J. Phys. Chem. 1994, 98, 9693-9696
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Electron Transfer Rates with Vibrational State Resolution Kenneth G. Spears,' Xiaoning Wen, and Steven M. Arrivo Department of Chemistry, Northwestern University, Evanston, Illinois 60208-3113 Received: June 28, 1994@
Charge transfer excitation at 600 nm of the ion pair [Co(Cp)~+lCo(C0)4-]prepares a neutral pair that can undergo spontaneous electron transfer. Electron transfer rates were measured by picosecond transient IR absorption for quantum numbers of 0 and 1 in the C O stretching mode of the Co(CO)4 species. The rate of electron transfer was 2 times faster with one quantum of energy in the C O stretch mode. The electron transfer returns the ion pair species, and we measured transient IR for levels having 2, 3, and 4 quanta in the ion pair. The rise time of these levels is consistent with the measured rates of leaving the neutral pair. A model calculation was done that shows approximate agreement with the observed ratio of electron transfer rates. This is the first observation of electron transfer rates with vibrational resolution.
Introduction Electron transfer is a widely studied and important phenomenon with an extensive The measurement of electron transfer (ET) rates as a function of vibrational state has been a long sought goal for testing the vibrational reorganization component of electron transfer. Prior insight into vibrational effects has been indirect, initially through correlations of rate versus exothermicity for a variety of corn pound^^^^ and more recently through Raman spectroscopic identification of important vibrational Identification of vibrational energy following ET has been demonstrated with transient IR absorption.* A direct electron transfer rate measurement for two vibrational states and subsequent identification of the final vibrational quantum numbers following electron transfer are demonstrated in this work for the first time. Preliminary measurements were reported in a conference pr~ceeding.~ Here we have used a different solvent and better time resolution to provide mechanistic confiiation by quantitative analysis of the product vibrational state rise times and model predictions for the ratio of ET rates with quantum numbers of 0, 1, and 2. The requirements for performing such measurements include a vibrational probe such as our ultrafast infrared transient absorption apparatus. The molecules must have fast ET compared with intramolecular vibrational redistribution (IVR) and vibrational relaxation (VR) for one or more molecular vibrations. We have used a tight ion pair complex with a well-defined geometry for these solution studies. The singly charged cation is a cobalt metal complex, cobaltocenium, that is a sandwich compound made from cyclopentadiene (Cp) with the formula Co(Cp)2+. The singly charged negative anion is a carbonyl metalate, Co(CO)d-, which is tetrahedral in free solution. The structure and photophysics for this carbonylmetalate has been previously studied by Bockman and Kochi,lo where they demonstrated that tight ion pairs [Co(Cp)2+lCo(CO)4-] can form in low and medium dielectric constant solvents. For this molecule, the two cobalt atoms interact sufficiently to form a new charge transfer band in the visible. While these ions interact relatively strongly, leading to a broad charge transfer (CT) absorption centered near 520 nm in dichloromethane, the oscillator strength is weak with a peak molar absorption of about @
Abstract published in Advance ACS Abstracts, September 15, 1994.
Coordinate Figure 1. Schematic of neutral pair [A D] and ion pair [A+D-] energy as a function of one vibrational coordinate. The high-frequency CO stretching mode is shown as a displaced oscillator, and optical excitation to near the zero level is shown by an arrow.
200 M-' cm-'. This CT interaction causes a small distortion of the carbonylmetalate anion to a CzV symmetry that shows the normal strong IR absorption of Co(C0)4- at 1888 cm-' with two shoulders at about 1908 and 1870 cm-' and a very weak absorption near 2008 cm-'. The experiments involve direct optical excitation of the CT absorption with a picosecond pulse at 600 nm, which converts the ion pair [Co(Cp)2+1Co(CO)4-] denoted as [A+D-] to the neutral radical pair [A D]. The neutral pair can then undergo electron transfer to regain the ion pair. This spontaneous electron transfer step is the key event that our experiments seek to understand. The initial optical excitation populates vibrational states of the neutral pair [A D] according to the Franck-Condon factors for the ion pair to neutral pair CT transition. These vibrational states have IVR and VR relaxation processes competing with ET processes; however, from prior workl1J2 we expected slow IVR compared with ET for CO stretching modes. Figure 1 shows a schematic of the reaction coordinate for ET, where the optical CT excitation provides excess energy in the upper neutral pair state[A D] with specific quantum numbers in the CO stretching mode and other low-frequency modes. The energy in the CO stretching mode remains for 50-100 ps, while moderate energy in the low-frequency modes is probably lost to solvent modes in about 1 ps (measurements in progress). The rate of ET from specific CO stretching modes is monitored by
0022-3654/94/2098-9693$04.50lO 0 1994 American Chemical Society
Letters
9694 J. Phys. Chem., Vol. 98, No. 39, 1994 Neutral Pair in Dichioroethane
transient IR absorption, where the anharmonicity is sufficient to resolve several levels. The exothermic ET populates CO stretch vibrations of [A+D-] according to the Franck-Condon factors for ET, and transient IR absorption is used to measure these populations. These ion pair vibrational states then decay by IVR and VR processes.
