Article pubs.acs.org/JPCA
Comparing the Energetic and Dynamic Contributions of Solvent to Very Low Barrier Isomerization Using Dynamic Steady-State Vibrational Spectroscopy Andrea N. Giordano† and Benjamin J. Lear*,‡ †
Department of Chemistry, St. John Fisher College, 3690 East Avenue, Rochester, New York 14618, United States Department of Chemistry, The Pennsylvania State University, State College, Pennsylvania 16801, United States
‡
S Supporting Information *
ABSTRACT: We report the solvent-dependent dynamics of carbonyl site exchange for Fe(CO)3(η4-norbornadiene) (FeNBD) in a series of linear and nonlinear alkanes. The barrier to exchange is very low (∼1.5 kcal/mol), and the resulting carbonyl dynamics are rapid enough to lead to a change in the vibrational spectra, which we use to extract the ultrafast rates of exchange from linear Raman spectra of FeNBD. The dynamics of the carbonyl exchange has a weak dependence upon the solvent, and we analyze this dependence in terms of energetic (reaction field) and dynamic (Kramers theory) models of solvent effects. We find that both models can reproduce the observed solvent dependence but that the dynamic model provides a more physically satisfying picture for the solvent effects than does the energetic model. Finally, we find that cyclohexane is more strongly coupled to the dynamics of FeNBD than are the noncyclic alkanes.
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INTRODUCTION The strength of the interaction between solute and solvent is a critical parameter for controlling solution-phase chemistry and impacts a host of molecular behaviors, from solubility to reaction kinetics. For instance, the polarity of solvent can control association constants between molecules, the enatomeric selectivity of organic reactions, and the rate of chemical and electrochemical transformations.1−7 The kinetic effects are often explained within the framework of transition state theory and its modifications, where the solute−solvent interactions are assumed to affect either the barrier height (EA) and curvature of the potential energy surface that underlies the reaction or the manner in which the reactive surface is explored. In general terms, we can classify these effects as either energetic or dynamic, respectively. Both of these effects impact the course of a reaction in different ways and are controlled by different properties of the solvent. Thus, it is important to understand, identify, and distinguish between the occurrence of energetic and dynamic effects of solvent upon reaction kinetics. It has long been common to treat the energetic effects on the rate constant of a chemical process (k) within the confines of transition state theory: k=
⎛E ⎞ ωR exp⎜ A ⎟ ⎝ RT ⎠ 2π
induce changes in the pre-exponential term via modification of the curvature of the potential energy surfaces. This latter effect alters the frequencies associated with the reactant well (ωR) and the top of the barrier (ωB). The dynamic aspects of solvent control continue to be the subject of considerable theoretical8−19 and experimental3,11,20−29 efforts. Much of the current theoretical framework is based upon modifications of the work by Kramers, which treated solvent dynamics as a frictional effect and proved effective at describing systems with reasonably large activation barriers. This original theory was subsequently modified to include processes with very low barriers (including zero barrier).13,14,29 With respect to experimental work, many of the predictions of these theories were validated for excited state transformations. However, for practical reasons, investigation of ultrafast (low barrier) ground state processes eluded experimentalists until recent spectroscopic developments enabled their study.30 There are, however, many reasons to focus on ground state processes, such as the importance and prevalence of thermally driven chemical transformations. Indeed, the vast preponderance of industrially relevant chemicals are produced in thermally driven processes. In addition, many enzymes have evolved to run chemical transformations via near barrier less
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Received: January 17, 2015 Revised: March 24, 2015 Published: March 26, 2015
where the interaction between the solvent and the solute results in a modification of the barrier height (EA), which may also © 2015 American Chemical Society
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DOI: 10.1021/acs.jpca.5b00510 J. Phys. Chem. A 2015, 119, 3545−3555
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The Journal of Physical Chemistry A
