Insights into Photoinduced Electron Transfer Between [Ru(mptpy)2]4+

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Insights into Photoinduced Electron Transfer Between [Ru(mptpy)2]4+ (mptpy ) 4′(4-methylpyridinio)-2,2′:6′,2′′-terpyridine) and [S2O8]2-: Computational and Experimental Studies Alexey L. Kaledin,*,† Zhuangqun Huang,‡ Qiushi Yin,‡ Emma L. Dunphy,§ Edwin C. Constable,§ Catherine E. Housecroft,§ Yurii V. Geletii,‡ Tianquan Lian,*,‡ Craig L. Hill,‡ and Djamaladdin G. Musaev*,† Cherry L. Emerson Center for Scientific Computation and Department of Chemistry, Emory UniVersity, Atlanta, Georgia 30322, and Department of Chemistry, UniVersity of Basel, CH 4056, Basel, Switzerland ReceiVed: January 28, 2010; ReVised Manuscript ReceiVed: April 9, 2010

The mechanism and electron transfer dynamics of the reaction [RuII(mptpy)2]4+ + hν + [S2O8]2- f [RuIII(mptpy)2]5+ + SO42- + SO4-• were studied using various computational (density functional and exciton interaction theories) and experimental (transient absorption, static and time-resolved fluorescence spectroscopy, and other) techniques. The results were compared with those recently reported for [Ru(bpy)3]2+ dye [ref 18]. It was found that the excitation energy of [Ru(mptpy)2]4+ is about 0.4-0.5 eV smaller than that of [Ru(bpy)3]2+, which is consistent with the measured absorption maxima of 445 and 507 nm, for [Ru(bpy)3]2+ and [Ru(mptpy)2]4+, respectively. The smaller excitation energy in [Ru(mptpy)2]4+ correlates with much slower electron transfer rates to persulfate compared to [Ru(bpy)3]2+. The quenching of the photoexcited [Ru(mptpy)2]4+ by [S2O8]2- occurs via a unimolecular mechanism with formation of a weak ion-pair complex {[Ru(mptpy)2]4+ · · · ([S2O8]2-)n}, where n ) 1 and 2. The initial photon is absorbed by the [Ru(mptpy)2]4+ fragment forming an MLCT state, e.g., the bright singlet state S1. This S1 state undergoes a fast spin-orbit coupling induced intersystem crossing to a lower-lying triplet and rapid subsequent relaxation down to the lowest triplet T1 via internal conversion and collisions with solvent molecules. At this stage, the electron transfer from [Ru(mptpy)2]4+ to a loosely attached [S2O8]2- occurs in a dark reaction via elongation of the O-O peroxo bond of the oxidant [S2O8]2-. The electron transfer lifetimes in water are calculated to be 1/κ1 ) 199.4 ns and 1/κ2 ) 108.4 ns, for the 1:1 and 1:2 complexes, respectively. The computed electron transfer lifetimes (1/κ1) are in reasonable agreement with their experimental values of 298 and 149 ns for the 1:1 and 1:2 complexes, respectively. The effect of solvent polarity on electron transfer rates is found to be significant: the less polar acetonitrile slows the rate by an order of magnitude compared to water. 1. Introduction The development of efficient and stable photocatalytic systems capable of splitting water into H2 and O2 by utilizing sunlight is one of the grand challenges in renewable energy research.1,2 These photocatalytic systems often consist of a water oxidation catalyst (WOC), photosensitizer, and H2 evolving catalyst (HEC).2-5 In the past two years, we have developed several all-inorganic, stable, molecular WOCs, namely, {[Ru4O4(OH)2(H2O)4](γ-SiW10O36)2}10- (1),6 {[RuIV4O5(OH)(H2O)4](γ-PW10O36)2}9- (2),7 and [Co4(H2O)2(B-R-PW9O34)2]10(3).8 Furthermore, we have demonstrated that complex 1 (containing a RuIV4O4 cluster stabilized by oxidatively resistant [SiW10O36]8- ligands) efficiently catalyzes visible-light-driven water oxidation using tris(2,2′-bipyridine)ruthenium(II), [Ru(bpy)3]2+, as a photosensitizer, and persulfate, [S2O8]2-, as a sacrificial electron acceptor.9 This soluble three-component homogeneous water oxidation system shows a ∼9% quantum yield (moles of O2 formed per two absorbed photons) under 420-520 nm illumination. However, the [Ru(bpy)3]2+ sensitizer * Corresponding authors: [email protected], [email protected], and [email protected]. † Cherry L. Emerson Center for Scientific Computation, Emory University. ‡ Department of Chemistry, Emory University. § University of Basel.

has a relatively narrow absorption window and is not oxidatively stable under the photocatalytic conditions. Therefore, one way to improve the performance of this homogeneous visible-light-driven artificial photosynthetic system is to replace the [Ru(bpy)3]2+ with a better light absorber. One candidate class of dyes are ruthenium 2,2′:6′,2′′-terpyridine (tpy) complexes, [Ru(tpy)2]4+, which generally (a) have high Ru2+/3+ potentials (>1.1 V vs NHE)10,11 as required for water oxidation, (b) have high extinction coefficients11-13 over a broad range of the visible light spectrum, (c) exhibit an absorption spectrum that overlaps very well with the solar spectrum,10,14 and (d) can be easily engineered to have a larger positive charge that facilitates strong (relative to [Ru(bpy)3]2+) bonding both to the negatively charged reductant, i.e., persulfate, and to the WOC, the Ru4O4-containing polyoxometalate (POM). Furthermore, because 4′-substituted tpy ligands in a [Ru(mptpy)2]4+ are linearly oriented with respect to the metal center, they may facilitate the construction of triads in which the WOC and HEC are connected via the photosensitizer in a colinear manner. Such a configuration of triad increases the distance between the reductant and oxidant, thus slowing the rate of charge recombination. In fact, previously, ruthenium tpy complexes have been shown to be good photosensitizers in various dye-sensitized TiO2 solar cells.15-17 In these solar cells, the photoinduced electron

10.1021/jp100850n  2010 American Chemical Society Published on Web 05/10/2010

Insights into Photoinduced Electron Transfer

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interacting fragments (i.e., electron donor and acceptor), coupled to each other by a perturbation is given by

Pmn ) (4π2 /h)| 〈ψm |V′|ψn〉 | 2 δ(Em - En)

