J. Chem. Phys. 142, 212441 (2015); https://doi.org/10.1063/1.4920953 142, 212441

© 2015 AIP Publishing LLC.

Correlating solvent dynamics and chemicalreaction rates using binary solvent mixturesand two-dimensional infrared spectroscopyCite as: J. Chem. Phys. 142, 212441 (2015); https://doi.org/10.1063/1.4920953Submitted: 05 February 2015 . Accepted: 29 April 2015 . Published Online: 14 May 2015

Brynna H. Jones, Christopher J. Huber, Ivan C. Spector, Anthony M. Tabet, RiAnna L. Butler, YingHang, and Aaron M. Massari

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THE JOURNAL OF CHEMICAL PHYSICS 142, 212441 (2015)

Correlating solvent dynamics and chemical reaction rates using binarysolvent mixtures and two-dimensional infrared spectroscopy

Brynna H. Jones, Christopher J. Huber, Ivan C. Spector, Anthony M. Tabet,RiAnna L. Butler, Ying Hang, and Aaron M. Massaria)Department of Chemistry, University of Minnesota—Twin Cities, Minneapolis, Minnesota 55455, USA

(Received 5 February 2015; accepted 29 April 2015; published online 14 May 2015)

Two-dimensional infrared (2D-IR) spectroscopy was performed on Vaska’s complex (VC) and itsoxygen adduct (VC-O2) in binary solvent mixtures of chloroform or benzyl alcohol in d6-benzene.The second order rate constants for oxygenation were also measured in these solvent mixtures. Therate constant in chloroform mixtures is linear with mole fraction within the error of the measurementsbut changes nonlinearly in benzyl alcohol mixtures, displaying a preference for the alcohol over ben-zene. The rate constants were compared with FTIR spectra of the carbonyl ligand and the frequency-frequency correlation function of this mode determined by 2D-IR. The line shape broadeningmechanisms of the linear spectra of the CO bound to VC and VC-O2 are similar to those previouslyreported for VC-I2. There is a particularly strong correlation between rate constants and homogeneouslinewidths of the carbonyl vibration on the VC-O2 product state. Concurrently, the FTIR spectraand spectral diffusion observed by 2D-IR corroborate an increase in solvent heterogeneity aroundthe product. We interpret these results in the context of the potential role of solvent dynamics infacilitating chemical reactivity. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4920953]

I. INTRODUCTION

Bis(triphenylphosphine)iridium(I)carbonyl chloride, orVaska’s complex (VC), has been extensively studied for itscatalytic ability and its willingness to oxidatively bind smallmolecules.1–15 The kinetics and mechanism of O2 additionto form the VC-O2 adduct (Scheme 1) have been the focusof many previous studies.2,8,12 The reversible side-on bindingof O2 to VC provides a small molecule mimic of biologicaloxygen transport systems1,5,16 and is also a simple model of thefirst mechanistic step in a catalytic cycle wherein the substrateis bound to the active site of a catalyst. As is true for mostchemical reactions, the rate of O2 addition to VC is sensitiveto the nature of the solvent.2,8,12,17 The entropy of this processwas found to be negative and the rate constant increasedwith increasing solvent polarity, suggesting the presence ofa polar transition state, similar to a Menshutkin reaction.2

This interpretation was disputed by early studies analyzingelectronic ligand effects,18–20 and more recently, it has beenshown by Wilson and coworkers that ligand properties candictate relative rates for this and analogous compounds.21

Thus, for the same reactant in different solvents, the mereincrease in rate with polarity does not in and of itself giveenough information to determine whether a polar transitionstate was present. A further computational study modeled themechanism and calculated transition states for the reaction ofO2 with the trimethylphosphine analogue of VC.22 This studyshowed that the mechanism begins with an end-on triplet O2approach, proceeds via a pincer motion of the CO and Clligands through a side-on O2 position (as surmised by Ugo),20

a)Author to whom correspondence should be addressed. Electronic mail:massari@umn.edu.

passes through another end-on state, and then undergoesintersystem crossing to the side-on singlet product.22 Thelargest energy cost (the transition state) comes at the pinchingstep, which was calculated to be structurally similar to theVC-O2 product and still fairly nonpolar.22 In this light, therole of the solvent in dictating the reaction kinetics is notimmediately clear.

An alternate explanation is that the dynamics of themolecules in the immediate solvation shell around the soluteimpact the rate of barrier crossing. The generalized Langevinequation provides a reasonable model for motion in thecase of a reaction with a barrier and describes the solventeffect as a time dependent frictional force.23 This force isrepresented as a correlation function of solvent fluctuationsexerted in the direction of the reaction coordinate.23 Thoughtransition state theory predicts that only the energies of thereactants and transition state will matter to the final rate, itis important to note that, for our system, the product givesmore information relevant to the reaction coordinate: the COfrequency in VC-O2 is uniquely attuned to the environmentaround the O2 ligand.24,25 It has also been shown in accordancewith Onsager’s linear regression hypothesis that the molecularmotions that comprise solvation dynamics (the movement ofsolvent molecules in response to a change in the solute) are notdistinct from the solvent dynamics (the movement of solventmolecules around a solute).26 With this understanding, it seemsreasonable to hypothesize that the dynamics that might bemeasured experimentally could at least partly capture the samedynamics that facilitate chemical reactivity, as long as theobservable has the appropriate sensitivity.