time, the high-energy band (which involves the totally symmetric stretch of all three ligands) remains relatively unchanged. This dynamic coalescence due to chemical exchange is similar to that observed for other spectroscopies, such as EPR37,38 and NMR.39 The aspects of vibrational coalescence that are unique to vibrational spectroscopy are addressed in detail in several recent publications.31,40 Just as in these other spectroscopies, the rate of exchange can be extracted from simulation of the observed spectra (Figure 1b). Thus, this behavior provides a simple and high-throughput means for obtaining picosecond molecular dynamic information on the FeNBD system. Prior work on FeNBD has established the barrier for exchange as 1.4 kcal mol−1 in 2methylpentane,31 which is close to the calculated gas phase value of 0.5 kcal/mol.41 However, what is unknown is if this observed barrier is dependent upon the solvent environment, to what extent solvent may couple to such a low-barrier process, and whether energetic or dynamic effects dominate any solvent dependence. It is also worth noting that recently Harris and co-workers have reported the 2D-IR of complexes similar to FeNBD (in which the norbornadiene is replaced by a 1,5-cyclooctadiene and 1,3-butadiene).42 In this paper, they find that the dynamics reported on by the 2D-IR spectra were dominated by intramolecular vibrational redistribution (facilitated by partial rotation and the resulting symmetry breaking), rather than chemical exchange. However, at the same time, they found that analysis of the linear spectra (similar to our approach described below) resulted in extraction of kinetics parameters (specifically the value of EA) consistent with those expected from DFT calculations on the molecules of interest. This provides additional support for the use of linear spectra to extract parameters associated with chemical exchange in FeNBD. In this article, we examine the changes to the dynamics of FeNBD that accompany changes in solvent. In order to simplify the analysis, this first effort focuses on the following series of alkanes: n-pentane, n-hexane, n-heptane, n-octane, n-decane, ndodecane, n-hexadecane, 2-methylpentane, and cyclohexane. Below, we report the temperature-dependent vibrational spectra of FeNBD in all of these solvents and analyze the changes in dynamics with respect to current theories of solvent effects. We find that both energetic and dynamic models can explain our results but that the dynamic model provides the most physically satisfying explanation. In addition, we also find that cyclohexane appears to couple to the dynamics of the solvent to a much greater extent than do the noncyclic alkanes.
ground state pathways. Thus, it is worth examining such reactions and their dependence upon the solvent environment. We felt it would be useful to examine ground state dynamics for a process with a barrier even lower than that previously analyzed,30 as this might allow us to identify an area in which the standard treatments of solvent effects would break down. In particular, we wondered about the extent to which solvent energetic and dynamic effects could be separated in such systems. To this end, we selected Fe(CO)3(η4-norbornadiene) (FeNBD, Figure 1) as a probe for understanding the relative
Figure 1. Structure of FeNBD. The experimental Raman spectra in 2methylpentane (a) show increased coalescence of the low-energy bands with increasing temperature. This is a result of the turnstile exchange of carbonyl ligands that give rise to dynamically coalesced band shapes. The resulting band shapes can be simulated (b) in order to extract the rate of carbonyl exchange.
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EXPERIMENTAL SECTION Materials. Norbornadiene and 2-methylpentane were purchased from Alfa Asear, and other solvents were obtained from VWR and were used as received. Iron(0) pentacarbonyl was purchased from Sigma-Aldrich and was filtered through a sterile syringe filter with 0.2 μm cellulose acetate membrane (VWR) before use. Synthesis of Fe(CO)3(η4-norbornadiene) (FeNBD). Synthesis of FeNBD was adapted from a previously published procedure.43 Under N2, Fe(CO)5 (2.9 g, 0.0148 mol) was added dropwise over 10 min to a flask of norbornadiene (2.7 g, 0.0294 mol) at 80 °C and stirred for 18 h. Flash column chromatography with hexanes over silica was used to purify the crude reaction mixture. The second yellow band off the column contained FeNBD. The solvent was removed under vacuum to yield an orange/yellow liquid (0.249 g, 7.25% yield).
