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Electron Transfer Dynamics for a DonorBridge-Acceptor Complex in Ionic Liquids Jessalyn A. DeVine, Marena Fekry, Megan E. Harries, Rouba AbdelMalak Rached, Joseph B. Issa, James F. Wishart, and Edward W. Castner J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.5b03320 • Publication Date (Web): 15 Jun 2015 Downloaded from http://pubs.acs.org on June 21, 2015

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The Journal of Physical Chemistry

Electron Transfer Dynamics for a Donor-Bridge-Acceptor Complex in Ionic Liquids Jessalyn A. DeVine,†,§ Marena Labib,‡ Megan E. Harries,‡,k Rouba Abdel Malak Rached,‡ Joseph Issa,† James F. Wishart,∗,¶ and Edward W. Castner, Jr.∗,† Department of Chemistry and Chemical Biology, Rutgers, The State University of New Jersey, Piscataway, NJ 08854, Department of Natural Science, Fordham University, New York, NY, 10023, and Department of Chemistry, Brookhaven National Laboratory, Upton, NY 11973-5000 E-mail: [email protected]; [email protected]

∗

To whom correspondence should be addressed Department of Chemistry and Chemical Biology, Rutgers, The State University of New Jersey, Piscataway, NJ 08854 ‡ Department of Natural Science, Fordham University, New York, NY, 10023 ¶ Department of Chemistry, Brookhaven National Laboratory, Upton, NY 11973-5000 § present address: School of Chemistry, University of California at Berkeley, Berkeley, CA 94720 k present address: Department of Chemistry, University of Colorado at Boulder, Boulder, CO 80309 †

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Abstract Intramolecular photoinduced electron transfer from an N,N -dimethyl-p-phenylenediamine donor bridged by a diproline spacer to a coumarin 343 acceptor was studied using time-resolved fluorescence measurements in three ionic liquids and in acetonitrile. The three ionic liquids have the bis(trifluoromethylsulfonyl)amide anion paired with the tributylmethylammonium, 1-butyl-1-methylpyrrolidinium, and 1-decyl1-methylpyrrolidinium cations. The dynamics in the two-proline donor-bridge-acceptor complex are compared to those observed for the same donor and acceptor connected by a single proline bridge, studied previously by Lee, et al. (J. Phys. Chem. C 2012, 116, 5197). The increased conformational freedom afforded by the second bridging proline resulted in multiple energetically accessible conformations. The multiple conformations have significant variations in donor-acceptor electronic coupling, leading to dynamics that include both adiabatic and nonadiabatic contributions. In common with the single-proline bridged complex, the intramolecular electron transfer in the two-proline system was found to be in Marcus inverted regime.

Introduction Electron transfer (ET) reactions are among the simplest chemical reactions and are ubiquitous in chemical and biological systems. 1 However, challenges remain for understanding electron-transfer reaction rates and heterogeneous dynamics in complex environments. Longrange electron transfer, in particular where the donor and acceptor are separated by a molecular linker that may or may not play a role in the reaction, is a fundamental process for understanding respiration and enzymatic catalysis, in addition to designing circuitry for molecular electronics. 2,3 photoinduced electron transfer reactions occur when one of the reactants is in an excited electronic state and thus is a crucial process in harvesting and converting natural light to energy in both natural and synthetic systems. 4,5 Donor-bridge-acceptor (D-B-A) systems provide favorable templates for investigating 2


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long-range and photoinduced ET reactions due to the ability to tune specific parameters of the ET dynamics, such as donor-acceptor distance, energy of solvation, donor-acceptor electronic coupling, and chemical nature and relative orientation of the reactants. 6–10 Another advantage of studying intramolecular donor-acceptor complexes is that the ET reaction in these systems is decoupled from other transport phenomena (such as diffusion) that tend to obscure the effects of local solvation environment on bimolecular ET reactions. 11 Donor-bridge-acceptor complexes using polyproline bridges have been used extensively to determine the distance dependence of ET in various systems, due to the conformational rigidity of the five-membered ring. 12,13 Issa, et al., analyzed the electron transfer kinetics in two series of D-B-A molecules with the N,N -dimethyl-p-phenylenediamine (DMPD) electron donor linked to the pyrene-1-sulfonyl (Pyr) electron acceptor by 0–3 glycines or prolines. 14 This work included an in-depth conformational analysis for each system, resulting in a detailed account of the distance and conformational dependence of ET in several traditional solvents. Ionic liquids (ILs), defined as ionic compounds having melting points less than 100 ◦ C, have attracted attention in recent years due to their deviation from traditional solvent behavior 15–17 and their applications to energy storage and generation technologies. 18 Use of fluorescent probes has provided interesting details of the polarity and solvation environments experienced by solutes in ILs. 11,19–27 The thermal and electrochemical stability of ILs combined with their intrinsic properties of negligible vapor pressures and high conductivities has sparked interest in implementation of these materials as media for energy transport, and they have been successfully featured as electrolytes in lithium-ion batteries and dye-sensitized solar cells. 28–30 Because of the interest in ILs as media for energy applications, a more detailed understanding of electron-transfer reactions in these solvents is desirable. Careful comparisons of ET dynamics in ILs and neutral solvents of similar viscosities indicate that the ionic character of the solvent does not seem to have a significant impact on kinetics for bimolecular

