Comparative Study of Cl-Atom Reactions in Solution Using Time

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A Comparative Study of Cl-Atom Reactions in Solution Using Time-Resolved Vibrational Spectroscopy Jae-Yoon Shin, Amanda S. Case, and F. Fleming Crim J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b01765 • Publication Date (Web): 05 Apr 2016 Downloaded from http://pubs.acs.org on April 10, 2016

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The Journal of Physical Chemistry

A Comparative Study of Cl-atom Reactions in Solution Using Time-resolved Vibrational Spectroscopy Jae Yoon Shin,† Amanda S. Case,* and F. Fleming Crim* Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53706 ABSTRACT A Cl atom can react with 2,3-dimethylbutane (DMB), 2,3-dimethyl-2-butene (DMBE), and 2,5dimethyl-2,4-hexadiene (DMHD) in solution via a hydrogen-abstraction reaction. The large exoergicity of the reaction between a Cl atom and alkenes (DMBE and DMHD) makes vibrational excitation of the HCl product possible, and we observe the formation of vibrationally excited HCl (v=1) for both reactions. In CCl4, the branching fractions of HCl (v=1), Γ (v=1), for the Cl-atom reactions with DMBE and DMHD are 0.14 and 0.23, respectively, reflecting an increased amount of vibrational excitation in the products of the more exoergic reaction. In addition, Γ (v=1) for both reactions is larger in the solvent CDCl3, being 0.23 and 0.40, as the less viscous solvent apparently dampens the vibrational excitation of the nascent HCl less effectively. The bimolecular reaction rates for the Cl reactions with DMB, DMBE, and DMHD in CCl4 are diffusion limited (having rate constants of 1.5 × 1010, 3.6 × 1010, and 17.5 × 1010 M1 -1

s , respectively). In fact, the bimolecular reaction rate for Cl + DMHD exceeds a typical

diffusion-limited reaction rate, implying that the attractive intermolecular forces between a Cl atom and a C=C bond increase the rate of favorable encounters. The two-fold increase in the reaction rate of the Cl + DMBE reaction from that of the Cl + DMB reaction likely reflects the effect of the C=C bond, while both the number of C=C bonds and the molecular geometry likely play a role in the large reaction rate of the Cl + DMHD reaction.

*A. S. Case, E-mail: [email protected] *F. F. Crim, E-mail: [email protected] † Present Address: Department of Chemistry, Stanford University, Stanford, California 94305

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1. Introduction The reactions of Cl atoms with organic molecules are important in atmospheric chemistry1-2 and as prototypes for understanding reaction mechanisms and testing theoretical models of reaction dynamics. Because the vast majority of experimental and theoretical studies of Cl-atom reactions investigate Cl atoms reacting with alkanes, their reaction mechanisms are known in detail. In particular, the gas-phase reactions of Cl atoms with methane (or its isotopologues) have been a platform for studies of the state-to-state reaction dynamics at various collision energies that have clearly established bond- and mode-specific chemistry in vibrationally mediated reactions.3-8 Reactions between Cl atoms and alkenes, on the other hand, are less well studied, and they offer richer chemistry than the reactions with alkanes. In alkane reactions, direct hydrogen abstraction is the only possible reaction channel, but in reactions with alkenes, addition of Cl to a C=C bond is also possible along with subsequent elimination of HCl (addition–elimination or indirect hydrogen abstraction). The direct and indirect abstraction pathways can compete, and in the gas-phase reactions of Cl + alkenes the relative contribution of each pathway depends on the thermodynamics of the reaction and on experimental conditions, such as temperature and pressure.9 The role of the potential addition–elimination processes in Cl + alkenes reactions remains unclear because of the difficulty in distinguishing between direct and indirect hydrogen abstraction.9-12 However, the latest quasi-trajectory calculations in the Cl + propene reaction suggest that indirect hydrogen abstraction plays a minor role in the reaction dynamics.12 Recent improvements in transient infrared (IR) absorption spectroscopy have provided new approaches to studying condensed-phase, bimolecular reactions,13-15 but these studies are still limited. Since Hochstrasser and coworkers first observed HCl formation from Cl-atom reaction with cyclohexane in real time (with ps time resolution),16 there have only been a few studies of Cl-atom reaction dynamics that monitor product formation.17-18 Recently, Orr-Ewing and coworkers investigated reactions of Cl atom with 2,3-dimethyl-2-butene (DMBE) and resolved, for the first time, both ground-state and vibrationally excited HCl products in solution.18


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Here, we report similar studies of the reaction of Cl-atoms with two additional molecules, 2,3dimethylbutane (DMB) and 2,5-dimethyl-2,4-hexadiene (DMHD), in two different chlorinated solvents. As shown in Figure 1, DMB has a similar structure to DMBE, but it is a saturated hydrocarbon. In DMHD, there are four methyl substituents as in DMBE, but it has one more C=C bond. Therefore, this series of molecules allows for a systematic comparison of reaction dynamics with an increasing number of C=C bonds and increasing molecular complexity. For the reaction of Cl atoms with DMHD, we observe more vibrationally excited HCl products than in the reaction between Cl atoms and DMBE. In addition, the reaction between Cl atoms and DMHD has a larger bimolecular reaction rate coefficient (~1011 M-1s-1) compared to the reaction of Cl atoms with DMBE, even though our quantum chemistry calculations show that the energy profiles of the two reactions are similar. Further, the bimolecular reaction rate coefficient for reaction of Cl atoms with DMHD exceeds that for a typical diffusion-limited reaction, suggesting that the presence of the C=C bonds and the difference in the molecular geometries may enhance the rate. Interestingly, the reaction rates we determine have a counter-intuitive solvent dependence that requires more sophisticated considerations than viscosity alone. 2. Experimental Methods We use 2,3-dimethylbutane (DMB) (Aldrich, 98%), 2,3-dimethyl-2-butene (DMBE) (Aldrich, 98%), 2,5-dimethyl-2,4-hexadiene (DMHD) (Aldrich, 96%), CCl4 (Sigma-Aldrich, Reagent grade 99.9%), and CDCl3 (Aldrich, 99.8 atom % D) as received. For these experiments, the concentrations of DMB and DMBE are 0.2, 0.5, and 0.75 M, but we use lower concentrations of DMHD (0.1, 0.2, and 0.35 M) to avoid the formation of photoproduct, as described below. The apparatus for broadband transient IR absorption measurements is similar to that used in our recent condensed-phase study of photoisomerization of polyhalomethanes.19 The third harmonic of an ultrafast Ti:sapphire laser provides 267-nm photolysis pulses at a 1 kHz repetition rate. We use 1 µJ of that light for two-photon photolysis of the CCl4 or CDCl3 solvent molecules, generating Cl atoms in solution for the reaction. For these broadband IR probe experiments, a continuum-seeded double-pass optical parametric amplifier using a potassium niobate crystal generates tunable probe light near 3.6 µm, which covers the fundamental (v=1 ← v=0) and excited-state (v=2 ← v=1) transitions of HCl. The photolysis and probe beams cross


