chem. B 2014, 118, 2164−2171

The Journal of Physical Chemistry B

Article

reference could not be found for confirmation. Thus, the vapor pressure is about one-third that of benzoquinone, which is reasonable, since perfluorocarbons have vapor pressures comparable to their hydrocarbon analogues.15 The above method could not be used for Cl2Q for which the vapor pressure is quite low.16 In this case, a solution is first prepared in tetrahydrofuran in a glovebox. An aliquot of this is added to the side arm of the evacuated conductivity cell from which the solvent has been removed. The cell valve is opened and the aliquot transferred into the cell. The THF is then pumped off on a vacuum line at a low temperature, leaving the solute and finally the solvent distilled in. Fluorescence Measurements. Spectra of substituted benzoquinone radical anions were measured at 77 K in MTHF glasses with a Spex Fluorolog spectrofluorimeter, as described previously.4 Anions were prepared by Cobalt-60 γirradiation. Excitation spectra were measured by monitoring the emission intensity near the peaks of the fluorescence spectra, which were found to be insensitive to the detection wavelength.

equilibrium reaction and the overall volume change is large, ≈ −200 cc/mol, as in the case of CO2. It is also an exoergic reaction in solution for which ΔG° = −0.43 eV. Our aim in this study is to further our understanding of the energy dependence of electron attachment utilizing continuous tuning of ΔG°. The ability to continuously tune ΔG° is a long sought-after goal for ET reactions.10 A particular focus here is on cases such as substituted benzoquinones for which there may be large inverted region effects. To do this, we studied several substituted benzoquinones which have different electron affinities. We also varied the energy of the electron in the solvent, ΔGs(e), by changing the pressure, temperature, or solvent, including use of mixtures of nonpolar solvents. For TMS, ΔGs(e) is considered the same as V0; for TMP, equilibrium studies11 indicate ΔGs(e) is below V0. Increasing pressure increases V0 in both solvents;5 in TMS, V0 changes from −0.56 eV at 1 bar to −0.43 eV at 2500 bar; in TMP, V0 changes from −0.24 eV at 1 bar to −0.045 eV at 2500 bar.5 In nonpolar liquids, ΔGs(e) increases with pressure in a manner similar to that of V0.6 The present study is the first to examine the pressure dependence of the rate of electron attachment to benzoquinone and its derivatives in TMS and TMP. The results indicate that electron attachment occurs to form an excited anion, and we conclude that the rate depends on the free energy of reaction as predicted by electron transfer theory.12

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RESULTS TMS as Solvent. Figure 1 shows the pressure dependence of the observed rate of electron attachment to three solutes in

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EXPERIMENTAL SECTION Electron Attachment. The rate of electron attachment to solutes is measured as a function of pressure in this study. The metal conductivity cell, equipped with a bellows to allow for volume change with pressure, is described elsewhere.13 For measurements, this cell is placed in a cylindrical pressure vessel capable of 3000 bar. The vessel and pressurizing apparatus was built by LECO Corp. Samples are exposed to a 30 ps pulse of X-rays generated from the 9 MeV electron pulse of the Laser Electron Accelerator Facility14 striking a metal beam stop. Conductivity signals due to mobile solvated electrons produced by the X-ray pulse are detected with a fast 10 ns rise time current sensitive amplifier, and recorded in a Lecroy 4820A scope. The rate constants, ks, for electron attachment to solutes are determined by a fit of the experimental current trace to the equation i(t ) = i0(1 − t /t D) exp(− (ks + k imp)t )

Figure 1. Observed rate constants for electron attachment to (red ●) BQ, (orange ◆) Cl2Q, and (green ■) F4Q in TMS as a function of pressure.