On3
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6 Experiments
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P)
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The transient absorption apparatus is similar to that described in prior publications12and is based on a 10 Hz active-passive mode-locked Nd:YAG laser and a tunable dye laser. The pulse duration of the dye laser pump pulse in the 600 nm region has been reduced to about 2 ps. The IR in the 2000 cm-' region has been generated by lithium iodate crystal mixing with 1064 nm and the dye pulse to generate a difference frequency in the near-infrared, followed by 1064 nm mixing with the nearinfrared in silver thiogallate to generate the infrared wavelength~.'~ The sample cell uses sapphire windows, and the sample is flowed through the cell with a gas-tight, dual-syringe pump system that is filled in a nitrogen atmosphere glovebox. The response function due to the pulse overlap of the visible pump and IR probe is obtained by using InP plates mounted to be at the center of the cell volume. The cell path was 1.0 mm in length. The optical arrangement used about 0.5 d for pumping the sample in a focal diameter of 0.4 mm, and 10 nT of IR was focused to about l/2 of this diameter. The laser system operated at 10 Hz, and each data point was an average of 64 shots per time delay point. The time delay was varied at 0.5 ps increments for the first 50 ps, and for longer scans another 100 points at 20 ps increments were usually added to the file. The IR detectors were of cooled PbSe, and a reference channel was used to reduce noise from shot fluctuations (about 10-15%) by forming a ratio of transmitted to reference signal. The sample has been prepared by literature methods1° using an inert atmosphere Schlenk line and glovebox methods, The sample must be handled in an inert atmosphere due to oxidation. The solvent is 12-dichloroethane labeled as 99+% pure and water-free (Aldrich); it was dried with 4 A sieves. The vibrational spectroscopy of the anion has been extensively studied as free ions14 and in ion pairs.15 Matrix isolation studies16 have shown that the Co(C0)4 radical has a symmetry with a strong band at 2011.5 cm-I and a weaker (l/3) band at 2029 cm-'. The frequency shift from the argon matrix to free solution has not been measured for the radical. The vibrational anharmonicity, which gives a red shift for consecutive infrared absorptions, is not well-known for these species. The assignments of Edge11 and Lyford14 suggest that the anion would have about 17 cm-l between the v = 0 v = 1 and the v = 1 v = 2 transitions. We can compare with other carbonyl data where there is a shift of 15-16 cm-' from our observation12 of vibrationally excited Cr(C0)sL species having various weakly bonded ligands, L, and CO frequencies near 1960 cm-'. We estimated the frequency of the Co(C0)4 radical to have a slightly greater anharmonic shift than the anion, and we assume about 20 cm-' for the transition shift in the neutral radical with about 16-18 cm-I for the transition shift in the anion. Preliminary spectral scans (not shown) have been made to more precisely identify the anharmonic shifts for the Co(CO)4 radical, and weak maxima support this assignment. The experimental requirement for well-separated frequencies is satisfied for this molecular system, and our experimental resolution of about 5-7 cm-' is sufficient to identify ET rates as a function of vibrational state.
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v=l -> v=2 at 1980 cm''
c
f.$
B c
0.1
(P
0.0
1 300 0
100 200 Time (ps)
Figure 2. Data for neutral pair [Co(Cp)zlCo(CO),] transient infrared absorption at 2000 and 1980 cm-' corresponding to the indicated transitions. For clarity the noise in the 1980 cm-' case is connected by lines. The absorbance is relative.