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reactions. 31 However, the intrinsic kinetics of bimolecular ET may be obscured by transport processes such as diffusion in viscous solvents, neutral or ionic. 32 To avoid this complication, intramolecular ET reactions have been studied by several groups. 11,33–36 In several cases, it was found that the reactions in ILs exhibit distributed dynamics and are often solventcontrolled. 11,36 Previously, Lee, et al., compared ET dynamics in ionic liquids and neutral solvents by investigation of a D-B-A complex consisting of DMPD as electron donor connected to the excited-state acceptor coumarin 343 (C343) by a proline bridge. Using time-resolved fluorescence, the excited state dynamics of DMPD-Pro1 -C343 (P1 ) was studied in the neutral solvents acetonitrile and methanol, and in two ILs based on the bis(trifluoromethylsulfonyl)amide 36 (NTf− 2 ) anion.

Figure 1: Reaction scheme for photo-induced intramolecular charge transfer for P2. State 0 (A) represents the D-B-A acceptor HOMO, state 2 (A∗ ) is the acceptor LUMO and state 1 (D) is the donor HOMO. In the present work, we extend the work of Lee, et al., and Issa, et al., by studying electron transfer in the two-proline complex DMPD-Pro2 -C343 (P2 ). The reaction scheme for photo-induced intramolecular charge separation in P2 is shown in Fig. 1. A bridge4


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acceptor complex that is lacking an electron donor, tBu-Pro-C343 (tBu), was used as a control. The molecular structures of P1, P2, and tBu are shown in Figure 2. The dynamics following photoexcitation of coumarin 343 were investigated in acetonitrile and three ILs using the NTf− 2 anion with three different cations. The IL anion and cations used in this work are shown in Figure 3. In addition to the two similarly sized IL cations studied by + Lee, et al., methyltributylammonium (N+ 1444 ) and 1-butyl-1-methylpyrrolidinium (Pyrr14 ),

we included the cation 1-decyl-1-methylpyrrolinidium (Pyrr+ 1,10 ) to investigate the effects of a longer alkyl chain on the electron-transfer rate and mechanism. In the case if this IL, the longer decyl chain causes a change in the structure of the liquid, resulting in distinct polar and nonpolar domains that set it apart from its butyl congener where such polarity segregation does not exist. 37–39 H N

O O N

N O

O

N O

DMPD-Pro1-C343

O N

O

N

O O

N H

O

O

N

tBu-Pro-C343

N O

O

N

DMPD-Pro2-C343

Figure 2: Structures of the P1, P2 donor-bridge-acceptor and the tBu bridge-acceptor molecules.

O F 3C

O

NS

S O O

N+

Pyrr1,10 +

N+

Pyrr14 +

CF 3 N+

NTf2-

N1444 +

Figure 3: Structures of the three ILs.

Experimental Methods − + − The ionic liquids N+ 1444 /NTf2 and Pyrr14 /NTf2 were purchased from IoLiTec and dried under − vacuum for 4-6 hours before use. Pyrr+ 1,10 /NTf2 was synthesized at Brookhaven National

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Laboratory. Acetonitrile (anhydrous, 99.8%) was purchased from Sigma Aldrich and used as received. The synthesis of the donor-bridge-acceptor molecules followed previously reported procedures. 14,36 A detailed description of the synthesis of P2 is given in the supporting information.

Time-Resolved Fluorescence Measurements Samples were prepared to have an absorbance of less than 0.15 at 430 nm to avoid multiple scattering. Acetonitrile samples were prepared by dissolving a small amount of the chromophore into the solvent and diluting until the desired absorbance was reached. Samples of P2 in IL solution were prepared by adding a small amount of a concentrated acetonitrile P2 stock solution to a previously dried IL, followed by removal of the acetonitrile under vacuum for 4-6 hours. Neat IL was then added to dilute the solution to the desired absorbance. Fluorescence cuvettes with a 10 mm optical path (Type 23H from NSG Precision Cells) were used for optical spectroscopy. Sample temperature was regulated to ±0.1 K using a Quantum Northwest TLC-50 thermoelectric controller. Steady-state fluorescence emission and excitation spectra were measured using a Fluoromax 3 fluorimeter.