TMS. The rate of attachment to BQ increases dramatically with pressure from 4 × 1010 to 3 × 1013 M−1 s−1, a change of nearly 3 orders of magnitude. Attachment to Cl2Q is much faster at 1 bar and increases with pressure to a lesser extent. The rate of attachment to F4Q is high initially but decreases with increasing pressure. None of these reactions are diffusion controlled; the diffusion limit is reported to be close to 1015 M−1 s−1 in TMS.2 The rate of electron attachment to BQ has previously been studied as a function of temperature, where the rate increases with decreasing temperature in TMS.1 Figure 2 compares that temperature data1 with the pressure data, both plotted versus V0. The two sets of results exhibit a similar dependence on V0, but the rate increases more with pressure. The largest rate constant, 3.21 × 1012, attained by temperature variation in Figure 2 occurs at V0 = −0.474 eV for T = −98 °C. When the same V0 is attained by raising the pressure, the rate constant is larger by a factor of 8.5. This difference cannot be attributed to the mobility of the electron which changes little with pressure13 or temperature17 over the ranges studied. The low rate at T = −94.4 °C may be a need for thermal activation. A detailed understanding is not available and might require considerations of complex effects that arise from factors like frequency

(1)

where tD is the drift time of the electrons and kimp is the rate of attachment to impurities determined prior to addition of solutes. The initial current, i0, and the drift time both depend on the applied voltage, typically between 2 and 20 V in the case of TMS. As eq 1 predicts, ks is found to be independent of the applied voltage. Fits of eq 1 to the data use Igor Pro software. Chemicals. TMS and TMP, both Aldrich 99.9+%, are further purified by degassing and passage through a Silica Gel/ molecular sieve column and storage over NaK. The electron lifetimes (1/kimp) in the pure solvents are typically 5 μs for TMS and >5 μs for TMP. 1,4-Benzoquinone (BQ), 2,5dichlorobenzoquinone (Cl2Q), and tetrafluoro-1,4-benzoquinone (F4Q) from Aldrich were further purified by sublimation prior to use. These solutes are added in one of two ways. For BQ and F4Q, which have significant vapor pressure, the amount of solute added is determined by measuring the pressure with an MKS baratron in a calibrated volume. The vapor pressure of F4Q at 22 °C was determined to be 0.03 Torr; a literature 2165



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30% TMS is added may reflect a balance of factors discussed below, including an increase in electron mobility with little change of ET rate. The rate also decreases as the temperature increases for all three mixtures as is the case for pure TMS. Spectra and Fluorescence Results. The fluorescence spectra of a series of substituted benzoquinone anions in solid MTHF are measured in Figure 4. The estimated high energy

Figure 2. Observed rate constant for electron attachment to BQ versus V0: (blue ●) pressure from 1 to 2500 bar at T = 20 °C; (red □) temperature from 35 to −98 °C (T in °C shown at first and last point), from ref 1.

changes.18 Increasing pressure causes the solvent V0 to increase and the rate to increase. With decreasing temperature, V0 increases and the rate increases. V0 for TMS was calculated from the density N (in cm−3) using the parabolic dependence given by a previous pressure study:5 V0 = −0.61 + (N − 3.39 × 1021)2 /2.48 × 1043

(2)

TMP as Solvent. The rate of attachment to BQ in TMP is quite high and changes little with both pressure and temperature. The results are shown plotted versus V0 in Figure 3. Figure 4. Fluorescence spectra of BQ•− * and radical anions of other substituted benzoquinones in MTHF at 77 K. The identity of each spectrum is indicated by the abbreviation in the figure.

emission band edge for BQ•− is at 593 nm,4 indicating that the energy of the fluorescent state lies at 2.1 eV. Similar analysis gives nearly the same energies for Cl2Q and F4Q, 2.1 and 2.0 eV, respectively. This series of spectra, along with excitation spectra, can enable predictions about states formed by electron transfer to a range of quinones. The excitation spectra of BQ•− and substituted benzoquinones recorded near the peak of the emission spectra are shown in Figure 5. The excitation spectrum for BQ•− is shown to be a good match for the absorption spectrum recorded by Shida19 under similar conditions. The low energy edges of the excitation spectra were used to estimate the upper π*−π* excited state energies. For BQ•−, the edge at approximately 475 nm gives an excited state energy of 2.6 eV. Similarly, the threshold for Cl2Q is at 495 nm (2.50 eV) and for F4Q at 530 nm (2.34 eV).

