Article pubs.acs.org/JPCB

Ultrafast Electron Transfer Dynamics in a Series of Porphyrin/ Viologen Complexes: Involvement of Electronically Excited Radical Pair Products Jonas Petersson and Leif Hammarström* Department of Chemistry − Ångström Laboratory, Uppsala University, Box 523, SE75120 Uppsala, Sweden S Supporting Information *

ABSTRACT: Ultrafast electron transfer was studied for a series of metalloporphyrin/ bipyridinium complexes in aqueous solution, using laser excitation in the Soret or Q-bands of the porphyrin. Electron transfer occurred before electronic and vibrational relaxation of the initial excited state. This allowed for a thorough investigation of the dependence of electron transfer rate constants on the driving force and the nature of the product state. The driving force dependence showed that electron transfer from the S2 state occurred to an electronically excited radical pair state, and the present results provide the most direct evidence to date for the formation of such states in photoinduced electron transfer reactions. We also found that subsequent recombination of the radical pair produced vibrationally excited ground states; the excess energy of the radical pair generated from the initial state is not completely dissipated during the lifetime of the radical pair. The porphyrin/bipyridinium complexes where recombination lies deeper in the Marcus inverted region show less formation of unrelaxed ground states, contrary to what is expected from equilibrium electron transfer theories. Instead, the rate of the electron transfer, which competes with vibrational relaxation, was the main parameter controlling the relative yield of unrelaxed ground states within this series of complexes.

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excited. Several reasons for this were discussed;19 among them were (i) rate limitation by, e.g., solvent dynamics; (ii) coincidental compensatory variation of two factors, e.g., electronic coupling and driving force; (iii) coincidental similarity of the ET barrier where the S1 reaction would be in the Marcus normal region and the S2 reaction in the inverted region; or (iv) the involvement of excited charge transfer (radical pair) states as reaction products. The latter explanation was preferred, which was supported by the similarity of the intermediate spectra with reference spectra of the excited viologen radical. Nevertheless, while we could exclude i, further experiments were needed to determine if also ii and iii could contribute to the observed behavior. Another interesting observation was that the subsequent back electron transfer (kBET = (700 fs)−1) produced vibrationally excited ground states to an extent that depended on the initial excitation wavelength. That is, the excess energy of the S2 state survived two steps of electron transfer, and there was even a memory of the small 0.15 eV difference between the two vibrational levels of the porphyrin S1 state (v = 0 and v = 1). These observations provided indirect evidence for the

INTRODUCTION The dynamics of electron transfer in systems where electron transfer occurs to or from nonthermalized states is of great interest. Fundamentally, it expands theories for electron transfer that mostly have been based on assumptions of equilibrium reactants1−4 Formation of excited radical pair states have been proposed as an explanation for the absence of a clear Marcus inverted region behavior in bimolecular electron transfer,5−7 in contrast to its clear demonstration in covalently linked systems.8 Nonequilibrium electron transfer is also relevant as a means for reaction control by excitation wavelength and excitation wavelength dependent molecular switches.9−11 Porphyrins have been shown to be very useful in these studies, both because of the high light absorbing capability (high extinction coefficient) and also due to the relatively long-lived (ps) second excited state of some porphyrins, which enables different electron transfer reactions depending on the excitation wavelength.9−16 We have previously reported on the ultrafast electron transfer (ET) reactions for a 1:1 complex of zinc(II) tetrasulfonatophenylporphyrin (ZnTPPS4−) and methylviologen (MV2+) in aqueous solution.17−19 The porphyrin was excited in the Soret or Q-bands to either the S2, S1(v=1), or S1(v=0) state, and the subsequent ET to the viologen violated Kasha’s rule of photochemistry and occurred directly from each initially excited state, prior to excited state relaxation. We also noted that the rate constant of forward electron transfer (kFET ≈ (180 fs)−1) was nearly independent of the state that was initially © XXXX American Chemical Society

Special Issue: John R. Miller and Marshall D. Newton Festschrift Received: November 11, 2014 Revised: February 4, 2015

