Electron Dynamics and IR Peak Coalescence in Bridged Mixed

Jul 23, 2015 - Dynamic IR peak coalescence and simulations based on the optical Bloch equations have been used previously to predict the rates of intr...
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Electron Dynamics and IR Peak Coalescence in Bridged Mixed Valence Dimers Studied by Ultrafast 2D-IR Spectroscopy Matthew C. Zoerb,†,∥ Jane S. Henderson,‡ Starla D. Glover,‡,⊥ Justin P. Lomont,†,° Son C. Nguyen,† Adam D. Hill,†,Δ Clifford P. Kubiak,*,‡ and Charles B. Harris*,†,§ †

Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, United States Chemical Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States ‡ Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, California 92093, United States §

S Supporting Information *

ABSTRACT: Dynamic IR peak coalescence and simulations based on the optical Bloch equations have been used previously to predict the rates of intramolecular electron transfer in a group of bridged mixed valence dimers of the type [Ru3(O)(OAc)6(CO)L]-BL[Ru3(O) (OAc)6(CO)L]. However, limitations of the Bloch equations for the analysis of dynamical coalescence in vibrational spectra have been described. We have used ultrafast 2D-IR spectroscopy to investigate the vibrational dynamics of the CO spectator ligands of several dimers in the group. These experiments reveal that no electron site exchange occurs on the time scale required to explain the observed peak coalescence. The high variability in FTIR peak shapes for these mixed valence systems is suggested to be the result of fluctuations in the charge distributions at each metal cluster within a single-well potential energy surface, rather than the previous model of two-site exchange.

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INTRODUCTION Ground state intramolecular electron transfer in symmetric transition metal dimers can have a very low barrier in systems with large electronic coupling and may proceed on the ultrafast time scale. As the barrier decreases, the odd electron can become delocalized across the molecule. The transition from well-defined, localized states to fully delocalized states has received significant attention among the electron transfer community.1−5 Near this transition, features expected of both delocalized and localized systems may be observed, and a comprehensive description of the electron dynamics is challenging. Knowledge of electron transfer rates is often critical to a full understanding of the electronic state. However, exchange kinetics are very difficult to measure at thermal equilibrium where there is no net change in reactants and products. In some cases, dynamical information may be revealed through peak coalescence. Peak coalescence is a spectral phenomenon caused by ground-state exchange.6−8 It is most often observed in NMR spectroscopy for systems undergoing geometrical exchange. As the rate of exchange increases, spectral features associated with each geometry first broaden, shift in frequency, and then collapse into a single peak reflecting an average configuration. Changes in temperature may be sufficient to modulate exchange rates enough to observe a wide range of coalescence from two well-resolved peaks to a single collapsed peak. The optical Bloch equations provide a means to extract quantitative © 2015 American Chemical Society

rate predictions and barrier heights for such reactions from the degree of spectral coalescence.6,9 In general, for peaks corresponding to two exchanging species to fully coalesce, the exchange rate constant must be on the order of the frequency splitting between the two peaks. This analysis can be quite successful in NMR spectroscopy where peak separation is typically in the Hz to MHz range, and exchange time constants on the order of seconds to microseconds are required to cause coalescence.6 Peak separation in IR spectroscopy is much smaller, in the THz range, and requires picosecond exchange to cause coalescence. On this much faster time scale, many other dynamical processes, such as fast geometric fluctuations, may contribute to IR lineshapes. Electronic dynamics may further complicate spectra through quantum effects such as tunneling or changes in electron density.10−12 It is not always possible to distinguish exchange from other dynamics affecting the IR line shape. Due to these potential interferences, the reliability of exchange rates determined from coalesced IR lineshapes has been questioned.13−17 A group of dimers of trinuclear ruthenium clusters (Figure 1) has been studied extensively for their mixed valence properties.18−35 In particular, infrared spectroscopic investigations have focused on peak coalescence of the carbonyl vibrations of the mixed valence species. The carbonyl ligand at each metal Received: July 13, 2015 Published: July 23, 2015 10738

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Figure 1. Bridging ligand (BL) and ancillary ligand (L) combinations for the dimers of ruthenium clusters in this work. The bridging ligand for compounds 1−3 is pyrazine (pz), for compounds 4 and 6 is 4,4′bipyridine (bpy), and for compound 5 is 1,4-diazabicyclo[2,2,2]octane (dabco). The ancillary ligand for compounds 1 and 6 is 4dimethylaminopyridine (dmap), for compound 2 is pyridine (py), for compounds 3 and 5 is 4-cyanopyridine (cpy), and for compound 4 is 1-azabicyclo[2,2,2]octane (abco).