With this in mind, we previously used two-dimensionalinfrared (2D-IR) spectroscopy to characterize the solventdynamics experienced by the carbonyl ligand on VC and

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212441-2 Jones et al. J. Chem. Phys. 142, 212441 (2015)

SCHEME 1. Reversible binding of oxygen to Vaska’s complex.

VC-O2 in pure solvents that had different oxidative additionkinetics.25 While we were able to extract time scales andamplitudes of some solvent shell rearrangements for thereactant and product species, extrapolating these resultsto explain the reactivity trends was speculative. However,building on the approaches of others,27–36 we found that binarysolvent mixtures were extremely useful in identifying whichsolvent shell properties were correlated.37,38

Binary solvents provide a common coordinate alongwhich to map many observables, both static and dynamic.In a mixture of two solvents, it is generally true that thecomposition of the first shell of solvent molecules arounda solute is different than that of the bulk solvent. This is dueto the relative interaction strength of each solvent with thesolute and neighboring solvent molecules, and the dynamicsof solvent exchange into and out of the solvation shell.27–30,39

If an observable varies linearly with the mole fraction of thesecond solvent in a binary mixture, then this indicates that thecomposition of the solvation shell in the regions that influencethat variable matches the bulk values. For example, thevibrational lifetimes of the metal-bound carbonyl on VC-O2and the iodine adduct (VC-I2) in binary solvent mixtures ofd6-benzene with chloroform (CHCl3) or benzyl alcohol (BA)showed a linear variation with mole fraction of either CHCl3or BA.37 As a counter example, the center frequency of thecarbonyl vibrational on VC-O2 varies in a highly nonlinearfashion in d6-benzene/BA mixtures, with a small mole fractionof BA causing most of the frequency shift.25,37 This showsthat there is preferential solvation of VC-O2 by BA in waysthat perturb the frequency of the metal-bound CO, but not itsvibrational lifetime. These two examples illustrate that forthe same solute in the same binary solvent mixtures, twodifferent observables can report the absence and presenceof preferential solvation. The solvatochromic frequency shiftis achieved through electrophilic interactions with the O2ligand, which has π bonds that interact with the back-bondingorbitals on the iridium,24,25,40 whereas vibrational relaxationprimarily occurs via solute-to-solvent energy transfer in thevicinity of the CO ligand.37 It also highlights the possibility ofdrawing connections between quantities that might otherwisebe difficult to correlate, such as solvent dynamics and reactionkinetics, when distinct nonlinear patterns are observed acrossthe binary solvent coordinate.

In the following work, we have carried out a compre-hensive binary solvent study of Vaska’s complex and itsoxygen adduct. The second order rate constants for O2 additionwere measured in binary solvent mixtures of d6-benzene withCHCl3 or BA to identify any preferential kinetic behaviors.Then, numerous FTIR and 2D-IR spectroscopic observableswere analyzed across the same solvent mixtures to identify

correlations between steady-state and dynamic quantities withthe reaction kinetics.

II. EXPERIMENTAL METHODS

Bis(triphenylphosphine)iridium(I)carbonyl chloride(Vaska’s complex, 99.99%, Sigma Aldrich, Strem Chemicals),chloroform (CHCl3, 99.8%, Sigma Aldrich), benzyl alcohol(BA, ≥99%, Sigma Aldrich; puriss. Sigma Aldrich), andperdeuterated d6-benzene (99.5% D, Cambridge IsotopeLaboratories, Inc.) were used as received without furtherpurification for laser studies. (We found that the majority ofcommercially available ≥99% BA lots contained impuritiesthat react with VC. Those who reproduce this work areadvised to use only puriss. BA or to purify the solventbefore use. The ≥99% lot used for all previous and partof this work was unusually pure, as found by GC-MS; theimpurity was most problematic for the dilute solutions usedin the kinetics experiments, causing loss of the CO stretchin the FTIR and the MLCT peaks present in the UV-visspectrum.) All solutions were filtered prior to data collection.For solutions of VC, the solvents were degassed by spargingwith nitrogen prior to mixing, and all subsequent steps ofsolution preparation were performed under nitrogen. Forsolutions of VC-O2, mixing and dissolution were carried outunder ambient conditions. The solutions were capped andcovered with parafilm and stored until completion of theoxygenation reaction (24-48 h). All measured samples were∼4 mM in VC or VC-O2.

