Ultrafast Observation of Isomerization and Complexation in the

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J. Phys. Chem. A 2010, 114, 1548–1555

Ultrafast Observation of Isomerization and Complexation in the Photolysis of Bromoform in Solution† Stacey L. Carrier, Thomas J. Preston, Maitreya Dutta, Andrew C. Crowther,‡ and F. Fleming Crim* Department of Chemistry UniVersity of WisconsinsMadison, Madison, Wisconsin 53706 ReceiVed: September 9, 2009; ReVised Manuscript ReceiVed: NoVember 6, 2009

Ultrafast photolysis of bromoform (CHBr3) with a 267 nm pulse of light followed by broadband transient electronic absorption identifies the photoproducts and follows their evolution in both neat bromoform and cyclohexane solutions. In neat bromoform, a species absorbing at 390 nm appears promptly and decays with a time constant of 13 ps as another species absorbing at 495 nm appears. The wavelength and time evolution of the first absorption is consistent with the formation of iso-bromoform (CHBr2-Br) by recombination of the fragment radicals within the solvent cage. The presence of an isosbestic point in the transient spectra indicates that this isomer is the precursor of the second absorber. The excess internal energy remaining in iso-bromoform permits release of the weakly bound Br atom to form a complex, CHBr3-Br, with other bromoform molecules. The features in the transient spectra are qualitatively similar in cyclohexane solutions of bromoform. The wavelength of the transition of iso-bromoform does not change upon dilution, but that of the CHBr3-Br complex systematically decreases with addition of cyclohexane. This trend agrees with the predicted dependence of the energy of a charge-transfer transition on the dielectric constant of the medium. Vibrational relaxation is likely to be the controlling feature of the evolution of the initially formed iso-bromoform. I. Introduction The atmospheric and synthetic importance of halomethanes has motivated a variety of experimental studies over the past several decades. For example, the ultraviolet photolysis of bromomethanes may be responsible for up to 30% of the ozone depletion in the atmosphere,1-3 and halomethanes are the precursors in many organic reactions.4-6 Ultraviolet excitation dissociates halomethanes into halogen and halomethyl radicals,7,8 and in solution, the radicals encounter the solvent cage and recombine to form either the precursor or an iso-halomethane, in which the returning halogen atom binds to a halogen of the halomethyl radical.8 Resonance Raman, time-resolved Raman, and ultrafast pump-probe experiments have provided a detailed view of these compounds.8-27 They show that the isocompounds form within a few hundred femtoseconds and live for at least several nanoseconds and that they are the primary reacting species in the cyclopropanation of olefins.6,11-14 Complexes of halogen atoms with solvent are often central to radical chemistry in solution.28-32 A variety of interactions are responsible for complexation, ranging from ones that approach chemical bonds in strength to ones that involve only van der Waals forces. Many complexes absorb an ultraviolet or visible photon to reach a charge-transfer state in which the transfer of an electron creates an ion pair that is bound by strong electrostatic attraction.28-42 The simplest charge-transfer model gives the energy of these transitions as

hνCT ) ID - EA - W

(1)

where ID is the ionization energy of the donor D and EA is the electron affinity of the acceptor A. The last term, W ) e2/εrAD, †

Part of the “W. Carl Lineberger Festschrift”. * To whom correspondence should be addressed. E-mail: fcrim@ chem.wisc.edu. ‡ Present address: Department of Chemistry, Columbia University, New York, NY 10027.

is the magnitude of the electrostatic interaction between the ions,33 where ε is the dielectric constant of the medium and rAD is the distance between the acceptor and donor in the complex. This model predicts that the energy of the charge-transfer transition is proportional to the ionization energy of the donor in a series of complexes having the same electron acceptor. For example, the energies of the transitions appearing after photolysis of either Cl2 or CCl4 in different solvents scale with the ionization energy of the solvent, which is the donor in a chlorine-solvent complex.28-30 These same studies find that the halogen-solvent complex, rather than a free halogen radical, is the reactive species in such systems. Complexes of a halogen atom with a solvent molecule are also important in the reactions of bromine. Transient spectra obtained a microsecond after flash photolysis or pulse radiolysis of Br-atom precursors in solutions of aromatic molecules, alkanes, and haloalkanes show that bromine radicals form complexes that are the reactive species in the subsequent chemistry.38-40 Variations in the reaction rates reflect the influence that the structure and stability of the complex have on the reactivity. In aromatic molecules, the π-system is an electron donor that stabilizes the complex by charge transfer,43 but alkanes, which share electrons poorly, do not complex extensively.44 By contrast, the interaction in the haloalkane complexes with halogen atoms apparently involve the lone-pair electrons, sometimes described as a three-electron bond analogous to those in S∴S and Se∴Se compounds.38 The experiments described here probe the time evolution of Br radicals in neat CHBr3 and in solutions of CHBr3 in cyclohexane. Ultrafast photolysis of bromoform generates Br radicals, and ultrafast broadband transient absorption between 310 and 700 nm monitors the evolution of the resulting species. One of the key observations is the initial formation of relatively strongly bound iso-bromoform (CHBr2-Br) and subsequent production of a relatively weakly bound complex of Br with