(2)

where h is Planck’s constant, and ψm and ψn are the two excited states with energies Em and En, respectively. The effect of a Coulombic perturbation V′ acting between the two states is evaluated using an exciton interaction theory injection into TiO2 is ultrafast (98%), lead dioxide (PbO2, >97%), and tin(II) chloride (SnCl2, 98%) were purchased from Aldrich. [Ru(mptpy)2][PF6]4 was prepared according to the literature method.15 Synthesis of the Dye. [Ru(mptpy)2][PF6]4 (0.20 mg, 0.15 mmol) was dissolved in a mixture of 9:1 MeCN/CH2Cl2 (5 mL). Tetrabutylammonium hydrogensulfate (0.20 g, 0.60 mmol) was added and the resulting mixture stirred for 30 min. The red precipitate was collected by filtration, washed with MeCN (2 × 10 mL), redissolved in H2O, and the solvent removed under reduced pressure to give [Ru(mptpy)2][HSO4]4 as a dark red solid (0.13 g, 0.12 mmol, 78%). 1H NMR (500 MHz, D2O) δ ppm: 9.28 (1 H, s, HB3), 9.11 (1 H, d, J 6.6, HC3), 8.80 (1 H, d, J 6.6, HC2), 8.70 (1 H, d, J 8.1, HA3), 7.98 (1 H, t, J 7.8, HA4), 7.45 (1 H, d, J 5.5, HA6), 7.28-7.18 (1 H, m, HA5), 4.55 (1 H, s, HCH3), 13C{1H} (125 MHz, D2O) δ ppm: 157.2 (CA2), 155.9 (CB2), 152.6 (CA6), 152.0 (CC4), 146.0 (CC2), 141.0 (CB4), 138.3 (CA4), 127.6 (CA5), 126.0 (CC3), 124.7 (CA3), 121.8 (CB3), 44.9 (CCH3). ESI-MS m/z: 375 [M - 2PF6]2+. UV/vis (MeCN, 2.00 × 10-5 mol dm-3) λmax/nm (εmax/103 dm3 mol-1 cm-1): 507 (38.2), 339 (35.4), 310 (30.1), 275 (73.2), 240 (43.7). Found: C, 39.55; H, 4.17; N, 8.56; C42H38N8O16S4Ru · 8H2O requires C, 39.28; H, 4.24; N, 8.73%. Nanosecond Transient Absorption Measurements. Nanosecond transient absorption was performed with an EOS spectrometer (Ultrafast Systems LLC). The pump pulses at 400 nm were from the femtosecond amplified laser system described above. The probe pulse (a 0.5 ns white-light source operating at 20 kHz) was synchronized with the femtosecond amplifier, and the delay time was controlled by a digital delay generator. The probe light was detected in a fiber-optics-coupled multichannel spectrometer with a complementary metal oxide semiconductor (CMOS) sensor. The absorbance change was calculated from the intensities of sequential probe pulses with and without the pump. Static and Time-ResolWed Luminescence Measurements. Steady-state emission spectra of the samples were measured using a SPEX FluoroLog-3 self-contained and fully automated spectrofluorometer. Time-resolved fluorescence measurements were performed in the time-correlated single-photon-counting

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Figure 1. Calculated (in water) frontier orbitals of [Ru(mptpy)2]4+ at its S0 minimum.

(TCSPC) mode under a right-angle sample geometry. A femtosecond laser pulse (100 fs) with a repetition rate of 80 MHz was generated from a mode-locked Ti:sapphire laser (Tsunami oscillator pumped by 10 W Millennia Pro, SpectraPhysics). The output centered at 800 nm was doubled through a BBO crystal to generate 400 nm excitation pulses. The emission was detected by a microchannel-plate photomultiplier tube (Hamamatsu R3809U-51), whose output was amplified and analyzed by a TCSPC board (Becker & Hickel SPC 600). Solutions of [Ru(mptpy)2]4+ and [S2O8]2- and their mixtures were prepared and stored in the dark to avoid photoreactions. We used 5 µM [Ru(mptpy)2]4+ and less than 10 mM [S2O8]2for all measurements due to the low solubility of the [Ru(mptpy)2]4+/[S2O8]2- mixture in the applied solvents. All solutions were degassed with N2 before measurements. Samples were excited at 500 nm, and emission intensity data were collected at 640-720 nm at 20 °C under vigorous stirring. 3. Results and Discussion of the Computational Studies For simplicity, we label [Ru(mptpy)2]4+ as fragment A and its electronic states as SAn and TAn, where S and T stand for singlet and triplet, respectively, and n ) 1, 2, ..., 6. Similarly, we label [S2O8]2- as fragment B and its electronic states as SBn and TBn. 3.1. Properties of [Ru(mptpy)2]4+ and [S2O8]2-. Most of the computed results on [S2O8]2-, at the given level of theory, that are relevant to the present work were reported in our earlier paper.18 Here, we will only mention the key details in passing and concentrate mainly on the complex ion, [Ru(mptpy)2]4+. The ground electronic state of [Ru(mptpy)2]4+ is a closed-shell singlet state, SA0. Its few uppermost doubly occupied MOs (HOMOs) are primarily Ru d-orbitals with a small mixing of N p-orbitals (see Figure 1). The first two LUMO orbitals are localized on the ligands and are π* orbitals of the mptpy rings. In Figure 2, one can see the overall structure and some key geometry parameters of [Ru(mptpy)2]4+ (full geometries of all calculated structures are given in Table S1 of the Supporting Information). The performed Mulliken charge analyses show that only +0.88 e charge is located on the metal center of [Ru(mptpy)2]4+, and the rest of the total +4.0 e charge of the system is distributed on the tpy ligands. For comparison, in [Ru(bpy)3]2+ the metal center carries a +0.73 e charge.18 Applying the effects of solvation in water causes very little change to the electronic density of the ground state of [Ru-