Figure 2. FTIR spectra of compound 3 in acetonitrile (Panel A) and compound 6 in dichloromethane (Panel B) in three different oxidation states.

normalized to reflect that each peak in a −1 spectrum corresponds to only one CO ligand on each molecule, whereas in the 0 and −2 states the lone peak in each spectrum has contributions from both CO ligands. The frequency maxima for the peaks in the −1 spectrum are slightly shifted relative to the 0 and −2 states; however, this frequency shift can be explained by overlap of the individual CO peaks. The −1 spectrum of compound 3 in Figure 2A (solid line) exhibits much more overlap than can be explained by a simple sum of the 0 and −2 lineshapes. In this spectrum, the peaks appear substantially broader and shifted toward the average frequency of the peaks in the 0 and −2 spectra. This broadening and frequency shift is typical of the general changes observed for dynamically coalescing spectra.6 In the mixed valence state of these systems, the degree of peak overlap has been tuned over a broad range of coalescence.18−35 Spectra of some mixed valence dimers show virtually no coalescence, whereas others have only one carbonyl peak. No single sample can be tuned through the full range of coalescence; however, changes in temperature and solvent can lead to large changes in the spectra for a given dimer. Using peak fitting procedures based on the Bloch equations, electron transfer time constants ranging from 0.35 ps to ca. 10 ps were predicted.19,32 For these compounds, the Bloch equations predict that any exchange taking longer than 10 ps will not affect the IR spectrum, and a single CO peak is expected for exchange faster than 0.35 ps. These experiments revealed several important correlations regarding the changes in peak coalescence. First, ligand substitution has a dramatic influence on the degree of peak coalescence. It is well-known that the identity of the bridging ligand (BL) in bridged dimers is critical in mediating electron transfer. 1,3 The most significant coalescence is observed when pyrazine is the bridging ligand.

cluster site serves as a spectator ligand to electron dynamics. The CO frequency is sensitive to changes in electron density at the metal sites due to the π-backbonding interaction between the metal d-orbitals and the antibonding π* orbital of the carbonyl ligand.36 Spectra of the neutral dimers (Figure 2) show a single carbonyl peak indicating that the electronic environment at each metal site is equivalent. Spectra of the doubly reduced systems also have a single carbonyl peak, indicating that the two extra electrons are shared equally between the two metal sites, or approximately a −1 charge resides at each site. The frequency of this CO peak is redshifted ca. 50 cm−1 due to the extra charge density at each site. In the singly reduced state, however, significantly different spectra are observed. Carbonyl spectra associated with mixed valence dimers range in coalescence from two clearly defined peaks to a single broad peak at the average CO frequency, indicating that the electronic environment at each site can be highly variable. The degree of peak overlap is highly sensitive to ligand substitution, solvent identity, and temperature near the solvent freezing point, particularly when pyrazine is the bridging ligand. The smallest degree of overlap is observed when the two mixed valence peaks coincide with the CO frequencies of the neutral and doubly reduced dimers. In this case, the odd electron is described as fully localized at one site. As coalescence increases, the two peaks appear broader and shift toward the average CO frequency of the neutral and doubly reduced dimers. The highly variable peak coalescence observed in these systems has been attributed to frequency averaging resulting from changing rates of ultrafast electron transfer between the metal cluster sites. The −1 spectrum of compound 6 in Figure 2B (solid line) can be described as a sum of the spectra for the other two oxidation states. As in previous work, the 0 and −2 spectra are 10739

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horizontal, permitting a correlation between the excitation frequency at t = 0 and the frequency at later times. In the case of electron site exchange, if the average charge distribution at each site switches, it should be apparent in the 2D-IR spectrum as the frequencies of the corresponding CO peaks will switch and result in cross peak growth. To our knowledge, 2D-IR spectroscopy has not previously been used to monitor the dynamics of ground-state electron transfer. This is primarily due to the scarcity of systems having both picosecond time scale electronic exchange and vibrations with sufficient sensitivity to a change in electron density. The current study of electron exchange in mixed valence dimers is generally similar to that of geometric chemical exchange in that a molecular rearrangement is expected to alter the frequency of the observed vibrations. We collected 2D-IR spectra for several ruthenium dimers in a variety of solvents. Interestingly, none of these samples showed evidence of exchange within the time scale of the experiment. The vibrational lifetimes of these compounds limited our measurements to ca. 15 ps. The lack of exchange in these experiments allows us to place a lower limit on the exchange time constant at ca. 15 ps. As mentioned previously, the Bloch equations predict that any exchange taking longer than 10 ps will have no effect on the IR spectrum. While we were unable to directly measure the kinetics of electron transfer in these systems, we can conclude that electron transfer is too slow to cause IR peak coalescence. The lack of electron site exchange on this time scale is consistent with a fluctuation-based mechanism as the origin of peak coalescence in these mixed valence dimers.