10.1021/jp908725t  2010 American Chemical Society Published on Web 12/07/2009

Photolysis of Bromoform in Solution

J. Phys. Chem. A, Vol. 114, No. 3, 2010 1549

bromoform (CHBr3-Br). The transient absorption data are consistent with initial formation of vibrationally excited isobromoform and its subsequent release of Br atoms that complex with the solvent. II. Experimental Approach The apparatus and approach for these ultrafast transient absorption experiments is similar to those we used to study CN radicals.45,46 A pulse of 267 nm light photolyzes either neat bromoform or a solution of bromoform in cyclohexane, and a pulse of broadband continuum light monitors the evolution of the products by transient electronic absorption. A Ti:sapphire oscillator and regenerative amplifier provide a 1 kHz train of 2.5 mJ, 100 fs pulses centered at 800 nm from which we generate the required light. Frequency doubling a portion of the 800 nm light in a β-barium borate (BBO) crystal (type I, 0.3 mm, θ ) 29°) produces 400 nm light that we combine with additional 800 nm light in another BBO crystal (type I, 0.3 mm, θ ) 42°) to generate 267 nm light. To minimize multiphoton processes and burning of the sample cell, we attenuate the pulses to 1.7 µJ at the sample. A 267 nm waveplate rotates the polarization of the pump light to an angle of 54.7° relative to that of the probe light to suppress the effects of orientational anisotropy. Most of the measurements use a continuum between 380 and 700 nm, generated by focusing a small amount of the 800 nm light into a 6 mm thick, UV-grade CaF2 substrate. However, in some cases, we also use a shorter wavelength continuum between 310 and 600 nm, generated using 400 nm light, to search for absorptions below 380 nm. We match these data to the longer wavelength data in the region where they overlap. The measured temporal chirp of the continuum limits the time resolution of the experiment to about 0.5 ps. A computer-controlled delay stage determines the arrival time of the probe pulse relative to the photolysis pulse. We divide the continuum into a probe beam and a reference beam in order to correct for laser fluctuations. Each beam enters a separate, matched spectrometer containing a 512-element, 0.5 in. wide silicon photodiode array. We collect 150 pulses with and without the photolysis pulse and average five of these exposure pairs for each time increment to obtain a time trace. The data are averages of 10 of these time traces, and the resulting signals vary linearly with the energy of the photolysis pulse. A Teflon gear pump circulates a 50 mL sample through a 1 mm thick flow cell with UV-grade MgF2 windows. We use 99+% CHBr3 from Sigma-Aldrich and 99.9% cyclohexane as received from Fisher Scientific. III. Results Excitation of the σ* r n transition of bromoform with a 267 nm photon deposits 448 kJ/mol of energy, which makes dissociation into several different products possible:7,11,47

CHBr3 f CHBr2 + Br

(∆rH° ) 267 kJ/mol)

(R1)

CHBr3 f CHBr + Br2

(∆rH° ) 349 kJ/mol)

(R2)

CHBr3 f CBr2 + HBr

(∆rH° ) 247 kJ/mol).

(R3)

The dominant channel (R1) in the gas-phase photolysis produces Br radicals with a quantum yield of at least 0.76 ( 0.03.48 Molecular beam photofragmentation experiments show that Br atom production is the primary channel with other channels involving multiphoton processes.7 In solution, the radicals can either recombine within their solvent cage or escape and complex with the solvent. Two possibilities for

Figure 1. (a) Transient absorption spectra following 267 nm photolysis of neat CHBr3. The open points are the measured absorption at different times (∆t) after the photolysis pulse. The dashed lines are fits to a simple sequential kinetics scheme, and the solid lines are the fits to the more elaborate model described in the text. (b) Spectra of the absorbers, AB(λ) and AC(λ), from the kinetic analysis. The dashed lines are from fits to a simple sequential kinetics, and the solid lines are from fits to the more elaborate model described in the text. (c) Time cuts through the transient absorption spectra at the indicated wavelengths. (d) Time cuts on an expanded scale showing the early time evolution. The points shown at negative times for the data at 380 and 500 nm are typical for all of the traces. The data for the other wavelengths are omitted for clarity. The structure in the short-wavelength part of the spectrum is an artifact, and the gap in the data below 380 nm is the region obscured by the 400 nm light used to generate the short-wavelength continuum.