Infrared spectra were collected on a Nicolet 6700 FTIRspectrometer (Thermo Scientific) with at least 16 scans and atypical resolution of 1 cm−1. Path lengths of both 150 µm and25 µm were used for FTIR measurements.

Kinetics data were measured by UV-visible spectroscopy(Perkin-Elmer Lambda 12). Disappearance of the VC absor-bance at 387 nm (ε = 4040 M−1 cm−1)41 was monitored overup to 33 hours under pseudo-first order conditions (ambientO2, 0.1 and 0.05 mM VC). The solubilities of O2 in purebenzene and CHCl3 were determined from their Henry’s lawconstants (benzene = 9.24 × 10−3 M/atm,42 CHCl3 = 9.225× 10−3 M/atm43). The Henry’s law constant for BA was notavailable, but we used the value for toluene as has beenreported by others44 (toluene = 1.914 × 10−3 M/atm42). TheHenry’s law constants for binary mixtures were determined asdescribed by Krichevsky.45,46 An ambient O2 partial pressureof 0.21 atm was used as the concentration of O2 in eachsolution. Under these conditions, the lowest concentration ofO2 for any solutions was 1.8 mM, which was at least an orderof magnitude larger than the concentration of VC or VC-O2to ensure pseudo-first-order kinetics. The resulting decayswere fit well by a single exponential decay. Second orderrate constants were determined using the method describedby Corbett.47 Representative UV-visible kinetics data areprovided in the supplementary material.57

The 2D-IR setup has been described in detail previously.25

Briefly, a beam of tunable IR pulses (1 kHz, ∼90 fs durationfull width at half maximum (FWHM), ∼200 cm−1 bandwidthFWHM, and 3 µJ/pulse) centered around 1950 cm−1 forthe VC and 2000 cm−1 for the VC-O2 experiments was

212441-3 Jones et al. J. Chem. Phys. 142, 212441 (2015)

split into three beams of ∼33% power and a fourth weakerbeam (local oscillator) of 1%. The three intense beamscombined at the sample with controlled arrival times. Theecho signal, emitted in the phase-matched direction, wascombined with the local oscillator at a MCT array detector toenable the recovery of phase information. The data acquisition(chopped at 500 Hz) took the echo + local oscillator signal,subtracted the local oscillator signal and divided the localoscillator signal to compensate for the excitation pulse spectralshape. A Fourier transform followed by phase correctionwas applied to the resulting data, which were then added toobtain the purely absorptive spectrum.48 Since the pump-probeprojection theorem was used in the phase correction process,49

and since in our setup the probe beam passes throughthe sample while the local oscillator does not, the FTIRtransmission spectrum was used as an absorption correctionprior to phasing. The frequency-frequency correlation function(FFCF) was obtained using the centerline slope (CLS)/FTIRfitting method described in the literature.50,51

III. RESULTS AND DISCUSSION

The second order rate constants for oxidative addition ofO2 to VC (Scheme 1) in binary solvent mixtures of d6-benzenewith CHCl3 or BA are shown in Figure 1 (numerical values areprovided in Table SI in the supplementary material).57 To ourknowledge, this is the first work to examine this reaction inmixed solvents. The rate constants in neat solvents followthe trends previously observed by Steiger and Chock,2,12

increasing with solvent polarity index (benzene < CHCl3< BA)52 as 1.9, 2.4, and 12.5 M−1 min−1. They also follow theexpected trend of anticorrelating with the solubility of Vaska’scomplex.53 The rate constant in BA is considerably greaterthan in pure CHCl3 or d6-benzene. Although the Henry’s lawconstant used here could affect this value, the toluene constantis generally considered a good surrogate for BA,44 and evenif the solubility of O2 in BA was twice that of toluene, thecalculated rate constant would still be a factor of 3 higher thanthat of CHCl3.

Examining the shapes of the kinetics data in mixedsolvents, neither shows a fully linear trend with mole fraction.This is highlighted by the black line connecting the firstand last data points. Positive deviation, or deviation abovethe black line, generally indicates that the higher endpointsolvent has a stronger effect on the observable, whereas fornegative deviation, the opposite is true. Considering the errorbars, CHCl3 mixtures only show significant deviations fromlinearity for 0.7 and 0.9 mole fraction (notably in oppositedirections), whereas BA mixtures show a sharp increase in k2with just a small increase in mole fraction but then continue toincrease more linearly as the BA concentration is increased.Even at a mole fraction of only 0.05 BA, the k2 is alreadyconsiderably faster than in pure CHCl3.