Kaledin et al. (mptpy)2]4+, and as a result, the geometry of the system in its SA0 state, as well as the charge distribution in it, is virtually unchanged. Calculations show that the low-lying SA1, SA2, SA3, TA1, TA2, and TA3 excited states of [Ru(mptpy)2]4+ at the SA0 equilibrium geometry are metal-to-ligand charge transfer (MLCT) states. Table 1 summarizes excitation energies in the gas phase and in aqueous and acetonitrile solutions. As seen from this table, in general, triplet states are slightly lower in energy than corresponding singlet states with the TA1 and TA2 states being the lowest. The measured (see section 4.1.) absorption peaks at 507 nm, in solution, which closely corresponds to the first two singlet states, SA1 and SA2, which are calculated to be 2.32 eV (534 nm) and 2.32 eV (534 nm) in the gas phase, 2.35 eV (527 nm) and 2.35 eV (527 nm) in water, and 2.36 eV (525 nm) and 2.36 eV (525 nm) in acetonitrile, respectively. Comparison of these data with the corresponding data for the [Ru(bpy)3]2+, reported in our previous paper,18 shows that the first excitation energy is ∼0.4-0.5 eV lower in [Ru(mptpy)2]4+ than [Ru(bpy)3]2+ (see also Table 2). As reported earlier,18 the calculated excitation energies of the [S2O8]2- anion are almost twice as high as those for [Ru(mptpy)2]4+ and/or [Ru(bpy)3]2+. To eliminate the possibility of computational artifacts due to an incomplete basis set, we studied the effect of the used basis sets by adding (a) more valence basis functions to the H, C, and N atoms (the 6-311G contraction) and (b) extra polarization functions (2d,f). Since Ru loses an electron during the SA0 f SA1/SA2/SA3/TA1/TA2/TA3 excitations, additional basis functions on the metal are not expected to be a significant factor. As can be seen in Table 2, both [Ru(mptpy)2]4+ and [Ru(bpy)3]2+ singlet and triplet excitation energies in water are reduced slightly, at most by 0.08 eV, a much smaller number than the mptpy-bpy difference, when compared to the 6-31G(d) basis set. This result gives us confidence in reporting that [Ru(mptpy)2]4+ absorbs at a longer wavelength than [Ru(bpy)3]2+, and as will be shown later, this difference leads to a substantially slower TA1 decay rate in the complex with [Ru(mptpy)2]4+ flanked by a single [S2O8]2-. Analysis of the SA0 f SA1/SA2/SA3/TA1/TA2/TA3 excitations shows that the SA1 and SA2 states are open-shell singlet states. The calculated largest amplitude (0.68, the amplitudes of all other possible excitations smaller than 0.10 are not presented in Table 3) of the SA0 f SA1/SA2 excitations corresponds to excitation from HOMO1 (primarily Ru d-orbitals) to LUMO1/LUMO2 (π* orbitals of the mptpy rings), respectively (see Table 3). However, the S3 state is a mixture of four excitations, with comparable amplitudes, involving HOMO2/HOMO3 and LUMO1/LUMO2 orbitals. Unlike the SA1/SA2 pair, the TA1/TA2 triplet states are strong mixtures of four excitations: HOMO3 f LUMO1/LUMO2 and HOMO2 f LUMO1/LUMO2. On the other hand, T3 is a mostly localized state involving mainly the HOMO1 f LUMO1 excitation (with an amplitude of 0.65). This pattern of configuration mixing is qualitatively different from [Ru(bpy)3]2+ where both the low energy singlet and triplet states were dominated by a single excitation. As will be shown in the Experimental Section, the emission spectrum of [Ru(mptpy)2]4+ is broad and has a maximum at 710 nm, which is most likely a transition from a vibrationally relaxed TA1 state to an excited vibrational state of SA0. A vertical transition from the TA1 minimum (the structure of [Ru(mptpy)2]4+ is fully optimized at its TA1 electronic state) to the SA0 is about 728 nm in the gas phase and 788 nm in water. The overall appearance of the TA1 minimum is very



Figure 2. Calculated structures and important geometry parameters (in Å) of [Ru(mptpy)2]4+, [S2O8]2-, {[Ru(mptpy)2]4+ · · · [S2O8]2-}, and {[S2O8]2- · · · [Ru(mptpy)2]4+ · · · [S2O8]2-}. Numbers given in parentheses are for triplet electronic states.

TABLE 1: TD-DFT/6-31+G(d) Calculated Excitation Energies for the First Three Singlet and Triplet States, Ionization Potential (IP), and Electron Affinity (EA) (all in eV) of [Ru(mptpy)2]4+ and [S2O8]2- in the Gas Phase, Water, and Acetonitrile (ACN) [Ru(mptpy)2]4+

a

[S2O8]2a

states

gas-phase

water

ACN

gas-phase

SA1/TA1 SA2/TA2 SA3/TA3 IP EA

2.32/2.20 2.32/2.22 2.41/2.37 15.57 10.88

2.35/2.04 2.35/2.10 2.41/2.23 5.96b 3.65

2.36/2.04 2.36/2.10 2.42/2.23 6.15 3.76

4.74/3.66 5.37/5.24 5.37/5.24 0.55 0.40

watera

ACN

5.19/4.12 5.80/5.39 5.81/5.67 6.27 4.73

5.17/4.11 5.74/5.36 5.75/5.61 6.18 4.67

Taken from our earlier work.18 b Experimentally measured oxidation potential for [Ru(mptpy)2]4+ in water is 5.83 eV.

similar to that of the SA0 minimum with the only notable difference being an elongation of one of the two short Ru-N bonds, from 2.015 to 2.068 Å, accompanied by local charge

redistribution (see Figure 2). The Ru center becomes more positive, +1.1 e (versus +0.88 e in SA0), while the six bonded N centers accept the migrated electron density (for comparison,

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TABLE 2: Effect of the Basis Sets on the H, C, and N Atoms on the Calculated Triplet Vertical Excitation Energies (eV) of [Ru(mptpy)2]4+ and [Ru(bpy)3]2+ in Water, Evaluated at Their Respective S0 Minimaa State

6-31G(d)

6-311G(d)

6-31G(2df)

6-311G(2df)

4+

SA1/TA1 SA2/TA2 SA3/TA3

2.35/2.03 2.35/2.09 2.41/2.22

SA1/TA1 SA2/TA2 SA3/TA3

2.73/2.55 2.73/2.56 2.75/2.60

a

[Ru(mptpy)2] 2.31/1.99 2.31/2.05 2.37/2.18 [Ru(bpy)3]2+ 2.67/2.50 2.67/2.51 2.68/2.56

2.32/1.97 2.32/2.04 2.36/2.19

2.30/1.95 2.30/2.02 2.33/2.17

2.69/2.52 2.69/2.53 2.70/2.56

2.64/2.48 2.65/2.49 2.66/2.53

Note: no polarization functions were added to the H atoms.