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wavelength was obtained (the higher absorbance is for excitations in the Soret band), giving concentrations of a few micromolar. Complexation Constants. The complexation constants of porphyrin/viologen complexes were determined from absorption spectra. A full expression for the complex equilibrium was used, as described in the Supporting Information. This has the advantage that the complexation constant can be determined even if complete complexation cannot be achieved. The resulting complexation constants are in the range of 1 × 103 to 1 × 105 M−1 as seen in Supporting Information Table S1. There is no clear dependence on the reduction potential, charge, or counterion of the viologens. In the transient absorption measurements the concentration of viologen was varied, ranging from a few micromolar to a few millimolar, depending on the complexation constant with the porphyrin.22 The aim is that all porphyrins should form a 1:1 (porphyrin/viologen) complex but the viologen concentration anyway has to be kept low enough to avoid a 1:2 complex formation. That implies that some of the samples will have a significant fraction of free porphyrin, but this can be separated in the time-resolved spectra due to the long lifetime of the S1 state. MgTPPS4− is unstable in pure H2O because of dissociation of the central Mg2+. The complexation constant was therefore not determined for the MgTPPS4− complexes. MgTPPS4− is stabilized in phosphate buffer and even further stabilized when forming a complex with a viologen which made ET studies possible. The 1:2 complexes could be avoided due to the characteristic absorbance that gives a shoulder at about 445 nm (see, e.g., Supporting Information Figure S5). Femtosecond Transient Absorption Spectroscopy. For a detailed description of the transient absorption setup, see Petersson et al.19 Briefly, the output from a Coherent Legend Ti:sapphire amplifier (1 kHz; λ = 800 nm; full width at half-maximum (fwhm), 100 fs) was split into a pump and a probe part. Desired pump wavelengths were obtained with an optical parametric amplifier (TOPAS, Light Conversion), and with neutral density filters the energy of each pulse was kept between 300 and 500 nJ. The white light continuum probe was obtained by focusing part of the 800 nm light on a moving CaF2 plate. Polarization of the pump was set at magic angle, 54.7°, relative to the probe. Instrumental response time depends on pump and probe wavelengths but is typically about 100 fs. Because the porphyrin triplet state has a millisecond lifetime, a flow cell was used to provide a fresh sample at each excitation. Data analyses are done in MATLAB (The Math Works, Inc.), a robust trust-region reflective Newton nonlinear-leastsquares method, used for the fits. Traces (ΔA vs t) are fitted to a sum of exponentials, ΔA(t) = ∑i cie−(t−t0)/τi, convolved with a Gaussian shaped response. Also included in the fits is an artifact signal that is due to cross-phase modulation during pump and probe overlap.23 All spectra are corrected for chirp in the white light probe; time zero is set at maximum pump−probe temporal overlap. The region around the pump wavelength is removed due to scatter of pump light.

involvement of electronically and/or vibrationally excited charge transfer states in the reactions. This work aims to further our understanding of these processes by studying a series of porphyrin/viologen complexes that differ in their redox potentials. An analysis of the free energy dependence of the forward and back ET (FET and BET) reactions may enable a distinction of the different preceding effects i−iv and provide evidence for the generation of excited radical pair states in the FET reaction.

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EXPERIMENTAL SECTION Samples. Schematic structures for the viologens are shown in Figure 1. Tetrasodium salts of zinc(II) meso-tetrasulfonato-

Figure 1. Schematic structure of the viologens and the porphyrin. Potentials are given vs NHE.

phenylporphyrin (Na4ZnTPPS, Porphyrin Products) and magnesium(II) meso-tetrasulfonatophenylporphyrin (Na4MgTPPS, Porphyrin Products), as well as methyl viologen dichloride ((MV)Cl2, Sigma-Aldrich) and benzyl viologen dichloride ((BV)Cl2, Sigma-Aldrich) were used without further purification. 1-Methylbipyridine chloride ((MB)Cl) was available from a previous study.20 1,1′-Bis(cyanomethyl)-4,4′bipyridinium dibromide ((MV)CNBr2) was synthesized according to literature.21 1,1′-Dimethyl-2,2′-bipyridine diiodide ((DM)I2) was obtained by heating 2,2′-bipyridine with methyl iodode in acetonitrile, and 1,1′,4,4′-tetramethyl-2,2′-bipyridine diiodide (4,4′-Me2-(DM)I2) was obtained by heating 4,4′dimethyl-2,2′-bipyridine with methyl iodide in ethanol, as described in more detail in the Supporting Information. The oxidation potential for MgTPPS4− is obtained from the 0.17 V difference between MgTPP and ZnTPP, subtracted from the ZnTPPS4− potential. With the oxidation potential of +0.87 V vs NHE for ZnTPPS4− it gives +0.70 V vs NHE for MgTPPS4−. All samples were dissolved in a 2 mM sodium phosphate buffer with H2O at pH = 7.0. The steady state absorption spectra were recorded on a Varian Cary 5000 UV−vis−near-IR spectrophotometer, and the ZnTPPS4− emission spectrum was recorded on a Horiba Fluorolog. In order to avoid selfabsorption in the emission measurement, a dilute (c = 1.4 × 10−7 M) ZnTPPS4− sample was used giving a maximum absorbance of 0.1.12 The ZnTPPS4− concentrations of the samples used in the transient absorption measurements were adjusted until an absorbance of 0.15−0.5 at the excitation