It is useful to define a preference parameter followingthe approach of Rosés and coworkers.35 In the simplest case,an observable, y , displays a preference for one solvent overthe other that is constant over the entire range of solventmole fractions, allowing the data to be modeled with a single

FIG. 1. Second order rate constant, k2, for O2 addition to VC as a functionof mole fraction of (a) CHCl3 in d6-benzene and (b) BA in d6-benzene. Errorbars represent the standard deviation of four trials at two concentrations ofVC. Black line is an aid to the eye connecting the first and last points. Redand blue dashed lines are the best fits to the data calculated from Eq. (2) forCHCl3 and BA mixtures, respectively.

preference parameter, f2/1,34–36

y = y1 +f2/1 (y2 − y1) X2(1 − X2) + f2/1X2 , (1)

where y1 and y2 are the values of the observable in puresolvents 1 and 2, respectively, and X2 is the mole fraction ofsolvent 2 in solvent 1 in the bulk solution. For this study,we consider solvent 1 to be d6-benzene and solvent 2 iseither CHCl3 or BA. Since the solvation shell influencesthe stability of molecular configurations, it is possible thatthe preference parameter is not constant over the entiremole fraction range but undergoes a crossover between twomolecular configurations having different solvent preferences.For this more complex case, we can define a crossovermole fraction, XC, and then modify Eq. (1) using preferenceparameters below ( f below2/1 ) and above ( f

above2/1 ) this point,

y = y1 +f below2/1 XC (y2 − y1) X2(1 − X2) + f below2/1 X2

+f above2/1 (y2 − y1 − XC (y2 − y1)) X2

(1 − X2) + f above2/1 X2. (2)

As expected, Eq. (1) is recovered when the crossover molefraction is set to unity. This equation can be used to quantify thepreference of a given observable for solvent 2 (CHCl3 or BA)versus solvent 1 (d6-benzene). For the simple single preferencecase, the data can be fitted by floating only a single preferenceparameter, f2/1, while three adjustable parameters are neededwhen a crossover is included ( f below2/1 , f

above2/1 , and XC).

Returning to the kinetics data in Figure 1, the overlaiddashed lines show fits to Eq. (2) for each solvent mixture.The data in CHCl3 mixtures (Figure 1(a)) were modeled bya single f2/1 of ∼2 (all preference parameters are tabulated

212441-4 Jones et al. J. Chem. Phys. 142, 212441 (2015)

in the supplementary material).57 For such a value, the rateof addition of O2 to VC increases in going from pure d6-benzene to pure CHCl3, but something about the propertiesof the solvation shell enables this to occur about twice asfast as would be expected from the bulk solvent composition.However, in light of the error bars on these data points, itis difficult to conclude that the rate constant increase is notlinear in mole fraction. Though the function with an f2/1 of2 is the best fit, and although the majority of deviations fromlinearity occur above the line between the endpoints, withinthe standard deviation the majority of the points do not deviatesignificantly from that line.

The kinetics in d6-benzene/BA mixtures in Figure 1(b)are not modeled well by a single preference parameter. Theaddition of small amounts of BA increases k2 with a preferencefor BA over d6-benzene by more than 13:1, followed by amore gradual rise to the pure BA value. This shows thatsmall quantities of BA preferentially modify the compositionand/or dynamics of the solvation shell in ways that favor O2addition to VC. Beyond a crossover point of about 0.2 molefraction BA, the solvation shell composition and/or dynamicscontinue to be modified in ways that have a smaller impacton the reactivity of the solute, exhibiting almost no solventpreference.

The nonlinearity of the BA kinetics could be becauseof preferential solvation, where the composition of the solventshell is different than that of the bulk solvent. Alternatively, thecomposition of the solvation shell may match that of the bulksolution but be heterogeneously distributed about the solutein ways that preferentially impact the reactivity of VC to O2.Another possibility, which is not exclusive of the previoustwo, is that the dynamic behavior of the solvent shell and/orsolute contributes to the addition reaction, and that these timedependent fluctuations are modified in a nonlinear fashion bythe added mole fraction of BA.

Figure 2 shows the trends for the FTIR peak centers for thecarbonyl stretching frequencies, νCO, on VC (top) and VC-O2(bottom) in mixed solvents. The vibrational spectra have beenpreviously reported for VC in pure solvents24 but not in binarysolvent mixtures. Numerical values of νCO are provided inTable SI in the supplementary material.57 Beginning withVC in Figure 2(a), we see that although this mode is lesssolvatochromic than when it is bound to VC-O2 (Fig. 2(b)),its frequency does shift nonlinearly with the mole fraction ofthe solvent system. The most unusual behavior is observed forVC in CHCl3 mixtures, in which the beginning and endingfrequencies are nearly identical but in the intermediate molefractions the center blue-shifts by about 1 cm−1. This clear,though small, increase in frequency occurs only when bothsolvents are present. Equation (2) cannot model a change inobservable that is outside of the range of the pure solvents.The νCO for VC in BA mixtures, however, provides a casethat can be analyzed. We find that the positive deviation fromlinearity for the νCO indicates f2/1 of 2.1 preferring BA overd6-benzene for the characteristics of the solvation shell thatinfluence the carbonyl frequency.