the recombination within the solvent cage are the Br atom bonding to the carbon atom to reform the precursor or

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bonding to one of the Br atoms of the CHBr2 radical to form the iso-compound, CHBr2-Br. As the results described below show, this isomer has a clear spectroscopic signature, as does the complex of Br with the solvent. We study both neat bromoform and bromoform diluted in cyclohexane to uncover the influence of the surroundings on these species. A. Neat CHBr3. Figure 1a shows the transient absorption spectra of neat bromoform at time intervals ranging from 1 to 50 ps after photolysis with a 100 fs pulse of 267 nm light. The small oscillations in the data at short wavelengths are an artifact arising from misalignment of a high reflector, which alters the registration of the probe and reference spectra on the photodiode arrays. A few test measurements made after identifying and correcting the problem show that the time evolution of the spectra is the same with or without the oscillations. The spectra show two prominent maxima. The feature near 390 nm appears promptly and then decays as a broad feature with a maximum near 495 nm grows. The presence of an isosbestic point at 425 nm suggests that the species responsible for the initial absorption at 390 nm is the precursor of the species that absorbs at 495 nm. The second feature decays slowly on a time scale that is much longer than our observation period. Figure 1c illustrates this behavior by showing the time evolution of the signal at several wavelengths between 380 and 500 nm for the entire 1 ns observation period, and Figure 1d shows the same data on an expanded scale of 100 ps. B. CHBr3 in Cyclohexane. The transient spectra following 267 nm photolysis of CHBr3 in cyclohexane solution, shown in Figure 2 for a 50% (5.7 M) solution, are qualitatively similar to those in neat CHBr3. In both cases, a feature appears promptly at 390 nm and another feature grows at longer wavelengths as the first disappears. The most striking aspect of the spectra for different dilutions is the change of the long-wavelength absorption with the concentration of CHBr3. In increasingly dilute solutions, the maximum systematically moves to shorter wavelengths. Figure 3 shows the spectra obtained 1 ns after photolysis for different concentrations of bromoform in cyclohexane ranging down to 2% by volume (0.23 M), a span over which the maximum moves monotonically from 495 to 430 nm. The attenuation of the probe light changes only modestly with concentration because the samples are optically thick at the 267 nm excitation wavelength. Because less than 1% of the excitation light passes through the sample even in the most dilute solution, the number of photons in the excitation pulse, rather than the concentration of the solution, determines the attenuation of the probe pulse. The spectrum we measure for a 1 ns delay after photolysis in 0.23 M CHBr3 agrees with the transient spectrum that Shoute and Neta measure at the same concentration for a 1 µs delay.40 The shift of the transition to higher energies with increasing dilution reflects a variation with the composition of the solvent that is consistent with the behavior of charge-transfer transitions,49-51 as described below. IV. Kinetic Analysis A. Neat CHBr3. The simplest approach to fitting the disappearance of one feature and the simultaneous appearance of a second feature is to use a sequential kinetic scheme

Carrier et al. kfast

kslow

A* f B† 98 C 98 in which the initially excited species A* rapidly forms species B†, which in turn evolves into species C. Species B† and C both contribute to the transient absorption

S(λ, t) ) AB(λ) · e-kfast · t + AC(λ) ·

(

)

kfast · (e-kslow · t kfast - kslow e-kfast · t)

(2)

Simultaneously fitting all of the data using the two rate constants, kfast and kslow, and the set of amplitudes, AB(λ) and AC(λ), from

Figure 2. (a) Transient absorption spectra following 267 nm photolysis of 50% CHBr3 in cyclohexane. The open points are the measured absorption at different times (∆t) after the photolysis pulse. The dashed lines are fits to a simple sequential kinetics scheme, and the solid lines are the fits to the more elaborate model described in the text. (b) Spectra of the absorbers, AB(λ) and AC(λ), from the kinetic analysis. The dashed lines are from fits to a simple sequential kinetics, and the solid lines are from fits to the more elaborate model described in the text. (c) Time cuts through the transient absorption spectra at the indicated wavelengths. The points shown at negative times for the data at 450 nm are typical for all of the traces. The data for the other wavelengths are omitted for clarity. The structure in the short-wavelength part of the spectrum is an artifact.