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each other in the sample solution at a small angle, and a computer-controlled mechanical translation stage controls the time delay between the two pulses. A peristaltic pump flows the sample solution through a cell with MgF2 windows and a 300-µm thick polytetrafluoroethylene spacer. After the cell, a 0.25-m Ebert monochromator equipped with a 300-grooves/mm grating disperses the IR probe light onto a 64-pixel mercury-cadmium-telluride array detector. We calibrate the array detector using the absorption features of 1,4-dioxane contained in a thin space between two CaF2 windows. The resolution of the array detector is about 2.1 cm-1/pixel in this wavelength region, giving a spectral width on the detector of roughly 134 cm-1. We take two separate scans, each using a different spectral window of the probe beam, and merge these two scans during data processing to obtain the requisite 200 cm-1 coverage for both ground-state and vibrationally excited HCl products. We calculate a transient absorption spectrum from the probe signals with and without the photolysis pulse using a mechanical chopper that operates at onehalf of the laser repetition rate. We average 10,000 spectra at each time delay and use a total of 46 time delay points to create one scan. The data presented in this study are the average of three such scans. A small DC gear motor translates the sample cell perpendicular to the direction of the probe beam between each data acquisition cycle of 1,000 spectra to avoid deposition of photoproducts on the cell windows. In addition, we randomly order the time-delay steps and block both the photolysis and probe beams while the translation stage moves to the next time delay position in order to minimize the effects of photoproduct formation. We are particularly careful with the DMHD solutions, as high concentrations and long irradiation times produce deposits on the windows. For the same reason, we clean the MgF2 windows before and after each scan and make a fresh sample solution for each experiment. We use transient electronic absorption as a complement to our vibrational absorption measurements, and the details of our broadband transient electronic absorption apparatus are the same as in our earlier experments.19 We generate ultraviolet (UV) and visible (VIS) continuum probe light by focusing a 400-nm pulse (which is the second harmonic of the Ti:sapphire laser) into a CaF2 substrate. The resulting continuum spans roughly 280 nm to over 600 nm. We split the continuum light using a neutral density filter to generate reference and signal beams and pass the signal, but not the reference, through the sample. A 600-grooves/mm holographic grating


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enclosed in a modified Czerny-Turner spectrometer disperses both beams onto a pair of 512pixel Si photodiode arrays. Fast mechanical shutters block and unblock the photolysis and probe pulses to permit determination of the transient absorption from the reference corrected probe signals with and without the photolysis pulse. We use KOALA (Kinetics Observed After Light Absorption), recently developed by Grubb et al.,20 for post data processing of both the transient IR and UV/VIS absorption data. For the analysis of the IR probe data, we subtract the negative-time signal and fit the baseline in the raw experimental spectrum to a linear or quadratic function to eliminate the contributions from baseline offsets. In the data processing of the UV/VIS continuum probe, we correct the negativetime signal of the raw spectrum and deconvolute the Cl-solvent complex absorption band from the absorption of unknown species by fitting Gaussian curves to the experimental transient absorption spectrum (see the Supporting Information for details).21 We use the Gaussian09 suite of programs22 to perform ab initio calculations on the isolated and implicitly solvated reactants, products, and possible entrance and exit channel complexes. Since there are no thermodynamic data available for the reactions of DMB, DMBE, and DMHD with a Cl atom, we use the CBS-QB3 method to estimate the overall reaction energy. This method extrapolates the energy to the complete basis set limit based on a series of single-point energy calculations with various basis sets and is widely used for the calculation of reaction energies due to its high thermochemical accuracy (~ 8 kJ mol-1).10-11, 23 To calculate the energy profiles, we use density functional theory (B3LYP) with a 6-311G++ (d,p) basis set to determine the energy of all local minima and the TS of each reaction and apply the integral equation formalism polarizable continuum model (IEFPCM), an implicit solvent model, to account for the solvent effects of CCl4, CHCl3, and CH2Cl2. We find stationary points with one imaginary vibrational frequency, and an intrinsic reaction coordinate calculation confirms that the TS connects the local minima for each reaction.


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3. Results Our goal is to understand the dynamics of Cl + alkene reactions in solution, and, to this end, we study a series of molecules with an increasing number of C=C bonds, with the most interesting reaction partner (DMHD) having two distinct types of H atoms, as shown in Figure 1. A. Quantum calculations for the reactions of Cl with DMB, DMBE, and DMHD Figure 1 shows the possible hydrogen-abstraction reaction pathways and their calculated overall energy changes (∆E). We calculate ∆E by taking the difference between the (CBS-QB3) energy of the reactants and the products, and we use this ∆E to estimate the endoergicity or exoergicity of the reactions. For DMB, there are two hydrogen-abstraction channels because it has two distinct types of H atoms. Abstraction of either an H atom bonded to a primary or tertiary carbon has a relatively small exoergicity, with the calculated ∆E being -13 or -31 kJ/mol (-3.1 or -7.4 kcal/mol), respectively. Abstraction from the tertiary position is more exoergic because it produces a more stable tertiary alkyl radical (in comparison to a primary alkyl radical generated by abstraction from a primary carbon). However, based upon the calculated exoergicity, neither abstraction channel provides enough energy to populate the HCl vibration, which requires 34.5 kJ/mol (8.2 kcal/mol). (Our energy profile calculations suggest that the hydrogen-abstraction reactions are barrierless; therefore, we do not consider the energies of the transition state or the entrance- and exit-channel complexes when calculating the energy available to the products.) The Cl-atom reaction with DMBE has only one abstraction channel, removal of an allylic H atom from one of the four methyl groups. The calculation gives ∆E = -80 kJ/mol (-19.1 kcal/mol) for this reaction with the large exoergicity arising from formation of a resonance stabilized allylic radical. Our calculated ∆E is consistent with that estimated by Preston et al. from their CBS-QB3 calculations.11 In gas-phase experiments, this reaction produces HCl with up to v=2 excitation, while reaction in solution populates only HCl in v=0 and v=1.18 In both phases, the highest vibration excited in the products is one quantum less than the energetic maximum. (The additional collisional energy in the gas phase provides enough energy to populate v=3.)