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RESULTS AND DISCUSSION The reaction dynamics following photoexcitation of ZnTPPS4−/MV2+ (complex 4 here) have been analyzed and described in detail in a previous publication.19 Here we present a study of a series of porphyrin/viologen complexes. The B

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The Journal of Physical Chemistry B Table 1. ET Time Constants for the Different Complexes and Excitations

ZnP and MgP denotes ZnTPPS4− and MgTPPS4−, respectively. bNo correction for the competing S2 → S1 IC pathway has been made; see the Supporting Information. cReduction potential from ref 24. dReduction potential from ref 20. eReduction potential from ref 25. fReduction potential from ref 21.

a

complexes are referred to with their numbers given in Table 1 (structures are seen in Figure 1). Ground State Absorbance and Free MTPPS4−. All porphyrin/viologen complexes show absorbances similar to that of ZnTPPS4−/MV2+. A typical ground state absorption spectrum is seen in Figure 2. The viologen itself has no

Figure 3. Transient absorption spectra of MgTPPS4− in H2O (2 mM sodium phosphate buffer) excited at 435 nm. Spectra at delay times 0.25 and 20 ps correspond to absorbance from the S2 and S1 states, respectively. Inset is a trace at probe wavelength 670 nm observing the onset of S1 → S0 stimulated emission, fitted with τ = 2.2 ± 0.4 ps.

previously reported ZnTPPS4−/MV2+ complex (see Figure 4, Figure 5, and Supporting Information Figure S11).18,19 Thus, FET occurs directly from the initially excited state (S2, S1(v=1), or S1(v=0)) to the radical ion pair state (D+/A−, possibly vibrationally and/or electronically excited). This is followed by back electron transfer (BET) to form the vibrationally unrelaxed ground state (S0v). While the transient spectra of the S1 and S2 M-TPPS4− states are similar, they show distinct differences that allow the ET processes to be followed. Stimulated emission from S1 and S2 show up around 670 and 450 nm, respectively, while the radical pair state has sharp absorption bands at 390 and 405 nm corresponding to reduced viologen and oxidized porphyrin. Vibrationally unrelaxed states will have a similar electronic absorption spectrum as its vibrationally relaxed state but shifted to slightly longer wavelengths due to the smaller energy gap to the higher electronic states.19 S0v is seen mainly as a sharp band to the red of the ground state Soret band. The ET time constants are summarized in Table 1. All ET reactions occur on a sub-

Figure 2. Ground state absorption spectrum of ZnTPPS4− (purple line) and the ZnTPPS4−/BV2+ complex 6 (yellow line). Included is also emission spectrum of ZnTPPS4− (dashed line).

absorbance at wavelengths > 370 nm, and the resulting absorption from the porphyrin/viologen complexes mainly resembles that of the free porphyrin, somewhat red-shifted due to the interaction with the viologen. The Soret band corresponds to the transition to the S2 state, and the Qbands corresponds to transitions to the different vibrational levels of the S1 state. The transient absorption spectrum of MgTPPS4− (Figure 3) is similar to that of ZnTPPS4− but with a slightly longer S2 lifetime; τS2 = 2.2 ± 0.4 ps compared to the τS2 = 1.3 ps lifetime of ZnTPPS4−. This is in agreement with what is observed for MgTPP and ZnTPP in various solvents.12 Transient Absorption Measurements of the Porphyrin/Viologen Complexes. The series of porphyrin/viologen complexes reported here show dynamics similar to that of the C

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Figure 4. Transient absorption spectra for complex 5 (a−c) and 1 (d−f). Top to bottom panel: Excitation is to the S2, S1(v=1), and S1(v=0) states. Arrows indicate the excitation wavelength. In 1 there is a substantial amount of uncomplexated porphyrin, as seen from the residual absorbance at 100 ps. Signs of the initially excited state can be seen from the stimulated emission at 670 nm for the S1 excitations and at 450 nm for the S2 excitations, resulting in a lower absorbance. This is most clearly seen for 1 due to the lower rate FET. The radical pair has absorbance at ca. 390 and 405 nm from the viologen and porphyrin, respectively. In complex 5 it is clear that the unrelaxed ground state has a higher intensity (see 440 nm) with higher excitation energy. This is also seen in complex 1 but with less intense signals that correlate with the higher lying radical pair state.