importance of energetic versus dynamic solvent effects. This molecule undergoes carbonyl site exchange on the picosecond time scale via a turnstile type mechanism (Figure 1a). The dynamics of this rotation are fast enough to lead to broadening and coalescence of bands in its vibrational spectraan effect that has been examined in detail by ourselves31 and others.32−36 In brief, the lowest energy conformation possesses C s symmetry, and the three carbonyl ligands are expected to produce three vibrational bands (from highest to lowest energy) of a′, a′, and a″ symmetry that are all IR- and Raman-active. At low temperature, these three bands are resolved. However, as the temperature increases, the two lowenergy bands are found to broaden and eventually coalesce, brought about by the exchange of carbonyl ligands. At the same 3546
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The Journal of Physical Chemistry A Characterization by IR in 2-methylpentane revealed two distinct ν(CO) bands at 1967 and 2035 cm−1, which correspond with previous literature values.36 The compound must be stored in an inert atmosphere to avoid decomposition. Though the compound is mildly air sensitive, it does remain chemically persistent in 2-methylpentane under ambient conditions for several days. Spectroscopic Measurements. Raman spectra were acquired using a Renishaw inVia Raman microscope equipped with an integrated microscope (Leica DM2500 M) and a Linkam LTS420 liquid nitrogen temperature controlled stage. The excitation source was a 647 nm CrystaLaser CL-2000 diode pumped laser (70 mW, model DL647-070). We employed a 1200 line/mm grating, yielding a resolution of 1.9 cm−1. The sample cell was home-built, and a description can be found in a previous publication.31 IR spectra were acquired using a PerkinElmer Spectrum 400 FT-IR/FT-NIR with a liquid cell with path length of 0.1 mm and a 1 cm−1 spectral resolution or with a Pike MIRacle ATR attachment at a spectral resolution of 4 cm−1. All samples were prepared by adding liquid FeNBD to 1 mL of alkane solvent and diluting until a reasonable IR spectrum was obtained. Spectral Analysis and Simulated Data. All data were analyzed in Origin 9.0. The band positions and full widths at half-maximum (fwhm) were acquired using the multiple peak fitting tool in Origin 9, and all three bands were fit using the Voigt function. Simulated data were acquired through the use of the Raman and IR Dynamics program (RAPID) described previously,31 which is freely available on the Web.44
where the naught indicates the gas phase (intrinsic) values and the prime indicates the values in solution. It is important to realize that this relationship is not intended as a definitive model but is merely suggested as a plausible example of how the barrier height and frequency factor could be linked under the energetic picture. With regard to dynamic effects, transition state theory assumes that solvent-coupling facilitates barrier crossings by providing a thermal bath from which energy can be borrowed to overcome the barrier and returned in order to relax into the products well.48 Such a behavior requires that the strength of the solvent−solute coupling be at least strong enough that energy can be readily exchanged. However, if the coupling between solvent and solute is too strong, then the solvent can impede molecular dynamics.49 Within this overdamped regime, the motion of a system along the reaction coordinate would be increasingly controlled by random fluctuations of the solvent. Thus, such a system would exhibit a Markovian walk along the reaction coordinate that could be described by the Langevin equation. Solving this equation, Kramers arrived at the following expression for the rate constant (kKramers):48 kKramers
(4)
where R is the gas constant, T is the temperature, and γ is the friction constant of the motion along the reactant coordinate. In this expression, the terms contained within the rightmost curly brackets are the familiar expression for the rate under transition state theory, revealing Kramers theory as a modification of transition state theory. In the strong coupling limit, eq 4 reduces to the Smoluchowski limit,48 which can be further modified to give