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There are two abstraction channels for the Cl reaction with DMHD because the Cl atom can abstract either an allylic or vinylic H atom. Because the vinylic hydrogen abstraction is endoergic by 10 kJ/mol (2.4 kcal/mol), it is unlikely to contribute significantly. As in the reaction with DMBE, the allylic hydrogen abstraction from DMHD is very exoergic, ∆E = -102 kJ/mol (24.4 kcal/mol). This calculated ∆E is well above the energy required to populate the v=2 state of HCl but is just below the energy of the v=3 state. UB3LYP/6-311G++(d,p) calculations elucidate the detailed reaction energetics, including the TS, and IEFPCM evaluates the solvent effects on each reaction. Each of these reactant pairs forms an entrance-channel complex in the gas phase, but the TS for all three channels lies below the asymptotes. Including solvent effects does not change the situation, and the overall reactions are barrierless in both cases. Solvation also has very little effect on the exoergicities of the reactions. The Supporting Information provides calculated energy profiles along with further details. B. Transient IR absorption measurements for the reactions of Cl with DMB, DMBE, and DMHD We initiate reaction by photolytically producing Cl atoms using two-photon photolysis of the chlorinated solvents CCl4 and CDCl3 at 267 nm. Abou-Chahine et al. have recently investigated the detailed dynamics of photodissociation and isomerization of liquid CCl4 and CHCl3.24 Twophoton excitation of CCl4 (or CHCl3) at 267 nm cleaves a C–Cl bond resulting in fragments of CCl3 (or CHCl2) and Cl. The nascent Cl atom immediately forms a van der Waals complex with surrounding solvent molecules, Cl…CCl4 (or Cl…CHCl3). The Cl-solvent complex can recombine to re-form the parent molecule or it can isomerize to form iso-CCl3–Cl (or iso-CHCl2–Cl). The authors assigned the bands at 330 and 500 nm to transient absorption of the Cl-solvent complex and the isomer, respectively. Using these spectral signatures, they mapped out a complete picture of photoinduced reactions in liquid CCl4 and CHCl3. Over the course of photodissociation, recombination, and isomerization, the Cl atoms react when they encounter a reaction partner, such as an alkane or an alkene. Most condensed-phase studies of Cl atom reactions use such a two-photon photolysis scheme for preparing Cl atoms and, thus, initiating a reaction in solution.17-18, 24-25


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i. Reaction of Cl atoms with 2,3-dimethylbutane (DMB) Figure 2 shows transient IR absorption spectra at different delay times for the reaction of Cl atoms with DMB in CCl4 and CDCl3. In the transient absorption measurements of a 0.5 M DMB solution in CCl4, an absorption band at 2830 cm-1 grows in as the time delay increases. In the CDCl3 solution, a broader band at 2820 cm-1 appears and grows in intensity with an increase in time delay. The peak positions of these bands match those of the steady-state absorption peaks of HCl in CCl4 and CDCl3,18 although there are interferences from the changing absorption of DMB in the transient absorption spectra. Since the HCl feature resides close to the large absorption feature of DMB that starts at 2780 cm-1, interference from DMB produces a negative-signal in the transient absorption spectrum. The negative-signal from absorption of DMB at 2807 cm-1 and the shift of the HCl absorption feature to higher energy in CCl4 make the transient absorption band appear to be narrower than in CDCl3. As expected from the calculated ∆E, we do not observe the v=2 ← v=1 transition that would appear about 105 cm-1 below the fundamental (v=1 ← v=0). In order to extract the reaction dynamics from the time evolution of the HCl molecule, we integrate the intensities of 10 pixels (corresponding to 21 cm-1) around the band maximum and display this integrated intensity as a function of the time after photolysis in Figure 3. The growth rate and magnitude of the HCl band depend on the DMB concentration, implying a bimolecular reaction. ii. Reaction of Cl atoms with 2,3-dimethyl-2-butene (DMBE) Figure 4 shows representative transient absorption measurements of the Cl + DMBE reaction in CCl4. An additional band at 2710 cm-1 appears in CCl4 along with the fundamental band of HCl at 2828 cm-1 (in CDCl3, these two bands shift to lower energy by 5 and 10 cm-1, appearing at 2705 and 2818 cm-1, as shown in the Supporting Information). Again, an interference from the changing absorption of DMBE results in the negative signals at 2725 cm-1 and above 2850 cm-1. Orr-Ewing and coworkers assigned the new feature appearing at 2710 cm-1 in CCl4 (and 2705 cm-1 in CDCl3) to the HCl (v=2 ← v=1) transition. This excited-state transition appears on a similar time scale to the rise of the fundamental band until ~20 ps and then decays at the rate of the vibration-to-vibration (V-V) energy transfer with DMBE. The close proximity of the C-H stretching band of DMBE (starting from 2820 cm-1) and the fundamental band of HCl (2828 cm-


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1

) makes near-resonant V-V energy transfer from HCl (v=1 → v=0) to DMBE (vC-H=0 → vC-