Results Figure 2 shows the transient IR absorptions for the CO(c0)4 radical created by CT absorption at 600 nm in 1,2-dichloroethane solvent. The absorptions are at 2000 and 1980 cm-I for vibrational absorptions v = 0 v = 1 and v = 1 v = 2, respectively. We use the notation that v is the quantum number of vibration. The v = 1 absorption at 1980 cm-l decays to the base line in 8 f 1 ps while the v = 0 level has a decay of 17 f 1 ps with a long component of about 400 ps. These data were fit to a three-level model where the initial populations were estimated by Franck-Condon calculations and the instrument response function was used to fit both transients simultaneously. Level zero ( v = 0) had decay rates due to ET and a source term by IVR from level one. Level one ( v = 1) had decay rates by ET and IVR, and level two (v = 2) was assumed to have small population. A long decay was added to the level zero decay kinetics to represent a diffusional contribution in level zero (see below). The fast decay times of 8 and 17 ps are nearly identical to those previously measured by us for dichloromethane? but in 1,2-dichloroethane the long component decay of about 400 ps is of smaller amplitude and faster. Consistent data fitting is not possible if an IVR decay rate is used for level 1 that is on the order of 8 ps or less, and the fitting supports an inverse rate much longer than this (also, see data for IVR of the ion pair). We assign these decays as almost pure electron transfer components, where the ET rate of a CO stretching vibration with 1 quantum of population is about 2 times faster than with zero population. We tested the conjecture that the long component is of diffusional character, where the neutral pair has some probability of both rotational correlation averaging and translational separation of the metal centers in the neutral pair. The long decay is a complex result of a slight distance separation (probably not solvent separation) and return to closer distances where the ET is more probable. The 0.78 CPviscosity of 1,Zdichloroethane shows 1.7 times less amplitude for this component than dichloromethane at a viscosity of 0.41. In addition, we studied a 30% mixture of dichloromethane and light mineral oil having a dielectric constant of 7.0 and an estimated viscosity of > 1.5
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J. Phys. Chem., Vol. 98, No. 39, 1994 9695 electronic state, a, has one specific vibration that is optically excited with quantum number v. The final electronic state, b, has v' quanta in the optical mode and a number of other acceptor modes, j . These other acceptor modes have a thermal distribution of populations so mj is the change in acceptor quantum number. The acceptor modes are assumed to have no frequency change, just a geometry change given by S', while the optically excited mode uses frequency and geometry changes to compute (vlv') and explicitly puts these frequencies into the Gaussian expression. The parameters x, and zj are used in eq 1 along with the dimensionless displacement parameter SJ and the modified Bessel function I&).
Co(Cp),* Co(C0)i in DCE
I
Om4
z, = Sj csch(x,) 1 , 0
, , ,
, , , ,
;, , ;
100 lime (picoseconds)
, , ,
,I 200
Figure 3. Data for ion pair [Co(Cp)2+lCo(CO)4-]transient infrared absorption at 1854, 1837, and 1815 cm-' corresponding to the indicated transitions. For clarity the data points are not shown for 1837 cm-' and the points for 1815 cm-' are connected by a line. The base lines have been adjusted to provide a common zero reference point.
CP where the percent of long component was reduced to 22% and the long decay reduced to 230 ps. For this case the ratio of ET rates was very similar to the other low dielectric solvents, and the increased viscosity changes the long component in the expected direction. The ET from the neutral pair results in vibrationally excited states of the ion pair. We have directly measured these transitions by infrared absorption, and in Figure 3 we show the highest populated levels for the v' = 4 v' = 5 , v' = 3 v' = 4, and v' = 2 v' = 3 transitions. The v' = 0 level of the ion pair recovers in a time of about 90 ps (not shown), and is a complex result of IVR within the multiple levels, but is dominated by IVR from v' = 1. These results directly confirm that fast ET has occurred from the neutral pair to reform the ion pair [Co(Cp)2+(Co(CO)4-]. In this work we have carefully analyzed the rise time of these transitions to see whether a match with decay times of the neutral pair is approximately correct. As we discuss below, any given level has a rise time composed of ET from several neutral pair levels. With better time resolution or slower rates a more complete, multilevel model with complex rise time might be done. However, we have found that the rise time of v' = 4 absorption is about 2.4-3.6 ps, the rise time of v' = 3 is about 4.8-6 ps, and v' = 2 is about 7.29.6 ps.