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THEORY In order to separate energetic from dynamic effects, we must first identify mathematical models that can be used to interpret and fit our data. In both the energetic and dynamic effects, transition state theory (eq 1) forms the foundation for this analysis. With regard to purely energetic effects, one must account for the strength of the interaction between the solute and solvent. Though many models have been forwarded,45 this is most readily accomplished for our work using the reaction field model,46 in which the solute is treated as a polarizable dipole that induces a field within the solvent (the reaction field) that, in turn, affects solute energies. To the extent that the reactant minimum and transition states of a reactive system possess different dipole moments, they will be differentially affected by the reaction field of the solvent. Thus, this effect provides a means by which to affect the activation energy of a chemical process and can be parametrized using a reaction field factor, f(ε), which is a function of the dielectric constant of the solvent (ε): f (ε) =
ε−1 ε+2
k Smoluchowski
⎛ ω b ⎞α ω R ⎛ −E ⎞ exp⎜ A ⎟ =⎜ ⎟ ⎝ RT ⎠ ⎝ γ ⎠ 2π
(5)
In the preceding expression, the equation for the Smoluchowski limit was modified by the inclusion of the α term.29,50 This term is a measure of the strength of the coupling between the solvent and the solute, and the value of α can vary between 0 and 1. In the limit α = 1, the true Smoluchowski limit is obtained, whereas in the limit α = 0, the transition state expression is obtained. For intermediate values of α, the expression found in eq 5 cannot be rigorously justified; however, it still yields insight into the behavior of a particular system. Specifically, it provides a very clear picture concerning how solvent−solute coupling impacts the Arrhenius parameters typically associated with an activated process, and the value of α provides a rough metric for quantifying the strength of the coupling between solvent and solute dynamics. Before we can consider exactly how coupling to solvent dynamics leads to control of reaction dynamics, we must first explore the definitions of γ. The most common choice for γ under the hydrodynamic model is based upon solvent viscosity (η). When dealing with molecular rotations, this dependence is expressed as51
(2)
At the same time, a change in the height of the activation barrier will change the curvature of the ground state potential energy surface. For instance, for a harmonic oscillator, one might expect the following relationship between the barrier height, the frequency associated with the barrier well, and the frequency associated with the top of the barrier (ωb):47 ⎡ ω ′ ⎤2 ⎡ ω ′ ⎤2 = ⎢ R0 ⎥ = ⎢ b0 ⎥ 0 EA ⎣ ωR ⎦ ⎣ ωb ⎦
⎧⎡ ⎫ 2 ⎤1/2 ⎪ ⎛ γ ⎞ ⎛ − E ⎞⎫ γ ⎪⎧ ωR ⎢ ⎥ ⎨ ⎬⎨ = ⎜ − exp⎜ A ⎟⎬ ⎟ +1 ⎝ RT ⎠⎭ ⎢ ⎥ ⎩ 2ω b ⎪ 2π ⎪⎣⎝ 2ω b ⎠ ⎦ ⎩ ⎭
EA′
γ=
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4πηdr 2 I
(6) DOI: 10.1021/acs.jpca.5b00510 J. Phys. Chem. A 2015, 119, 3545−3555
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The Journal of Physical Chemistry A and I, d, and r are the moment of inertia, diameter, and radius of gyration associated with the rotating group, respectively. Though other parameters can be used,30,51 this article focuses on the use of viscosity. Thus, the friction constant is proportional to η in the solvent-controlled limit. However, it is also important to recognize that viscosity is itself an activated process, and the viscosity of a solvent at any temperature, η(T), is given by ⎛ Eη ⎞ η(T ) = η0 exp⎜ ⎟ ⎝ RT ⎠
(7)
where η0 is the viscosity in the limit of infinite temperature and Eη is the barrier associated with viscosity. By combining eqs 5, 6, and 7, and assuming that ωb does not depend upon solvent viscosity, we arrive at the following simple expressions for how the observed barrier height (Eobs) and frequency factor (Aobs) for an activated process depend on coupling to the viscosity of the solvent: Eobs = EA + αEη
(8)
ln(Aobs) = −α ln(η0) + ln(ν0)
(9)
where we have set ν0 = (ωbI/4πdr2)α(ωR/2π). Thus, analysis of either the values of Eobs or Aobs, as a function of solvent viscosity, will give an indication of the relative strength of coupling between solvent and solute in terms of α.