Figure 3. Electron attachment to BQ in 2,2,4-trimethylpentane plotted versus V0: (blue ●) pressure dependence data at T = 20 °C; (red □) temperature data from ref 1.

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Mixture Results. Table 1 shows the rate of attachment to BQ for several mixtures of TMS and TMP as a function of temperature. As the percentage of TMS increases in the mixtures, the rate of attachment decreases, with the exception of the first addition of TMS at 20 °C. The small increase when

DISCUSSION Rates and Free Energy Changes. The free energy change for electron attachment to benzoquinone to form the ground

Table 1. Rate Constants (M−1 s−1) for Reaction of Electrons with BQ in TMS/TMP Mixtures TMS/TMP mixtures T (°C) 20 30 40 50

1/T 0.003412 0.003299 0.003194 0.003095

100% TMP 1.80 × 10

13

30% TMS

55% TMS

75% TMS

100% TMS

× × × ×

× × × ×

× × × ×

4.40 × 1010

2.70 1.71 1.18 7.68

13

10 1013 1013 1012 2166

3.69 2.40 1.67 1.23

12

10 1012 1012 1012

8.55 5.87 3.71 3.21

11

10 1011 1011 1011



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Figure 5. Excitation spectra of the radical anions of 1,4-benzoquinone, 2,5-dichlorobenzoquinone, and F4Q in MTHF at 77 K measured by monitoring the fluorescence intensity at 643, 620.5, and 670.5 nm, respectively, are compared to the absorption spectrum of BQ•− from Shida.19

Figure 6. Schematic diagram of the ground state and three types of excited states. In the ground state, an electron is added to the LUMO, π1*. In the π*−π* state, it is added instead to a higher orbital, π2*. In the n−π* state, which is the lowest excited state of BQ•−, an electron is added to π1* and a second electron is promoted to π1* from an n orbital. The π−π* state is similar, but an electron is promoted from a π orbital.

state anion is estimated to be −2.43 eV (Table 2) in TMS based on redox potentials and equilibria described below. This should place the reaction well into the inverted region, making it very slow. Indeed, negligible formation of the ground state was observed upon electron attachment at 1 bar in isooctane or THF.4 Instead, excited anions were produced, which later relaxed to their ground states. Figure 6 is a schematic diagram of orbital occupancies in the ground and excited states of a quinone anion.

type of excited state, a π−π* state, promotes an electron from an occupied π orbital to pair with the electron in the lowest π* orbital. Photoexcitation of BQ•− in its strongly allowed band at 450 nm produces BQ•− ** which relaxes in two steps:

Table 2. Redox Potentials and Free Energy Changes for the Reaction e− + M → M−• in TMS at 1 bar to Form Anions in Their Ground States compound (M)

E0 a (V)

ΔG° b (eV)

BQ 2,5-Cl2BQ F4 Q anthracene naphthalene biphenyl

−0.90222 −0.59122 −0.39622 −2.40224 −2.99125 −3.04725

−2.42 −3.91 −2.93 −0.92 −0.3311 −0.3023

e− + BQ → BQ•− ** → BQ•− * → BQ•−

With energies deduced above and the reduction potential of BQ, E0 = −0.9 V vs ferrocene (Fc),22 we may estimate reduction potentials for formation of BQ•− * and BQ•− ** to be −3.0 and −3.5 vs Fc+/0. These can be related to the electron in TMS with the free energy change for e− + naphthalene in TMS (−0.33 eV)23 and E0 = −2.991 eV vs Fc for reduction of naphthalene. Energies and redox potentials of relevant species are shown in Table 2. These redox potentials along with the free energy change for equilibria observed for e− in TMS with naphthalene11 (ΔG° = −0.33 eV) yield ΔG° = −2.42 eV for reaction of e− with BQ in TMS at 1 bar. Similarly, one finds −2.45 and −2.42 eV for reaction of e− with BQ based on biphenyl23 and anthracene, respectively, also shown in Table 2. These estimates utilize differences, ΔE0, between reduction potentials of BQ and of naphthalene or biphenyl in polar solvents to estimate ΔE0 in nonpolar TMS. The −2.42 eV estimate based on naphthalene is preferred because the size of naphthalene is close to that of BQ, which should minimize any difference between ΔE0 in TMS and ΔE0 in polar solvents. We estimate that this possible difference and other sources give some uncertainty, so ΔG° = (−2.42 ± 0.1) eV. This estimate places the electron slightly below the 2.6 eV energy of the π*−π* excited state of BQ, BQ−• **, but well above that of the lowest, n−π* excited state, BQ−•*. The energetics for electron attachment to form BQ−• ** is thus compatible with the observation of a rate that is slow at 1 bar but increases with pressure. The observed attachment rates and estimated energetics are incompatible with reaction to produce the n−π* excited state. Electron transfer reactions to produce that state were reported to be