Substitution of the ancillary ligands (L) also strongly influences the spectrum. Most of the dimers have a substituted pyridine ligand in the ancillary position. The extent of peak coalescence in these compounds has been shown to follow the electron donating character of the ligands; for example, a more highly electron-donating ligand such as 4-dimethylaminopyridine (dmap) results in more highly coalesced IR spectra. Electron transfer reactions in solution are usually highly sensitive to the surroundings.1−3 Not surprisingly, the extent of coalescence in the dimers is also very dependent on temperature and solvent. As the temperature is reduced near the solvent freezing point, the degree of coalescence increases. This anti-Arrhenius behavior is consistent with decoupling the solvent modes from the exchanging system and was taken as evidence of low barriers to electron transfer.32,33 This has also been described in terms of the loss of ergodicity near solvent crystallization.37 No further increase in coalescence occurs past the freezing point of the solvent. The degree of spectral coalescence upon freezing is similar for all solvents but is quite different at room temperature. Changes in coalescence are also observed with changes in solvent and can be correlated with the rate of solvent relaxation.32 The solvent relaxation parameter, t1e, is a measure of how quickly a solvent can rearrange to accommodate a change in charge distribution.38 Any significant change in ground-state charge distribution within a molecule is only possible if it is accompanied by a reorientation of the dipoles of nearby solvent molecules. The faster a solvent can reorganize, the faster the electron density can change. In the dimers, faster solvent reorganization rates are associated with more highly coalesced IR spectra.32 This relationship is particularly important as it broadly correlates the degree of peak coalescence with charge mobility in the solution. In pursuit of a more direct measurement of electron dynamics, we implemented two-dimensional infrared spectroscopy (2D-IR). 2D-IR is an ultrafast time-resolved technique capable of monitoring the kinetics of ground-state exchange reactions where the reactants and products are spectroscopically identical.39−42 We have previously used the doubleresonance implementation43 of 2D-IR in experiments to determine the time scale, mechanism, and transition state of fluxional rearrangement in iron pentacarbonyl44 and the role of torsional motion in vibrational population transfer in iron diene tricarbonyl compounds.45 This technique extends the vibrational information to two frequency axes representing an initial excitation (pump) and probe interaction with the molecule. A variable time delay between the pump and the probe pulses allows us to monitor spectral changes over time. The pump interaction excites a single normal mode of the system, providing a vibrational label analogous to isotopic labeling in NMR. An important difference is that the vibrational label is temporary, and decay mechanisms such as vibrational energy relaxation (VER) or intramolecular vibrational redistribution (IVR) determine the time scales accessible to the technique. If no exchange occurs, the vibrational label remains at the same frequency and will result in a peak along the diagonal of the 2D spectrum. If the chemical environment around the vibration changes, the frequency of the vibrational label will change. If the frequency shift is small, e.g. from a change in solvation, the result may only be a change in the inhomogeneous line width of the peak (spectral diffusion). For larger frequency shifts, e.g. from an isomerization reaction, a new peak will appear reflecting the vibrational frequency of the second isomer. This off-diagonal peak, or cross peak, will be shifted along the

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METHODS Sample Preparation. The syntheses of compounds 1−6 have been reported elsewhere.18,19 Most neutral compounds for the 2D-IR experiments have one isotopically labeled carbonyl ligand (13C16O) resulting in two carbonyl peaks in the spectra with a similar frequency splitting to the mixed valence compounds. Spectroscopic-grade acetonitrile, dichloromethane, and DMSO solvents were purchased from Fischer Scientific and used without further purification. The singly and doubly reduced samples were prepared by chemical reduction with cobaltocene or decamethylcobaltocene (purchased from Strem and Sigma-Aldrich, respectively) under anaerobic conditions. The oxidation state for each sample was confirmed spectrally by FTIR (Thermo Fisher Nicolet 6700). Airtight sample cells were purchased from Specac with CaF2 windows and a path length of 500 μm. Frequency Domain 2D-IR Spectroscopy. The experimental apparatus consists of a Ti:sapphire regenerative amplifier (SpectraPhysics, Spitfire) seeded by a Ti:sapphire oscillator (SpectraPhysics, Tsunami) to produce a 1 kHz train of 100 fs pulses centered at 800 nm. The output is split 50:50 between two mid-IR OPAs. The OPAs are independently tunable from 3 to 6 μm with a spectral width of ca. 200 cm−1. The output of the first OPA is used to generate IR pump pulses by passing the beam through a Fabry−Perot interferometer to produce narrowband Lorentzian pulses at ca. 15 cm−1 fwhm with an exponential time decay of ca. 1 ps. The output of the second OPA is split into equal intensity probe and reference lines. The polarization between the pump and probe lines is set to magic angle (54.7°) by a zero-order half-wave plate. The pump and probe pulses are focused onto the sample with a 1 in. off-axis parabolic mirror. Time delays between the two pulses 10740