H=1)

likely. Our transient absorption measurements (taken at three different concentrations)

show the same dynamics as Orr-Ewing and coworkers reported.18

iii. Reaction of Cl atoms with 2,5-dimethyl-2,4-hexadiene (DMHD) The reaction of Cl + DMHD in CCl4 and CDCl3 produces both ground-state and vibrationally excited HCl (see Figure 5), consistent with the calculated exoergicity. In CCl4, we assign the feature at 2717 cm-1 as the v=2 ← v=1 excited-state transition and the band at 2830 cm-1 as the fundamental transition of HCl. In CDCl3, these bands appear at 2709 and 2816 cm-1, respectively. As with the DMB and DMBE solutions, the transient absorption spectra show negative-going signals near the high-energy side of each band because of the changing absorption of the DMHD. The excited-state transition grows in during the first 20 ps and then decays, while the fundamental transition grows monotonically. The time dependence of these spectral signatures is analogous to those of the excited and fundamental transitions of HCl observed in the DMBE reactions with Cl, further supporting their assignment as HCl product signals of the v=1 and v=0 vibrational states. Figure 6 shows the time-dependent integrated intensities for the v=0 and v=1 HCl signals. We find no evidence of a transition from the v=2 state of HCl, despite a careful search below 2600 cm-1. The fundamental transition grows monotonically, as in the Cl + DMBE reactions, in both CCl4 and CDCl3, and, more important, the hot band decays on the same time scale as in the Cl + DMBE reactions, again suggesting that the V-V energy transfer governs the decay. Because the C-H stretching transition of DMHD lies close in energy to the fundamental transition of HCl, it is likely that a near-resonant V-V energy transfer also occurs between the HCl (v=1) product and the DMHD reactant. The time dependence of both the ground- and excited-state HCl signals in the DMHD reaction are qualitatively similar to those in the DMBE reactions. Both reactions show the monotonic growth of the HCl (v=0) band and the rise-and-decay of the HCl (v=1) band. Their concentration and solvent dependences are also similar. However, the maximum intensities of the HCl (v=1)


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signal relative to the HCl (v=0) signal from 10 to 20 ps are much larger than for the DMBE reactions, indicating that the reaction of Cl atoms with DMHD produces more vibrationally excited HCl than the reaction with DMBE.

C. Kinetics analysis of Cl-atom reactions with DMB, DMBE, and DMHD We model our analysis of the reaction of Cl with DMB, DMBE, and DMHD, on the kinetic scheme of Orr-Ewing and coworkers.18 Their model accounts for three categories of processes: in-cage reaction, diffusion, and in-bulk reaction. The Cl atoms created via photolysis can promptly react with their nearest reaction partners, and these reactions can occur rapidly before the Cl atoms can escape the first solvation shell (in-cage reactions). Other Cl atoms can diffuse out of the cage to the bulk solvent (diffusion) and react more slowly with reaction partners in the solvent (in-bulk reactions). The model describes these processes as a series of chemical reactions with associated rate constants. In-cage reaction and relaxation: c

Clc + RH HCl (v=0)c + R c

Clc + RH HCl (v=1)c + R rc

HCl (v=1)c HCl (v=0)c

(1a) (1b) (1c)

Diffusion:

Clc Clb d

HCl (v=0)c HCl (v=0)b d

HCl (v=1)c HCl (v=1)b

(1d) (1e) (1f)

In-bulk reaction and relaxation: b

Clb + RH HCl (v=0)b + R

(1g)


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b

Clb + RH HCl (v=1)b + R rb

HCl (v=1)b HCl (v=0)b

(1h) (1i)

We follow the notation of Orr-Ewing and coworkers18 where the subscripts of c and b denote a species (or a reaction) in the cage and in the bulk, respectively, the subscript d denotes a diffusion process, and the subscript r denotes the vibrational relaxation of HCl (v=1). In addition, the subscript 0 and 1 denotes a reaction producing HCl (v=0) and (v=1), respectively. We assume that the concentration of RH (the reactive partner that loses an H atom) is much larger than that of Cl, thus making k0c, k0b, k1c, and k1b pseudo-first-order rate constants. The corresponding bimolecular reaction rate constants, K0c, K0b, K1c, and K1b, are the pseudo-firstorder rate constants divided by the solute concentrations. The bimolecular reaction rate in the bulk, Kbi, is the same as K0b for the DMB reaction because there is no formation of HCl (v=1). However, Kbi = K1b + K0b if a reaction produces both HCl (v=0) and (v=1), as is the case for the DMBE and DMHD reactions. Our global fitting constrains the diffusion rate constant, kd, to values that lie within the error range obtained by Orr-Ewing and coworkers from the fit of their DMBE experimental data.18 We also fix krc to 0 for the same reason that they found: it is always negligible when running fits treating it as a free parameter. This result suggests that the nascent HCl (v=1) diffuses out of the solvent cage before vibrational relaxation can occur. In our analysis, we use the vibrational relaxation rate in the bulk solvent that Orr-Ewing and coworkers estimate from IR pump-probe experiments, krb = 2 × 1010 s-1M-1.18 (This rate of vibrational relaxation is 5 times slower than diffusion in CDCl3 and 10 times slower than diffusion in CCl4, supporting our notion that diffusion occurs too quickly to allow for vibrational relaxation in the cage.) We also use a scaling factor of two to account for the difference in the transition probabilities of the excitedstate transition (v=2 ← v=1) and the fundamental transition of HCl in extracting relative populations of HCl (v=1) from the signal intensities. Since the HCl (v=0) signal that we observe comes from population difference between HCl (v=1) and HCl (v=0), we subtract the corrected population of HCl (v=1) from the population of HCl (v=0) in the kinetic model to fit the experimental HCl (v=0) signal.


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We use a global-fitting program to analyze simultaneously the time evolution for three different concentrations for each reaction and summarize the resulting rate coefficients in Table 1. For the Cl + DMB reaction, we remove k1c, krc, k1b, and krb from the analysis, as it cannot form vibrationally excited products. This modified kinetic model fits nicely with our experimental data, as illustrated by the solid lines in Figure 3. The Kbi for the reaction of DMB and Cl in CCl4 and CDCl3 are 1.5 (± 0.5) × 1010 M-1s-1 and 0.7 (± 0.1) × 1010 M-1s-1, respectively. These values are comparable to bimolecular reaction rate constants for other alkanes in the condensed phase.17, 25

The reactions of Cl atoms with alkenes produce vibrationally excited HCl. Our fits to the Cl + DMBE data give a total bimolecular reaction rate constant in the bulk solvent, Kbi, of (3.6 ± 0.3) × 1010 M-1s-1 in CCl4 and (1.7 ± 0.6) × 1010 M-1s-1 in CDCl3, in agreement with previously reported values.18 We also define a branching fraction for HCl (v=1) as

v = 1 =

K1c +K1b HCl(v=1) = (2) HCl(v=1)+HCl(v=0) K1c +K1b +K0c +K0b

This quantity, which is the fraction of all the HCl molecules produced that are vibrationally excited (in v=1), shows the energy disposal in the reaction. The branching fractions, Γ, are 0.14 ± 0.01 in CCl4 and 0.23 ± 0.05 in CDCl3, again consistent with those reported in the previous study.18 We make one convenient assumption in fitting the Cl + DMHD data. Although we did not carry out IR pump-probe experiments of an HCl solution in the presence of DMHD to estimate the vibrational relaxation (or V-V energy transfer) rate of HCl (v=1), we assume that it is roughly the same in DMBE and DMHD and, thus, use the vibrational relaxation rate determined by Orr-Ewing and coworkers for HCl (v=1) in a DMBE solution as the krb for the reactions of Cl + DMHD. As a test of this assumption, we fit the decay of the HCl (v=1) signal from its maximum at ~ 20 ps to a single-exponential function and obtain a decay time of τ ≈ 250 ps for the 0.2 M DMHD solution in CCl4. This decay rate matches the V-V energy transfer rate of HCl (v=1) in the DMBE reactions.