Driving Force Dependence of the ET Rates. The FET rates are analyzed with the classical expression for nonadiabatic electron transfer (eq 1).26,27 NA = kET

⎛ (ΔG° + λ)2 ⎞ exp⎜ − ⎟ 4λkBT ⎠ ⎝ ℏ 4πλkBT 2πHRP 2

(1)

Here, HAB is the electronic coupling, λ is the total reorganizational energy, and ΔG0 is the driving force. We assume that the variation in HRP and λ is small within the series of porphyrin/viologen complexes examined and that the main variation is that of the driving force ΔG0. The driving force for the FET reactions is to a first approximation calculated from the redox potentials and excited state (E00) energy by 2

0 0 ΔG° = e(Eox (D/D+) − Ered (A/A−)) − E00

Figure 5. ΔA vs t for different probe wavelengths of complex 5 excited to the S2 state (λexc = 438 nm); cf. Figure 4a. Wavelength 390 nm probes the rise and decay of the radical pair, 425 nm probes the ground state recovery, and 440 and 445 nm both probe the rise and decay of the S0v state. The S0v state grows in with the same rate as the BET. Time constants for FET and BET are 0.15 and 0.63 ps (see Table 1). The dynamics of the S0v state is multiexponential and probe wavelength dependent. At the red side of the S0v absorption band the signal grows in with the rate of BET while it at shorter probe wavelengths includes some extra rise time. The decay of the S0v state occurs with time constants as long as 5 ps.

(2)

Equation 2 neglects the effect of electrostatic interaction in the product and reactant state, but that effect should be relatively small and not affect the trends within the series of complexes. There are some differences in both charge and structure of the different viologens that might influence the electronic coupling. However, there is no clear correlation between the complexation constants and the charge or acceptor strength (E0), only that the viologens based on 2,2-bipyridine give somewhat lower values. Electrostatic interaction seems not to be of large importance since the monocationic MB+ binds equally well as the dicationic viologens. A caveat is that MB+ may coordinate axially to the Zn2+ ion even in water, which may give a different electronic coupling than for the other complexes. The results below suggest that this is not the

picosecond time scale, except for the slowest BET reactions (complexes 1−3). The vibrational relaxation of the unrelaxed ground state occurs on a 1−10 ps time scale.19 D

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The Journal of Physical Chemistry B case, as the complex with MB+ does not deviate from the general correlation within the series. From the shift of the Soret band and smaller shift of the Q-bands upon complexation we assume that the interaction instead has some charge transfer character. Free Energy Dependence of FET: Formation of Electronically Excited Radical Pair Products. The rates of FET vs driving force are shown in Figure 6 for the S2 and S1

Figure 7. S2 FET rates vs driving force, where ΔG° is shifted 0.89 eV to give th esame λ = 0.9 eV for both S2 and S1(v=0) FET reactions. The coupling then also gets lower; HRP = 183 cm−1.