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The Journal of Physical Chemistry B are adjusted with a computer controlled translation stage (Newport). The probe and reference lines are spectrally resolved in a spectrograph and collected on a 2 × 32 pixel mercury cadmium telluride (MCT) array detector with a spectral resolution of ca. 3 cm−1. The sample cell is translated perpendicular to the beam axes during the experiment with computer controlled translation stages (Standa) to avoid local heating effects. Theoretical Calculations. Density functional theory (DFT) calculations were performed in Gaussian 09 using the BP86 functional, the LANL2DZ basis set for Ru, and the 6-31G basis set for all other atoms.46 Geometry optimization calculations were performed on the neutral and singly reduced states of compound 2. Two energy minima were observed corresponding to a conformer with a nearly perpendicular bridging ligand (relative to the plane of the ruthenium atoms) and a conformer with a nearly parallel bridging ligand. Singlepoint energy calculations were performed on neutral compound 2 to approximate the potential energy due to torsional motion of the bridging ligand. The torsional angle between atoms 63 (Ru), 60 (Ru), 119 (N), and 121 (C) was adjusted (see Supporting Information for full atom list). Single point energy calculations were chosen over constrained geometry optimization primarily due to computational expense. For the perpendicular conformer, single-point energies were calculated for dihedral angles 26.9° to 146.9° in 3° steps. For the parallel conformer, single-point energies were calculated for dihedral angles −67.7° to 52.3° in 3° steps. Due to the planarity of the pyrazine ring, the same energy values are used for torsional angles 112.3° to 232.3° (+180° rotation) in Figure 6. Molecular orbital composition analysis at each torsional angle was performed using Multiwfn.47 This analysis allowed us to determine the atomic orbital contributions to the molecular orbitals using the Becke partition method. Due to computational expense, molecular orbital analysis focused on the LUMO orbital of the neutral dimer. In addition to the decreased expense, this is also beneficial as a closed shell calculation because DFT often overestimates delocalization in open shell species.48,49 This composition analysis allowed us to observe how changes in bridging ligand torsional angle can be expected to affect contributions from different atoms and functional groups. In addition to the total orbital extent on each metal cluster, we were able to isolate the orbital extent on each carbonyl ligand and the bridging ligand. Atomic orbital contributions from all atoms, including carbonyl ligands and the bridging ligand fragments, as a function of torsional angle are included in the Supporting Information (SI).

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RESULTS AND DISCUSSION 2D-IR spectra were collected for compounds 1−5 at room temperature with samples representing the neutral, mixed valence, and doubly reduced states and three different solvents. No cross peak growth was observed in any sample. Spectra of neutral and mixed valence compound 3 in dichloromethane are presented in Figure 3. The spectra for all samples are qualitatively similar, and therefore, all other spectra are contained in the SI. In some 2D-IR spectra, weak intensity may be observed in the cross peak regions. This intensity does not grow in with time and is an artifact of the highly overlapped IR bands (see SI). The neutral dimers exhibit a single carbonyl peak in the FTIR spectrum. As a control, we wanted to observe any interaction between the two carbonyl ligands in a neutral dimer

Figure 3. 2D-IR spectra of isotopically labeled neutral (A) and unlabeled mixed valence (B) compound 3 in dichloromethane at four delay times, TW. The spectra show no significant cross peak intensity.

where no electron dynamics are expected. In all of the neutral samples presented in this work, one of the carbonyl ligands has been isotopically labeled (e.g., 13C16O). The more massive ligand appears in the spectrum at a lower frequency. The splitting between the two carbonyl ligands is approximately 50 cm−1, similar to the peak splitting observed in the unlabeled mixed valence samples. The lack of 2D-IR cross peak formation in the labeled neutral samples indicates that there is no 10741

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peak). The rate of this peak shift would correspond to the rate of electron transfer. The lack of cross peak formation in the mixed valence samples indicates that no electron transfer is observed in the 2D-IR spectra. When SA is vibrationally labeled, all members of the subsample initially have the same CO frequency reflecting the electron density of the metal site. The average frequency of this vibration stays constant throughout the experiment; therefore, the average electron density at this site is effectively constant. Fluctuations of this charge density may occur, but the equilibrium charge densities at the two sites do not exchange for the duration of the experiment. The only population dynamics observed in the 2D-IR experiments were peak amplitude loss due to vibrational relaxation or redistribution. For large molecules, with many degrees of freedom, decay of vibrational excitations can be very fast.50 For the mixed valence dimers, we observed vibrational relaxation ranging from ca. 5−12 ps for the lower frequency vibration and ca. 15−21 ps for the higher frequency vibration. A faster relaxation time was also observed for the lower frequency vibration in the neutral isotopically labeled systems (Tables S1−S5). The difference in CO relaxation time constants depends on frequency in both neutral and mixed valence samples but may also be influenced by differences in electron density at each site in the mixed valence compounds. The pyrazine bridged mixed valence dimers exhibited a biexponential decay with a faster component of ca. 1.6−3 ps. No clear relationship was observed between vibrational relaxation time constants and degree of coalescence (Figure 4). Due to the