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The kinetic scheme fits the DMHD data well for all three concentrations, as shown by the solid lines in Figure 6 (the data for the 0.2 M DMHD solution are available in the Supporting Information). The total bimolecular reaction rate constants, Kbi, show that the abstraction of a H atom from DMHD by Cl is very fast, Kbi = (17.5 ± 1.6) × 1010 M-1s-1 in CCl4 and (6.7 ± 1.6) × 1010 M-1s-1 in CDCl3. These values are four- or five-fold larger than those of Cl + DMBE reactions. The branching fractions of HCl (v=1), Γ are 0.23 ± 0.06 in CCl4 and 0.40 ± 0.12 in CDCl3, showing a two-fold increase over those of Cl + DMBE. Furthermore, there is clear difference between reaction in CCl4 and CDCl3, with the Cl + DMHD reaction in CDCl3 being slower and producing more vibrationally excited HCl. D. Broadband transient electronic absorption measurements for the reaction of Cl with DMHD We have established transient electronic absorption as a means of following the reaction of Cl atoms in solution,17, 25 and here we use it as a complement to the IR absorption data for the Cl + DMHD reaction in CCl4 by monitoring the absorption of the Cl…CCl4 complex at 330 nm. Without reaction partners in solution, as in neat CCl4, Cl atoms (or Cl…solvent complexes) recombine to the parent CCl4 or isomerize to iso-CCl3–Cl molecules that have a broad absorption band with a maximum near 500 nm. However, for the DMHD solution in CCl4 another absorption band emerges at 300 nm, which we assume comes from an unidentified photoproduct (see Supporting Information). This feature is intense and masks the Cl-solvent complex absorption at 330 nm, but we use the fitting procedure described in the Supporting Information to disentangle the evolution of these features. Figure 7 shows the time-dependent integrated intensity of the Cl-solvent complex band with and without DMHD in CCl4. In neat CCl4, the intensity decays due to recombination and isomerization of the Cl…CCl4 complex. The decay rate increases when DMHD is present in solution and depends on the concentration of DMHD, consistent with a bimolecular reaction between the Cl…CCl4 complex and DMHD. We use the Smoluchowski model to fit the time-dependent dynamics of the Cl…CCl4 complex band and obtain the bimolecular reaction rate coefficient from the disappearance of the Cl…CCl4 complex (a reactant), as in previous work by the Crim17, 25-28 and Orr-Ewing24 groups. The Smoluchowski model is useful for describing geminate recombination of radical photoproducts


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and diffusion-controlled reactions in the condensed phase.29-31 In the transient electronic absorption measurements, we observe both diffusive geminate recombination and reaction with solute by monitoring the evolution of the Cl…CCl4 complex. Each of these processes gives rise to the signal, showing a non-exponential and exponential decay, respectively. We describe the detailed fitting procedure in the Supporting Information. Separate fits of the Cl…CCl4 complex band for the 0.5, 1.0, and 2.0 mM DMHD solutions, give an averaged bimolecular reaction rate constant, Kbi = (23.3 ± 5.7) × 1010 M-1s-1 (solid lines in Figure 7). (The data for 1.0 mM solution are in the Supporting Information). This value, obtained by monitoring the disappearance of reactants, also indicates that the bimolecular reaction rate of Cl + DMHD is very fast. Both the IR and electronic transient absorption measurements produce consistent rate constants, and their agreement confirms that the loss of Cl atoms (or complexes) is directly associated with the formation of HCl in the v=0 and v=1 states. 4. Discussion The transient absorption measurements provide rate constants and branching fractions that allow us to examine the inherent differences and similarities in these reactions and associated the solvent effects. A. Effects of solvation on the reactions of Cl atoms The rates of Cl reactions with alkanes in solution are, in general, an order of magnitude smaller than those in the gas phase. For Cl-atom reactions with n-pentane, n-hexane, n-heptane, and cyclohexane, the difference is a factor of ~ 10 to 20.25, 32 The bimolecular reaction rates of the Cl + DMB reaction follow the same trend. We measure its condensed-phase reaction rate constant to be (1.5 ± 0.5) × 1010 M-1s-1 in CCl4 and (0.7 ± 0.1) × 1010 M-1s-1 in CDCl3, values that are roughly 8 and 18 times smaller than those of the gas-phase congener. The gas-phase reaction rate constant for DMB with Cl is (12.4 ± 0.4) × 1010 M-1s-1.32 The absence of gas-phase data makes a direct comparison of the bimolecular reaction rates between gas and condensed phases impossible for the Cl + DMBE and the Cl + DMHD. However, we can compare the gas-phase reaction rate constant for the Cl-atom reaction with 2-