could be localized on either the viologen or porphyrin, or delocalized over both. We have previously shown that differences in the transient spectra for the ZnTPPS•−/MV•+ radical pair for the different initial excitations suggest that at least part of the electronic excess energy is localized on the viologen radical.19 Inclusion of high-frequency acceptor modes in the fit of kFET vs − ΔG0 (see eq 3 later) has little effect in the normal region and would give marginal differences in the estimate of λ compared to the classical result of eq 1. Because none of the data points in Figure 6 are in the inverted regime, the value for λ is difficult to determine with accuracy. Nevertheless it is clear that for the fit of the S2 data using the apparent driving force the value of λ must be at least 2 eV, and as already discussed, this is an unreasonably large value. These findings therefore provide good evidence that the ET reactions from the porphyrin S2 excited state occur to an electronically excited state of the radical pair. This is so far the strongest evidence for the involvement of electronically excited charge transfer (radical pair) states involved in intramolecular electron transfer that is found in the literature. Koch et al. recently reported on a series of electron donor and acceptor molecules where hot ground states were observed as a result of bimolecular charge separation and recombination.7 From the dependence of the vibrational temperature that was transferred to the acceptor molecule it could be reasoned that for some of the DA pairs an electronically charge separated state was involved in the process and gives a clear but indirect proof of electronically charge separated states as product states in the bimolecular charge separation process. Of the different possible reasons given in the Introduction for the very similar FET rate constants from the S2 and S1 states, Numbers i−iii fall short: kFET follows the driving force dependence of eq 2 with no rate limitation up to at least 1 × 1013 s−1; the S2 reaction is not in the inverted region, and there is no compensatory difference in coupling and barrier for the S2 and S1 reactions. Instead, only number iv remains to explain the similar FET rates from the S2 and S1 states: because of the excited radical pair products the driving force is similar for FET from the different states. The fitted parabolas also indicate that the electronic coupling, which limits the maximum of the parabola, must be similar for the S1 and S2 FET reactions. Back Electron Transfer in the Inverted Region. Figure 8 shows the rate constant of BET vs apparent driving force. There is a clear inverted region effect with a slower rate at larger driving force. It was concluded previously that FET from the S2 state formed electronically excited charge transfer states. If these have not relaxed to the ground state radical pair prior to BET, the data from S2 excitation should have a larger driving

Figure 6. FET rates vs apparent driving force from the S2 state and the S1 states. Numbers refer to the complex listed in Table 1. Included is also the Marcus parabola: S1(v=0) (solid green line), λ = 0.90 eV and HRP = 162 cm−1; S1(v=1) (dashed green line), λ = 1.07 eV and HRP = 176 cm−1; S2 (purple line), λ = 1.93 eV and HRP = 232 cm−1.

excitations. In the calculation of driving forces it is assumed that all reactions occur from the thermalized state of the reactants to the ground state of the products (i.e., that S1(v=1) is thermalized in all other modes). This is denoted “apparent driving force” in Figure 6. For the ET reactions presented here that assumption is probably not valid, as will be shown later. It is clear from Figure 6 that the S2 and S1 FET reactions fall on different Marcus parabolas and also that both reactions lie in the Marcus normal regime (|ΔG0| < λ) of their respective parabola. A fit of the data with eq 1 (nonadiabatic electron transfer) gives a reorganizational energy of 0.90 eV for the S1 reaction and 1.96 eV for the S2 reaction. It is however unlikely that λ is very different for the two different excitations, since both S2 and S1 states of the porphyrin have small and similar fluorescence Stokes shift. It is also expected that λ < 1 eV for such shortrange ET, even in water. We therefore conclude that the S2 reactions produce an electronically excited charge transfer state (radical pair), which effectively lowers the driving force for FET compared to the apparent values used in Figure 2. We note that the good agreement with a parabolic fit according to eq 2 suggests a well-defined electronically excited product state, instead of a broad distribution of vibrationally excited products that presumably would vary within the series of complexes. Marcus explained the observation of chemiluminescence with the presence of electronically excited states as product states of electron transfer in the inverted region already in the 1960s.28 Electronically excited states have also been observed as product states of intermolecular charge recombination.11,29,30 By assuming that the FET reactions from the S2 state have the same value of λ as those from the S1 state, the energy of the excited charge transfer state produced by the S2 FET is estimated to be about 0.9 eV above the lowest charge transfer state. This value is obtained by fitting the S2 FET data according to eq 1 with the value of λ fixed to 0.90 eV and instead allowing for a constant shift of the apparent ΔG° values within the series (Figure 7). The shift equals the electronic excess energy of the excited charge transfer state. The energy E

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Figure 8. BET rates vs apparent driving force. Driving force is obtained from D+/A− ground state to S0. The rates are fitted to eq 3 with HRP = 96 cm−1, λ = 0.9 eV, ℏω = 827 cm−1, and λv = 0.1 eV.

force than indicated in Figure 8. Moreover, they would not show a thermal (Boltzmann) distribution of reactant states as assumed by eq 2. The rather similar rates of BET for the different initial excitations indicate that significant relaxation, i.e., (D+/A−)* → D+/A− internal conversion, has taken place prior to BET. There are still some differences in the S2 and S1 BET rates that will be discussed later. The BET reactions clearly involve high-frequency acceptor modes as seen by the formation of unrelaxed ground states S0v. This may also be the case for the initial FET, so, e.g., a Jortner− Bixon type modification of the Marcus equation might be more appropriate.31,32 kNA =