significant interaction between the carbonyl ligands such as IVR or vibrational coupling. This is not surprising given the large distance (>15 Å) and number of bonds (>10) between them. This isolation is advantageous for these experiments since any vibrational interaction would interfere with the measurement of exchange cross peaks. FTIR spectra of the mixed valence dimers typically exhibit two peaks (or a single broad peak resulting from two highly overlapped features). The mixed valence samples in this work were not isotopically labeled; however, previous work has examined the effect of isotopic labeling on FTIR spectra.27,29,30 The peak separation in unlabeled samples arises from electronic asymmetry. The carbonyl ligand on the metal cluster with greater electron density will experience greater π-backbonding, resulting in a lower IR frequency. The previous explanation of the coalescence of these CO peaks treats the extra electron as localized on one of the two metal clusters, with the carbonyl ligands having an IR frequency associated with this electron distribution, e.g. one carbonyl ligand at ca. 1890 cm−1 and one at ca. 1940 cm−1. If the electron transferred between the two metal clusters, the carbonyl frequencies would switch. If the rate of exchange were similar to the frequency splitting of the CO ligands, the observed IR frequencies would begin to shift to the average frequency, and the peaks would become broader. If exchange was fast enough, FTIR could no longer resolve the two peaks, and the frequency of the two CO ligands would appear identical and at the average frequency. The optical Bloch equations attempt to quantify the degree of peak coalescence and, therefore, the rate of reaction. This approach requires the assumption that the IR peaks are only affected by exchange. This assumption is not generally valid, because geometric or electronic fluctuations on the femto- to picosecond time scale may result in significant changes in IR spectra as experimental conditions such as solvent and temperature are changed. The ability to directly monitor the time dependent frequency of each carbonyl ligand offers much deeper insight into the electron dynamics at each cluster site in the mixed valence dimers. In a 2D-IR experiment, the dimers are effectively sorted into two subsamples: subsample A (SA) and subsample B (SB). In SA, the vibrational label is imparted to the carbonyl ligand at the site with greater electron density (lower frequency), while in SB, the vibrational label is imparted to the carbonyl ligand at the site with less electron density (higher frequency). SA is never converted to SB; however, SA may evolve to become spectroscopically identical to SB. Each subsample is defined by a single carbonyl ligand, selected by the initial IR pump frequency. The frequency of this carbonyl ligand can then be monitored over time. For a given subsample, at time zero, the frequency of the vibrational label is the same as the frequency of the IR pump pulse. Each horizontal slice across the spectrum represents a change in initial conditions corresponding to the excitation frequency. At time zero, only one peak pair (representing the v = 0 → 1 and v = 1 → 2 vibrational transitions) is present along the horizontal slice. If SA is vibrationally labeled, initially all members of this subsample will have the same CO frequency reflecting the fact that the ligand is on the metal cluster with higher electron density. If electron site exchange occurs, the CO frequency will shift to the frequency associated with SB, reflecting the change in electron density at the metal site. A change in CO frequency would result in a decay in the intensity of the diagonal peak pair and a simultaneous growth of a new peak pair off diagonal (cross

Figure 4. Plot of the time constant predicted by simulations based on the Bloch equations versus the vibrational relaxation time constants measured in the 2D-IR experiments. No correlation is observed between the degree of peak coalescence (predicted exchange time constant) and the rates of vibrational relaxation.

time scale and the lack of correlation to the FTIR line shape, we attribute the additional, faster time constant to an IVR process. Enhanced rates of IVR have previously been correlated with the presence of geometric fluctuations,51 potentially explaining why the biexponential decay is only seen in pyrazine bridged mixed valence samples. The differences in vibrational relaxation between different oxidation states underscore difficulties with predicting the mixed valence lineshapes based on the peak parameters of neutral compounds. The use of the Bloch equations requires some knowledge of the peak parameters in the absence of exchange. For geometric exchange, this may be achieved by lowering the temperature of the sample, thereby reducing the reaction rate and removing exchange effects from the 10742

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The Journal of Physical Chemistry B spectrum.52 For the mixed valence dimers, lowering the temperature can increase the observed coalescence, making it harder to extract stopped exchange peak parameters. The lower frequency CO peaks of the mixed valence dimers have shorter vibrational lifetimes compared to the higher frequency CO peaks, resulting in different natural line widths, and the two peaks should be modeled with different parameters. CO ligand vibrational lifetimes in the neutral dimers are different than those in the mixed valence dimers, also resulting in different natural line widths of the CO ligand peaks, which makes a comparison of neutral and mixed valence peak shapes problematic. Additional FTIR line shape analysis with other methods such Kubo theory53 could prove useful to account for these differences in vibrational lifetimes and natural line widths. Additional dynamical information may be available through peak shape analysis of the 2D-IR spectra. Spectral diffusion, a feature commonly encountered in 2D-IR spectroscopy, can yield detailed information about changes in the homogeneous and inhomogeneous contributions to the peak shape. This information can be valuable for gaining a better understanding of dynamics such as ground-state fluctuations and changes in solvation. These features are much more accessible through the Fourier-transform implementation of 2D-IR. Double-resonance 2D-IR requires a spectrally narrow IR pump pulse, resulting in temporally longer pulses. This not only affects the time resolution of the measurement but also elongates peaks along the pump frequency axis in 2D-IR spectra. The population information yielded by the two techniques is equivalent,43 but 2D peak shape analysis of data collected with double-resonance 2D-IR is difficult. Several spectra in this data set, most prominently those of the mixed valence pyrazine bridged compounds, show evidence of spectral diffusion and increased inhomogeneous broadening. Although a quantitative analysis of these features was not possible, some additional insights are possible. Spectral diffusion represents a redistribution of the statistical ensemble observed at time zero. In the absence of full site exchange, this may indicate small changes in geometric or solvent structure or changes in the electronic distribution. However, these dynamics are expected to be coupled to one another in the current systems. Further, the increased inhomogeneous broadening in mixed valence samples is present in both carbonyl ligand peaks, not just the peak corresponding to a higher electron density. Fourier-transform 2D-IR and 2D peak shape analysis could potentially yield additional insights into the role of spectral diffusion and inhomogeneous broadening in these complexes. Recent work has investigated spectral diffusion and its sources in mononuclear rhenium carbonyl compounds with Fouriertransform 2D-IR.54,55 Changes in solvent and in the excitedstate charge distribution corresponded to differences in solvent friction and molecular flexibility that introduced changes to the rates of CO ligand spectral diffusion. FTIR spectral simulations based on the Bloch equations depend largely on the separation of the two peaks in addition to the rate of exchange. The peak widths and functional forms are also very important. For extremely rapid exchange, even peaks with a large frequency splitting can be affected. If exchange is too slow, no change to the spectrum can be observed even if the peaks are very close in frequency. Based on our spectral simulations and previously reported work using the Bloch equations, any exchange slower than 10 ps will have no effect on the IR spectra of the mixed valence dimers.19,56 The observation of any dynamics in a 2D-IR experiment requires