Photolysis of Bromoform in Solution

J. Phys. Chem. A, Vol. 114, No. 3, 2010 1551 TABLE 1: Time Constants from Sequential Kinetic Fits of the Spectra Obtained in Neat CHBr3 and in Cyclohexane Solutions of CHBr3 CHBr3 concentration (M) CHBr3 volume % 11.5 10.31 8.02 5.73 3.44 1.15 0.23

Figure 3. Transient absorption spectra at a delay of 1 ns in increasingly dilute solutions of CHBr3 in cyclohexane. The maximum moves from 495 nm in neat bromoform to 430 nm in a 2% solution.

1 to 1000 ps yields a fast decay time of τfast ) kfast-1 ) 13.0 ( 0.2 ps and a slow decay time of τslow ) kslow-1 ≈ 3700 ps. The reported uncertainty is two standard deviations of the fit taken from the covariance matrix. The determination of the slow decay constant is very imprecise because we follow only a small portion of the total evolution, as the time cuts through the data in Figure 1c illustrate. However, changing the magnitude of kslow by 20% or more produces a noticeably poorer fit. The dashed lines in the figure, which are virtually coincident with the solid lines from the more elaborate model presented below, show that the agreement between the fit and the data is very good. The exception is the region near 500 nm for the shortest (1 ps) delay times. The fit also yields the spectra of the two absorbers, shown as dashed lines in Figure 1b, which is a plot of AB(λ) and AC(λ) from the fit. The following discussion proposes that the rapidly formed species B† is vibrationally excited iso-bromoform, in analogy to observations in time-resolved studies of other haloalkanes.6,10,13,14,20-23,27 Iso-halolkanes can survive for many nanoseconds in dilute solutions, and indeed, we clearly observe iso-bromoform at long times in solvents such as acetonitrile.52 Thus, we also fit the data with a more elaborate kinetic scheme that includes relaxation and slow loss of the iso-species. In this scheme, the excited species (B†) formed from the initially excited precursor A* decays to two different species (B and C) with time constants kvib and kesc, respectively. In the dilute solutions,

species B, formed by vibrational relaxation of B†, potentially survives for a long time compared to the duration of our observation, but it eventually decays with a rate constant kloss. As in the simpler scheme, species C decays with a rate constant kslow. If we assume that B† and B absorb at similar wavelengths, the corresponding transient signal S(λ,t) is

((

)

kvib e-(kvib+kesc)t + kvib + kesc - kloss kesc kvib e-klosst + AC(λ) · (e-(kvib+kesc)t + kesc - kloss kvib + kesc

S(λ, t) ) AB(λ) · 1 kvib

)

e-(kslow)t) †

(3)

where AB(λ) is the spectrum of both B and B and AC(λ) is the spectrum of C. The fast decay of one absorption and the

100 90 70 50 30 10 2

τfast (ps)

τslow (ps)

13.0 ( 0.2 13.3 ( 0.2 13.7 ( 0.2 14.1 ( 0.2 14.2 ( 0.2 14.4 ( 0.2 15.3 ( 0.2

3700 4650 5400 7550 13 000 93 000 415 000

corresponding growth of the other are the primary features of the data, and in this model, the rate constant for that decay and growth is the sum of those for the two parallel decay channels, kfast ) kvib + kesc ) τfast-1. Because the escape rate and the vibrational decay rate compensate for each other to maintain the value of τfast in the fitting, we cannot extract them independently. A vibrational decay time of 10-50 ps is consistent with vibrational relaxation times in a variety of systems,53-56 and we fix the vibrational relaxation time as τvib ) kvib-1 ) 40 ps in the fits. Using a larger vibrational relaxation rate produces a correspondingly smaller escape rate because the total decay rate is the parameter to which the fits are sensitive. We use the value of the slow decay constant (τslow ) 3700 ps) from the simple sequential fits and simultaneously fit all of the data using the rate constants, kesc and kloss, as free parameters along with the set of amplitudes, AB(λ) and AC(λ). Fitting the transient spectra from 1 to 1000 ps to this more elaborate model yields a fast decay time of τfast ) 12.7 ( 0.2 ps, and a loss time of τloss ) kloss-1 ≈ 3000 ps, a value that is on the order of the slow decay time of species C. The fast decay is essentially the same for both fitting schemes and is insensitive to the other parameters. The solid lines in Figure 1 show the results for this more elaborate scheme. The quality of the fits is virtually indistinguishable for the two kinetic schemes. The role of kloss is to remove species B, the vibrationally relaxed isobromoform, as required by the slow decay of the absorption that we observe at 390 nm. As the curves in Figure 1d show, the slow decay of either species B or C is unimportant during the early times that are the focus of the measurements and analysis. B. CHBr3 in Cyclohexane. We use the same fitting procedures for the cyclohexane solutions because of the qualitative similarity of the spectra to those for neat bromoform. The dashed lines in Figure 2 show the results of the simple sequential fit, and Table 1 collects the time constants for all concentrations. Because of the imprecision of the rate constant for the slow decay, we use the same concentration dependent values from the simple sequential fits in the more elaborate fitting scheme, in analogy with our approach for neat CHBr3. Table 2 collects the corresponding fitting parameters, and the solid lines in Figure 2 show the resulting fits. The Supporting Information shows the plots with the corresponding fits for all of the concentrations. The quality of the fits at each concentration is comparable to those shown in Figures 1 and 2. Comparing the time constants for the fast decay, τfast, in the two kinetic schemes shows that their decrease is rather small, about 15 and 25%, respectively, in going from a 2% solution to a neat sample, as summarized in Tables 1 and 2. The rate constant for the slow decay increases linearly with the concentration of CHBr3, corresponding to an effective bimolecular reaction rate constant of 2 × 107 M-1 s-1. It is possible that the slow decay comes from reaction of the weakly bound CHBr3-Br complex either with other com-