2πHAB 2 ℏ 4πλclkBT ∞

×

∑ n=0

Figure 9. Schematic free energy parabolas for the involved states: S0 (black), S1,v=0 (light green), S1,v=1 (dark green), S2 (purple), D+/A− (dark yellow), and (D+/A−)* (light brown). Thin gray lines denote vibrational levels of the S0 and D+/A− states. As the driving force for ET gets smaller, the D+/A− parabolas will be shifted to higher energies (the dotted lines).

netics.33−35 The dielectric response of water is very fast,36 and most of the slow relaxation probably lies in vibrational motions of the complex. Influence of Excitation Wavelength on the S0v Yield. It is obvious from Figure 4 that S2 excitation produces a larger S0v signal upon recombination than does S1 excitation of the same complex. There is even a difference between S1(v=0) and S1(v=1) excitations, as was noted for complex 4 before.18,19 Here we show this result to be general for the series of complexes. We note that between S1(v=0) and S1(v=1) excitations there is no significant difference of the FET and BET rates, which excludes that the effect is due to differences in the kinetic competition with vibrational relaxation, discussed previously. Still the observed S0v absorbance is more intense following the more energetic S1(v=1) excitation. Some of the excess energy of the initial S2 and S1(v=1) states is apparently conserved during the two-step FET and BET processes, but converted into different degrees of freedom. These ultrafast ET processes are clearly not occurring from thermally equilibrated reactants. The excess reactant energy in both reactions provides stronger coupling to vibrationally excited product states. For S2 excitation, the excess electronic energy is converted into an electronically excited radical pair, but after BET it has been converted into excess vibrational energy, compared to the experiments with S1 excitation. Also for S1(v=1) excitation, the additional medium frequency quantum appears to be converted into lower frequency excitations in the resulting S0v state, as the ground state spectral shift is more modest than the energy shift between the two Q-bands. With the available data for these large molecules we cannot be more precise on the identity of these vibrational modes. Many studies of ET, such as this one, are made with UV−vis spectroscopy, and in order to observe vibrationally excited states with that technique, it requires that the corresponding electronic states have sharp absorption peaks in order for the vibrational excess energy to sufficiently shift the electronic spectra. The porphyrin Soret band is excellent in that respect, but unfortunately there is no ground state absorbance in the detectable wavelength region that can be attributed to only the viologen dication. Attempts to identify the nature of the excited radical pair by femtosecond stimulated Raman spectroscopy have proven unsuccessful.37 Apart from the

exp( −S)

⎛ (ΔG° + λ + nℏω)2 ⎞ Sn cl ⎟⎟ exp⎜⎜ − n! 4λclkBT ⎝ ⎠

(3)

This is essentially a sum of the classical expression for nonadiabatic electron transfer over different vibronic transitions. The electronic coupling is multiplied with nuclear coupling to vibrational levels, |⟨0|n⟩|2 = (Sn/n!)e−S, and the product state includes increasing vibrational levels of one highfrequency mode (nℏω, with kBT ≪ nℏω) of the electronic ground state. S is the Huang−Rhys factor, S = (λv/ℏω), λv is the intramolecular reorganization energy of the high-frequency mode, and λcl is the reorganization energy for the remaining classical coordinates. This refined model does not change the present conclusions, however, which are semiquantitative and drawn from the general trends rather than the exact value of the parameters in the Marcus equation. The preceding findings of the ET processes can be rationalized with the schematic free energy parabolas in Figure 9. The S2 state is energetic enough to produce electronically excited radical pairs (D+/A−)*. Some of the excess energy is conserved during the FET and BET reactions to produce a significant amount of S0v. More correctly a multidimensional model should probably be used, similar to the Sumi−Marcus model, that treats the solvent coordinates and vibrational coordinates separately. It should also be noted that excited states are of importance in both the reactant and product states of the FET and BET reactions. In most models of electron transfer, vibrational relaxation is assumed to be much faster than the electron transfer reactions so that all reactions take place from the relaxed reactant state. This is also what is assumed in the Barbara hybrid model that has been used to explain the wavelength dependent recombination of photoexcited ion pairs, and temperature independent ET kiF

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For comparison between the complexes the general trend is that complexes with smaller driving force for FET are observed to give a less intense S0v maximum absorbance (Figure 10).