a

Reduction potentials vs Fc+/0 reported by Prince22 for quinones or Shalev24 for anthracene. Values for naphthalene and anthracene used differences relative to anthracene reported by Streitweiser.25 bFree energy changes to form ground state anions calculated from equilibria reported for naphthalene11 and the differences in redox potentials: ΔG°(M) = ΔG°(Nap) − E0(M) − E0(Nap).

When quinone, Q in Figure 6 is BQ, electron attachment to form the lowest excited anion state (BQ•− *) an n−π* state, involves a transition of a second electron which has been reported to greatly slow the electron transfer either into or out of that state.20 While the n−π* state seems to not be directly formed in electron attachment, the π*−π* state (BQ•− **), approximately 0.5 eV higher, is readily formed.4,20 The absorption spectra (Figure 5) show indeed that the energy of this state for BQ•− is 2.6 eV above the ground state. A gas phase photodetachment study found this state to be located at 2.5 eV.21 This upper state is presumed to relax rapidly to the lower weakly fluorescent state. In nonpolar fluids, photodetachment also occurs.1 The lowest excited state is 2.1 eV above the ground state (BQ•−) as noted previously4 and seen in the observed fluorescence spectra shown in Figure 4. One other 2167



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Table 2). The spectral data show that transition to the π*−π* state is even lower in F4Q, 2.34 eV, making the attachment even more favorable. All of the above data are combined in Figure 7

slow due to the requirement of transition of a second electron.20 The energy of the upper excited anion state, BQ−• **, is estimated to be 0.17 ± 0.1 eV above the energy level of the electron in TMS at room temperature and 1 bar. Thus, attachment to create this state is uphill energetically. Electron attachment to ethyl bromide in TMS is uphill energetically by 0.32 eV, and the rate is similarly slow,2 3.7 × 1010 M−1 s−1. As mentioned in the Introduction, the energy level of the electron increases as the pressure increases, which brings the electron level closer to the level of the BQ−• ** state. This qualitatively explains the results for BQ in Figure 1. To estimate the dependence of ΔG° on pressure, we must also take into account both the known effect of pressure on the energy of the electron, ΔGs(e), and the change with pressure of the polarization energy of the negative ion. The changes in polarization energy are calculated from the Born equation using for BQ a radius of the negative ion of 0.32 nm. Table 3 shows

Figure 7. Bimoleular rate constant for electron attachment as a function of free energy change to form anions of quinones in their π*−π* excited states. The solid red line is a fit of electron transfer theory eqs 4 and 5 to the rates for BQ and F4Q in TMS. Parameter values: V(r) = 348 ± 4 cm−1, λs = 0.105 ± 0.006, λv = 0.24 ± 0.007, T = 296, ω = 1296 cm−1. The fit was performed with the mobility μ = 100. Dashed lines change μ while keeping all other parameters fixed to the values from the fit.

