How Do Strain and Steric Interactions Affect the Reactions of Aromatic

Article pubs.acs.org/JPCA

How Do Strain and Steric Interactions Affect the Reactions of Aromatic Compounds with Free Radicals? Characterization of the Radicals Formed by Muonium Addition to p-Xylene and [2.2]Paracyclophane by DFT Calculations and Muon Spin Spectroscopy Iain McKenzie,*,†,‡ Robert Scheuermann,§ and Kamil Sedlak§ †

Centre for Molecular and Materials Science, TRIUMF, 4004 Wesbrook Mall, Vancouver, B.C. Canada V6T 2A3 Department of Chemistry, Simon Fraser University, 8888 University Drive, Burnaby, B.C. Canada V5A 1S6 § Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institute, CH 5232 Villigen, Switzerland ‡

S Supporting Information *

ABSTRACT: Muoniated radicals were produced by the addition of muonium (Mu) to the aromatic compound p-xylene (1) in the solid and liquid states and to the strained aromatic compound [2.2]paracyclophane (2) in the solid state. The radicals were characterized by avoided level crossing muon spin resonance spectroscopy and identified by comparing the experimentally determined muon hyperfine coupling constants with values obtained from DFT calculations. Mu was observed to add to both the secondary and tertiary carbons of 1, with the relative yield of the Mu adduct of the tertiary carbons estimated to be ∼10% in the liquid phase. The relative yield of the tertiary adduct is much higher in the solid state although this cannot be calculated exactly due to the overlap of resonances and the apparent nonuniform distribution of the radical orientations. There are three possible addition sites in 2 due to the lower symmetry of the six-membered ring compared with 1. Mu can add to the secondary carbons either from the outside of 2, generating the “exo” adduct, or from the inside, generating the “endo” adduct. The relative yields of the exo, endo, and tertiary carbon adducts are 67.1(1), 21.8(1), and 11.1(1)%, respectively. The barriers to Mu addition at the different sites of isolated molecules were determined from DFT calculations. The barriers for Mu addition to 2 are lower than the barriers for Mu addition to 1, except for addition to the “endo” position, where the unfavorable steric interactions with the second ring of 2 raise the addition barrier considerably. The measured relative yields do not reflect the distribution of products calculated using the activation energies obtained from the DFT calculations due to strong steric interactions with neighboring molecules.

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INTRODUCTION The hydrogen atom (H), the most abundant in the universe, has played a significant role in the development of our understanding of the material world.1 H is arguably the simplest free radical and there is considerable interest in studying how it reacts with other atoms and molecules. Unfortunately, H is not a common reagent, largely because of complications inherent in its generation. Most commonly, the H atoms are produced by photolysis or radiolysis of a material, but this usually results in the production of other radical species. Rather than use H atoms to generate the radicals and ESR to observe them,2 we have chosen to generate radicals using a light isotope of hydrogen called muonium (Mu = [μ+,e−]) and characterize the radicals by avoided level crossing muon spin resonance (ALCμSR).3 The utility of Mu as a surrogate for the hydrogen atom is well documented.4 The radicals produced by Mu addition to polyaromatic hydrocarbons (PAH) in the liquid state have been extensively © 2012 American Chemical Society

studied. Mu adds exclusively to unsaturated secondary carbons of PAH such as pyrene,5 triphenylene,6 and fluoranthene.7 Only when there are no unsaturated secondary carbons does Mu add to tertiary unsaturated carbons, as in dodecahydrotriphenylene.6 What is less well understood is how H or Mu adds to aromatic compounds in the solid state or how strain affects reactivity. There have been many studies on the reactions of radicals with fullerenes,8,9 but there have been, to the best of our knowledge, no investigations on systems where it was possible to study both strained and unstrained versions of a molecule. The studies on radicals reacting with planar polyaromatic hydrocarbons cannot be compared directly with the fullerene experiments as they are dominated by reactions at Received: June 7, 2012 Revised: June 25, 2012 Published: July 16, 2012 7765