Figure 2(b) shows that VC-O2 exhibits larger solva-tochromic carbonyl frequency changes than VC due to changesin iridium backbonding caused by electron density changes

FIG. 2. FTIR peak centers for the carbonyl stretch, νCO, on (a) VC and (b)VC-O2 as a function of the mole fraction of CHCl3 (red circles) or BA (bluesquares) added to d6-benzene. Black lines are aids to the eye connecting thefirst and last points. Red and blue dashed lines are the best fits to the datacalculated from Eq. (2) for CHCl3 and BA mixtures, respectively.

at the O2 ligand.24 The FTIR spectra for VC-O2 have beenpublished and discussed previously for these neat solvents24

and binary solvent mixtures37 but were reanalyzed here withimproved solvent subtraction. The trends with mole fractionare readily fit by Eq. (2) using f2/1 values of 2 and 9 for CHCl3and BA, respectively. The positive deviation from linearity isnotably greater for BA, which provides some support for thepolar transition state hypothesis since the geometry of VC-O2is believed to be similar to the transition state. The centerfrequency always has a greater influence from the more polarsolvent (positive deviation), but to differing degrees dependingon the adduct.24

The FWHMs in Figure 3 increase with increasing molefraction of either CHCl3 or BA. This could be due to anincreased number of environments around the carbonyl ligandwith a more polar solvent; however, it is impossible todistinguish inhomogeneous broadening from an increase inwidth due to homogeneous broadening (faster dephasing orrelaxation). VC shows only a slight preference ( f2/1 = 1.3)for CHCl3 over d6-benzene and VC-O2 is effectively linear.Clearly whatever produces nonlinearity in the frequency doesnot have as strong of an influence on the peak widths for thesemixtures.

In BA mixtures, VC shows a similar preference tothe center frequency ( f2/1 = 2), but VC-O2 shows a strongbimodal preference as described above with f below2/1 = 76 andf above2/1 = 0.11 and a crossover of 0.7 mole fraction. This is aconsiderably greater preference at low mole fractions thanνCO shows in Figure 2(b). The VC-O2 carbonyl FWHMvalues in BA mixtures all have very similar widths, whichis considerably wider than the value in pure d6-benzenebut narrower than that in pure BA. This indicates a stronginteraction with BA that is inhibited by even small amounts ofbenzene. The carbonyl widths of VC and VC-O2 are similarin value; VC-O2 is always slightly larger than VC in BAmixtures and the reverse is true in CHCl3 mixtures. Neither

212441-5 Jones et al. J. Chem. Phys. 142, 212441 (2015)

FIG. 3. FTIR FWHMs for the carbonyl vibration on (a) VC and (b) VC-O2as a function of the mole fraction of CHCl3 (red circles) or BA (blue squares)added to d6-benzene. Black lines are aids to the eye connecting the first andlast points. Red and blue dashed lines are the best fits to the data calculatedfrom Eq. (2) for CHCl3 and BA mixtures, respectively.

VC nor VC-O2 shows the dramatic width changes exhibitedby VC-I2.38 Surprisingly, considering the more open squareplanar configuration, the VC FTIRs show less preferentialsolvation in both width and frequency than those of VC-O2.This is a reflection of the preferential solvation of the dioxygenligand, communicated via changes in electron density of theiridium.

These trends in the carbonyl FTIR parameters can becompared to those observed in the kinetics traces. First, theνCO for VC in either solvent system in Figure 2(a) showsno qualitative resemblance of the k2 changes with solventmole fraction, so we can conclude that the factors thatincrease the rate constants in Figure 1 are likely unrelatedto those that impact the center frequency of the reactantspecies. Next, we note that although the linewidth on VC isresponsive to a change in solvent composition (Figure 3(a)), itexhibits no particular behavior that would correlate it withthe kinetic trends. On the other hand, the νCO for VC-O2shows a mild preference for CHCl3 and a strong preferencefor BA (Figure 2(b)), which at least matches the kineticsdata qualitatively. The FWHM perhaps shows the strongerrelationship (Figure 3(b)) with a mostly linear trend in CHCl3mixtures, a fast rise at low mole fractions of BA, and acrossover point at higher concentrations.