Table 3. Rates and Free Energies vs Pressure in TMS P (bar)

V0 (eV)

P− (eV)

ΔG° (eV)

1 100 250 500 750 1000 1250 1500 1750 2000 2250 2500

−0.574 −0.565 −0.554 −0.537 −0.523 −0.509 −0.497 −0.486 −0.476 −0.466 −0.456 −0.447

−1.023 −1.041 −1.061 −1.087 −1.107 −1.123 −1.137 −1.149 −1.160 −1.169 −1.178 −1.186

0.170 0.144 0.112 0.069 0.035 0.005 −0.021 −0.044 −0.065 −0.085 −0.103 −0.120

k(e + BQ) (M−1 s−1) 4.28 5.50 3.63 1.55 4.62 8.77 1.33 2.19 2.72 3.04 3.55 3.58

× × × × × × × × × × × ×

1010 1010 1011 1012 1012 1012 1013 1013 1013 1013 1013 1013

as a plot of rate constant versus ΔG°. The rate of attachment increases as ΔG° decreases from 0.2 to −0.2 eV and then levels off, and at values of ΔG° more negative than −0.4 eV, it starts to decrease. The rate constants observed for BQ in 2,2,4-TMP are in the range (4−5) × 1013 M−1 s−1. One might expect higher values in this case, since the diffusion limited rate, kD, is estimated as ∼1014 from eq 3, taking the reaction radius, Re, as 0.72 nm and the drift mobility, μD, as 7 cm2/Vs:2

how both quantities change with pressure in TMS. At 1 bar, the free energy is positive and the rate of attachment is low. At high pressure, the free energy is negative, i.e., exothermic, and the rate is high. A similar analysis for the TMS/TMP mixtures is shown in Table 4. For TMP, the energy level of the electron is higher

E(e−) (eV)

P− (eV)

ΔG° (eV)

75% 55% 30% 0%

−0.53 −0.49 −0.45 −0.42

−1.038 −1.053 −1.068 −1.088

0.111 0.056 0.001 −0.049

K (M−1 s−1) 8.55 3.66 2.70 1.80

× × × ×

(3)

ka = 4πR eμD kBT /(1 + τA /τD)e

(4)

However, for most aromatic compounds, the attachment rate constants, ka, in 2,2,4-TMP are at or lower than this 1014 estimate.2 In TMS with μD = 100 cm2/Vs,2 most rates fall further below the prediction of eq 3. The observation that rates are well below the diffusion limit of eq 3 in high mobility liquids has been attributed to the fact that the residence time, τD = Re2/ 2D, of an electron within a reaction radius is short compared to the attachment time τA in contact.26 Thus, for high mobility liquids, rate constants tend to level off at a value below the diffusion limit, defined by eq 3 with Re = 0.72 nm.26,27 In TMS where μD = 100 cm2/Vs, one finds τD = Re2/2D ∼ 1 fs; similarly, τD ∼ 15 fs in 2,2,4-TMP with ∼15 times lower drift mobility. Thus, the picture26,27 of eq 4 estimates that the rate of electron transfer in contact >1015 s−1 is needed to obtain the diffusion controlled limit. Fit to Electron Transfer Theory. Reactions of electrons in nonpolar fluids have been studied for a number of years. Although no one unifying theory has emerged to explain all the results, various concepts have emerged. In some cases, the reactions are diffusion controlled; this applies usually for liquids like cyclohexane in which the electron mobility, 0.24 cm2/Vs,2 is only ∼50 times larger than that of diffusing molecules. In many cases, the reaction may be characterized by activation energy. That is not the case for electron attachment to BQ

Table 4. Rates and Free Energies vs Pressure for Mixtures at 20 °C TMS %

kD = 4πR eμD kBT /e

1011 1012 1013 1013

than that in TMS. Thus, for neat TMP, the energetics are favorable and the rate is high. As the percentage of TMS in the mixture increases, the free energy increases and the rate of reaction decreases. The data obtained for electron attachment to Cl2Q in TMS, as shown in Figure 1, were treated similarly. The reduction potential of Cl2Q in THF is 0.335 eV higher than that of benzoquinone.22 Also, the absorption and excitation spectra suggest that the transition energy to the π*−π* state is 2.5 eV. These two factors make the excited anion state more accessible. Electron attachment to F4Q is even more exothermic. The redox potential of F4Q is 0.5 eV higher than that of BQ (see 2168