dx.doi.org/10.1021/jp305610g | J. Phys. Chem. A 2012, 116, 7765−7772

The Journal of Physical Chemistry A

Article

DFT calculations were performed to isolate the effect of strain on the reactivity of the compounds from other factors. This was quantified by calculating and comparing the barriers for Mu addition at the different sites of 1 and 2. Information about the reactivity of the aromatic compounds is obtained by determining the structures and yields of the resulting muoniated radicals. The muoniated radicals are identified by measuring the hyperfine coupling constants (hfccs) and comparing these values with hfccs obtained from DFT calculations for possible structures. The relative yield of each product could in some cases be determined by measuring the relative amplitudes of the ALC resonances. ALC-μSR spectra were obtained of 1 in the solid and liquid state, which allows us to determine the effect of steric interactions from neighboring molecules. 2 is not sufficiently soluble in any solvent suitable for muon spin spectroscopy, so ALC-μSR spectra were obtained for polycrystalline samples of 2. The distribution of products of the reaction of Mu with 2 is due to the combination of both strain and steric interactions and by comparing the experimental yields with the predicted values we can infer the relative importance of each effect. We are also interested in the structures of the resulting radicals for their own sake. The magnitude and temperature dependence of the hfccs give information about the geometry of the radicals and this is supported by the DFT calculations. By comparing the structures of the muoniated radicals, we will be able to ascertain what effect strain has on the structure of the cyclohexadienyl-type radicals.

the edges of the molecules, something that fullerenes obviously do not possess. In this experiment we have chosen to study how Mu reacts with p-xylene (1) and [2.2]paracyclophane (2) through a combination of DFT calculations and ALC-μSR experiments. These molecules were chosen as the focus of this study due to the similarities in their structures, except with a key difference; the phenyl rings of 2 have a boatlike shape due to the strain imposed by the C2H4 linkers.10,11 The chemistry of 2 and related compounds have been intensively investigated, although we are not aware of any studies on the reactions with free radicals. Radical anions have been produced by single electron transfer to 2 and they have been characterized by electron paramagnetic resonance spectroscopy.12,13 Two possible types of cyclohexadienyl radical can form by Mu addition to 1; an adduct of the secondary carbons and an adduct of the tertiary carbons. The structures of 1 and the two types of Mu adducts are shown in Figure 1. Three types of radical can form by Mu

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MUON SPIN SPECTROSCOPY μSR is an acronym for muon spin rotation, relaxation, and resonance, which is a collection of spectroscopic techniques that are extremely useful for characterizing transient free radicals. The μSR techniques and their role in free radical chemistry have been extensively reviewed, so only a basic description of it is given here.3 These techniques involve injecting a beam of spin-polarized positive muons into a sample and detecting the positron produced by the decay of each muon. Muons can pick up a radiolytic electron and form Mu, which can then react with unsaturated molecules to produce a muoniated radical, where the ensemble of muons are ∼100% polarized spin labels. The parity-violating decay of the muon provides a convenient way to monitor the evolution of the muon spin and its lifetime (2.2 μs) is comparable to many molecular processes. The ALC-μSR technique involves measuring the asymmetry of the muon decay as a function of a magnetic field applied parallel to the initial direction of the muon spin. The asymmetry parameter is defined as (nB − nF)/(nB + nF), where nF is the total number of positrons detected in the forward counters and nB is the total number of positrons detected in the backward counters, and is proportional to the time-averaged muon polarization, Pz. In high magnetic fields the eigenstates of the radical can be approximated by pure Zeeman states, so there is no evolution of the muon’s spin with time and the asymmetry is independent of the magnetic field. At specific values of the applied magnetic field nearly degenerate pairs of spin states can be mixed through the isotropic and anisotropic components of the hyperfine interaction. The muon polarization oscillates between the two mixing states and this leads to a loss of time-integrated asymmetry. There are three types of resonances, which are characterized by the selection rule ΔM = 0, ±1, and ±2, where

Figure 1. Structures of p-xylene (1) and the possible Mu adducts of pxylene (1a and 1b).

addition to 2 and their structures are shown in Figure 2. The symmetry of the phenyl rings of 2 is broken so Mu can add to the secondary carbons of 2 to give either radicals 2a or 2b (referred to hereafter as the “exo” and “endo” adducts, respectively). Mu can also add to the tertiary carbon of 2 to give radical 2c.