spectral properties, the key factor that allows for these unusual observations are the high rate constant for both FET and BET that can outcompete vibrational relaxation, and the availability of several relatively long-lived local excited states. The following section discusses the competition between ET and vibrational relaxation and how this varies within the series of complexes. Competition between Electron Transfer and Vibrational Relaxation. The back electron transfer is in the inverted region (−ΔG0 > λ) where the effects of nuclear tunneling to vibrationally excited product states are expected also when the reactants are in their vibrational ground states. For the BET reactions vibrationally excited product states are represented by the S0v state. As described in more detail in our previous publication,19 the absorption band due to transitions from the S0v state is influenced both by the yield of S0v production and which vibrational modes and levels are excited. Formation of S0v occurs in competition with recombination directly to S0. A higher yield of S0v will give a larger magnitude of its ΔA signal. An S0v state that contains higher vibrational excitation will show a larger red shift relative to S0 and also a more intense ΔA signal. Since the BET is in the inverted region, a larger driving force is expected to give both a higher yield of S0v as well as more energetic S0v states, both of which will result in a more intense ΔA signal. This prediction is based on reaction of a thermally equilibrated radical pair state, however. Since this is not the case here, we need to consider two effects of a kinetic competition between BET and vibrational relaxation. First, the observed S0v signal will depend on the relative rates of BET and intramolecular vibrational energy re-distribution (IVR) in the S0v state(s). IVR is expected to occur faster in higher vibrational energy levels, and hence the red side of the S0v absorption bands is expected to decay faster than the blue side.38−40 With BET in the inverted region a larger driving force is expected to also give a slower BET rate. Then the highest vibrational excitations of the S0v state might have decayed by IVR before they could be observed in the spectra. This will make the apparent yield of S0v larger for highly exoergonic BET reactions, but the spectral shift compared to the ground state is smaller. Hence a larger driving force for BET is still expected to give a larger ΔA signal for S0v, as discussed previously. Second, the observed S0v signal will depend on the relative rates of BET and vibrational relaxation in the radical pair. The radical pair is produced with excess energy, and BET occurs on a time scale similar to that of radical pair relaxation.41,42 A faster BET will therefore conserve more of the vibrational energy of the radical pair state, yielding a more energetic S0v state after BET. But a faster BET is associated with a smaller driving force for BET, with less excess energy to conserve. Therefore, the two kinetic effects predict opposite trends for the yield of S0v as a function of driving force for BET. With these effects in mind we compare and discuss the relative S0v yield in the series of complexes. Influence of ET Driving Force on the S0v Yield within the Series of Complexes. When comparing the results for different complexes, we note that the driving forces and rates are different when the same excitation wavelength is used but also that the excess energy for each complex when going to the shorter excitation wavelengths is the same. Therefore, it is useful to compare the S0v yields between complexes for the same excitation wavelength; also, a comparison for the same complex but with different excitation energies was made earlier.

Figure 10. Relative yield of S0v after S2 excitation vs the energy of the radical pair state, E(D+/A−). The yield is obtained as the observed S0v peak maxima (at ca. 435 nm) relative to the D+/A− maxima at ca. 450 nm. Complexes 8 and 9 are not included due to the high amount of free porphyrin that obscures the S0v dynamics.

Following the reasoning of the previous paragraph, this can be explained by the slower rates of electron transfer (both FET and BET) for complexes with smaller driving force for FET. The slower rate means that vibrational relaxation takes place to a larger extent, both in the initially excited state and in the charge transfer state (radical pair), which reduced the S0v yield. Furthermore, a slower BET could run into competition with vibrational cooling of the S0v state that will deplete the S0v state. Without knowledge of the exact vibrational modes that are involved in these processes we cannot make a more quantitative analysis, but the trends observed here are expected to be the result of a more general scheme that is present in many reactions. Both of these observations of the dependence of the S0v yield on both the initial excitation and the driving force for ET point to the importance of considering the rate of vibrational relaxation in relation to the rate of electron transfer. Most expressions for the rate of electron transfer, including those that take into account nuclear tunneling from the reactant state, assume thermal equilibrium of the reactant state. Ivanov and co-workers developed a model that, in analogy with the Sumi− Marcus model, treats the solvent and vibrational degrees of freedom separately. Rather than using one single relaxation time, a distribution of solvent relaxation times is accounted for and also a full quantum mechanical treatment of all vibrational modes.43,44 With this model they could reproduce the kinetics observed by Wallin et al.; initial FET from the ZnTPP S2 state resulted in unrelaxed charge transfer states that recombined to the ZnTPP S1 state where further FET to the relaxed charge transfer state occurred.11,45 That is highly relevant also for the results presented here where we have shown that electron transfer can be faster than vibrational relaxation and that not only excited product states but also excited reactant states need to be accounted for in the processes. Influence of Excitation Wavelength on kBET. Other evidence for the involvement of excited radical pairs is that the rate of BET in the same complex depends on the initially excited state. This is a consequence of the fact that the radical pair state does not have time to relax fully after FET before BET takes place. BET is in the inverted region, so more excess energy in the D+/A− state should give a lower BET rate G