the vibrational label to persist for longer than the time required to complete the reaction. The given time constants are 1/e values of the peak amplitude. Sufficient intensity to observe a change in signal is usually maintained for a few times the efolding time. We can conservatively say that we measured no exchange within ca. 15 ps in any sample. Although we were unable to directly measure site exchange in these systems, placing the lower limit for electron transfer at 15 ps indicates that site-to-site electron exchange is too slow to affect the spectrum, and the observed peak coalescence must have some other origin. The pyrazine bridged dimers were all expected to undergo electron transfer in less than 1 ps as predicted by the Bloch equations. If exchange proceeded on this time scale, the vibrational label would be equally distributed between the two vibrations long before the vibrational label had decayed. This would have been marked by a large increase in intensity at both cross peak positions and a similar decrease in the intensity at both diagonal peak positions. Cross peak growth is the most obvious signature of exchange in a 2D-IR spectrum, but the decay rates of the diagonal peaks can be revealing as well. In addition to the lack of significant cross peak growth in these spectra, the decay kinetics of the diagonal peaks are also not consistent with the predicted exchange rates. Assuming exchange is not the source of IR peak coalescence, the previously predicted exchange time constants still represent a quantitative measure of the degree of coalescence. It is useful here to compare the degree of coalescence to the rates of our observed vibrational dynamics. In Figure 4, we have plotted the degree of peak coalescence (as predicted exchange time constant32) against the vibrational relaxation times measured in the 2D-IR experiments. If electron site exchange occurred in under 10 ps, the exchange rate should be correlated to both the degree of peak coalescence as well as the decay of the 2D-IR diagonal peaks. The degree of peak coalescence is unrelated to any of the observed changes in population within ca. 15 ps. Because the degree of peak coalescence is not correlated to the decay of the diagonal peaks, electron site transfer cannot be the source of IR peak coalescence. Previous work on dynamic IR peak coalescence has detailed how ground-state fluctuations may lead to changes in IR spectra that strongly resemble coalescence due to chemical exchange.13−17 The mechanisms leading to this pseudocollapse phenomenon do not cross any reaction barrier and are termed “intrawell” dynamics. In other words, fluctuations within a single potential well can perturb the vibrational frequencies enough that the peak widths and positions change in a way resembling exchange-induced coalescence. The lack of exchange on the sub-15 ps time scale in the dimers suggests coalescence may be the result of a fluctuation-based mechanism. Previous FTIR analysis has shown that the degree of coalescence is correlated with ability of the solvent to accommodate changes in charge distribution.32 Fast fluctuations in the charge densities at each metal cluster site could explain both the modulation in average CO frequency as well as the dependence on the solvent relaxation time. These dynamics would also be expected to result in spectral diffusion in 2D-IR spectra, rather than cross peak formation. Although discussions of coalescence and pseudocollapse typically focus on geometric changes that cause a change in the vibrational frequencies, the dependence of coalescence on solvent suggests that changes in electron density are central to any fluctuations. 10743

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The Journal of Physical Chemistry B To explore the electronic and geometric structure of the dimers in more detail, we performed several density functional theory (DFT) calculations. We based the initial geometry on a crystal structure of a neutral dimer with a pyrazine bridging ligand and abco ancillary ligands.21 Due to the computational expense associated with the calculations, we focused on the dimer with fewest atoms, compound 2. Significant coalescence is only observed when pyrazine is the bridging ligand, and we were interested in the role of bridge torsional angle in mediating charge dynamics. The orientation of the pyrazine bridging ligand can be expected to have a strong effect on orbital overlap as the angle between the delocalized π system and the metal-based d orbitals changes. DFT geometry optimizations resulted in two conformations of compound 2, one with a nearly perpendicular bridging ligand (relative to the plane of the ruthenium atoms) and another with a nearly parallel bridging ligand. The difference in total energy for the two conformers was ΔE = 4.4 kcal/mol for the neutral and ΔE = 1.4 kcal/mol for the singly reduced structures. For both oxidation states, the perpendicular structure is lower in energy, and we expect the ground-state dynamics to be dominated by this conformer. The two conformers of neutral compound 2 are shown in Figure 5, along with the LUMO.