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Figure 4. Kinetic scheme illustrating the formation of iso-bromoform and its evolution following photolysis of bromoform.

TABLE 2: Parameters for Fits of the Spectra Obtained in Neat CHBr3 and in Cyclohexane Solutions of CHBr3 Using the Kinetic Scheme Including Vibrational Relaxation CHBr3 concentration (M)

CHBr3 volume %

τviba (ps)

τesc (ps)

τfastb (ps)

τslowc (ps)

τloss (ps)

11.5 10.31 8.02 5.73 3.44 1.15 0.23

100 90 70 50 30 10 2

40 40 40 40 40 40 40

18.5 ( 0.2 19.7 ( 0.2 20.5 ( 0.3 21.4 ( 0.3 22.2 ( 0.3 23.2 ( 0.4 25.8 ( 0.6

12.7 ( 0.2 13.2 ( 0.2 13.6 ( 0.3 13.9 ( 0.3 14.3 ( 0.3 14.7 ( 0.4 15.7 ( 0.6

3700 4650 5400 7550 13 000 93 000 415 000

3000 2090 1650 1700 1400 1080 930

a

Fixed value. b τfast-1 ) τvib-1 + τesc-1. c Fixed at the same value as obtained in the simple sequential fit (Table 1).

plexes or with the approximately 1% impurity in the CHBr3, about half of which is aliphatic hydrocarbons and alkenes.52 The latter react with the CHBr3-Br complex at near diffusion-limited rates in favorable cases.39 V. Discussion The primary ultraviolet photodissociation channel of gasphase CHBr3 produces CHBr2 and Br radicals by direct dissociation of the C-Br bond,7,47,48 but in solution, interactions with surrounding molecules complicate the evolution of these initially formed products. The transient spectra show that one species appears promptly and evolves into another longer-lived species. A 267 nm photon provides 181 kJ/mol of excess energy for deposition into the relative translation and internal degrees of freedom of the fragments. Because this energy is unlikely to dissipate into the surroundings during the prompt appearance of the absorbing species, vibrational excitation of the polyatomic radical fragment is potentially important in the evolution of the products.10,22,23 Identifying the absorbing species is the first step to understanding their temporal evolution. A. Neat CHBr3: The 390 nm Feature. The short-wavelength absorption appears within our 0.5 ps time resolution and decays in about 13 ps to a nearly constant level, as the trace for λ ) 380 nm in Figure 1d shows. There are several candidates for this absorbing species such as the halomethyl radical23,57 or a radical cation58 resulting from the absorption of two photons. However, comparison of resonance Raman measurements with density functional theory (DFT) calculations for the halomethanes CH2Br2,8,11 CHBr3,8,15 CH2I2,8,18-20 and CHI38,12 provides compelling evidence that a halomethane isomer is the absorbing species. The kinetic scheme in Figure 4 shows the proposed absorbing species and their evolution. In this picture, the Br radical forms iso-bromoform, CHBr2-Br, by returning to bond to one of the bromines of the CHBr2 radical, as illustrated on the left of the figure. The calculated 395 nm transition wavelength8 of CHBr2-Br is consistent with the 390