Based on these correlations, one could hypothesize thatthe changes in the solvation shell of VC-O2 that perturb theνCO and FWHM when small amounts of BA are added tobenzene are also important to facilitating the addition of O2.As noted in the introduction, calculations by Yu and coworkersindicated that the VC-O2 structure is a better surrogate for thetransition state structure and therefore might be influenced bythe solvent composition in similar ways.22

The vibrational lifetimes (T1) of the CO stretch were alsomeasured and are recorded in Table SI in the supplementarymaterial.57 Those for VC-O2 have been published previously37

but the T1 values for VC have not been measured in these

mixtures before. In keeping with previous observations, allof the carbonyl lifetimes are significantly shorter for VCthan those of VC-O2 or VC-I2 due to the lower frequencyof the vibration. The range over which the lifetimes changein the same mixtures is also considerably smaller than eitherof the octahedral adducts. Curiously, the lifetime decreasesslightly in the CHCl3 mixtures, rather than increasing. Thismay indicate a more intramolecular mechanism than wassuggested for VC-O2 and VC-I2. For the current study, we aremost interested in dynamic parameters that vary nonlinearlywith mole fraction so that distinct correlations might be foundwith kinetic data. The trends in T1 for VC are linear with molefraction and will not be discussed further here.

Figure 4 shows representative 2D-IR plots for VC atshort (Tw = 0.3 ps, top row) and long (Tw = 30 ps, bottomrow) waiting times. In each 2D-IR spectrum, the positive peak(red) arises from the vibrational coherence between the groundand first excited states for the metal-bound carbonyl, and thenegative peak (blue) arises from the coherence between thefirst and second excited states. The horizontal axis is theexcitation frequency and the vertical axis is the vibrationalecho emission frequency. Starting with the neat d6-benzenespectra (center column, (e) and (f)), it is clear that increasingthe Tw causes both peaks to evolve from diagonally elongatedto symmetric and round. At Tw = 0.3 ps, the vibrationaloscillators are correlated with their starting frequencies, butby Tw = 30 ps, they have diffused spectrally and samplednearly the entire FTIR linewidth. These dynamics that arenormally obscured by the inhomogeneous FTIR line shapecan be characterized by analyzing the CLS from each 2D-IRspectrum as a function of Tw, which has been shown in manycases to be proportional to the FFCF.50,51

To the left from the center column in Figure 4, the 2D-IRspectra are shown for 0.5 mole fraction and pure CHCl3. To theright from the center are 0.5 mole fraction and pure BA. Theincrease in FTIR linewidth in Figure 3(a) is manifested in theincrease of the diagonal widths with addition of either CHCl3or BA in Figure 4. Comparing the antidiagonal widths inFigures 4(a)–4(i) shows that the dynamical contributions to theline shape are different for these two solvents. The narrowingalong the antidiagonal direction for BA mixtures indicatesthat the homogeneous linewidth is growing narrower, a trendseen previously for VC-I2.38 The antidiagonal broadeningfor CHCl3 mixtures cannot immediately be attributed to ahomogeneous linewidth change since the diagonal width isalso increasing; however, this will be determined below in thequantitative analysis of the CLS plots.50,51 It is also apparentthat spectral diffusion dynamics are different for these solventssince the long Tw data in Figures 4(b) and 4(j) show the CHCl3spectrum to be symmetric and round while the BA spectrumis still diagonally elongated. We can predict that some ofthe spectral dynamics will exhibit preferential behavior sincethe 0.5 mole fractions of both solvents (Figures 4(c), 4(d),4(g), and 4(h)) look quite similar to the neat solvent spectra.Hence, whatever dynamics result in frequency fluctuations ofthe carbonyl ligand, they appear to have been mostly developedby this mole fraction.

The same 2D-IR plots for the VC-O2 adduct are shownin Figure S1 in the supplementary material.57 In both solvent

212441-6 Jones et al. J. Chem. Phys. 142, 212441 (2015)

FIG. 4. 2D-IR spectra collected for VC at Tw= 0.3 (top row) and 30 ps (bottom row) for ((a) and (b)) neat CHCl3, ((c) and (d)) 0.5 mole fraction CHCl3 ind6-benzene, ((e) and (f)) neat d6-benzene, ((g) and (h)) 0.5 mole fraction BA in d6-benzene, and ((i) and (j)) neat BA.

mixtures, the same qualitative trends hold as were describedfor VC. In total, for VC and VC-O2 in all solvent mixturesstudied at all Tw values, more than 600 2D-IR spectrawere collected and analyzed. All spectra are provided in thesupplementary material.57 The CLS treatment was applied tothe 0-1 carbonyl transition in every spectrum to distill thisenormous dataset into a tractable form.

Figure 5 shows the CLS decays as a function of Tw foreach of the mixture series and adducts. A first observationis that the addition of CHCl3 (Figures 5(a) and 5(b)) has anotably smaller effect on the dynamics than addition of BA. Ingeneral, CHCl3 mixtures look more similar to pure d6-benzenethan BA mixtures, with any deviations appearing at longer Twvalues. Spectral diffusion in BA (Figures 5(c) and 5(d)) isconsiderably slower than in d6-benzene or CHCl3. The overallspectral diffusion for VC-O2 in BA shows the same trends asthe FTIR FWHM; the endpoints are distinct while the mixturesare very similar. Also the y-intercept of the CLS, which insome situations is related to the homogeneous linewidth, ishigher for BA mixtures than for CHCl3. It is also generallyhigher in VC mixtures than in VC-O2, so the homogeneouslinewidth is likely larger for VC-O2. Looking at Figure 5as a whole, aside from differences in the y-intercepts, thedynamical data extracted from the 2D-IR spectra look fairlysimilar for VC and VC-O2 in a given solvent system. Thissupports the notion that the carbonyl vibrational mode mostlyreports on the dynamics of the proximal solvation shell ratherthan the intramolecular dynamics of the molecule to which itis bound, which was also recently concluded for a family ofrhenium catalysts.54