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This analysis thus finds that electron attachment to BQ overwhelmingly forms the upper π*−π* excited state, consistent with previous results in THF.4 We attribute the absence of ground state formation to suppression of rate by a Marcus inverted effect by a factor of at least 103, due to a nuclear overlap (Franck−Condon) effect. Calculations of eqs 4 and 5 will illustrate this in Figure 8. In the case of the n−π*

which has a negative temperature coefficient in TMS.1 It was suggested early on by Henglein26,28 that the concepts of electron transfer in solution be applied to solvated electron attachment reactions. Here we follow this path applying theories of electron transfer29−34 cast in forms we discussed earlier.12 The results obtained here for TMS as solvent were fit using an expression for the rate of electron transfer given in eq 5,12 which depends on the attachment free energy, ΔG°, and the reorganization energies, λs and λv. Equation 5 is a simplified form with only one high frequency molecular vibration at frequency ω. kET =

2π |Hab(r )|2 FCWD ℏ ∞

FCWD = (4πλskBT )−1/2

(5)

⎛

∑ ⎜⎝e−S S

w=0

w⎞

⎟ w! ⎠

exp{−[(λs + ΔG° + wℏω)2 /4λskBT ]}

S = λ v /hω Figure 8. Calculated rate constants (eqs 4 and 5) for electron attachment to BQ by a hypothetical electron whose energy can vary over a wide range. The rates are plotted vs ΔG° to form BQ−• ground states. Mobility and electron transfer parameters are those for TMS in Figure 7. The electronic coupling into the n−π* excited state was assumed to be small, decreasing the rate by 1000, the minimum decrease needed to be consistent with observed rates in Figure 7. The arrow indicates that the actual rates to n−π* may be lower.

Equation 5 gives the ET rate at one distance, taken here as the “contact” distance, Re = 0.72 nm, to give kET. Here we set τA in eq 4 to kET−1 to fit eqs 4 and 5 to the observed attachment rate constants. The contact distance may not be well understood or defined for high mobility electrons. We propose that, while the reaction occurs over a range of distances, the average ⟨ReHab2⟩ is pertinent. The fit to rates of attachment to BQ and F4Q in TMS is shown in Figure 7 above. The parameters (see legend to Figure 7) all have reasonable values, though the reorganization energies are somewhat smaller than typically found for electron transfer between molecules. The reorganization energy for high-frequency molecular vibrations, λv = 0.24 eV, compares to λv = 0.45 eV found for intramolecular35 or λv = 0.4 eV for intermolecular12 ET from biphenyl anion to BQ and other acceptors. The larger λv in those previous studies is plausibly due to reorganization of biphenyl. It seems reasonable that little reorganization energy might be associated with the electron in TMS and that the total solvent reorganization energy would be small in this nonpolar liquid. In Figure 7, we see that electron transfer theory provides a good description of the dependence of rate constants on ΔG° for electron attachment to BQ and F4Q. An important issue is which electronic state is formed by electron attachment. Analysis given below will conclude that observable attachment rates to BQ and F4Q occur only into the second π* orbital. ΔG° was therefore calculated for electron attachment to form the corresponding π*−π* excited states, BQ−• ** and F4 Q−• **. Consistent with previous results,4,20 the n−π* excited states, BQ−• * and F4 Q−• *, appear to play no role in the kinetics. For BQ−•, the n−π* excited state lies 0.5 eV below the π*−π* state, so electron attachment to form the n−π* state would be more exoergic by 0.5 eV. At p = 1 bar, where electron attachment to form the π*−π* excited state is endoergic by 0.17 eV, the observed rate constant is almost three decades below the maximum. Attachment to form the n−π* state would have been exoergic by 0.33 eV. With reorganization energies similar to those in Figure 7, the rates to form the n−π* state are predicted to be near the maximum at 1 bar, but the observed rates are much slower, and can be fully accounted for by formation of only the higher, π*−π* excited state.