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methyl-2-butene (the closest analogue of DMBE with a reported rate) to Kbi for the Cl + DMBE reactions we study. Ezell et al. investigated the gas-phase reactions of Cl atom with a series of alkenes, and determined a bimolecular rate constant for the Cl + 2-methyl-2-butene reaction of (2.38 ± 0.19) × 1011 M-1 s-1.33 Using this gas-phase value for comparison, we might consider the condensed-phase reaction rate constant for the Cl + DMBE reaction (3.6 ± 0.3) × 1010 M-1 s-1 in CCl4 to be roughly 10 times smaller than its gas-phase analogue. However, the reported gasphase reaction rate for 2-methyl-2-butene includes contributions from the Cl addition reaction (which forms a chlorinated radical adduct) and both the direct and indirect (addition–elimination) hydrogen-abstraction reactions (which form HCl and an alkyl radical). Ezell et al. developed a structure–reactivity model to separate the contributions of these reaction pathways in the reactions of Cl atoms with alkenes.33 They describe the overall reaction rate constant as the sum of the addition reaction (kadd), the hydrogen-abstraction reactions from allyl carbons (kallyl), and the hydrogen abstractions from all other carbons that can donate a H atom (kalkyl). They calculate kalkyl using the structure–reactivity model already developed for the Cl + alkane reactions.32, 34 Once they have determined kalkyl they fit their data with a generalized reduced gradient nonlinear optimization code and minimize the difference between the calculated and measured reaction rates to obtain the best fit for kadd and kallyl. According to their model, the hydrogen-abstraction reaction rate constant for the Cl + 2-methyl-2-butene reaction is 6.14 × 1010 M-1 s-1. 33 We can further extend their model to the Cl + DMBE reaction by adding the contribution of one more methyl group to the hydrogen-abstraction reaction rate constant for the Cl + 2-methyl-2-butene reaction to obtain a calculated reaction rate constant of 8.2 × 1010 M-1 s-1. There is no distinguishing between direct abstraction and the addition–elimination pathway when estimating the hydrogen-abstraction reaction rates with this model. In a recent crossed molecular beam velocity-map imaging study of the Cl + isobutene reaction, Jolland et al. find that the indirect hydrogen abstraction occurs via a roaming mechanism and suggest that these roaming dynamics play a prominent role in the reaction.10 In a parallel molecular beam velocitymap imaging study, Orr-Ewing and coworkers observed a bimodal rotational distribution of HCl (v=0) products from the reaction of Cl atoms with propene.11 Based on direct-dynamics simulations on a limited number of trajectories, they attributed this two-component distribution to the role of both direct and indirect hydrogen abstraction, but they note that only 10% of the


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trajectories follow the indirect route.11 More recent quasi-classical trajectory calculations by OrrEwing and coworkers, which use an empirical valence bond (EVB)-fit potential energy surface to run a much larger number of trajectories, show that only a small fraction (less than 10%) of the trajectories sample the addition–elimination pathway in the Cl + propene reaction.12 Although these calculations are for a collision energy of 27 kJ mol-1, they still agree well with experiments having a mean collision energy of 2.4 kJ mol-1,12 supporting the idea that direct hydrogen abstraction at the methyl site dominates the Cl + propene dynamics.12 Further, these calculations suggest that the degree of rotational excitation of HCl cannot be used to distinguish between direct and indirect abstraction, and they indicate that the roaming pathway is only a minor contributor to the dynamics.12 For the Cl + DMBE reaction, the addition pathway is likely to be even more unfavorable because of the larger number of allyl carbons, which not only provide energetically accessible H atoms but, also, sterically hinder the Cl atom’s approach to the double bond. This speculation agrees with a recent gas-phase study of the Cl + DMBE reaction, which strongly suggests that the contribution of the addition–elimination reaction channel is insignificant even under single-collision conditions.11 Therefore, we expect that the actual gas-phase reaction rate constant for the direct hydrogen abstraction of the Cl + DMBE reaction is larger than the value estimated by the structure–reactivity model above (8.2 × 1010 M1 -1

s ). While this estimated gas-phase reaction rate is more than a factor of two larger, the

comparison with the condensed-phase rate is still likely much closer than in the alkane case. Electrostatic and other intermolecular influences of a solvent can affect a reaction rate by shifting energy levels and changing the activation energy. In addition to these static effects, the solvent can also dynamically influence a reaction through interactions that occur during the course of a reaction.14 The results of our quantum calculations (see Supporting Information) indicate that the energy profiles of the reactions in the condensed phase are not substantially different from those in the gas phase for all three reactions, and that all three are barrierless reactions regardless of the phase. Therefore, the static effects of the solvent on these reactions appear to be small. This observation suggests that the dynamic effects of the solvent play an important role in reducing the reaction rates in the condensed phase, which all appear to proceed at the encounter-limited rate.


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The relatively small amount of data available to compare vibrational energy disposal in condensed-phase reactions and gas-phase reactions indicate that the former yield fewer vibrationally excited products.15, 18, 35-36 While a recent gas-phase study demonstrated that the Cl + DMBE reaction produces HCl products in higher vibrational levels in the gas phase than the condensed phase,11 the gas-phase branching fractions for the Cl + DMBE reactions are unknown. However, the values we find are significantly smaller than the branching fraction of an illustrative gas-phase reaction: the Cl + propene reaction (Γ (v=1) = 0.48 ± 0.06).37 This comparison implies that while the solvent does not completely suppress the production of vibrationally excited products, it does perturb the reaction dynamics and, in this case, diminishes the fraction of vibrationally excited products. A recent review proposed three possible explanations for this reduced vibrational excitation of the HCl products in condensed-phase reactions.15 The dampening could occur because of (1) a coupling of the post-TS motions of the developing products and the solvent bath modes, (2) displacement of the TS arising from a modified reacting form of Cl atoms in solution, such as a Cl-solvent complex, or (3) differing contributions of the addition–elimination reaction pathway. However, as described above, the recent gas-phase study of Cl + DMBE and the quasi-classical trajectory calculations of Cl + propene encourage us to discount the last possibility.11-12 While there is no comparable gas-phase study for the Cl + DMHD reaction, it is likely that this reaction also follows the general trend because the calculated ∆E is larger than the Cl + DMBE reaction yet we detect the same vibrationally excited products (v=0 and v=1). Within the condensed phase, the branching fraction of vibrationally excited HCl products, Γ (v=1), clearly depends on viscosity in the reactions of Cl atoms with both DMBE and DMHD. The less viscous solvent, CDCl3, has a larger fraction of vibrationally excited molecules, Γ (v=1). Our electronic structure calculations predict that the locations of the TS for both reactions are nearly the same with little change for the different solvents and that the TS for both reactions are always lower in energy than the reaction products (see Supporting Information). The H-Cl bond lengths at the calculated TSs are roughly 1.50 to 1.60 Å for the Cl + DMBE reactions and roughly 1.52 to 1.65 Å for the Cl + DMHD reactions, depending on the solvent used. Therefore, it seems that it is the weaker interactions with the solvent that lead to the increased Γ (v=1) in CDCl3. Furthermore, the nearly two-fold increase in Γ (v=1) obtained in CDCl3 is consistent