nm absorption maximum that we observe soon after photolysis. This same calculation predicts that the transition for the CHBr2 radical is weak and lies below 220 nm8,17 and that the stronger transition for the cation (CHBr2+) is near 230 nm. Thus, we ascribe the 390 nm transition to the iso-compound. The halomethyl radical should retain a substantial fraction of the energy available as internal excitation. An impulsive energy release model59 predicts that the polyatomic radical retains 81% of the available energy as internal excitation in the gas-phase photolysis of bromoform, a prediction in reasonable accord with experiment.7 The radical fragments are likely to continue interacting within the solvent cage, both to reform bromoform, whose absorption at shorter wavelengths we do not observe, and to form iso-bromoform with large amounts of internal energy. Prior to dissipation of that energy into the surroundings, the highly excited recombination products can potentially dissociate and recombine to sample many geometries. During this time, the radicals can also escape the cage and form a complex with the surrounding solvent, as indicated for the Br radical in the second step of the kinetic scheme in Figure 4. As demonstrated below, this solvent-Br complex absorbs at 495 nm and appears as the initially formed species disappears. Molecular dynamics simulations of the photolysis of CH2I2 in acetonitrile paint a similar picture of the early time dynamics, in which some of the recombination within the cage yields the vibrationally excited iso-compound.60 Simulations of the photolysis of ICN61 and OClO62 in solution find that ballistic cage escape and geminate recombination occur in about 1 ps and that translational thermalization of the escaped species is comparably fast, in general agreement with the corresponding measurements.63-66 The calculated probability of ballistic escape is not very large in these systems, being only 16% for ICN in chloroform. Some amount of prompt cage escape is likely after photolysis of bromoform in our experiments and may be responsible for the discrepancy between the fits and measurements at the shortest time delay (1 ps) shown in

Photolysis of Bromoform in Solution Figures 1 and 2. There is clearly some absorption near 500 nm that is missing from the kinetic model. Simulations also find that relaxation of excited or recombined fragments is slower than cage escape, taking about 30 ps for OClO in ethanol67 and about 15 ps for ICN in chloroform.68 Relaxation of the vibrationally excited species can control the subsequent dissociation and overall escape probability. For example, the simulation for OClO shows that the extent of vibrational relaxation determines the escape probability for electronically excited OClO, which has a barrier to dissociation. Only molecules with vibrational excitation can overcome the barrier, and thus, vibrational relaxation reduces the dissociation yield.62 An analogous competition might be important in the endothermic dissociation of iso-bromoform, in which only vibrationally excited molecules have enough energy to release Br atoms. The time constant τfast for loss of the initial absorber in our experiments is consistent with vibrational relaxation times observed and calculated for various halomethanes,53-56 and vibrational relaxation is likely to play an important role in the decay, as illustrated in Figure 4. Dissociation of the energized iso-compound can release Br atoms that complex with the solvent, forming the species that absorbs at 495 nm. Once relaxation has removed enough energy, the relaxed iso-CHBr3, which is bound by about 88 kJ/mol,69 survives in solution to produce the slowly decaying absorption at 390 nm for periods longer than 1 ns. Although vibrational relaxation can alter the shape of an absorption feature, we see no dramatic changes in our data. The growth of the broad 495 nm absorption during the decay of the 390 nm feature potentially obscures changes on the long-wavelength side of the 390 nm feature, where vibrational relaxation should influence the electronic absorption most strongly. In many cases where the shape changes during vibrational relaxation, the location of the absorption maximum does not.22,23 B. Neat CHBr3 and CHBr3-Cyclohexane Solutions: The 495 nm Feature. The long-wavelength absorption that we observe is consistent with slower flash photolysis and pulsed radiolysis measurements38-40 that assign the absorption to a charge-transfer transition of a complex of Br with the bromoalkane solvent. As shown in Figure 3, dilution in cyclohexane moves the absorption to shorter wavelengths, with the transition maximum changing from 495 nm for neat CHBr3 to 430 nm for 0.23 M CHBr3 in cyclohexane. In laser flash photolysis and pulse radiolysis studies, Shoute and Neta assign the 430 nm absorption to the charge-transfer transition of the CHBr3-Br complex in preference to the cyclohexane-Br complex, and the complexes they observe for different bromoalkanes diluted in cyclohexane are stable for microseconds.38 In agreement with these longer time scale measurements, we see no evidence of a new absorption in the region of 370 nm corresponding to the cyclohexane-Br complex. Formation of Br2 is also an energetically available channel for bromoform, and there is an analogous example of production of molecular halogen in the formation of I2 by photolysis of CF2I2 in solution.25,26 However, because the absorption maximum of Br2 is near 410 nm in both the gas phase70 and in CHBr3 and cyclohexane solutions,52 it cannot be the origin of the long-wavelength absorption. The sensitivity of a charge-transfer transition to the environment of the complex49-51,71,72 explains the change in the absorption maximum we observe upon addition of cyclohexane, and its analysis supports the assignment of the long-wavelength feature to the CHBr3-Br complex. Mulliken and Person have modeled charge-transfer transitions in terms of two weakly interacting species that, upon absorption