Figure 2. Structures of [2.2]paracyclophane (2) and the possible Mu adducts of [2.2]paracyclophane (2a, 2b, and 2c). These will be referred to as the exo, endo, and bridge adducts, respectively. 7766



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M is the sum of the mz quantum numbers of the muon, electron, and proton spins. The resonances are referred to as Δ0, Δ1, and Δ2 resonances, respectively. The Δ2 resonance is extremely weak and is rarely observed. The Δ1 resonance field is given by Δ1 = Bres

⎡ Aμ ⎤ 1 ⎢ Aμ ⎥ − γe ⎥⎦ 2 ⎢⎣ γμ

functional and the EPR-II basis set as these methods have been demonstrated to give hfccs close to the experimental values.17 Mu is almost chemically identical to H but the lower mass of Mu means that the vibrationally averaged C−Mu bond is longer than the corresponding C−H bond. A complete treatment of vibrational averaging effects for the radicals in this study would be computationally expensive, so we have treated the vibrational motion empirically. The vibrationally averaged C−Mu bond is estimated to be 4.9% longer than the corresponding C−H bond18 and the methylene C−H bond of a muoniated cyclohexadienyl radical is estimated to be reduced by 0.3% compared with its optimized value. The C−Mu and C−H bonds were lengthened or shortened by the appropriate amount for the single point calculations. The muon hfccs also include a factor of 3.183 to account for the larger gyromagnetic ratio of the muon. Distinguished coordinate paths for addition of Mu to the unsaturated secondary and tertiary carbons of 1 and 2 were obtained by optimizing the geometry for fixed distances between H(Mu) and the site of addition. Although it has been shown previously that DFT methods have difficulty locating and estimating the transition state, they are sufficient to obtain qualitative information about competing reaction paths. The computed values of ⟨S2⟩ ranged from 0.75 to 0.80 along the distinguished coordinate path, indicating negligible spin contamination. The zero-point energy (ZPE) of each structure was calculated using the “Frequency” keyword in Gaussian 09. The Frequency calculations confirmed that each of the partially optimized structures has only one imaginary frequency. The quoted energy is the sum of the internal energy and the ZPE. The ALC-μSR experiments were performed using the ALC spectrometer at the πE3 beamline of the Paul Scherrer Institute in Villigen, Switzerland. 1 was purchased form Sigma Aldrich and used without further purification. It was degassed by bubbling with N2 gas for 1 h and then sealed in an aluminum cell with an internal volume of 3 mL and a 20 μm thick titanium foil window. 1 crystallizes in the monoclinic system, with a = 5.806(2) Å, b = 5.023(1) Å, c = 11.215(2) Å, and β = 100.48(2)° in the space group P21/n.19 The molecules form infinite chains along b and layers are formed parallel to (001). 2 was also purchased from Sigma Aldrich and used without further purification. It was sealed in a packet made of 25 μm thick aluminum foil and had a surface area of 2 × 2 cm2 and a thickness of ∼2 mm. 2 crystallizes in the tetragonal system with a = 7.781(1) Å, c = 9.290(2) Å in space group P42/mnm with two molecules per unit cell.20 ALC-μSR spectra have a large field-dependent background that is very sensitive to the stopping position of the muons. It was not possible to remove the background by subtracting the spectrum of a substance that does not have resonances in the ALC-μSR spectrum (such as water) as the background is very sensitive to the density of the sample. Instead, a fifth-order polynomial was used to model the background. The fitting was performed with the MINUIT function minimization library in the ROOT package from CERN.

(1)

where Aμ is the muon hfcc, γμ is the muon gyromagnetic ratio, and γe is the electron gyromagnetic ratio.3 The Δ1 resonance arises from mixing between spin states with the same electron and proton spins but different muon spin directions and is only observed in the solid state or when there is anisotropic motion. The time-averaged polarization as a function of field for a radical with an axially symmetric muon dipolar tensor ([D∥μ, D⊥μ , D⊥μ ] where D⊥μ = −0.5 D∥μ) is given by14 Pz(B) = 1 −

∫0

Pz0πq2 sin θdθ

π

Δ1 2 (λ /2π )2 + q2 + γμ 2(B − Bres )

(2)

where P0z is the muon polarization at time zero of the species of interest, θ is the angle between the unique axis of the hyperfine tensor and the applied magnetic field, λ is the rate for a reaction to a state outside resonance, and

q=

3 ⊥ Dμ sin θ cos θ 2

(3)

The shape of the resonance is sensitive to the motion of the radical14 and has a characteristic asymmetry depending on the sign of D⊥μ , with the steep side being at a lower field that for D⊥μ < 0 and at a higher field for D⊥μ > 0. The Δ0 resonance is due to mixing between spin states that have the same electron spin but opposite muon and proton spins and is observed for muoniated radicals in the solid, liquid, or gas phases. The Δ0 resonance field depends on both the muon hfcc and the proton hfcc, Ap, and is given by Δ0 = Bres

⎡ Aμ + A p ⎤ 1 ⎢ Aμ − A p ⎥ − ⎥⎦ γe 2 ⎢⎣ γμ − γp

(4)

where γp is the proton gyromagnetic ratio. the Δ0 resonance is given by

15

amplitude ∝

The amplitude of

Pz0ωLCR 2 λeff 2 + ωLCR 2

(5)

where ωLCR is the frequency at resonance and λeff is the effective relaxation rate (muon decay rate plus any additional relaxation contribution)15 ωLCR =

c π Aμ A p Δ0 γeBres

(6)

and c is the number of magnetically equivalent protons at resonance.