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with the ratio of the room temperature viscosities between CCl4 (0.908 cP) and CDCl3 (0.537 cP).38 Thus, the first explanation, solvent friction dampening the vibrational excitation, accounts for the more viscous solvent producing a smaller Γ (v=1). While the trend in the branching fractions mirrors the solvent viscosity, the bimolecular reaction rates do not follow solvent viscosity. A simple diffusion model predicts that these encounter-limited reactions should have rates that correlate with the solvent viscosity and that the more viscous solvent should have the smaller reaction rate. However, our results show that the reaction rates increase in the more viscous solvent, CCl4. By photolytically generating the Cl atoms from two different sources (solvents), we complicate the simple diffusion picture as the initial translational energy of the Cl atoms is different and, potentially, influences the diffusion and complexation rates. A deeper understanding of the observed solvent effects requires more sophisticated models and simulations. For example, Glowacki et al. demonstrated the need for a model that includes the role of the co-product, cyclohexyl at early times, to describe the vibrational excitation relaxation of the nascent HCN product formed in the reaction of the CN radical with cyclohexane.39 We may also need to consider the co-product or the Cl-solvent complexation to better understand the solvent dependence of these bimolecular reaction rates. B. Comparisons of the reactions of Cl atoms with DMB, DMBE, and DMHD All three of the Cl-atom reactions that we study are encounter limited with the TS playing a minimal role in their reaction dynamics, and, thus, the exoergicity and molecular structures are likely responsible for the differing energy disposal and reaction rates. In both solvents, the reaction rates for Cl + DMBE are about twice those of the Cl + DMB reaction, even though DMB has two more H atoms available for abstraction. Since the molecular structures of DMB and DMBE are similar and, again, these reactions are in the encounter-limited regime, the difference in the reaction rates likely reflects the effects of the C=C bond on the encounter rate. If we add one more C=C bond, as with DMHD, the bimolecular reaction rates become even faster. In fact, while the reaction rate constants for Cl + DMB or DMBE approach the diffusion limit, the reaction rate constant for Cl + DMHD in CCl4 seems to surpass it (~ 1011 M-1s-1 vs. ~ 1010 M-1s-1).


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A condensed-phase bimolecular reaction rate can be faster than the nominal diffusion limit when there are sufficient intermolecular forces between the reactants or a long-range transfer occurs.29 Reactions of solvated electrons are good examples.29 The interaction between a charge and permanent dipole of solvated electrons with aromatic molecules can produce rate constants on the order of 1011 M-1s-1.40 Similarly long-range electron transfer reactions also occur in the reactions of solvated electrons.29 In the reaction of Cl atoms with alkenes, the strongly electrophilic Cl atoms and the electron density and π character of the C=C bonds may make the attractive forces substantial. Perhaps, a long-range potential directs the Cl atoms and DMHD molecules toward one another. Indeed, Hornung et al. calculated the ab initio potential energy surface for the reaction of a Cl atom with propene, and the calculation shows a basin that connects the deep wells of the 1-chloropropyl and 2-chloropropyl radicals.12 This area extends to 4 – 5 Å of separation between the Cl atom and the C=C bond, corresponding to a π-complex. They also found that including this extended attractive potential in their quasi-classical trajectory calculations makes reactive collisions occur at larger impact parameters,12 showing the effect of the attractive interaction between the Cl atom and the C=C bond on the dynamics. If we assume that the two-fold increase in the reaction rates of the Cl + DMBE reactions (versus Cl + DMB) arises from the effects of the C=C bond, then we could adopt a generic doubling of the reaction rate with each additional C=C bond. Even so, the magnitude of the rate of increase in the Cl + DMHD reactions is still about twice that amount. It is conceivable that this discrepancy comes from the differences in molecular geometries. Figure 8 compares the optimized structures for DMBE and DMHD. The DMBE structure is more compact than that of DMHD. In the DMBE structure, the closest H–H distances between adjacent methyl groups are 1.9 Å for the direction parallel to the C=C bond and 2.5 Å for the direction perpendicular to the C=C bond. In the DMHD structure, the closest H–H distances between adjacent methyl groups are 2.6 Å, and the closest H–H distances between methyl groups and the vinyl H atoms are 2.3 and 2.0 Å, respectively. These calculations show that in DMHD there is an easier approach for the Cl atoms. These steric effects specify the cone of acceptance for the reactions and the possible steering of the intermolecular interactions. Such considerations would favor a faster rate for the Cl + DMHD reactions and may be, in part, responsible for the


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unexpectedly high four- or five-fold increase of the bimolecular reaction rate as compared with the Cl + DMBE reactions. Considering the branching fractions of HCl (v=1), we find that Γ (v=1) is larger in the Cl + DMHD reaction than in the Cl + DMBE reactions by roughly a factor of two. Since both reactions are barrierless, the exoergicity of the reaction appears to dictate the difference in the vibrational excitation of the products. The Cl + DMHD reaction is more exoergic and, thus, has more energy available to go into vibration.

5. Summary We investigate the reactions of Cl atoms with a saturated hydrocarbon (DMB) and an unsaturated hydrocarbon having two C=C bonds (DMHD) in chlorinated solvents, building on a recent study of the Cl + DMBE reactions.18 We photolyze CCl4 and CDCl3 to generate Cl atoms in solution and follow the hydrogen-abstraction reactions of these Cl atoms by monitoring the formation of the HCl products with transient IR absorption measurements. Based on CBS-QB3 calculations, the Cl + DMHD reaction is highly exoergic (102 kJ/mol), while the Cl + DMB reaction is mildly exoergic (13 or 31 kJ/mol). As a result, the Cl + DMHD reaction produces vibrationally excited HCl (up to v=1), in analogy with the Cl + DMBE reaction, but the Cl + DMB reaction produces only ground state HCl. The bimolecular reaction rate constants of all three reactions are encounter-limited: in CCl4, they are (1.5 ± 0.5) × 1010 M-1s-1 for Cl + DMB, (3.6 ± 0.3) × 1010 M-1s-1 for Cl + DMBE, and (17.5 ± 1.6) × 1010 M-1s-1 for Cl + DMHD. Detailed energy profile calculations indicate that all three reactions are barrierless, consistent with these large rate constants. Overall, the reaction dynamics of Cl-atom reactions in the condensed phase are akin to those in the gas phase. The reactions are fast without significant energy barriers, and energy disposals into the products grow with the exoergicity of the reaction. However, the solvent still plays a crucial role in damping the vibrations of the nascent HCl products, allowing for more vibrational excitation in a less viscous solvent. Calculations suggest that dynamic solvent effects are mainly responsible for the reduced reaction rates in the condensed phase, while exoergicity and solvent


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friction dictate the branching fractions of the HCl (v=1) product. Interestingly, the bimolecular reaction rate of the Cl + DMHD reaction in CCl4 seems to exceed those of common diffusionlimited reactions, perhaps suggesting an attractive long-range interaction. Acknowledgments We gratefully acknowledge support from the National Science Foundation (1321931). We also thank Professor Andrew Orr-Ewing for enthusiastic discussions about this work.