Figure 6. DFT potential energy curves for changes in the bridging ligand torsional angle for the two conformers of compound 2.

the 2D-IR experiments. The difference in transition-state energies for the two conformers is a result of using singlepoint energy calculations rather than constrained geometry optimizations. This choice was made primarily due to computational expense. We expect that the bridging ligand torsional angle will vary by less than ±12°, and overall geometry will be minimally influenced by small fluctuations around the equilibrium torsional angle. A change in torsional angle by ±12° was calculated to increase the energy by 1.3 kBT (at 25 °C). To assess the possible changes in charge distribution during this torsional motion, we performed molecular orbital composition analysis with the software Multiwfn. These calculations focused on the LUMO orbital of the perpendicular conformer of neutral compound 2. We attempted similar calculations on singly reduced compound 2, but satisfying the DFT convergence criteria was challenging for many of the structures. Additionally, changes in bridging ligand torsional angle of 2 resulted in negligible changes to the symmetry of the HOMO or the atomic orbital populations. Exaggerated delocalization is a common problem in DFT calculations of open-shell systems with unpaired electrons.48,49 Here, we focus on orbital changes in the LUMO of the neutral compound to approximate the orbital changes expected in the singly reduced HOMO. Future work may be able to more explicitly calculate these orbital changes in both electronic states. Molecular orbital composition analysis allowed us to isolate atomic contributions from the different molecular fragments to the total molecular orbital. The dimer was split into three main fragments; the two metal centered clusters and the bridging ligand. Orbital contributions from each of the carbonyl ligands were also determined. Contributions from the carbonyl ligands were primarily antibonding π* in nature and most directly represent the anticipated electron density that will affect the carbonyl ligand vibrational frequency. The extent of molecular orbital density on each cluster as a function of bridging ligand torsional angle is shown in Figure 7. At the equilibrium geometry, the two clusters have slightly asymmetric orbital contributions. However, even a 3° rotation

Figure 5. LUMO orbitals of the two conformers of neutral compound 2.

The parallel conformer has much higher orbital density on the bridging ligand; however, both equilibrium structures have nearly symmetric LUMO orbitals. Despite the similarity in orbital symmetry between the two conformers, the change in bridging ligand torsional angle has a significant impact on the size and shape of the molecular orbital as well as which atomic orbitals contribute to it. To assess the possibility of fluctuations in the bridging ligand torsional angle, we performed a series of energy calculations around the equilibrium geometries of each conformer of neutral compound 2 (Figure 6). We changed the torsional angle in steps of 3° from −60° to +60° relative to the equilibrium angle from the optimized geometries and performed a single-point energy calculation at each step. Based on the barrier heights, we do not expect any conformational exchange on the time scale of 10744

DOI: 10.1021/acs.jpcb.5b06734 J. Phys. Chem. B 2015, 119, 10738−10749

Article

The Journal of Physical Chemistry B

Figure 7. Sum contributions of the atomic orbitals on each cluster to the LUMO orbital of neutral compound 2 as the bridging ligand torsional angle varies. Each cluster is defined as [Ru 3 (O) (OAc)6(CO)py]; clusters a and b are arbitrary labels to differentiate the two clusters. The lower panel plots the potential energy along the same torsional axis and is a close-up of the minimum in Figure 6.

Figure 8. Three-state potential energy surfaces for compound 2. In panel A, the ground-state adiabatic surface has a barrier large enough to prevent electron transfer on the sub-15 ps time scale. Fluctuations on the nuclear coordinate within either of the two adiabatic minima will result in charge redistribution as shown in Figure 7. In panel B, the reorganization energy is reduced to allow a qualitative comparison to the gas phase DFT results of compound 2. The nuclear coordinate in both panels is scaled to that in Figure 7 and can be interpreted as deviation from the equilibrium torsional angle of the bridging ligand.