Time-correlated single-photon counting (TCSPC) measurements

were performed using an experimental setup described previously. 23 A fs Ti:sapphire laser (Spectra-Physics Tsunami) was tuned to 860 nm, which was then frequency doubled to provide the 430 nm excitation pulses used for our measurements. Sample emission was observed for a series of emission wavelengths centered around the steady-state maximum. The emission bandpass of the Acton SP-150 monochromator was set to 2.5 nm.

Analysis of Time-Resolved Fluorescence Transients The convolute-and-compare method was used to fit TCSPC data to two models. The first and more conventional model used was a multi-exponential model,

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I(t) =

Z

N X

t 0

R(t − t′ )

Ai e

−t′ /τ

i

i=1

!

dt′

(1)

where R(t) is the instrument response function and N was set to 4 or 5. Our version of the convolute-and-compare method 23,40 was implemented in Igor Pro. 41 The second model used for analysis of the TCSPC fluorescence transients, used previously by Lee, et al., considers the sample response as arising from a continuous distribution of exponential decays. 36 I(t) =

Z

t ′

0

R(t − t )

Z

∞

g(τ )e

−t′ /τ

dτ dt′

0

(2)

The distribution fitting was performed using a quadratic programming (QP) method 36 implemented in MATLAB. 42 All fitting methods were identical for the experiments on the P1 samples by Lee, et al., who provided a more detailed description of these models and their implementations. 36

Electronic Structure Calculations To explore the conformational degrees of freedom of the P2 D-B-A complex relative to P1, calculations of structural properties such as donor-acceptor coupling and the driving force of electron transfer were performed for the lowest-energy conformations of P2. Conformational conventions were adapted from the work of Issa, et al., and account for differences in orienO

O

O

H C1

N2

C3

!

cis (c) α up (U )

H C4

: : :

N

N1

5◦ < |φ| < 20◦ |ψ| < 150◦ ϕ < 0◦

O

O

H

C2

"

H C3

#1 C2

N4

trans (t) β down (D)

O

H C3 C4

: : :

N1

H C2

N1

C3 C 4

#2

170◦ < |φ| < 180◦ |ψ| > 150◦ ϕ > 0◦

Figure 4: Criteria used for classification of diproline conformations. Adapted from Issa, et al. 14

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tation about the carbonyl between the two prolines (cis, c or trans, t), peptide backbone dihedral angle (α or β), and proline ring puckering (up, U or down, D). 14 The conformations and dihedral angle criteria are defined in Figure 4. All geometry optimizations were carried out using Gaussian09. 43 Semi-empirical geometry optimizations using the PM6 Hamiltonian 44 were performed on a proline dipeptide to obtain the 16 possible conformations. Optimized structures of the donor and acceptor were then connected to each of these bridges and the resulting D-B-A molecule was further optimized. Calculations were run both for gas phase molecules and using the Integral Equation Formalism Polarizable Continuum Model (IEF-PCM) with a dielectric constant of 36, chosen to model acetonitrile and the typical polarity experienced by coumarin solvatochromic probe molecules in IL solutions. 23 DFT ground state geometry optimizations of P2 were performed using the B3LYP functional and 6-31+G(d,p) basis set. Time-dependent DFT calculations (using the same functional and basis as in the optimizations) were then performed on the resultant geometries. Atom-centered charges were obtained from fits to the electrostatic potential using the CHelpG algorithm 45 in Gaussian09. 43 To obtain all the required diagonal and off-diagonal transition dipole matrix elements, the Dalton quantum chemistry package was used. 46 These results were used as input to the Generalized Mulliken-Hush algorithm 47 for evaluating the donor-acceptor coupling element (HDA ) for each conformation. From the 16 starting conformations, 8 distinct conformations corresponding to local energy minima were obtained. The five lowest-energy conformations and energies relative to the lowestenergy conformer are shown in Figure 6.