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RESULTS AND DISCUSSION Optimized Structures. The structures of 1 and 2 were calculated and compared with values obtained by X-ray crystallography to verify the reliability of our chosen computational methods. The optimized structures of both 1 and 2 are in good agreement with experiment, except that the calculated

EXPERIMENTAL SECTION All ab initio calculations were performed using the Gaussian 09 package.16 The geometries of the radicals were optimized with the unrestricted B3LYP density functional and the 6-311G(d,p) basis set. The hfccs were calculated using the unrestricted PBE0 7767



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C−C bond lengths are slightly longer than the experimental values, with the maximum difference being ∼0.07 Å (Figure 3).

Table 1. Calculated (UB3LYP/6-311G(d,p)//UPBE0/EPRII) Muon and Proton Hyperfine Coupling Constants (|Ap| > 5 MHz) and the Corresponding ALC Resonance Fields for the Mu Adducts of p-Xylene (1)

Figure 3. Distances and angles in the optimized structures of 1 and 2. Calculated values are reported in brackets. Distances are in angstroms and angles are in degrees.

radical

position

AX/MHz

Bres/T

1a

muon methylene ortho ortho CH3 meta meta CH3 para muon ortho meta para CH3

461.8a 129.9b −29.1 26.9c 12.2 −10.8c −41.4 455.9a −30.3 12.3 40.5c

1.6951 1.7745 2.6325 2.3303 2.4095 2.5333 2.6985 1.6737 2.6076 2.3777 2.2254

1b

Given the good agreement between theory and experiment, we have concluded that the chosen computational methods are sufficient to generate accurate geometries and have used these methods to determine the minimum energy geometries of the radicals. The optimized structures of radicals 1a, 1b, 2a/b, and 2c are shown in Figure 4. Both 1a and 1b have planar six-membered

a Aμ was calculated by lengthening the C−Mu bond by 4.9% to account for the primary isotope effect and multiplying the DFT value by 3.183 to account for γμ/γp. bAp was calculated by decreasing the C− H bond by 0.3% to account for the secondary isotope effect. cAverage value of three methyl protons.

radicals and suggests that the computational methodology is appropriate. The calculated muon hfcc of 1b is 1.3% lower than 1a, indicating that the methyl substituents have very little effect on the distribution of spin density around the six-membered ring. EPR measurements of 2−• in 1,2-dimethoxyethane found that the unpaired electron spin density is evenly distributed over both rings.13 DFT calculations were performed on the radical anion of 2 to confirm that the chosen methodology could reproduce the transfer of spin density between the benzene rings. The calculated hfccs of 2−• agreed well with the values measured by EPR (Table 2), so we can conclude that our methodology is suitable for the Mu adducts of 2. Table 2. Calculated (UB3LYP/6-311G(d,p)//UPBE0/EPRII) and Measured Proton Hyperfine Coupling Constants of the Radical Anion of [2.2]Paracyclophane (2−•)

Figure 4. Optimized structures of (a) 1a, (b) 1b, (c) 2a/b, and (d) 2c.

rings. The Cortho−Cmeta−Cortho bond angle is 114.9° in 1a and 111.8° in 1b, a little larger than tetrahedral, whereas the remaining C−C−C bond angles of 119−123° are all close to 120°. The Cortho−Cmeta bonds of both radicals are longer than the corresponding bonds in 1, indicating that the methylene carbon does not participate in the conjugation. The remaining C−C bond lengths are typical for aromatic bonds. These results are consistent with calculations on the C6H7 radical reported by Chipman.21 The cyclohexadienyl rings of radicals 2a/b are nonplanar, with the methylene carbon adopting a nearly tetrahedral geometry and the ortho carbons adopting pyramidal geometries. Addition of Mu to the tertiary carbon of 2 preserves the mirror symmetry and leads to an increase of the separation between the rings at the site of addition (2.83−3.13 Å) and a decrease to 2.79 Å at the para end of the ring. The cyclohexadienyl ring of 2c is more planar than that of 2a/b. DFT Calculations of Hyperfine Coupling Constants. The calculated hfccs and ALC resonance fields for the Mu adducts of 1 are listed in Table 1. Roduner et al. determined the Aμ of 1a at 298 K to be 482.8(5) MHz using transverse field muon spin rotation spectroscopy.22 The calculated Aμ of 1a is 5% smaller than the experimental value, which we consider to be a reasonable amount for the purpose of identifying the