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RESULTS AND DISCUSSION Vibrational Spectroscopy. We began by examining the solvent-dependent IR spectra of FeNBD at room temperature (Figure 2a). For comparison (Figure 2b), we also show the spectra for Fe(CO)3η4-cyclooctatetraene (FeCOT). This molecule is structurally analogous to FeNBD but has a barrier for CO rotation that is large enough (8.1 kcal/mol) to prevent dynamic effects in its vibrational spectrum.52 We have previously examined the spectra of FeCOT in these alkanes and concluded that the band position exhibited a small dependence upon solvent.53 Compared to FeCOT, the spectra of FeNBD depend strongly upon changes in solvent. In particular, the resolution of the low-energy bands increases with the length of the alkane solvent molecules. Considering the mechanism of coalescence for these bands, this observation suggests that the rate of carbonyl site exchange slows upon increasing the chain length of the alkane solvent. If we are to interpret band shapes in a dynamic context, care must first be taken to ensure that changes in solvent do not simply result in changes in inhomogeneous or homogeneous broadening, which might mimic dynamic coalescence. The lack of significant broadening of FeCOT in these same solvents suggests that homogeneous and inhomogeneous broadening are not responsible for the observed behavior of FeNBD; however, temperature-dependent spectra of FeNBD (Figure 3 and Supporting Information) allow us to further address these concerns. Figure 3 shows the temperature-dependent Raman spectra of FeNBD in the shortest (pentane) and longest (hexadecane) alkane solvents that we investigated, while the temperature-dependent spectra for the remainder of the solvents can be found in the Supporting Information. For clarity, Figure 3 presents only three temperatures for each solvent. Spectra for all temperatures can be found in the Supporting Information. We use Raman spectroscopy for collecting these temperature-dependent spectra rather than IR
Figure 2. (a) IR spectra of FeNBD in the linear alkanes solvents used in this study. There is a clear dependence of the degree of coalescence of the low-energy band upon solvent. (b) IR spectra of FeCOT in all solvents used in this study. The carbonyl ligands of FeCOT give rise to three well-resolved bands in all solvents. The bands of FeCOT display only slight solvatochromism.
as was used for the survey spectra in Figure 2 due to problems with our IR cryostat. We have already demonstrated that identical results can be obtained using either IR or Raman spectroscopy on this system.31 All of the temperature-dependent Raman spectra show the same trends. Namely, at lower temperature, the carbonyl bands are most resolved, and the observed coalescence of the bands increases with increasing temperature. This behavior is fully consistent with coalescence resulting from thermally activated exchange of the carbonyl ligands. In addition, the observed behavior is not consistent with coalescence due to changes in either inhomogeneous or homogeneous broadening (in the absence of chemical exchange) with temperature. If the coalescence was due to inhomogeneous broadening in a solution phase, then we would expect an increase in bandwidth with decreasing temperature. However, this is not observed in pentane. At the same time, if homogeneous broadening (in the absence of exchange) were responsible for changes in apparent coalescence with changes in solvent, then we would expect an increase in width with increasing temperatures. Again, this is not consistent with the behavior of FeNBD in hexadecane, 3548
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observed barrier to exchange (Eobs), and the observed frequency factor (Aobs). Figure 4a shows Arrhenius plots for
Figure 3. Temperature-dependent Raman spectra of FeNBD in both pentane and hexadecane. Shown are both experimental spectra (open circles) and simulated spectra (solid lines) of the two coalescing lowenergy bands.