Results and Discussion Lee, et al., characterized the dynamics of electron transfer from DMPD to C343 in a D-B-A system utilizing a single proline bridge (DMPD-Pro-C343, P1 ). 36 In this system, only a single low-energy conformation was obtained using geometry optimization methods similar

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to those used here. The ET kinetics were measured for two neutral solvents, methanol − + − and acetonitrile, and two ionic liquids, N+ 1444 /NTf2 and Pyrr14 /NTf2 . The fluorescence

rate distributions obtained in that work showed that the dynamics in ILs were significantly more distributed than in the neutral solvents. 36 Analyses of the temperature dependence for the observed rates using the Marcus and Arrhenius equations show that the ET reaction was nearly barrierless, with barrier heights of ∆G∗ ∼ 0.1 eV in all four solvents. Electron transfer in this system was found to be in the Marcus inverted regime for all solvents, using the previous estimate for the total reorganization energy for P1 of λ=1.0 eV. Lee, et. al. reported ∆G0 values in the range of 1-2 eV, indicating that the use of Marcus theory to analyze kinetics in a DMPD-Pron -C343 system is likely to be well-founded. Shim and Kim used molecular dynamics (MD) simulations to explore the kinetics and dynamics of unimolecular ET reactions in the IL 1-ethyl-3-methylimidazolium hexafluo− 33,34 rophosphate (Im+ They found that the derived activation free 21 /PF6 ) and in CH3 CN.

energy as a function of reaction free energy was consistent with that predicted by Marcus theory for reactions with reasonably low reaction free energies (|∆G0 | < 2 eV). 33,34 Free energies, solvent reorganization energies, barrier transmission coefficients, and diabatic free energy surfaces were found to be quite similar in the two solvents, and inclusion of solvent relaxation dynamics in the simulations did not significantly alter the diabats, in spite of the − high viscosity of Im+ 21 /PF6 . Rate constants derived from the simulations were slightly slower

in the IL than in CH3 CN, and showed slightly more variation with changing the activation − free energy for charge transfer in Im+ 21 /PF6 than in CH3 CN. Shim and Kim clearly demon-

strated that a Grote-Hynes approach to calculating the molecular friction that determines reactive barrier crossing is a reasonable approach, while Kramers theory fails in this aspect. 33,34 Shim and Kim also studied adiabatic intramolecular electron-transfer for a model diatomic reactive complex in solution of the IL 1-butyl-3-methylimidazolium dicyanamide (bmim+ /DCA− ) and in CH3 CN, to find that for both systems, the Grote-Hynes theory for barrier crossings gives a reasonable description. 35 They point out that the biphasic nature

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of the solvation dynamics, including a very rapid sub-picosecond component as well as the much slower ns-scale dynamics, is the reason why the friction that determines barrier crossings for adiabatic electron-transfer reactions can be similar for CH3 CN and the IL, despite the large difference in shear viscosities. 33–35 − Figure 5 compares the fluorescence transients for P1, P2, and tBu in Pyrr+ 14 /NTf2 . It is

clear from this figure that the introduction of an additional proline significantly increases the lifetime of the observable fluorescence for P2 relative to P1 ; from the ET rate distributions (Figure 7), we see that this is likely due to a higher probability of radiative emission relative to any other form of relaxation. Unsurprisingly, this indicates that increasing the distance between donor and acceptor results in a decrease in electron transfer efficiency in each of the solvents. The fluorescence transients for P2 in all four solvents for the temperature range from 283 to 333 K are given in the supporting information.

4

10

3

10

2

10

0

10

20 ns

30

40

Figure 5: Fluorescence transients from TCSPC for tBu (black), P2 (red), and P1 (blue) in − Pyrr+ 14 /NTf2 at 298.2 K.

Conformational Analysis of DMPD-Pro2 -C343 As described in the methods section, a conformational analysis in the spirit of Issa, et al., was performed for P2, the two-proline D-B-A molecule. 14 Use of proline as a linker restricts the number of possible D-B-A conformations relative to more flexible peptides; in the one-proline oligomer, only one low-energy conformation need be considered to adequately account for 10


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any realistic population of D-B-A molecules at temperatures of interest. We note that in our analysis of ET kinetics in the DMPD-Pron -C343 systems, in particular the two-proline oligomer, it is assumed that the conformations obtained from the geometry optimization methods described earlier account for all possible conformations, regardless of the specific solvation environment. Calculations were only done for a dielectric continuum solvation model, which cannot account for the microscopic heterogeneity that is − likely to be experienced by solutes in ionic liquid solvents, in particular Pyrr+ 1,10 /NTf2 , which

is known to exhibit alkyl tail segregation leading to polar and non polar domains within the liquid on a molecular scale. 37–39 Assuming Boltzmann statistics, the five lowest-energy conformations of P2 obtained by our methods should account for more than 99.5% of the observable population. These conformations are shown in Figure 6 along with their energies relative to the lowest-energy conformation and HDA values. The three higher energy P2 conformations, – cαDD, cβUU, and cβDD with relative energies ∆E=0.149, 0.158, and 0.291 eV, respectively – were not included in our kinetic analysis because of the low probability that a D-B-A molecule will assume these high-energy conformations. The values of HDA are calculated using the 3-state Generalized Mulliken-Hush method introduced by Cave and Newton. 47 The three lowest-energy conformations have HDA values less than 50 cm−1 , which corresponds to the nonadiabatic electron transfer regime. However, cαUU and tβUD have strong donor-acceptor coupling, and so these conformations are in the adiabatic electron-transfer rate regime. The two groups of conformations are likely to give rise to different ET rates, which will be discussed later.