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Figure 5. Energy diagram illustrating the mixing of the wave functions ψ0(D,A) and ψ1(D+ · · · A-) for the “no-bond” and “dative” states in solution to form the ground ψG and excited state ψE wave functions of the charge-transfer complex. ID is the ionization energy of the gasphase donor D, EA is the electron affinity of the gas-phase acceptor A, and W is the electrostatic attraction of the gas-phase ions. The wave functions ψ∞(D,A) and ψ∞(D+,A-) correspond to the separated neutral and ionic species. The vertical dashed arrow shows the predicted energy of the charge-transfer transition for gas-phase species without the inclusion of state mixing.

of a photon, transfer an electron to create an electrostatic attraction.73-75 This model describes the ground state (ψG) and the excited state (ψE) as a linear combination of a “no-bond” wave function, ψ0(A,D) ) ψ0, corresponding to the two separated species, and a “dative” wave function, ψ1(D+ · · · A-) ) ψ1, corresponding to the ion pair arising from transfer of an electron. Figure 5 schematically illustrates the mixing of the two states in which the wave functions for the separated neutral and ionic species are ψ∞(A,D) and ψ∞(D+,A-), respectively.36 Solving the secular determinant gives the transition energy34,37

hνCT )

1 (I - C1)2 + 4β0β1 2√ D 1-S

(4)

where ID is the ionization energy of the donor and S is the overlap integral between the two wave functions, ∫ψ0ψ1 dτ. The two terms, β0 and β1, are the resonance integrals describing the stabilization and destabilization of ψG and ψE from the mixing of ψ0 and ψ1 and are related to each other by the expression35,37,74,76

β1 ) β0 - S(ID - C1)

(5)

The term (ID - C1) in eq 4 contains all of the contributions to the energy difference between the ground and excited states in solution except for the portion arising from state mixing, which the resonance and overlap integrals describe. Using the energy associated with formation, solvation, and complexation of the ion pair to calculate C1 gives37

C1 ) EA +

)(

)

e2 1 1 1 e2 1+ + 2 ε rD+ rArADε

(

(6)

where EA is the electron affinity of the acceptor and the remaining terms are the solvation energy of the ions and the electrostatic attraction between the ion pair.36,37 The parameters in this expression are the optical dielectric constant of the medium ε, the radii of the solvent cavities around the donor rD+ and acceptor rA-, and the distance between the acceptor and donor in the complex rAD.37 Because changes in the van der Waals interactions between ground and excited states are small compared to the changes in the electrostatic interactions, this term includes only the electrostatic contributions.

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TABLE 3: Calculated and Experimental Energies and Wavelengths of the Transition Energies in the CHBr3-Br Complex hνCT (eV)

λCT (nm)

CHBr3 concentration (M)

CHBr3 volume %

mole fraction, X

ε

calculated

observed

calculated

observed

11.5 10.31 8.02 5.73 3.44 1.15 0.23

100 90 70 50 30 10 2

1.00 0.92 0.75 0.56 0.36 0.13 0.03

2.56 2.52 2.42 2.32 2.21 2.09 2.05

3.11 3.13 3.16 3.20 3.24 3.30 3.32

2.51 2.53 2.56 2.64 2.73 2.81 2.88

399 397 392 388 382 376 374

495 490 485 470 455 440 430

The concentration dependence of the dielectric constant introduces a significant variation in the transition energy through the electrostatic terms, from which we can predict the trend in the transition energy upon addition of cyclohexane. To include this variation, we estimate the effective dielectric constant ε for the binary mixtures using the mole fraction X of a continuum composed of polar and nonpolar constituents77 X ε ) εCHBr ε1-X 3 cyclohexane