The full FFCFs were found by fitting to the FTIR spectraas well as the CLS decays.50,51 With only a few exceptions, thedata in Figure 5 and their corresponding FTIR spectra werewell fit by a double exponential function (Eq. (3)), includinga motionally narrowed term (for the homogeneous line shape)as shown in

FFCF(t) = δ(t)T2+ ∆21e

−t/τ1 + ∆22e−t/τ2 + ∆20. (3)

A few of the datasets did not require a static offset to fitwell and one did not need a second exponential term. Thestatic offsets for these solution-phase samples do not trulyrepresent static inhomogeneity, rather they capture dynamicsthat perturb the CO vibration on time scales that are slowerthan we are able to resolve. The 2D-IR peaks for VC in 0.7mole fraction and pure BA mixtures do not run straight alongthe diagonal (see, for example, Figure 4(i)), and as a result,the CLS shows a kink around 1970 cm−1. This is indicativeof non-Gaussian dynamics.55 Though the CLS method is notstrictly accurate when non-Gaussian dynamics are present,51

it has been shown to still give a reasonable approximationof the dynamics.55 In these two cases, the CLS method wasapplied twice, once centered around 1966 cm−1 and the othercentered around 1973 cm−1. The population at 1966 cm−1

represents the majority of the FTIR linewidth and so theCLS values from this region were plotted in Figure 5(c). Theend result of this analysis is a collection of amplitudes, ∆,and time constants, τ, for spectral diffusion as well as theinhomogeneity and homogeneous linewidths of the carbonylmode for both molecules in all solvent mixtures studied. Theseparameters are all tabulated in Tables SIII through SVI in thesupplementary material57 but will be presented and discussedgraphically below.

Returning to the purpose of this study, we seek todetermine how the dynamic parameters vary with the molefraction of the solvent to identify similarities and correlationsin the solvent dynamics with the reaction kinetics introducedin Figure 1. Since the strongest relationship of the FTIRparameters was with the FWHM, it seems reasonable to alsocarry out an inspection of the broadening sources, as was donepreviously for VC-I2.38

For fits involving multiple exponentials (i.e., Eq. (3)), itcan often be difficult to claim uniqueness for a fit; an increasein one time constant or amplitude can be compensated forby another. We have attempted to clarify these relationshipswith the error calculations for each parameter,38 but it isnot always obvious in the averaged values. Figures S32

212441-7 Jones et al. J. Chem. Phys. 142, 212441 (2015)

FIG. 5. CLS decays for VC (top row)and VC-O2 (bottom row) as a func-tion of Tw for binary solvent mixturesof CHCl3 (left column) and BA (rightcolumn). Panels (a) and (b) show bi-nary mixtures of 0 (black), 0.1 (red),0.3 (blue), 0.5 (green), 0.7 (orange), 0.9(lavender), and 1 (purple) mole frac-tions CHCl3 in d6-benzene; panels (c)and (d) show 0 (black), 0.05 (brown),0.1 (red), 0.2 (pink), 0.3 (blue), 0.4(lavender), 0.5 (green), 0.7 (orange),and 1 (purple) mole fractions BA ind6-benzene. Overlaid solid lines are themultiexponential fits to the data mark-ers. Error bars on each point representthe standard deviation of two or threetrials.

through S35 in the supplementary material present each of theFFCF parameters graphically, followed by some discussion ofparameter correlations and uniqueness.57 In order to minimizethe possibility of such errors influencing our correlation, wefocus the following discussion on the homogeneous linewidth,Γ, and the inhomogeneous amplitude, Ω, as defined in

Ω =

2n=0

∆2n, (4)

Γ =1πT2=

12πT1

+1πT∗2+

13πTor

. (5)

In these equations, T∗2 is the pure dephasing time and Tor isthe orientational relaxation time. Generally, Tor is on the orderof hundreds of picoseconds for molecules of this size31,56 andso does not contribute significantly to Γ.