position

Acalcd p /MHz

|Ameasd |/MHz p

benzene CH bridging CH2

−11.81 2.86

8.27 2.89

The calculated hfccs and ALC resonance fields for the Mu adducts of 2 obtained from the DFT calculations are listed in Table 3. In all of the radicals 2a−2c there is very little unpaired electron spin density ( 5 MHz) and the Corresponding ALC Resonance Fields for the Mu Adducts of [2.2]Paracyclophane (2)a radical

position

AX/MHz

Bres/T

2a

muon methylene ortho meta para ortho CH2 meta CH2 muon methylene ortho meta para ortho CH2 meta CH2 muon ortho meta para CH2

530.9b 47.9c −22.3 21.2 −39.9 30.0 −5.9 169.9b 150.9c −22.4 30.0 −40.2 30.5 −5.9 469.0b −28.3 14.6 16.2

1.9489 2.5873 2.9661 2.7314 3.0614 2.6840 2.8777 0.6237 0.0965 1.0314 0.7978 1.1277 0.7462 0.9424 1.7219 2.6672 2.4357 2.4269

2b

2c

Figure 5. Distinguished coordinate reaction paths (UB3LYP/ 6-311G(d,p)) near the transition states for Mu addition to the secondary and tertiary carbons of 1 and the exo, endo, and bridging sites of 2.

Table 4. Calculated (UB3LYP/6-311G(d,p)) Transition State C−Mu Bond Lengths and Energy Barriers for the Addition of Mu to 1 and the Predicted Relative Yields

a

The C−Mu bond was increased by 4.9% and the C−H bond decreased by 0.3% from their optimized values. bAμ was calculated by lengthening the C−Mu bond by 4.9% to account for the primary isotope effect and multiplying the DFT value by 3.183 to account for γμ/γp. cAp was calculated by decreasing the C−H bond by 0.3% to account for the secondary isotope effect.

position

C−Mu distance/Å

Ea/kJ mol−1

predicted relative yield/%

secondary tertiary

1.766 1.728

23.8 34.8

98.8 1.2

Table 5. Calculated (UB3LYP/6-311G(d,p)) Transition State C−Mu Bond Lengths and Energy Barriers for the Addition of Mu to 2 and the Predicted Relative Yields

on the reactivity of aromatic compounds toward Mu. Mu addition is exothermic to both the secondary (−42.6 kJ mol−1) and tertiary carbons (−26.5 kJ mol−1) of 1. Mu addition to all three types of sites in 2 is also exothermic, with the exo adduct being the most favored (−62.6 kJ mol−1), followed by the endo adduct (−59.5 kJ mol−1), and the bridge adduct being the least favored product (−56.7 kJ mol−1). The distinguished coordinate paths near the transition states for addition of Mu to the different sites of 1 and 2 are shown in Figure 5, and the addition barriers and C−Mu distances at the transition state are listed in Tables 4 and 5. The barrier for Mu addition at the secondary carbon of 1 is 11.0 kJ mol−1 smaller than the barrier for Mu addition at the tertiary carbon of 1. This would imply that a negligible amount of 1b should form in the liquid phase near room temperature. The barriers for addition to 2 (except at the endo site) are smaller than those for addition to 1 and this is likely a result of the strained geometry requiring less reorganization to generate the preferred tetrahedral geometry. The barrier for addition at the endo site of 2 is very large and this results from the unfavorable steric interaction between Mu and a proton on the opposite ring, which are 2.09 Å apart at the transition state. On the basis of the DFT calculations we expect that the major product of the reaction of Mu with 2 is 2a, due to the small barrier to addition and the 8 possible sites of addition, then with a smaller amount of 2c due to the slightly larger barrier and fewer number of addition sites and negligible amounts of 2b because of the large addition barrier. The DFT calculations indicate that the partial release of strain increases the rate of reaction between an aromatic molecule and a simple free radical. μSR of p-Xylene. The ALC-μSR spectrum of liquid 1 was measured at 300 K (Figure 6). Six resonances were observed,

position

C−Mu distance/Å

Ea/kJ mol−1

predicted relative yield/%

exo endo bridge

1.832 1.817 1.825

17.2 48.6 20.4

87.7 ∼0 12.3

Figure 6. Background subtracted ALC-μSR spectrum of p-xylene at 300 K.