(7)

where the dielectric constant for each component is the optical dielectric constant εop obtained from the index of refraction (εop ) n2) with εCHBr3 ) 2.56 and εcyclohexane ) 2.03.78 Both the interactions that mix the no-bond and dative wave functions and the electrostatic interactions contribute to the calculated energy of the charge-transfer transition, but these contributions are not completely independent. By adjusting the resonance integral β0 and the overlap integral S, it is possible to reproduce the transition frequencies for reasonable values of the radii. Because our goal is to understand the solvent-induced changes in the transition energy, we do not adjust those parameters but use the values S ) 0.1 and β0 ) -0.94 eV, obtained from analysis of a series of bromine atom π-complexes.34 We use the ionic radius of bromide (rA- ) rBr- ) 1.96 Å)78 for the acceptor anion and use the molar volume of CHBr3 to calculate the radius of the donor cation (rD+ ) rCHBr3 ) 3.26 Å) under the assumption that removing an electron from a nonbonding orbital does not change the size significantly. We also use that radius along with the covalent radius of bromine (rBr ) 1.14 Å)78 to estimate the radius of the complex (rAD ) rCHBr3-Br ) 4.40 Å). Table 3 shows that this formulation predicts an increase of the transition energies for dilute solutions, and the analysis supports the assignment of the long-wavelength feature to the charge-transfer transition of the CHBr3-Br complex in both neat bromoform and cyclohexane solutions. C. Time Evolution. The kinetic scheme in Figure 4 is consistent with the time evolution we observe. The scheme includes vibrational relaxation of the initially formed isobromoform in order to account for the rapid decay of the 390 nm feature to an asymptote corresponding to vibrationally relaxed iso-bromoform. The species recombining in the solvent cage contain large amounts of internal energy that ultimately dissipates into the solvent, and in the kinetic model, there is a competition between dissociation of vibrationally excited isobromoform and vibrational relaxation. Bromine atoms that escape the cage form a complex with the other CHBr3 molecules, which we detect as the charge-transfer transition at 495 nm. Subsequent processes, likely reaction to form Br2, HBr, or other Br adducts,39,40 remove this complex over a time that is longer than 1 ns. Diluting bromoform in cyclohexane does not change the absorption wavelength of the iso-compound but does decrease the absorption wavelength of the solvent complex, as we expect for a transition to a charge-transfer state. Because formation of

the CHBr3-Br complex that we probe on the charge-transfer transition requires an encounter between a Br radical and a CHBr3 molecule, the complex should form more slowly in dilute solutions. The rise time τfast of the absorption of the complex increases by about 20% upon dilution, and consequently, τesc increases by 40% in going from neat bromoform to a 2% solution. However, we would expect an even larger increase if the process were controlled solely by diffusion. At the lowest concentration of 0.23 M (2% by volume), there is about one CHBr3 molecule for every 50 cyclohexane molecules, corresponding to an average separation of about 20 Å between CHBr3 molecules. Because a diffusive encounter requires several nanoseconds at this concentration, our observation of a relatively small change upon dilution suggests that diffusion does not completely control complexation of Br with CHBr3. The presence of bromoform clusters in cyclohexane solution, which place the Br atom close to another CHBr3 molecule after photolysis, is likely responsible for this effect. Ultrafast extended X-ray absorption measurements show that Br has a coordination number of 3.3 ( 0.2 in its second shell in a 0.17 M solution of CHBr3 in cyclohexane, suggesting that CHBr3 molecules are not uniformly distributed.79 Thus, a CHBr3 molecule is readily at hand for complexation even in a dilute solution. VI. Summary The combination of ultrafast photolysis of bromoform with time-resolved broadband transient absorption allows us to follow the evolution of the photofragments in both neat bromoform and in cyclohexane solutions. A 100 fs pulse of 267 nm light produces CHBr2 and Br fragments that lead to characteristic spectroscopic signatures as they evolve. In neat bromoform, a 390 nm absorption appears promptly and disappears in about 15 ps as a 495 nm absorption appears. The presence of an isosbestic point in the transient spectra indicates that the first absorber is the precursor of the second one. The wavelength of the first transition is consistent with absorption by the isomer of bromoform, CHBr2-Br, formed by recombination of the fragments within the solvent cage. The excess internal energy remaining after photolysis allows dissociation of iso-bromoform to release a Br atom that subsequently complexes with other CHBr3 molecules. Excitation of this solvent complex to a charge-transfer state produces the second feature at 495 nm. Release of Br is most efficient for the vibrationally excited isobromoform, and the competing relaxation of the vibrationally excited isomer is an essential part of the time evolution of the system. The transient spectra are qualitatively similar in dilute solutions of CHBr3 in cyclohexane. The absorption of isobromoform appears promptly at 390 nm, but the second absorption occurs at progressively higher energy in more dilute solutions. This systematic shift to shorter wavelengths is consistent with predictions of the effect of solvent dielectric constant on the charge-transfer transition of the CHBr3-Br complex.

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