Estimation of Driving Force The free energy or driving force for photoinduced electron transfer is defined as

∆G0 = NA {e E 0 (D+• /D) − E 0 (A/A−• ) + w(D+• A−• ) − w(DA)} − ∆E0,0

11


(3)


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where NA is Avogadro’s number, e is the elementary unit of charge, E 0 (D+• /D) and E 0 (A/A−• ) are the reduction potentials of the isolated donor and acceptor, and ∆E0,0 is −1 the photon energy, which is taken to be ∆E0,0 = 12 hc(λ−1 abs + λem ), where λabs and λem are

the maxima in the steady-state excitation and emission spectra, respectively. 1,48 The electrostatic work terms, w(XY ) = (e2 ZX Zy )/(4πǫ0 ǫs RXY ), account for the interactions between the donor and acceptor in the ground (DA) and charge-transfer (D+• A−• ) states. In this expression for w(XY ), ǫ0 is the permittivity of free space, ǫs is the dielectric constant of the medium, Zi is the charge on molecule i, and RXY is the separation between the centers of mass for X and Y . 48 For the case of bimolecular electron transfer, the charges on donor and acceptor are 0 in the ground state and ±1 in the charge-transfer state. However, for systems in which the ET is intramolecular, such as P2, it is more accurate to consider the reaction as a charge shift from the donor to the acceptor moiety of the molecule. In the ground state, the donor and acceptor are dipolar and polarizable so that the magnitude of charge transfer is most likely less than 1. To account for this, rather than using the bimolecular values for the charges on donor and acceptor, we estimated the charges on DMPD and C343 from the SCF population analysis generated by Gaussian following optimization for the ground state and TD-DFT calculations for the charge transfer state. To obtain an estimate for the charges needed to calculate the electrostatic work terms in Eq. 3, the charges were first obtained from fits to the electrostatic potential using the CHelpG algorithm 45 on the gas-phase optimized geometries of P2, then summed over the atoms corresponding to donor and acceptor to obtain an estimate for ZX ZY . Details of this process are reported in the supporting information. An average value of the work term was found using Boltzmann statistics, neglecting the three higher-energy conformations not shown in Fig. 6, which constitute less than 1% of a thermal population.

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Table 1: Thermodynamic and electrochemical parameters relevant to electron transfer of P2. ∆ED−A ∆E0,0 λo ∆G0 ∆G∗ λ Ea (V) (eV) (eV) (eV) (eV) (eV) (eV) CH3 CN 1.19 2.81 0.19 -1.64 0.089 1.03 0.075 − Pyrr+ /NTf 0.99 2.76 0.17 -1.71 0.167 0.92 0.153 14 2 + − Pyrr1,10 /NTf2 – 2.77 0.15 -1.71 0.073 1.13 0.059 + − N1444 /NTf2 1.01 2.77 0.15 -1.71 0.200 0.87 0.186 0 +• 0 −• ∆ED−A is E (D /D) − E (A/A ), the difference between the reduction potentials, for which the values were reported by Lee, et. al. 36 ∆E0,0 is the photon energy for the ground to first excited singlet states of P2, and λ0 are the estimates for the outer-sphere reorganization energies. ∆G0 values are a Boltzmann average over the five lowest-energy conformations. ∆G∗ , defined in Eq. 6, is the barrier height and Ea is the Arrhenius activation energy. ∆G∗ and Ea were calculated from the temperature-dependence of the fluorescence data, with details provided in the Supporting Information.

Analysis of the time-resolved fluorescence transients Figure 7 presents the results of fitting the TCSPC fluorescence transients for P2 as described in the methods section, using both the discrete sum of exponentials and the distribution of exponentials models. Further details regarding the fitting results are provided in the supporting information. The presence of two fluorescence rate regimes is likely due to the presence of multiple conformations, which can lead to different lifetimes for the singlet photoexcited acceptor. Fig. 7 shows that the analysis of the fluorescence transients represents distributed dynamics over time scales from 50 ps to 4 ns. Using a discrete five-exponential model results in fits that are equally as good as those obtained from the distribution model. The distribution model generally shows three broad peaks, providing confidence that the discrete exponential fits will be suitable for analyzing the ET rates. The general shape of the distribution of rates for P2 shown in Fig. 7 was similar in all four solvents (see Fig. 7). The distributions indicate the presence of three distinct excited state relaxation processes. The slowest process (τ ≈ 3 ns), which was also observed for each of the control samples, was attributed to the non-reactive radiative decay of the coumarin moiety.