the Ru center in [Ru(bpy)3]2+ in its first triplet state has the charge of +1.4 e).18 The small changes in geometry facilitate the slow spin-orbit-mediated nonradiative decay of SA1 to TA1 via favorable Franck-Condon overlaps. Calculations in the less polar acetonitrile reveal no major changes in geometry for SA0 and TA1 compared to their structures in water. Removing an electron from [Ru(mptpy)2]4+ leads to formation of [Ru(mptpy)2]5+ with a doublet ground electronic state. This process requires 359.2 and 137.6 kcal/mol (15.57 and 5.96 eV, respectively: experimental measurements in water yield 5.83 eV (vs a vacuum) which is in an excellent agreement with its calculated value) of energy in the gas phase and in water, respectively (see Table 1). Placing the removed electron on [S2O8]2- results in the breakup of the latter to SO4-• and SO42-: the resulting reaction [S2O8]2- + 1 e f SO4-• + SO42- is found to be exothermic by 9.3 and 109.3 kcal/mol in the gas phase and water, respectively (cf. Table 4). In other words, the overall reaction [Ru(mptpy)2]4+ (SA0) + [S2O8]2- f [Ru(mptpy)2]5+ + SO4-• + SO42- requires (is endothermic by) 349.9 and 28.3 kcal/mol in the gas phase and water, respectively. Given that the computationally estimated band origin, i.e., the adiabatic SA0-TA1 transition, is 45.2 kcal/mol in gas phase and 42.5 kcal/mol in water, the photoinduced charge transfer reaction from [Ru(mptpy)2]4+ to [S2O8]2-, i.e., [Ru(mptpy)2]4+ (TA1) + [S2O8]2- f [Ru(mptpy)2]5+ + SO4-• + SO42-, seems to be possible only in water and is exothermic by 14.2 kcal/mol. Effects of a less polar solvent were also elucidated by performing the same set of calculations using acetonitrile as solvent: the dielectric constant of acetonitrile, ε(CH3CN) ) 36.64, is about half that of water, ε(H2O) ) 78.39. In acetonitrile, the reaction [Ru(mptpy)2]4+ (SA0) + [S2O8]2- f [Ru(mptpy)2]5+ + SO4-• + SO42- is found to be endothermic by 33.4 kcal/mol, and the adiabatic SA0-TA1 gap was calculated to be 42.8 kcal/mol. Thus, in acetonitrile the photoinduced electron transfer from [Ru(mptpy)2]4+ to [S2O8]2-, i.e, the reaction [Ru(mptpy)2]4+ (TA1) + [S2O8]2- f [Ru(mptpy)2]5+ + SO4-• + SO42-, is exothermic by only 9.4 kcal/mol. In other words, the photoinduced electron transfer from [Ru(mptpy)2]4+ to [S2O8]2- becomes thermodynamically less favorable as the polarity of the solvent is reduced. This conclusion is in good agreement with our experimental findings (see below). 3.2. Geometry and Electronic Structure of the LowerLying Singlet and Triplet States of the {[Ru(mptpy)2]4+ · · · ([S2O8]2-)n} Complex, where n ) 1, 2. Addition of an [S2O8]2anion to the [Ru(mptpy)2]4+ cation leads to formation of a {[Ru(mptpy)2]4+ · · · [S2O8]2-} ion pair complex, called the 1:1 complex (see Figure 2). The calculated [Ru(mptpy)2]4+[S2O8]2- interaction energy is 385.2 kcal/mol in the gas phase, which can be attributed entirely to Coulomb interaction between

a -2 e charged anion and +4 e charged cation. As expected, in water and acetonitrile solutions this interaction is much weaker due to solvent screening. Indeed, in water and acetonitrile solutions, the calculated fragmentation energy of the optimized {[Ru(mptpy)2]4+ · · · [S2O8]2-} complex in its ground singlet S0 state (we label the electronic states of the {[Ru(mptpy)2]4+ · · · [S2O8]2-} complex as Sn and Tn) is 4.8 and 8.6 kcal/mol (see Table S2 of Supporting Information), which are in good agreement with their experimental values (see below). The geometry of the S0 complex (see Figure 2) in solvent shows only a slight distortion in the two fragments relative to their individual geometries. The small changes can be explained by the fact that the fragments [Ru(mptpy)2]4+ and [S2O8]2- of the complex do not form chemical bonds, but rather exhibit long-range interactions. One should note that, in contrast to the ground S0 state, the T1 of the {[Ru(mptpy)2]4+ · · · [S2O8]2-} complex in the gas phase exhibits spontaneous electron capture by a LUMO of a mptpy ligand from the persulfate. This drastic change in electron density distribution leads to significant geometrical changes in both the mptpy ligands and persulfate. Briefly (not shown in Figure 2), the terminal pyridines bend toward the persulfate, while the bridging O-O bond of [S2O8]2- shortens (to 1.298 Å) and its O3S-O bond elongates (to 2.00-2.07 Å). In water and acetonitrile, on the other hand, the triplet-state structure assumes a geometry quite similar to the singlet-state structure, and the calculated {[Ru(mptpy)2]4+ · · · [S2O8]2-} bonding energies for the T1 state, 4.9 and 8.0 kcal/mol, respectively, are closer to their values for the S0 state of the complex, 4.8 and 8.6 kcal/mol, respectively. The +2 e total charge of the complex {[Ru(mptpy)2]4+ · · · [S2O8]2-} facilitates association of another (the second) [S2O8]2dianion to its Ru center to form a 1:2 complex, i.e., {[S2O8]2- · · · [Ru(mptpy)2]4+ · · · [S2O8]2-}. In our studies of the 1:2 complex, we placed the second persulfate opposite the first one (see Figure 2), reflected through the Ru center as the approximate center of inversion, to minimize Coulomb repulsion from the other persulfate. As the total charge of the 1:2 complex becomes zero, the binding energy of the second persulfate to {[Ru(mptpy)2]4+ · · · [S2O8]2-} is somewhat reduced relative to that in the 1:1 complex: from 4.8 to 3.6 kcal/mol in water and from 8.6 to 6.1 kcal/mol in acetonitrile, which are in good agreement with their experimental values (see below). The electronic spectra of the 1:1 and 1:2 complexes are very similar to that of the free [Ru(mptpy)]4+, i.e., a few low-lying MLCT states followed by [S2O8]2- π-σ* excitations. For example, the vertical excitation energies in water for S1/T1 pairs are 2.36/2.04 and 2.35/2.03 eV for 1:1 and 1:2, respectively. These values are to be compared with 2.35/2.04 eV for [Ru(mptpy)]4+ reported in Table 1. After optimizing the triplet state of each complex, {[Ru(mptpy)2]4+ · · · [S2O8]2-} and {[S2O8]2- · · · [Ru(mptpy)2]4+ · · · [S2O8]2-} in water, we determined that the respective adiabatic excitations of T1 are 1.84 and 1.82 eV (42.4 and 42.0 kcal/mol). Thus, the coordination of persulfates (especially, the first of them) significantly deforms the geometry of the [Ru(mptpy)2]4+ core and, consequently, reduces the S0-T1 energy gap (see further discussion below). The effect of acetonitrile on the geometry of the 1:2 and 1:1 complexes is manifested primarily in the relative positions of [Ru(mptpy)2]4+ and [S2O8]2-. Namely, in the 1:1 complex the Ru-S distances are 0.05-0.08 Å shorter in the less polar solvent, while in the 1:2 complex, they are shorter in water by about the same margin (see Figure 2 and Table S1 of Supporting Information for geometries of these structures in acetonitrile).



TABLE 3: TD-DFT-PCM/6-31G(d) Calculated Orbital Excitation Amplitudes for the Lowest Three Singlet and Triplet States of [Ru(mptpy)2]4+ and [Ru(bpy)3]2+ a [Ru(mptpy)2]4+ SA1 H1 H1 H1 H2 H2 H3 H3 a

f f f f f f f

L1 L2 L3 L1 L2 L1 L2

SA2

SA3

TA1

[Ru(bpy)3]2+ TA2

0.68

TA3 0.65 0.11

0.68 0.36 -0.31 0.31 0.36

-0.31 -0.35 0.35 -0.30

-0.41 0.21 0.21 0.42

SA1

SA2

0.68 -0.13

0.13 0.68

SA3

TB1

TB2

-0.17 0.64

0.64 0.17

-0.70

TB3 0.65

-0.11

Only amplitudes with absolute values greater than 0.1 are shown. To shorten the notation, H ) HOMO and L ) LUMO.