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The Journal of Physical Chemistry B constant; i.e., kBET(S2) < kBET(S1(v=0)). As is seen in Figure 11, that is true for complex 8 with the smallest BET driving force

initially excited state, radical ion-pair state, and ground state. Complexes for which the recombination reaction is deeper into the Marcus inverted region and therefore expected to be more dependent on nuclear tunneling to vibrationally excited ground states showed instead a relatively low yield of unrelaxed ground states. Instead the complexes that displayed a high rate of BET showed the most production of unrelaxed ground states. It was therefore concluded that the rate of ET, competing with vibrational relaxation, rather than the nuclear tunneling to excited states, was of greater importance for the observation of unrelaxed ground states.

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ASSOCIATED CONTENT

S Supporting Information *

Figure 11. Ratio of S2 and S1(v=0) kBET vs. energy of the D+/A− state (apparent BET driving force). Numbers refer to the complex (Table 1).

Text describing the synthesis of MVCNBr2, DMI2, and 4,4′Me2-DMI2, complexation, data analysis, and transient absorption data, table listing complexation constants for all ZnTPPS4−−viologen complexes, and figures showing the corresponding titration spectra, complexation curves, and transient absorption spectra. This material is available free of charge via the Internet at http://pubs.acs.org.

(D+/A− state lower in energy), and for 4−6 we found that kBET(S2) ≈ kBET(S1(v=0)), but for 1−3 the opposite situation is observed, which is quite unexpected. A tentative explanation is that, in the inverted region, population of higher initial vibrational levels in the reactant state results in a better coupling to the product state. Indeed, the potential surfaces are nested and for the higher vibrational levels the wave function has most of the amplitude at the ends, away from the equilibrium position. For sufficiently large driving forces, it is then possible that higher levels of the reactant state give a faster rate due to better coupling to the product state and that this could explain the trend observed in Figure 11.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Prof. Michael R. Wasielewski and Prof. Dick T. Co at Northwestern University for their efforts studying the ZnTPPS4−−MV2+ complex with femtosecond stimulated Raman spectroscopy (FSRS). This work was supported by the Knut & Alice Wallenberg Foundation and the Swedish Energy Agency.

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CONCLUSION We have studied the photoinduced electron transfer reactions of a series of porphyrin/viologen complexes. From the rate vs free energy correlation we could conclude that forward electron transfer from the porphyrin localized S2 excited state produced an electronically excited radical ion pair state, ca. 0.9 eV above the ground state radical pair. Electronically excited radical pair states have been inferred but not directly observed for intramolecular electron transfer. The present evidence is the strongest published so far for the involvement of excited radical pair products of a photoinduced electron transfer reaction. The reaction to form electronically excited radical pair intermediates from the S2 state reaction, and the formation of vibrationally unrelaxed ground states upon charge recombination, may explain the very similar rates of forward ET from the S1 and S2 states, and the similar recombination rates, in spite of the ca. 0.9 eV excess energy generated from the S2 reaction. For the forward ET, very similar free energy dependences of the rate were observed from the S1 and S2 states, which were both found to lie in the Marcus normal region. For the subsequent recombination, the excess energy in the S2 reaction resulted in excess vibrational energy of the resulting ground state. This decreased the effective free energy difference between the reaction initiated by the S1 and S2 states and at least partially explains their similar rates. The study also revealed the intricate interplay of vibrational relaxation in competition with electron transfer, as evidenced by the observation of unrelaxed ground states depending on both initial excitation and driving force for the ET reactions. In the present complexes both forward and back electron transfer are fast enough to compete with vibrational relaxation in the

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REFERENCES

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