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Discussion The expected sensitivity of ET to vibrational level depends on the details of vibrational contributions to an ET rate. The ratios of vibrational rates are excellent tests of molecular parameters for exothermic electron transfer. This subject will be discussed more fully elsewhere, l7 but comparisons are made below with our data. Several groups have made a semiclassical analysis of ET in terms of the Fermi golden rule separation of electronic and vibrational terms. In eq 1 we have included the optically excited mode as well as the possibility of several acceptor modes in a conventional semiclassical calculation of acceptor contributions.18-22 Applications of this model and other quantum models will be discussed more fully elsewhere." The initial
+m
where A, is the solvent reorganization energy, AE is the effective energy gap (negative sign), andfj is the force constant for a normal mode j with frequency vj = wj12n and a normal coordinate change AQj. We have computed the ET rate using a model similar to eq 1 with the following parameters. The electrochemical datal0 show a computed free energy of - 10 300 cm-I in acetonitrile, which we assume is similar in 1,2-dichloroethane. The work of ion pair formation changes this energy gap to about - 11 900 cm-' in the 10.3 dielectric constant environment of 1,2dichloroethane. The solvent reorganization energy is calculated to be about 5500 cm-' for ion radii of 3.5 and 4.0 and a separation of 6.9 A. The vibrational geometry changes in the CO stretching mode will be obtained by Raman analysis in the future, but for now we have made rough estimates. The cobaltocene to cobaltocenium transformation has been previously studied,23and small amounts (490 cm-') of vibrational reorganizational energy is thought to be present in this molecule. We note that the nearly tetrahedral structure of Co(CO)4- is distorted to a C3" symmetry structure of unknown geometry so that the ET has both geometry, frequency, and coordinate transformations. We have assumed a geometry change of 0.035 A with a force constant of 16.9 mdyd8, to compute a reduced geometry change of 0.2605 for the 2000 cm-' frequency of the neutral pair. With the experimental frequency reduction to 1888 cm-' we can use Franck-Condon factors having both geometry and frequency changes in this mode. Other acceptor modes were 430, 525, and 555 cm-' having dimensionless geometry changes of 1.4634, 0.4315, and 0.1633. These parameters can be summarized using the product of frequency and dimensionless geometry change to give 1467 cm-' of total vibrational reorganization energy for these frequencies. Another calculation was done where the change in dimension of the 2000 cm-I mode was 0.055 8,(total of 2233 cm-' of vibrational reorganization).
A
9696 J. Phys. Chem., Vol. 98, No. 39, 1994 The electronic coupling matrix element cancels in a rate ratio, but the value of 100 cm-’ in the H d matrix element is reasonable for this case, and based on bandwidth estimates this element could easily be 5-6 times larger according to the Hush model.24 The computed ET rate constants for 0.035 8, geometry change are 0.105,0.222, and 0.355 in ps-’ for quantum numbers of 0, 1, and 2. For 0.055 8, change the rates are 0.333, 0.640, and 0.873 ps-’. The ratios of rates, where subscripts denote quantum numbers, are predicted for 0.035 8, as kllko = 2.11 and for 0.055 8, as k l l b = 1.92. Both sets of geometry assumptions give kl/ko predictions similar to the experimental value of 2.1 f 0.3. Clearly, more accurate experimental values would be useful, but the ratio k2/kl would be even more useful since the predicted value is 1.92 or 1.36, depending on geometry. Preliminary data for v = 2 levels obtained in our earlier work show a lifetime of about 3 ps, which would give k2/kl = 2.7; however, that data was for a longer path cell and also may have had a contribution from optical pumping of vibrationally excited ion pairs. Other experiments are in progress to examine this key experimental quantity. The model calculation shows that the rise time of the v’ = 2 v’ = 3 absorption in the ion pair is dominated by ET from the v = 1 level of the neutral pair (3.5 times more contribution from v = 1 than v = 0). This rise time of 7-10 ps agrees with the experimental ET time about 8 ps. The rise time of level v’ =3 v’ = 4 absorption in the ion pair is dominated by ET from level v = 2 (2.2 times as much as v = l), while level v’ = 4 v’ = 5 has most contribution from levels v = 2 and v = 3. The shorter rise times of these levels agree with the observed decay estimates, where complex rise time fitting is simplified only when one component dominates. The computed absolute rate is reasonable but would be 40 times faster if the Hush bandwidth estimate is correct for this system. Rates of such large value would not allow any population of neutral pairs to observed with our time resolution. While the experimental data seem to be internally consistent with the proposed interpretive framework, more complete ET modeling that includes VR and IVR is being done to model these measurements. Future experiments with better time resolution and in frozen solvent will help remove any ambiguity based on geometry changes in the neutral pair. In addition, calibration of the oscillator strength of the neutral pair and other experiments will help confirm that the signals we observe are due to the dominant ion pair and not some secondary structural species. Additional measurements are needed to understand if vibrational interchange between the totally symmetric CO stretching mode and IR-active mode is occurring in this system. Such effects have been seen in carbonyl^,^^,^^ but in our case the vibrational coordinate change between the two electronic states mixes these modes. For large quantum numbers such as seen for the CO modes in the ion pair, we expect that CO stretching may be better described in a local mode basis set, as has been analyzed for Ni(C0)4 and Co(C0)3NO by Milk2’ Despite the need for supporting experiments, the observation of two different rates of electron transfer for two different vibrational states is definitive and is the first such measurement for electron transfer.