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0.01

0.1 2

4

6 8

1 2

4

10

6 8

2

4

0.1 2

CH3CN

333 K

0.01

6 8

1.0

0.4

0.5

0.2

0.0 1.0

0.0

4

6 8

1 2

4

6 8

10 2

4

6 8

+

-

N1444 /NTf2

333 K

1.0

Distribution Fit Probability

323 K 0.5

0.5 0.0

0.0 1.0

313 K 0.5

0.5 0.0

0.0 1.0

303 K 0.5

0.5 0.0

0.0 1.0

293 K

0.4

0.5 0.0 1.0

323 K

0.5

0.2 0.0 0.4

0.0 1.0

313 K

0.5

0.2 0.0 0.4

0.0 1.0

303 K

0.5

0.2 0.0 0.4

0.0 1.0

293 K

Multiexponential Fit Amplitude

0.0


0.5


0.5

0.0

283 K

0.5

0.2

0.0 1.0

0.0

0.5

0.2

0.0

0.0

0.4

0.5 0.0 1.0

283 K

0.5

0.0 2

4

0.01

6 8

2

4

6 8

0.1

2

4

0.5 0.0

6 8

1

2

10

4

0.01

6 8

0.01

0.5

4

6 8

1 2

4

4

6 8

2

4

6 8

1

10

tau (ns)

0.1 2

2

0.1

tau (ns)

6 8

10 2

4

0.01

6 8 -

+

Pyrr1,4 /NTf2

333 K

0.1 2

0.5

1

4

6 8

1 2

4

6 8

10 2

4 +

6 8 -

Pyrr1,10 /NTf2

333 K

1.0 0.5

0.0 0.5

0.0 0.5

0.0 0.5

323 K

1

0

313 K

1

0

303 K

1

0

293 K

0.0



0.5

0

0.5

1.0 0.5

0.0 0.5

0.0

313 K

1.0 0.5

0.0 0.5

0.0

303 K

1.0 0.5

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1

0.0

323 K

0.0

293 K


0.0


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1.0 0.5

0.0 0.5

0

283 K

0.0 0.5

1

0.0

283 K

1.0 0.5

0.0

0 2

0.01

4

6 8

2

4

0.1

6 8

2

1

4

0.0

6 8

0.0 2

10

0.01

4

6 8

2

4

6 8

0.1

tau (ns)

2

1

4

6 8

10

tau (ns)

Figure 7: Distributions (solid lines) and multi-exponential (dots and sticks to zero) fit− ting results for P2 in all four solvents- top: left, CH3 CN; right, N+ 1444 /NTf2 ; bottom: left, − + − Pyrr+ 14 /NTf2 ; right, Pyrr1,10 /NTf2 . The solid curves represent fits to the distributed exponential model, while fits to the discrete exponential model are shown as vertical lines and circles, with the axes for these normalized amplitudes shown on the right. The dashed curves in the graphs for 293 K represent the complete solvation response for coumarin 153, calculated from the parametrization of the measured solvation response from Zhang, et al. 27

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The middle component of the P2 fluorescence rate distributions (τ ≈ 1 ns) displayed Arrhenius behavior with changes in temperature, enabling calculation of dynamic parameters from the temperature-dependent results. The temperature dependence of the intermediate time scale dynamics represented by this fluorescence lifetime component can be analyzed using the Arrhenius or Marcus rate equations, with details described in the supporting information. As was the case for the P1 system, electron transfer in P2 is nearly barrierless with values of ∆G∗ in the range from 0.1-0.2 eV. This photo-induced reaction is in the inverted Marcus rate regime, since −∆G0 > λ. The fastest components of the P2 fluorescence rate distributions are scattered about a value of τ ≈ 0.1 ns. The fastest fluorescence lifetime component for P2 did not display any clear temperature dependence in any of the four solvents, consistent with a near-barrierless process for small values of ∆G∗ . The photodynamics for the C343 chromophore in the tBu control molecule in CH3 CN displayed a lifetime component of about 0.1 ns in its multiexponential distribution, so more consideration is needed to identify a likely assignment for this lifetime component in P2. As described below, this peak likely results from electron transfer that occurs only for certain conformations of P2. Another possible ET mechanism could result from tunneling in the inverted Marcus region. There are several reports in the literature describing specific solvation effects for aromatic chromophores in ionic liquid solutions. 49–51 Khatun and Castner used 2D NOE NMR methods to compare structures for IL cations having shorter and longer alkyl substituents, 51 showing that the longer n = 10 chain for Pyrr+ 1,10 decreased the probability of anion proximities to a Ru2+ (bpy)3 solute relative to the n = 4 group on Pyrr+ 14 . There are clear differences in the intermediate range order displayed in the bulk structure of ILs as a function of the length of the cationic alkyl groups. 52–56 With increasing alkyl chain lengths of n = 5 for imidazolium cations or n=6 for pyrrolidinium cations, intermediate range order appears in the bulk X-ray and neutron scattering as a first sharp diffraction peak in the range of 0.250.5 ˚ A−1 . 37–39,52–54,57–64 ILs having longer cationic alkyl tails show increased viscosities for