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ASSOCIATED CONTENT Supporting Information The Supporting Information contains quantum calculations, more transient IR absorption data for DMB, DMBE, and DMHD solution with different concentration, and the details about the deconvolution of the Cl…CCl4 complex band in transient UV/VIS absorption measurements of the Cl + DMHD reaction and the fit with Smoluchoski model. This material is available free of charge via the Internet at http://pubs.acs.org.


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Greaves, S. J.; Rose, R. A.; Oliver, T. A. A.; Glowacki, D. R.; Ashfold, M. N. R.;

Harvey, J. N.; Clark, I. P.; Greetham, G. M.; Parker, A. W.; Towrie, M.; et al., Vibrationally Quantum-State–Specific Reaction Dynamics of H Atom Abstraction by CN Radical in Solution. Science 2011, 331 (6023), 1423-1426. 36.

Dunning, G. T.; Glowacki, D. R.; Preston, T. J.; Greaves, S. J.; Greetham, G. M.; Clark,

I. P.; Towrie, M.; Harvey, J. N.; Orr-Ewing, A. J., Vibrational Relaxation and Microsolvation of DF After F-Atom Reactions in Polar Solvents. Science 2015, 347 (6221), 530-533. 37.

Pilgrim, J. S.; Taatjes, C. A., Infrared Absorption Probing of the Cl + C3H6 Reaction:

Rate Coefficients for HCl Production between 290 and 800 K. J. Phys. Chem. A 1997, 101 (32), 5776-5782. 38.

CRC Handbook of Chemistry and Physics. 87th ed.; CRC Press: Boca Raton, FL, 2012-

2013. 39.

Glowacki, D. R.; Rose, R. A.; Greaves, S. J.; Orr-Ewing, A. J.; Harvey, J. N., Ultrafast

Energy Flow in the Wake of Solution-Phase Bimolecular Reactions. Nat. Chem. 2011, 3. 40.

Schindewolf, U.; Wünschel, P., Comparison of Solvated Electron Reaction Rates in

Water and Ammonia. Can. J. Chem. 1977, 55 (11), 2159-2164.


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Table 1. Bimolecular reaction coefficients (in 1010 M-1s-1) and HCl (v=1) branching ratios for the reaction of Cl with DMB, DMBE, and DMHD in CCl4 and CDCl3. The uncertainties of each rate coefficient are the standard deviations from the average of each rate coefficient obtained by fitting three sets of data, where each set contains three different concentrations. DMB

DMBE

DMHD

CCl4

CDCl3

CCl4

CDCl3

CCl4

CDCl3

K1c

-

-

8.1 ± 0.4

9.1 ± 2.5

22.3 ± 1.1

21.7 ± 5.8

K0c

6.7 ± 1.9

4.4 ± 0.3

54.5 ± 0.6

30.3 ± 1.9

66.8 ± 3.4

26.2 ± 4.7

K1b

-

-

0.9 ± 0.2

0.4 ± 0.2

2.2 ± 0.7

0.3 ± 0.1

K0b

1.5 ± 0.5

0.7 ± 0.1

2.7 ± 0.1

1.3 ± 0.4

15.3 ±0.9

6.4 ± 1.5

Kbi

1.5 ± 0.5

0.7 ± 0.1

3.6 ± 0.3

1.7 ± 0.6

17.5 ± 1.6

6.7 ± 1.6

Γ (v=1)

-

-

0.14 ± 0.01 0.23 ± 0.05

0.23 ± 0.06

0.40 ± 0.12


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Figure 1. Hydrogen abstraction reaction channels of DMB, DMBE, and DMHD and their calculated ∆E values.


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Figure 2. Transient absorption spectra, at select time delays, for the reaction of Cl with 0.5 M DMB in (a) CCl4 and (b) CDCl3. The black curve is the (inverse) steady-state IR absorption spectrum of DMB.


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Figure 3. Time-dependent integrated intensities of the HCl (v=0) band for the reaction of Cl with varying concentrations of DMB in (a) CCl4 and (b) CDCl3. The concentrations of DMB are 0.2 M (black), 0.5 M (red), and 0.75 M (blue). The solid lines are the fit from the kinetic model.


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Figure 4. Representative transient absorption measurements of the Cl + DMBE (0.5 M) reaction in CCl4: (a) contour plots, (b) the corresponding spectra at select time delays, and (c) timedependent integrated intensities of the HCl (v=0, black) and the HCl (v=1, red) bands. The inset shows an enlarged view of early time. The solid lines are the fit from the kinetic model.


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Figure 5. Contour plots of transient absorption (top) and the corresponding spectra at select time delays (bottom) for the reaction of Cl with 0.2 M DMHD in (a) CCl4 and (b) CDCl3.


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Figure 6. Time-dependent integrated intensities of the HCl (v=0, black and grey) and the HCl (v=1, red and blue) bands for the reaction of Cl with varying concentrations of DMHD in (a) CCl4 and (b) CDCl3. The DMHD concentrations are 0.1 M (open triangles) and 0.35M (circles). In both (a) and (b), the lower plot shows an enlarged view of early time. The solid lines are the fit from the kinetic model.


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Figure 7. The time-dependent integrated intensity of the Cl-solvent complex band for neat CCl4 (black) and 0.5 mM (red), and 2 mM (blue) DMHD solutions. The solid lines are the fit using the Smoluchowski model.


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Figure 8. Energy optimized structures of DMBE (left) and DMHD (right).


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Table of Contents Figure


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Comparative Study of Cl-Atom Reactions in Solution Using Time

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