state, Franck−Condon factors for formation should be nearly optimal, so the absence of a contribution indicates slowing of rates by a factor of >103 due to a small electronic coupling, Hab. As described by Zamadar,20 this small Hab may be understood in terms of the two-electron rearrangement in the formation of the n−π* excited state. Zamadar found several reactions that were slowed by factors >10 due to the need for a coupled transition of a second electron. The present experiments find a factor of 103 or larger. Figure 8 illustrates the role of the ground state and n−π* and π*−π* excited states for a hypothetical electron whose energy can be varied not over 0.3 eV but over ∼4 eV. At low energies, only ground states are formed. At higher electron energies, ΔG° is sufficient to form the n−π* and π*−π* excited states. In Figure 8, we can see that the parameters describing the data in Figure 7 predict a negligible contribution to the rate from ground formation at the energies of actual electrons in TMS. The figure predicts that a high mobility electron with an energy adjusted to give ΔG° = −0.25 eV the attachment rate to form BQ−• ground states would be nearly 1014 M−1 s−1 but for ΔG° = −1.9 eV the rate will have fallen by six decades to 108 M−1 s−1. This would require our hypothetical electron to have a ground state energy a few hundred meV below that in TMS; such a high mobility electron is not presently known. In the present experiments, high electron mobilities reduced or eliminated the effects of diffusion control to reveal the dependence of rates on free energy in Figure 7. Thus, within the description utilized here, what would be the effect of lower mobility? Calculated rate constants for lower electron mobilities are shown in Figure 7 as dashed lines. These curves use eqs 4 and 5 with the same parameters that fit the data but with decreasing electron mobilities. These calculated curves display weak sensitivity of the rates to mobility, μ, when μ is 2169



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high, but for μ ≪ 1, the rates become diffusion controlled: at these low μ’s, the rates decrease linearly with decreasing μ and lose their sensitivity to ΔG° over most of the range, forming wide, flat plateaus in Figure 7. The poor reactivity to create the n−π* excited state seen here was reported earlier for reaction of solvated electrons in tetrahydrofuran (THF) with substituted benzoquinones.20 The rate of electron attachment in THF is slowest for duraquinone and fastest for 2,5-dichlorobenzoquinone. The rate increases with the driving force of the reaction similar to the results found in this study. In that work, it was also concluded that solvated electrons in THF react with substituted benzoquinones to form the upper excited state BQ−• **. Figure 7 also shows rate constants for electron attachment to BQ in 2,2,4-trimethylpentane (TMP). These reactions are more exoergic because ΔGs is higher in TMP than in TMS by 0.32 eV.5 The rate constants are (4−5) × 1013 M−1 s−1 at all pressures, and seem well-described by the fit curve for BQ and F4Q in TMS, although the electron mobility is smaller by a factor of 15 in TMP. Despite this large difference in mobility, a curve from eqs 4 and 5 based on the TMP mobility falls below the TMP data and the TMS fit curve by less than a factor of 2 due to suppression of the effect of mobility of eq 4. The predictions of eqs 4 and 5 can match the observed rates in TMP if the electronic coupling, Hab, in TMP is increased by ∼30% compared to Hab = 348 cm−1 that fit the data in TMS. Little is known of the quantum description of electrons in these two liquids, but it seems conceivable that such an increase might arise from changes in the properties of the electron in TMP. For positive values of ΔG°, the fact that the electron attachment to BQ in TMS is uphill might suggest the rate constants should increase with temperature, but the opposite is observed. This can be understood as a combined effect of the energy level of the electron, which increases as the temperature decreases, and the polarization energy, which decreases as the temperature decreases. Both make the reaction more exoergic at low T, causing the rate to increase (see Figure 2) despite the decrease in temperature. We have no quantitative description for the more complex behavior of rates of electron attachment to Cl2Q shown in Figure 7. We can speculate that these rates reflect attachment to form two different excited states of Cl2Q−•. In this explanation, the weakly absorbing transition at ∼525 nm in Figure 5 is not a transition to the π*−π* state but instead perhaps to an optically forbidden π−π* state, as suggested by TD-DFT and MP2 calculations. Attachment to such a state may be slow as it is to the n−π* state, because the calculations predict it requires a similar rearrangement of two electrons to populate, as seen in Figure 6. If electron attachment to form this state reaches a maximum rate constant of only ∼2 × 1012 M−1 s−1 due to poor electronic coupling, the slow rates would be explained. The sharper rise at ∼485 nm in Figure 5 could actually be the transition to the π*−π* state, which gives fast electron attachment. If correct, the free energies to the π*−π* state of Cl2Q that can be formed rapidly would be ∼0.2 eV more endoergic than were used to make Figure 7; correcting for this would shift the points for Cl2Q in Figure 7 to less negative ΔG°, to lie nearly on top of those for BQ. Broad View of Electron Attachment in Nonpolar Liquids. Holroyd summarized2 the broad range of rate constants for electron attachment in nonpolar liquids, for which no clear systematic explanation has emerged. In