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Conclusion We have studied the vibrational state dependence of electron transfer between two neutral species to form an ion pair. The initial neutral pair was formed by charge transfer excitation at 600 nm of the ion pair [Co(Cp)2+1Co(CO)4-]. Electron transfer rates were measured by picosecond transient IR absorption for quantum numbers of 0 and 1 in the neutral Co(C0)4 species. The rate of electron transfer was 2 t i e s faster with one quantum of energy in the CO stretch mode. The electron transfer returns the initial ion pair species, and we measured transient IR for absorptions from levels having 2, 3, and 4 quanta. The rise time of these levels is consistent with the measured rates of electron transfer from the neutral pair. A model calculation was done that shows approximate agreement with the observed ratio of electron transfer model, and such work is underway. This is the first observation of electron transfer rates with vibrational resolution, and we expect that further measurements can provide a precise test of how molecular geometry controls some electron transfer rates.
Acknowledgment. We thank the U S . Department of Energy, Office of Energy Research, Division of Chemical Sciences (Contract FG02-91ER14228), for support of this research. References and Notes (1) (2) (3) (4)
Marcus, R.; Sutin, N. Biochim. Biophys. Acta 1985, 811, 265. Newton, M. Chem. Rev. 1991, 91, 767. Newton, M.; Sutin, N. Annu. Rev. Phys. Chem. 1984, 35, 437. Closs, G. L.; Miller, J. R. Science 1988, 240, 440. ( 5 ) Wasielewski, M. R.; Niemczyk, M. P.; Svec, W. A,; Pewitt, E. B. J . Am. Chem. SOC.1985, 107, 1080. (6) Doom, S. K.; Hupp, J. T. J. Am. Chem. SOC.1989,111,4704. See also: J. Am. Chem. SOC.1991, 113. 1060. (7) Markel, F.; Ferris, N. S.; Gould, I. R.; Myers, A. B. J. Am. Chem. SOC.1992, 114, 6208. (8) Doom, S. K.; Stoutland, P. 0.;Dyer, R. B.; Woodruff, W. H. J. Am. Chem. SOC.1992, 114, 3133. (9) Spears, K. G.; Arrivo, S. M.; Wen, X. SPIE Proc., in press. (10) Bockman, T. M.; Kochi, J. K. J. Chem. SOC.1989, 111, 4669. (11) Heilweil, E. J.; Cavanagh, R. R.; Stephenson, J. C. Chem. Phys. Lett. 1987, 134, 181. (12) Sprague, J. R.; Arrivo, S. M.; Spears, K. G. J. Phys. Chem. 1991, 95, 10528 and references therein. (13) Spears, K. G.; Zhu, X.; Yang, X.; Wang, L. Opt. Commun. 1988, 66, 167. (14) Edgell, W. F.; Lyford N, J. J. Chem. Phys. IWO,52, 4329. (15) Edgell, W. F.; Hegde, S.; Barbetta, A. J. Am. Chem. SOC.1978, 100, 1406. (16) Crichton, 0.;Poliakoff, M.; Rest, A. J.; Tumer, J. J. J. Chem. SOC., Dalton Trans. 1973, 1321. (17) Spears, K. G. To be published in J. Phys. Chem. (18) Kestner, N. R.; Logan, J.; Jortner, J. J. Chem. Phys. 1974, 78,2148. (19) Ulstrup, J.; Jortner, J. J. Chem. Phys. 1975, 63, 4358. (20) Van Duyne, R. P.; Fischer, S. F. Chem. Phys. 1974, 5, 183. (21) Siders, P.; Marcus, R. A. J. Am. Chem. SOC.1981, 103, 741, 748. (22) Brunschwig, B. S.; Sutin, N. Comments Inorg. Chem. 1987,6,209. (23) McManis, G. E.; Nielson, R. M.; Gochev, A,; Weaver, M. J. J. Am. Chem. SOC.1989, I l l , 5533. (24) Hush, N. S. Prog. Inorg. Chem. 1967, 8, 391. (25) Tokmakof, A.; Sauter, B.; Kwok, A. S.; Fayer, M. D. Chem. Phys. Lerr., in press. (26) Grubbs, W. T.; Dougherty, T. P.; Heilweil, E. J. Chem. Phys. Leu., in press. (27) Mills, I. M. Mol. Phys. 1987, 61, 711.