TABLE 4: Relative Energies (in kcal/mol) of Intermediates and Various Asymptotic Limits of the Reaction of [Ru(mptpy)2]4+ with [S2O8]2- in its S0/SA0 and T1/TA1 Electronic States, Calculated in Various Media (Gas Phase, Water, and Acetonitrile)a asymptote\medium

gas phase

[Ru(mptpy)2] (SA0) + [S2O8] {[Ru(mptpy)2]4+ · · · [S2O8]2-} (S0) [Ru(mptpy)2]5+ + SO42- + SO4-• [Ru(mptpy)2]3+ + [S2O8]-• {[Ru(mptpy)2]4+ · · · [S2O8]2-}* (T1) [[Ru(mptpy)2]4+*(TA1) + [S2O8]24+

a

The [Ru(mptpy)2]

5+/3+

2-

0.0 -385.2 349.9 -238.3 45.2 (1.96)

water

acetonitrile

0.0 -4.8 28.3 65.2 37.6 (1.63)b 42.5 (1.84)

0.0 -8.6 33.4 60 34.7 (1.5) 42.8 (1.86)

species are calculated in their doublet electronic states. b Numbers given in parentheses are in eV.

These small differences can be easily rationalized by the solvent screening of Coulombic interactions between the fragments. Similarly, excitation energies change little compared to their values in water. 3.3. Mechanism and Rate of Electron Transfer in the {[Ru(mptpy)2]4+ · · · ([S2O8]2-)n} Complexes, where n ) 1, 2. As seen from Table 4, the electron transfer reaction [Ru(mptpy)2]4+ + [S2O8]2- f [Ru(mptpy)2]5+ + SO4- + SO42- is endothermic by 28.3 and 33.4 kcal/mol, in water and acetonitrile, respectively. Previously, the mechanism of the photoinduced charge transfer reaction between [Ru(bpy)3]2+ and [S2O8]2- has been studied extensively using various experimental25 and computational approaches.18 On the basis of these thorough studies, two distinct mechanisms, called “unimolecular (or static quenching)” and “bimolecular (dynamic quenching)”, have been proposed. The “unimolecular” mechanism results from the ground-state association of donor with acceptor to yield the weakly bound {[Ru(bpy)3]2+ · · · [S2O8]2-} complex. In the “bimolecular” mechanism, the initial photoinduced electron transfer occurs in a collision between the excited [Ru(bpy)3]2+* and [S2O8]2-. An unusually strong dependence of bimolecular and unimolecular quenching rates on the solvent employed was reported.25a As we have shown above, [Ru(mptpy)2]4+ and [S2O8]2- form weakly bound {[Ru(mptpy)2]4+ · · · ([S2O8]2-)n} complexes even in aqueous solution. Furthermore, our experiments, given below, strongly point to the unimolecular mechanism for this reaction (see section 4.2). Therefore, below we only discuss the “unimolecular” electron transfer mechanism between [Ru(mptpy)2]4+ and [S2O8]2-. For the sake of simplicity, we separate our discussion of the {[Ru(mptpy)2]4+ · · · ([S2O8]2-)n} complexes for 1:1 (with n ) 1) and 1:2 (with n ) 2) complexes. 3.3.1. 1:1 complex, {[Ru(mptpy)2]4+ · · · ([S2O8]2-)n} with n ) 1. The excited states of the complex {[Ru(mptpy)2]4+ · · · [S2O8]2-} in the Franck-Condon region mirror those of the fragments. For example, the first three excited singlet and triplet states of the 1:1 complex, in water, are MLCT states localized entirely on the [Ru(mptpy)2]4+ fragment. This result is consistent with two weakly interacting fragments (A and B). Thus, one should expect that the initial photon with a wavelength near

507 nm will be absorbed by the [Ru(mptpy)2]4+ fragment of {[Ru(mptpy)2]4+ · · · [S2O8]2-} to excite it to an MLCT state, e.g., the bright state SA1. Then, based on our previous18 calculations of the [Ru(bpy)3]2+, the SA1 state undergoes a fast intersystem crossing to a lower-lying triplet. The system eventually trickles down to the lowest triplet TA1 via internal conversion and collisions with solvent molecules. At this stage, the electron transfer from [Ru(mptpy)2]4+ (fragment A) to a loosely attached [S2O8]2- (fragment B) occurs in a dark reaction. Following our earlier work18 on photoinduced electron transfer between [Ru(bpy)3]2+ and persulfate [S2O8]2- where the bridging O-O bond of the oxidant [S2O8]2- was shown to be a convenient “global” coordinate for mediating electron transfer from [Ru(bpy)3]2+* to the persulfate, here we performed relaxed scans along the O-O bond in the triplet T1 state of the complex {[Ru(mptpy)2]4+ · · · [S2O8]2-}* while monitoring fragment excitation energies (from SA0 and SB0 to TA1 and TB1, respectively) at each of the relaxed triplet-state complex geometries (see Figure 3). After encountering SCF convergence difficulties in the triplet states, as emphasized by the multiexcitation character of TA1 and TA2 states of [Ru(mptpy)2]4+, all subsequent geometry optimizations of T1 state of the 1:1 complex were done at the TD-DFT level using the ground-state singlet as reference. Several values of O-O bond length within the 1.6-1.8 Å range were used to make a scan. The curves of the lowest triplet state of the two fragments cross at ∼1.44 eV (33.2 kcal/mol, vertically above S0) and ∼0.47 eV (10.8 kcal/ mol) above the T1 minimum when the O-O bond approaches 1.77 Å, marking this geometry as the “transition state” for electron transfer. Examination of atomic charges and atomic spin populations offers a revealing insight into fragment interactions and charge migration. These analyses show that up to R(O-O) ) 1.7 Å, the complex is still in its Franck-Condon triplet state: {[Ru(mptpy)2]4+(TA1) - [S2O8]2-(SB0)}* with no unpaired spin on the persulfate fragment. Over a R(O-O) of 1.7-1.75 Å, however, [S2O8]2- abruptly changes into a triplet (with two unpaired spins) mirroring a simultaneous counter-change of [Ru(mptpy)2]4+ into a singlet. When R(O-O) exceeds 1.75 Å, [S2O8]2- captures an electron from a mptpy ligand, completing

6290


Kaledin et al. with the usual normalization condition for expansion coefficients Σnci,n2 + Σmci,m2 ) 1. Here and below, the TCDM calculated eigenstates are labeled using the same notation but with an added prime, e.g., S1′, T1′, and so forth. The cumulative rate for a given eigenstate is simply a sum over individual channels weighed by initial electronic state populations

rate(Ti′) ) F exp(-∆Ei/kBT)