where the overall width of the low-energy carbonyl band decreases with increasing temperatureconsistent with the dynamically induced coalescence of carbonyl bands. Finally, we also note that dynamic exchange of vibrational bands also leads to a spectroscopic signature for the exchange: an extra intensity is present between bands, which cannot be accounted for by two overlapping (but nonexchanging) Voigt profiles.34 The spectra that we observe contain this extra intensity. Thus, all of the above observations support the conclusion that the observed changes in coalescence result primarily from changes to the rate of thermally activated exchange of the carbonyl ligands in FeNBD. Simulation of the temperature-dependent data also allows us to extract the kinetic parameters for FeNBD in each solvent and directly yields lifetimes for exchange that we convert to an observed rate constant, kobs. The results of these simulations are shown in Figure 3 for pentane and hexadecane, and the simulations for the remaining solvents can be found in the Supporting Information. Using these extracted rate constants to make an Arrhenius plot, we can verify that the rates follow trends associated with activated kinetics, as well as extract an
Figure 4. (a) Arrhenius plot of the extracted rates for each solvent. (b) Eyring plot of the data from each solvent.
all solvents. Individual Arrhenius plots can be found in the Supporting Information. Because the Arrhenius plots were wellbehaved, we also constructed Erying plots of the data (Figure 4b) in order to obtain estimates of the enthalpies (ΔH‡) and the entropies of activation (ΔS‡). The Supporting Information contains individual Eyring plots for all the solvents. The values Eobs, Aobs, ΔH‡, and ΔS‡ for each solvent together with values of viscosity at room temperature (η(298)), the energetic term associated with the viscosity (Eη), the pre-exponential associated with the viscosity (η0), and the reaction field parameter, f(ε), are summarized in Table 1 and will be used to analyze the solvent dependence of FeNBD’s dynamics. 3549
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Table 1. Energetic and Dynamic Parameters of the Solvents Employed as Well as the Dynamic Parameters Obtained for FeNBD in Each Solventa solvent properties Eη (kcal mol−1)
solvent pentane hexane heptane octane decane dodecane hexadecane 2-methylpentane cyclohexane a
1.36 1.62 1.86 2.08 2.49 2.81 3.29 1.66 2.98
η0 (mPa s) 22.5 19.4 17.0 15.4 12.9 11.7 10.7 17.0 5.86
η(298) (mPa s) 0.24 0.31 0.42 0.55 0.93 1.51 3.48 0.29 0.89
system properties f(ε)298
Eobs (kcal mol−1)
0.219 0.228 0.235 0.240 0.248 0.253 0.260 0.226 0.256
± ± ± ± ± ± ± ± ±
1.50 1.48 1.55 1.58 1.60 1.66 1.73 1.41 2.04
0.07 0.09 0.06 0.07 0.03 0.05 0.04 0.02 0.17
ΔH‡ (kcal mol−1)
Aobs (s−1) 1.63 1.54 1.40 1.29 1.22 1.44 1.73 1.18 2.31
× × × × × × × × ×
13
10 1013 1013 1013 1013 1013 1013 1013 1013
± ± ± ± ± ± ± ± ±
7.50 9.40 5.20 5.80 2.20 3.60 3.30 4.20 2.45
× × × × × × × × ×
10
10 1010 1010 1010 1010 1010 1010 1010 1011
0.94 0.80 1.06 1.00 1.14 0.95 1.00 0.92 1.44
± ± ± ± ± ± ± ± ±
0.05 0.04 0.06 0.04 0.02 0.03 0.02 0.04 0.15
ΔS‡ (kcal mol−1 T−1) 0.04 −0.56 −0.03 −0.48 −0.09 −0.68 −0.39 −0.35 0.58
± ± ± ± ± ± ± ± ±
−4.70 −4.71 −4.70 −4.71 −4.72 −4.71 −4.71 −4.71 −9.92
× × × × × × × × ×
10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2
Error in η0 is