of the bridging ligand results in a significant shift of orbital density to one cluster or the other depending on the direction of rotation. The maximum difference in orbital density occurs at ±12°, with 99% on one cluster and 3.1% on the corresponding carbonyl ligand. Approximately 0.7% of the molecular orbital is on the bridging ligand over the range −12° to +12°, but much higher bridge contributions can be seen with larger rotations or in the parallel conformer. Prior experimental and computational work by other groups has similarly established that the torsional angle between the bridging units and intramolecular redox active sites is highly influential on the electron dynamics.57−66 This effect is dominated by changes in orbital overlap between the adjacent redox units. These DFT calculations are gas phase and introduce no contributions from solvent effects. For nearly delocalized systems, it has been shown that the barrier to electron transfer may be dominated by solvent reorganization.67−69 The DFT potential energy surface in Figure 7 corresponds to a groundstate adiabatic surface in the absence of solvent effects.49 As solvent effects are introduced, it is expected that a barrier to ground-state electron transfer will form along the nuclear coordinate. Similar to previous work, a three-state model can be used to calculate the adiabatic electron transfer surfaces (Figure 8).35 Here, a simplified two-dimensional model is presented using a single nuclear coordinate. In general, the nuclear coordinate in this type of model consists of many molecular and solvent degrees of freedom and is not necessarily trivial to describe; however, it can be approximated in some cases with the choice of a more convenient and intuitive coordinate.70 In this model, the bridging ligand torsional angle is chosen as the nuclear coordinate. This nuclear coordinate is plotted as the deviation from the equilibrium torsional angle, defining zero as the equilibrium angle. The abscissae of Figures 7 and 8 are identical, but centering the plot at zero simplifies the math of the three-state model. Based on the DFT results in Figure 7, a

torsional angle of +12° (relative to the equilibrium angle) results in full charge localization on cluster a and a torsional angle of −12° results in full charge localization on cluster b. The values −12 and +12 are used to define the minima of the two outer diabatic states on the nuclear coordinate. The minimum of the third diabatic state is set at 0. Full details of the three-state model parameters used here are available in the SI. Three-state adiabatic surfaces for solvated and solvent-free mixed valence dimers are given in Figures 8A and 8B, respectively. For the solvated system, the vertical energy splitting values between the adiabatic surfaces were constrained using experimental optical absorption data reported previously.35 In the case of the solvent-free system, the solvent reorganization energy was lowered to allow comparison to the gas phase DFT results. The change in solvent interaction, while holding all other parameters constant, results in ground-state adiabatic surfaces that are qualitatively very different. The ground-state adiabatic surface in Figure 8A has two minima and a significant barrier to electron transfer. On the basis of this barrier height, an electron transfer time constant can be approximated as ca. 160 ps using simple transition-state theory.71 Although an approximation, exchange on this time scale is over an order of magnitude too slow to result in 2D-IR cross peaks for these systems. This time constant is not meant as a quantitative prediction but rather serves to demonstrate that with reasonable parameters and constraints based on experimental values, the model predicts charge localization on time scales less than 15 ps. 10745

DOI: 10.1021/acs.jpcb.5b06734 J. Phys. Chem. B 2015, 119, 10738−10749

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The Journal of Physical Chemistry B

introduce a barrier height and a source of charge (and frequency) fluctuations consistent with our spectroscopic results. Importantly, this description of fluctuations in structure and charge density does not preclude the possibility of full electron site exchange on longer time scales. Due to the structural symmetry in these compounds, we expect that any localized charge could move between the metal cluster sites through thermal and optical mechanisms. In extreme cases (e.g., lowered temperature), reduced barrier heights could result in spectral effects due to both the torsional fluctuation mechanism and electron site exchange. In this case, it would be difficult to differentiate the relative contributions of the two mechanisms on IR peak shape, and coalescence would likely be too high to resolve the peaks in 2D-IR spectra. Previous work detailing the three-state model of electron transfer, the role of metal-to-metal and metal-to-bridge charge transfer transitions, and bridging ligand vibrations are still important and may continue to contribute to the understanding of the overall electronic landscape in these systems.24−26,28,35 On faster time scales, fluctuations in charge density could be considered electron transfer events involving the exchange of only partial electronic charge. In large molecules, the electron density often resides in molecular orbitals that span many atoms. An electron transfer event does not necessarily involve an integer change in electronic charge, and the donor and acceptor molecular orbitals may contain contributions from the same atomic orbitals. In the present case, the magnitude of the charge fluctuation, rather than the rate of electron transfer, may best define the electronic state. From this perspective, analysis of the IR spectrum is still useful in that it relates the average charge density (by peak center frequency) and magnitude of charge fluctuation (through peak width) at each site. However, application of the Bloch equations does not permit a quantitative analysis of the time scales of electron transfer if the changes in the IR spectrum do not correspond to changes in the rate of a barrier crossing reaction.

In Figure 8B, a single minimum is observed at the center point of the nuclear coordinate. The DFT potential energy is plotted along with this surface for comparison. The curvature of the DFT well is steeper; however, this is partially due to the use of single-point energy calculations rather than constrained geometry optimizations. Qualitatively, the single minimum represents a symmetric, delocalized electron distribution with approximately 50% of the density on each metal cluster. For thermal electron transfer to proceed on the adiabatic ground-state surface, the system randomly moves along the nuclear coordinate until the transition state is reached, after which electron transfer may occur. For a large barrier, such as that in Figure 8A, thermal energy at room temperature is insufficient to cross the barrier in