∑ ci,n2Pnm

(6)

nm

Figure 3. Energy profiles of S0 (open circles) and the first 4 triplet states (closed circles) of [Ru(mptpy)2]4+ · · · [S2O8]2- complex along the O-O peroxo bond with all the other parameters optimized in T1 (the curve is emphasized with a thick line) at the TD-DFT/6-31+G(d) level of theory. The T1 minimum (O-O ) 1.46 A) and the CT point (O-O ) 1.77 A) are indicated by arrows. The zero of energy is at the S0 minimum.

the electron transfer process. Figure S1 and Table S3 in the Supporting Information present the four orbitals involved in the electron transfer and the cumulative charge and spin population on the persulfate. To estimate the electron transfer rate in, and the nature of the calculated electronic states of the species {[Ru(mptpy)2]4+[S2O8]2-}, we turn to the TCDM model, which previously was tested and successfully applied to study the excited states of {[Ru(bpy)3]2+ · · · [S2O8]2-}. Taking into account that the first excitation energy of {[Ru(mptpy)2]4+ · · · [S2O8]2-} far exceeds the [Ru(mptpy)2]4+ · · · [S2O8]2- complexation energy, it is suitable to use a perturbation theory approach for interpreting excited states of the complex {[Ru(mptpy)2]4+ · · · [S2O8]2-}. The zero-order states are chosen as noninteracting fragment states at the geometries defined by their positions in the complex. Perturbation of a pair of singly excited singlet or triplet states of {[Ru(mptpy)2]4+ · · · [S2O8]2-} is described by the exciton interaction model

〈TAn|V′|TBm〉 )

∑ qn(rA,i)qm(rB,j)/|rA,i - rB,j|

(4)

i,j

where TAn and TBm are zero-order states of the [Ru(mptpy)2]4+ and [S2O8]2- fragments, respectively. V′ is the electrostatic perturbation acting between pairs of atoms i (on fragment A, i.e., [Ru(mptpy)2]4+) and j (on fragment B, i.e., [S2O8]2-) whose positions are given by the Cartesian 3D vector r. The charges qn/qm are transition charges, which are calculated by taking the difference between the atomic charge in state n/m and the ground-state SA0 or SB0. Taking the N and M states of respective fragments leads to an interaction matrix of size (N + M) × (N + M) whose eigenvalues and eigenvectors (see below) represent excited states of the 1:1 complex |Ti′〉 )

∑c

i,n |TAn〉

n

+

∑c

i,m |TBm〉

i ) 1, 2, ..., N + M

m

(5)

where F is the density of exit states, which is estimated near the transition structure to be approximately 3 eV-1, and ∆Ei is the energy of eigenstate i above the T1 minimum. The total rate of electron transfer from A to B is a sum over the eigenstate index in eq 6. In order to estimate the exciton interaction between [Ru(mptpy)2]4+ and [S2O8]2- (i.e., fragments A and B), we construct a small interaction Hamiltonian consisting of 6 excited singlet and 6 excited triplet states of each fragment, a 12 × 12 matrix for each spin symmetry. The diagonal elements of this matrix are the excitation energies of the individual fragments (zeroorder energies) calculated at the geometry of the complex {[Ru(mptpy)2]4+ · · · [S2O8]2-} using the TD-DFT/PCM method. The off-diagonal elements are computed using eq 4. These calculations result in weakly mixed T1′ (T1) states of the complex with 90% arising from the first MLCT triplet state of fragment [Ru(mptpy)2]4+ and 8% from the first triplet of [S2O8]2-. The matrix element for the resonant pair, as defined by eq 2, is -0.013 eV, which leads to a T1′ (T1) rate of 1.34 × 10-3 fs-1 at 300 K. Summing the cumulative rates over the 12 eigenstates and using ∆E1 ) 10.8 kcal/mol (i.e., T1 activation energy) produces the total rate of 6.21 × 10-11 fs-1, or the electron transfer lifetime, τ1′, of ∼16 µs, about 2 orders of magnitude greater than the experimentally determined electron transfer lifetime of 298 ns in aqueous solution. Table 5 summarizes the calculations. Calculations in acetonitrile reveal very similar geometrical parameters and, therefore, similar electronic coupling matrix elements. The main difference is in the height of the “transition point” relative to the T1 minimum, which leads to a rate about 10 times slower, and the electron transfer lifetime correspondingly longer, than in water. This finding is consistent with the asymptotic analysis presented earlier (cf. Table 4). It is also consistent with experimental measurements where a gradually increased concentration of CH3CN in a water solution leads to decreased electron transfer rates (see below). One should note that the calculations using Marcus’s electron transfer theory based on solvent reorganization energy produce similar dependence of the electron transfer lifetime on the solvent effect; however, the absolute values of the electron transfer lifetimes are substantially overestimated. Details of these calculations can be found in Supporting Information. The large overestimation of the experimental electron transfer lifetime can be a result of several factors including: (i) nonadiabatic (fast) electronic effects following photoexcitation possibly playing a significant role in electron transfer involving higher triplet states; and (ii) binding of a second persulfate possibly facilitating the electron transfer rate. Here, we find it constructive to speculate about the first point before moving on to address the second point and propose a mechanism where the excess energy of the photon stored initially in vibrational modes of [Ru(mptpy)2]4+ is converted to thermal energy that promotes the activation of the O-O bond.



TABLE 5: Summary of Key Parameters in Electron Transfer Reactions for {[Ru(mptpy)2]4+ · · · ([S2O8]2-)n} and {[Ru(bpy)3]2+ · · · [S2O8]2-} Complexes in Water and Acetonitrile at 300 Ka water R

E

V11′(AB)

n)1 n)2

1.77 1.59

10.8 7.9

-0.013 -0.003

n)1

1.61

6.9

0.023

acetonitrile τ1′/τ2′ 16.1 µs 9.4 µs 47 ns

τ1/τ2 [Ru(mptpy)2] 199.4 ns 108.4 ns

R

∆E

V11′(AB)

τ1′/τ2′

τ1/τ2

1.77 1.59

12.1 16.5

-0.012 -0.003

144.5 µs 16.4 s

710.8 ns 43 µs

N/A

N/A

N/A

N/A

N/A

4+

[Ru(bpy)3]2+ N/A

a

Here, R is the peroxo bond distance (in Å) at transition point; ∆E (in kcal/mol) is the energy of the transition point relative to T1 minimum; V11′(AB) is the interaction matrix element (in eV) at the transition point; τ1′/τ1 and τ2′/τ2 are the uncorrected/corrected lifetimes (1/ κ1 and 1/κ1, respectively) for 1:1 and 1:2 complexes, respectively. All results are calculated at the TD-DFT-PCM/6-31+G(d) level of theory.