cyclohexane (μ = 0.24 cm2/Vs), many attachment reactions are diffusion controlled, following eq 3. In TMP (μ = 6.7 cm2/ Vs) and especially in TMS (μ = 100 cm2/Vs), the rates are scattered, often falling below the diffusion limit of eq 3. The success seen in Figure 7 in describing electron attachment as a function of free energy, using electron transfer theory (eq 5) in combination with Warman’s assumption (eq 4), leads to the following question: Can this approach yield insight into sometimes wildly varying rate constants? In the description of eq 4, the escape time, τD, should be almost independent of solute. It is also plausible that many solutes will behave like the quinones in Figure 7, for which the rates vary little from ΔG° = 0−0.4 eV, so the reorganization paramaters may have little effect on rates over a substantial range. We suspect that this description will be appropriate for many solutes, leaving the electronic coupling, Hab, as the principle variable that might cause widely varying rate constants. In TMS where the diffusion controlled limit with Re = 0.72 nm is 1.4 × 1015 M−1 s−1, some of the fastest electron attachment reactions may be dissociative. One example, CH3I (ka = 1.6 × 1014),36 is almost certainly dissociative. Fast dissociation could play a role in achieving fast, nearly diffusion controlled rates. By the same reasoning, however, one might expect that e− attachment to BQ would be more rapid, as the initially formed π*−π* state is expected to be very short-lived, possibly decaying to the n−π* state at similar rates to dissociation in molecules like CH3I. On the other hand, the lifetime of the initially formed state may not dominate the observed kinetics in either case, if the attachment and subsequent excited state decay or dissociation reactions are not concerted; capture must occur as a first step and may be dominated by the value of Hab as suggested above. If so, a large electronic coupling may be an essential ingredient needed for obtaining superfast near diffusion controlled attachment rates.

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CONCLUSIONS Pressure tuning was used to continuously adjust free energy changes for electron attachment to BQ over a 0.3 eV range. Use of different quinones extended this range to almost 1 eV. The dependence on free energy is derived from that used for electron transfer reactions initially suggested by Marcus, showing both increases in attachment rate with driving force as well as decreases at larger driving force. This inverted region behavior decreases the rate constants by a factor less than 10, but it is apparent that an inverted effect decreases rates to form the ground state by a factor >1000. The data also support the idea that upon changing the solvent from TMS to TMP the rate constants are decided by the free energy change with little effect from the factor of 15 change in mobility of the electron, supporting the use of Warman’s assumption used in eq 4. The energy dependence of the rate constant is shown here to be accounted for by assuming attachment occurs to an upper excited π*−π* state, taking into account the shifts in V0 and polarization that occur as the pressure changes. The equilibrium explanation for the temperature dependence of the rate of attachment to BQ, which was posited in an earlier paper2 and mentioned in the Introduction, can now be ruled out. That explanation assumed fast attachment to form the n−π* excited state as well as a fast detachment from this state. As shown, attachment forms the π*−π* instead and electron transfer either to or from the n−π* excited state is slower than required for this mechanism. 2170



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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Jack Preses for help with the experimental studies. Also, we gratefully acknowledge the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences, of the U.S. Department of Energy for support through Grant No. DE-AC02-98-CH10886 and for use of the LEAF Facility of the BNL Accelerator Center for Energy Research.

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