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n > 4. 65 Because of the clear possibility that an increased chain length could lead to a sig− nificantly different solvation environment, we included the n = 10 Pyrr+ 1,10 /NTf2 IL in this

study. The intermediate rate for photoinduced electron transfer for P2 of τ ≈ 1 ns showed a decrease in activation barrier by about a factor of 2 on changing from the Pyrr+ 14 to the Pyrr+ 1,10 cation. Studies of solvation dynamics in ILs reveal strongly non-exponential relaxation phenomena, with broad distributions of rates that span 3–4 orders of magnitude. The fact that solvation dynamics in ILs include rate processes that are both very fast and very slow relative to photoinduced reactions leads to significant additional complexity in understanding reaction dynamics in these media. 36 Using the experimental results for the solvation dynamics of coumarin 153 from Zhang, we fit the solvation time correlation function to a rate distribution to facilitate a direct comparison with the rate distribution of photoinduced electron-transfer for P2. The comparison is shown in Fig. 7 as the dashed line in the distributions for 293 − + − + − 21,27 K for the three ILs N+ While the solvation 1444 /NTf2 , Pyrr14 /NTf2 , and Pyrr1,10 /NTf2 .

dynamics of CH3 CN are very well characterized, the sub-picosecond time constants for the solvation time correlation function are much faster than the the fastest excited-state dynamics for P2. 66 It is clear that the solvation dynamics measured for coumarin 153 in the ionic liquids span the entire temporal range of the electron-transfer dynamics for P2.

Non-Adiabatic and Adiabatic Rate Limits The Marcus equation for nonadiabatic (or weak ) electron-transfer reaction rates is given by 67–69 kET,N A

1 2π = exp |HDA |2 √ h ¯ 4πλkB T

−∆G∗ kB T

.

(4)

Zusman investigated the rate regime for strong donor-acceptor coupling to show that when solvation dynamics can be described by a single relaxation time constant τs , the Marcus equation becomes

17



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kET,SC

1 = τs

r

λ exp 16πkB T

−∆G∗ kB T

Page 18 of 30

(5)

where the free energy barrier for electron transfer, ∆G∗ , is related to the reaction free energy ∆G0 by 1 ∆G∗ =

(∆G0 + λ)2 . 4λ

(6)

The adiabatic limit of the Marcus theory, Eq. 5, applies when the adiabaticity parameter g ≫ 1, where g = (4π/¯h)(|HDA |2 τs /λ). 70 − The description for the complete solvation dynamical response for Pyrr+ 14 /NTf2 and − Pyrr+ 1,10 /NTf2 is reported by Zhang, et. al., who showed that an excellent fit to the sol-

vation time correlation function is obtained using an ultrafast Gaussian response plus a much longer time-scale broadly distributed stretched-exponential response. Thus, the question of whether the photo-ET rates for P2 are in the non-adiabatic or solvent-controlled − regime depends on what kind of solvation response is being considered. For for Pyrr+ 14 /NTf2 − and Pyrr+ 1,10 /NTf2 at 293 K, the relevant parameters are τG = 0.38 and 1.16 ps and hτstr i

= 0.37 and 1.49 ns , respectively. 27 An averaged solvation time constant of hτ i=0.35 ns for − Pyrr+ 14 /NTf2 at 293 K was previously reported by Funston, et al., while a longer time con− 23 stant of hτ i=3 ns was observed for N+ Thus, the slower, distributed exponential 1444 /NTf2 .