Above, we have shown that the vertical excitation from S0 to the first bright S1 state requires 54.3 kcal/mol (2.36 eV) of energy. The S1 state later relaxes to the T1 state via a fast intersystem crossing facilitated by strong spin-orbit coupling. The calculated adiabatic S0-T1 excitation is 42.4 kcal/mol (1.84 eV). Thus, the S0 f S1 f T1 electron transfer leaves 11.9 kcal/mol energy stored in the [Ru(mptpy)24+] vibrational modes to activate the O-O bond of the persulfate, enough to cross the charge transfer transition point. (As shown above, the energy needed to reach the transition point from the T1 global minimum is ∼10.8 kcal/mol). If the rate of energy flow from [Ru(mptpy)24+] to the solvent is much slower than vibrational energy redistribution, this excess energy can be used to activate the O-O bond via interactions between [Ru(mptpy)2]4+ and [S2O8]2-. Examining in more detail the change of geometries between the S0 minimum and the T1 transition point of the complex reveals that only a few vibrational modes change significantly during the process. Namely, one of the two pyridines rotates by ∼30° around the interannular C-C bond, while the persulfate undergoes obvious structural changes along the O-O peroxo bond, the S-S distance and along an angle that tilts the two sulfates relative to each other. All four coordinates are slow modes (low frequency modes) that behave classically at 300 K, allowing us to use a Hinshelwood-like correction factor to the usual Arrhenius form of eq 6, i.e., the factor of (∆E/kT)p-1/(p - 1)! Distributing the activation energy ∆E ) 10.8 kcal/mol among the p ) 3 ( 1 vibrational modes (where one of them is the reaction coordinate, the O-O elongation) produces a correction factor of 18 (for p ) 2), 162 (for p ) 3), and 800 (for p ) 4). So, the error bar of our estimation is relatively large. Below, we use the value of 162 corresponding to the p ) 3 case. Applying this correction to eq 6 reduces the triplet-state electron transfer lifetime (1/κ1) to 199.4 ns (from τ1′ ) 16.1 µs), bringing it into much better agreement with the experiment value of 298 ns. We label the corrected lifetime τ1 in Table 5. We should note that this calculation holds on the assumption that the excess energy has not had time to dissipate to the solvent. Further DFT calculations in explicit water are needed to address this issue more accurately. 3.3.2. 1:2 Complex, {[Ru(mptpy)2]4+ · · · ([S2O8]2-)n} with n ) 2. As we have discussed in section 3.2, the coordination of another (the second) [S2O8]2- anion to the 1:1 complex to form a 1:2 complex, i.e., {[S2O8]2- · · · [Ru(mptpy)2]4+ · · · [S2O8]2-} is feasible. The binding energy of the second persulfate to {[Ru(mptpy)2]4+ · · · [S2O8]2-} is calculated to be 3.6 and 6.1 kcal/mol in water and acetonitrile, respectively. Since these binding energies are also relatively small, as in the 1:1 complex, the electronic spectrum of the 1:2 complex in the Franck-Condon region is expected to be very similar to that of the 1:1 complex. Therefore, we may expect that the electron transfer in the two complexes (i.e., 1:1 and 1:2 complexes)

occurs via similar pathways. We note, however, that since either one of the two identical persulfates is available for electron capture, the electron transfer rate in eq 6 must be multiplied by a factor of 2. Repeating the procedure for the 1:1 complex, we scanned the O-O peroxo bond length of one of the persulfates (the “active” one) in the T1 state of the complex using TD-DFT gradient, while relaxing all other parameters, to locate geometries at which fragments have resonant excitations. These calculations show that the resonance between the lowest triplet states of [Ru(mptpy)2]4+, TA1, and an activated persulfate, TB1, is achieved approximately at the O-O value of 1.59 Å (i.e., approximately 0.18 Å shorter than in the 1:1 complex, discussed above). At this geometry, the excitation energy of T1 relative to S0 is ∼2.0 eV, ∼0.5 eV higher than (∼1.44 eV) in the 1:1 complex, while the required energy for O-O bond activation (energy difference between T1 minimum and triplet state of the “transition point”) is ∼7.9 kcal/mol, almost 3 kcal/mol lower than (∼10.8 kcal/mol) in the 1:1 complex. The reason that the triplet states of [Ru(mptpy)2]4+ and [S2O8]2- come into resonance at a shorter O-O peroxo bond distance in the 1:2 complex can be traced to smaller geometry distortions of [Ru(mptpy)2]4+ at the transition point in the 1:2 complex compared to those in the 1:1 complex. In the former, [Ru(mptpy)2]4+ remains nearly at the same geometry as the global S0 equilibrium, while in the latter, a terminal azobenzene rotates by 43° about the bridging CdC bond. This rotation is expected to destabilize SA0 relative to TA1 (which is being optimized along the O-O stretch) and thus maintain the S0-T1 gap in [Ru(mptpy)2]4+ smaller and force further elongation along O-O to stabilize TB1 on persulfate. In the 1:2 complex, the second persulfate acts as a counterforce to the active persulfate in balancing geometrical distortions of the dye core. The quantum mechanical aspect of electron transfer in the 1:2 complex was elucidated at the TCDM level using a threefragment interaction model: A, [Ru(mptpy)2]4+; B, [S2O8]2-(active); C, [S2O8]2-(spectator). The active persulfate is expected to capture the electron from [Ru(mptpy)2]4+ by activating its peroxo bond, while the spectator remains near its equilibrium geometry (i.e., O-O ) 1.46 Å). The resulting eigenstates of this three-component system are similar to eq 5, with added zero-order states of the spectator

|Ti′〉 )

∑ ci,n|TAn〉 + ∑ ci,m|TBm〉 + ∑ ci,k|TCk〉 n

m

k

(7) In order to estimate the exciton interaction between {[Ru(mptpy)2]4+(A) · · · [S2O8]2-(C)} and [S2O8]2-(B), we construct a small interaction Hamiltonian consisting of 6 excited triplet

6292


Figure 4. Illustrative 6 × 6 interaction matrix consisting of two triplets from each of the three fragments [Ru(mptpy)2]4+(A), “active” [S2O8]2-(B), and “spectator” [S2O8]2-(C). The diagonal contains (zeroorder) excitation energies calculated for isolated fragments. The offdiagonal matrix elements are fragment exciton interactions, Vij′(AB), Vij′(AC), Vij′(BC), evaluated using eq 4.