Figure 6 shows the values for Γ calculated from the CLSanalysis of the 2D-IR spectra for VC and VC-O2 in CHCl3 (redcircles) and BA (blue squares) mixtures. The general trends arevery similar to those previously observed for VC-I2,38 wherethe homogeneous linewidth changes very little in CHCl3 (redcircles) and decreases in BA (blue squares) mixtures. In spiteof the differences in y-intercepts for the CLS decays notedabove, the homogeneous linewidths are not very different forthe two solutes. In the CHCl3 mixtures at low mole fraction,VC-O2 is broader, but the distinction disappears after 0.7mole fraction, when the linewidth of VC rises slightly. Thebroadening noticed in the FTIR for VC with increasing amountof CHCl3 could be partly coming from this increase in thehomogeneous linewidth; however, it does not show the samepreference for CHCl3. The notable outlier in this figure isthe Γ for VC-O2 in BA mixtures (blue squares, Figure 6(b)).The homogeneous linewidth variations for this adduct andthis solvent mixture are clearly nonlinear, displaying a quickdecrease with the addition of a small amount of BA to d6-benzene. Since the T1 values for this adduct range from 56 to92 ps (see Table SI), the vibrational lifetime contribution to Γ isminor (

212441-8 Jones et al. J. Chem. Phys. 142, 212441 (2015)

FIG. 7. Inhomogeneous amplitude, Ω, for (a) VC and (b) VC-O2 as a func-tion of the mole fraction of CHCl3 (red circles) or BA (blue squares) added tod6-benzene. Black lines are aids to the eye connecting the first and last points.Red and blue dashed lines are the best fit to the data calculated from Eq. (2)for CHCl3 and BA mixtures, respectively.

in k2 with small quantities of BA is accompanied by acorresponding increase in the spectral inhomogeneity aroundthe product species (VC-O2). At the same time, beneath theinhomogeneous line shape, Figure 6 shows that the fast puredephasing events that dominate the homogeneous line shapeslow down. Returning to the view that VC-O2 reflects thetransition state structure,22 the preferential behavior of thekinetics in BA/d6-benzene mixtures is mirrored by a generalincrease in chemical heterogeneity in the solvation shell and aslowing of fast solvent dynamics. It is curious that these veryfast motions around the product should be correlated withthe nonlinearity when those occurring around the reactantdo not. This confirms that the product-like transition statecalculated by Yu and coworkers is an accurate picture of theactual reaction mechanism.22 If these fast motions aroundthe product carbonyl behave in the same fashion aroundthe activated complex, then it may be that they somehowassist the pincer motion and enable reactivity. Identifying themolecular origins of these dynamics is an important next stepthat would be facilitated by molecular dynamics simulations.Molecular dynamics simulations of the solute and its solvationshell during oxidative addition would enable one to confirmthis hypothesis. It could also be useful to determine whetherthese correlations exist for other additions to VC, such as theaddition of I2, which is considerably faster as well as beingirreversible.

IV. CONCLUSIONS

We performed an extensive spectroscopic and kineticstudy on the oxidative addition of O2 to Vaska’s complex.We measured the solvent dynamics around both product andreactant species at equilibrium. This work is a departure fromthe majority of 2D-IR/kinetics studies, as the reaction is not inthe low-friction limit of solvent-solute interactions, and it thusprovides an opportunity to examine a reaction that is squarelyin the range where transition state theory works well.

The kinetics for mixtures of CHCl3 and d6-benzeneshowed a linear trend with solvent mole fraction, precludingany distinct correlations with steady-state and dynamicparameters. However, binary mixtures of BA and d6-benzeneprovided a case in which the rate constant varied nonlinearlywith a rapid change upon addition of small quantities ofBA. This preferential kinetic behavior was closely mirroredby increases in the FTIR linewidth of the metal-boundcarbonyl ligand. Extraction of the FFCF from 2D-IR spectrarevealed that beneath the linear line shape, the homogeneouslinewidth for VC-O2 in BA mixtures was anticorrelated withthe preferential kinetics, meaning that the fast dephasingdynamics slow down as the inhomogeneity of the solvationshell increases. An exciting hypothesis that can be drawn fromthese results is that the nonlinearity in the rate constant is infact driven or facilitated by changes in the ultrafast solvationdynamics around the product, which in this case happensto closely resemble the transition state. A greater variety ofsolvation environments may increase accessibility to favorableconfigurations, and slowing of the microscopic motions thatlead to pure dephasing of the carbonyl could decrease thesolvent friction around the transition state. Correlation doesnot guarantee causality, and we cannot rule out the possibilitythat the kinetic and spectroscopic observables are simplyslaved to a common source. Nonetheless, it is remarkable, andpotentially important, that such a particular correlation existsotherwise unseen without the benefit of multidimensionalspectroscopy.

ACKNOWLEDGMENTS

The authors gratefully acknowledge funding from theNational Science Foundation under CHE-0847356. C.J.H. wasgraciously supported in part by a University of MinnesotaDoctoral Dissertation Fellowship. I.C.S. was supported by theNSF Graduate Research Fellowship Program (GRFP) (No.00039202). B.H.J. thanks Sean Ross in the Hoye researchgroup for running mass spectra to verify BA impurities.

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