solvation responses for each of the three ILs puts them solidly into the solvent-controlled regime with values of g ≫ 1, using the values for the donor-acceptor coupling for each of the five lowest energy conformations of P2 shown in Fig. 6. However, for the faster vibrational (or inertial) part of the IL solvent responses on the order of 1 ps, only the most strongly coupled conformations of P2 are expected to be in the solvent-controlled regime. The lower values of the donor-acceptor coupling HDA for the cαDD, cβUU and cβDD conformations of P2 lead to values of g ≪ 1, placing these conformations solidly in the non-adiabatic rate regime. While the Boltzmann factors for the two higher energy conformation of P2 are 4.2% for the cαUU and 1.1% for tβUD, their strongly coupled calculated estimates of HDA are 326

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and 134 cm−1 , respectively. Thus any P2 excited states adopting either of these two higher energy conformations could be expected to display solvent-limited ET rates on timescales of about 1 ps, while the majority (94%) of P2 conformations are in the solvent-limited rate regime, but with broad distributions of relaxation timescales that center about 1 ns, with faster dynamics occurring with increasing temperatures as the viscosities decrease and hence solvent relaxation accelerates. Such behavior is clearly consistent with what is shown in Fig. − + − + − 7 for Pyrr+ 14 /NTf2 and Pyrr1,10 /NTf2 . For N1444 /NTf2 , the shoulder in the distribution near

1.5 ns for P2 at 293 K is seen to sharpen and become faster with increasing temperature. Thus, the intermediate-time scale excited-state dynamics of P2 are fully consistent with most of the photo-induced reactions proceeding via a solvent-limited mechanism. For photoinduced reactions occurring from either of the two higher energy conformations predicted for P2, we expect that these will occur on ultrafast time scales that combine both solvation on 1 ps timescales combined with fluctuations of the donor-acceptor coupling that occur on similar timescales. 71 For sufficiently high temperatures, the thermal energies will exceed the torsional barriers between the conformations shown in Fig. 6, further complicating the task of unraveling the overlapping electron-transfer and solvation dynamics. Future studies of these systems below the glass transitions of the ILs would be desirable for two reasons. First, the distribution of P2 conformations would be frozen in place. Second, the solvation dynamics in the inertial regime are expected to be only very weakly temperature dependent, but the slower distribution of solvent relaxation would be expected to extend to ms and longer timescales.

Conclusions The photoinduced electron transfer dynamics of the P2 donor-bridge-acceptor molecule DMPD-Pro2 -C343 have been characterized and compared to those observed previously for the single-proline complex P1, DMPD-Pro-C343. 36 As for the P1 system, electron-transfer

19



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dynamics in P2 exhibited multi-exponential kinetics and are shown to be in the Marcus inverted rate regime. However, the conformational freedom allowed by the additional proline linker introduced additional complexity into the ET dynamics of P2 relative to P1. A fast component which showed little correlation with temperature is attributed to a nearly barrierless rate process. This fastest observed ET rate process likely arises from a superposition of non-adiabatic electron transfer from the three lowest energy conformers of P2, while two higher energy conformers, expected to account for about 5% of the ground-state distribution, account for a smaller fraction of the rate distributions limited by solvent reorganization and conformational fluctuations. The slower photoinduced electron transfer components of the rate distributions occur on time scales of about 1 ns, consistent with inverted regime dynamics with a barrier in the 0.1–0.2 eV range, with a notable decrease of the barrier by more than a factor of two observed on increasing the length of the cationic alkyl chain from − + − n=4 for Pyrr+ 14 /NTf2 to n=10 for Pyrr1,10 /NTf2 . We speculate that this may arise from a

difference in the ionic solvation environment surrounding the acceptor chromophore, since clear evidence of specific solvation has been shown in the molecular simulations from Terranova and Corcelli. 50 Thermal accessibility of multiple conformations of P2 leads to both strongly coupled and weakly coupled values of HDA . Because solvation dynamics span both an ultrafast inertial component as well as slower dynamics on the nanosecond time scale, the electron-transfer mechanism can be different for different conformations of P2.

Acknowledgement The authors would like to thank Dr. Min Liang for measuring the steady-state fluorescence spectra of tBu-Pro-C343. This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences under contracts DE-SC0001780 (E.W.C.), DE-AC02-98CH10886 (J.F.W.) and DE-SC0012704 (J.F.W.).

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Supporting Information Available The supporting information provides tables listing the fit parameters for the 4-exponential fits to the TCSPC fluorescence transients for P2, the distribution fits from the quadratic programming method to sums of Gaussians, a comparison between the fits for TCSPC transients for P2 and tBu, Arrhenius and Marcus plots for the temperature-dependent fluorescence rates for P2, how the solvation dynamics from Zhang, et al. 27 were computed for comparison with the fluorescence dynamics, and a description of how we evaluated the donor-acceptor coupling HDA and the electrostatic work terms required to calculate ∆G0 . This material is available free of charge via the Internet at http://pubs.acs.org/.

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