states of the each three fragments, a 18 × 18 matrix. The diagonal elements of this matrix are the excitation energies of the individual fragments (zero-order energies) calculated at the geometry of the complex {[S2O8]2- · · · [Ru(mptpy)2]4+ · · · [S2O8]2-} using the TDDFT/PCM method. The off-diagonal elements are computed using eq 4. To clarify this protocol, we show as an example a 6 × 6 matrix of fragments A and B and C in Figure 4. These studies show that, despite the earlier transition state and the lower barrier, the value of the interaction matrix element V11′(AB) for the resonant first triplet states of {[Ru(mptpy)2]4+ (A) · · · [S2O8]2-(C)} (i.e., mainly of [Ru(mptpy)2]4+(A)) and [S2O8]2-(B) is only 0.003 eV for the 1:2 complex, compared with -0.013 eV in the 1:1 complex. The small interaction matrix element can be understood by analyzing Mulliken transition charges in the TA1 state. Indeed, in the 1:1 complex the charge transition from Ru to the ligands has a more pronounced polar character where a majority of the negative charge migrates to one of the N ligand atoms. This creates a sizable transition dipole moment, 4.44 bohr*e, favorable for a strong exciton interaction with an excited dipole on [S2O8]2-. In contrast, in the 1:2 complex, the negative charge is more evenly (symmetrically) distributed across the ligand atoms. Such a distribution is indicative of a smaller transition dipole, 0.15 bohr*e, and a weaker interaction with excited triplet on [S2O8]2-. Diagonalization of the 18 × 18 matrix with 6 triplets from each of the three fragments whose geometries, charges, and excitation energies were taken at the transition structure, yields essentially unmixed eigenstates. The weights for configuration TA1 are 0.3%, 96%, and 2.3% in the T1′, T2′, and T3′, respectively; thus, T2′ contributes the most to the electron transfer rate. Using the symmetry factor of 2 (two available pathways in the 1:2 complex), the uncorrected results for the electron transfer rate and electron transfer lifetime, τ2′, are 1.1 × 10-10 fs-1 and 9.4 µs, respectively. This finding is qualitatively consistent with experimental measurements where the 1:2 complex is observed to react a little faster than 1:1. The Hinshelwood correction factor is smaller in the 1:2 complex due to the fact that there is 3 kcal/mol less energy to be put into the active vibrational modes. We use the correction factor of 86 at 300 K, bringing the corrected corrected electron transfer lifetime, τ2, down to 108.4 ns, virtually indistinguishable from the 1:1 corrected electron transfer lifetime, given the large error bars on the τ1 and τ2 values. 3.3.3. Comparisons of [Ru(mptpy)2]4+ and [Ru(bpy)3]2+, and Their Photoinduced Oxidation by Persulfate [S2O8]2-. Comparisons of the above presented computational data on photoinduced electron transfer between [Ru(mptpy)2]4+ and

Kaledin et al. persulfate [S2O8]2- with our earlier findings18 on [Ru(bpy)3]2+ reveal some differences and similarities in electronic structures, mechanism, and electron transfer rate. The most important difference in electronic structure of these two dyes is the appreciably (0.4-0.5 eV) smaller excitation energy of TA1 in [Ru(mptpy)2]4+. This necessitates further (relative to the 1.61 Å, reported for reaction with [Ru(bpy)3]2+) elongation of the activated peroxo bond of [S2O8]2- in order to bring its triplet (TB1) state in resonance with the TA1 state of [Ru(mptpy)2]4+. Indeed, as shown above, the calculated O-O distance, 1.77 Å, at the “transition point” of the reaction [Ru(mptpy)2]4+* with [S2O8]2- is 0.16 Å longer than that obtained for the reaction of [Ru(bpy)3]2+* with [S2O8]2-. In turn, this difference in O-O bond distance leads to the larger energy barrier (calculated relative to T1 minimum of the complex), which was calculated to be 10.8 and 6.9 kcal/mol for the [Ru(mptpy)2]4+ and [Ru(bpy)3]2+ complexes, respectively. Consequently, the difference in the calculated barrier heights correlates with much slower electron transfer rates to the persulfate for [Ru(mptpy)2]4+ compared to the [Ru(bpy)3]2+. The electron transfer rates (κ1) in water are calculated to be 1/κ1 ) 199.4 and 47 ns for the 1:1 persulfate complexes of [Ru(mptpy)2]4+ and [Ru(bpy)3]2+, respectively. Thus, the larger the excitation energy of the dye, the faster electron transfer from the photoexcited dye to persulfate. Another difference in electronic structure of these two dyes is a much stronger configuration mixing found in the low-lying triplets of [Ru(mptpy)2]4+. This multireference character of electronic wavefunction manifests itself in a highly complicated curve crossing behavior along the electron transfer reaction coordinate and involvement of at least four triplets over the range of geometries covering the Franck-Condon region and including the transition point. From a purely theoretical point of view, this property of [Ru(mptpy)2]4+ poses serious computational problems as straightforward single determinant DFT calculations may fail due to multiple determinants (we encountered such problems for the T1 state of the 1:1 complex). It is thus encouraging that TD-DFT was shown here to be adaptable to multireference excited-state wavefunctions provided that the ground state is a well-defined single-reference wavefunction. Previously, it was shown that photoinduced electron transfer between [Ru(bpy)3]2+ and [S2O8]2- could occur via both “unimolecular” and “bimolecular” pathways.18,25a The former assumes formation of a stable complex before electron transfer occurs, while the latter requires the persulfate collisions with dye molecules to be much faster than intermolecular relaxation times. Under typical experimental conditions, both of these mechanisms are likely to compete with each other. This competition depends on concentrations, ionic strength (or buffer conditions), solvent composition, and other factors. This distinction between the mptpy and bpy dyes arises due to a weak interaction between the two reactants. Since the calculated [Ru(mptpy)2]4+-[S2O8]2- binding energy, 4.6 kcal/mol, is almost two times larger than that for the [Ru(bpy)3]2+-[S2O8]2bond, 2.1 kcal/mol,18 one may expect the probability of a “unimolecular” pathway to be much higher for [Ru(mptpy)2]4+ than [Ru(bpy)3]2+ at room temperature. While we observed no major difference between the two mechanisms for the electron transfer rate in the bpy dye, the rate could be faster via the bimolecular mechanism in the mptpy dye. Indeed, if the two fragments collided before the [Ru(mptpy)2]4+ in its TA1 state could readjust its geometry (ring rotation) due to interactions wih [S2O8]2-, the SA0-TA1 gap would be closer to that in the persulfate, and electron transfer would occur at shorter values



TABLE 6: Results of Kinetics Fitting of the {[Ru(mptpy)2]4+ · · · ([S2O8]2-)n} (n ) 0, 1, 2) CH3CNa b

τ0 (ns) kq (M-1 s-1)c τ1 ) 1/κ1 (ns) τ2 ) 1/κ2 (ns) K1 (M-1)e K2 (M-1)f ∆G1 (kcal/mol)e ∆G2 (kcal/mol)f

0%

10%

20%

30%

174 (4.1 ( 0.2) × 107 298 ( 2 149 ( 1 (8.9 ( 0.1) × 103 180 ( 9 -5.28 ( 0.01 -3.012 ( 0.002

176

Insights into Photoinduced Electron Transfer Between [Ru(mptpy)2]4+

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