five of which could be assigned to 1a, and a sixth, at 2.2790(1) T, due to the para CH3 protons of 1b (Table 6). From the 7769



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= 466.8(1) MHz. Peaks due to other orientations of 1b could be hidden under the Δ1 resonances of 1a. The origin of the peak at 2.1545(5) T is most likely due to the para methyl protons in 1b. Calculating the relative amounts of 1a and 1b that are formed in the solid state is difficult due to the overlapping peaks and the nonuniform distribution of radicals. The amplitudes of the Δ1 resonances cannot be used as these depend on the angle between the unique axis of the hyperfine tensor and the applied magnetic field (eq 2), which is not known. The best that can be done in this situation is a rough estimate of the relative amounts of 1a and 1b based on the amplitudes of the Δ0 resonances, as this should be independent of the radical orientation. At 280 K the relative yields of 1a and 1b are estimated to be ∼60% and ∼40%, respectively. The relative yield of the tertiary adduct appears to be significantly larger in the solid state than in the liquid and the predicted value based on the calculated addition barriers. μSR of [2.2]Paracyclophane. There are three strong resonances in the ALC-μSR spectrum of paracyclophane (Figure 8). The resonances have an asymmetric line shape

Table 6. Resonance Fields and Hyperfine Coupling Constants Obtained from the ALC-μSR Spectrum of 1 at 300 K Δ

Bres0 /T

Ap/MHza

assignment

1.94915(2) 2.2790(1) 2.47170(2) 2.6282(1) 2.72166(4) 2.78346(2)

118.4 51.2b 21.6 −7.4 −24.7 −36.2

1a methylene 1b para CH3 1a ortho CH3 1a meta CH3 1a ortho 1a para

In each case the error in Ap is ∼0.5 MHz and is dominated by the large error in Aμ. bThe Aμ of 1b was not measured by Roduner et al.22 Aμ of 1b was estimated to be 476.6 MHz by scaling the experimental Aμ of 1a by the ratio of the calculated Aμ values of 1a and 1b. a

amplitudes of the Δ0 resonances we estimate that the relative amounts of 1a and 1b are 89.2:10.8. The relative yield of the tertiary adduct is considerably higher than was predicted from the DFT calculations and the results of the TF-μSR measurements where 1b was not observed. There are multiple overlapping resonances in the ALC-μSR spectra of solid 1 (Figure 7). The dominant feature in the

Figure 8. Background subtracted ALC-μSR spectrum of [2.2]paracyclophane at 300 K showing the Δ1 resonances of the three types of muoniated radical. The error bars for the data are smaller than the symbols.

Figure 7. Background subtracted ALC-μSR spectrum of p-xylene at 280 K.

spectra was fit with three Lorentzian peaks. The following discussion refers to the resonance field positions measured at 280 K. The Δ1 resonance field of 1a is expected to be ∼1.7724 T on the basis of the TF-μSR measurement in the liquid phase. We propose that the overlapping peaks at 1.7884(6) and 1.8375(12) T are the Δ1 resonances of 1a with two distinct orientations with respect to the magnetic field. Using the DFT calculated dipolar hfccs of 1a we have calculated that the maximum splitting of Δ1 resonances due to different radical orientations would be ∼0.08 T, which is smaller than the observed splitting. Measurements made on p-xylene in the liquid phase show that A′μ/Ap = 1.281, so we would expect the methylene proton Δ0 resonances for the different orientations at 1.9669 and 2.0206 T. There are small resonances at 1.9671(4) and 2.0262(9) T that we have assigned as the methylene proton Δ0. The DFT calculations show that the muon hfcc of 1b is slightly lower than that of 1a, so we suggest that the peak at 1.7136(4) T is the Δ1 resonance of 1b, with Aμ

and the best fit was obtained using eqs 1 and 2, which assumes a uniform distribution of molecules and an axially symmetric hyperfine tensor. The assignment of the resonances is based on a comparison of the experimental and calculated resonance fields. The discussion refers to the resonance fields at 300 K. The resonance at 0.6928(2) T is the Δ1 of 2b, the resonance at 1.7309(2) T is the Δ1 of 2c and the resonance at 1.89355(5) T is the Δ1 of 2a. The corresponding muon hfccs at 300 K are 188.71(5), 471.49(7), and 515.79(1) MHz, respectively, and there is very close agreement between the experimental and calculated muon hfccs. The average D⊥μ values for radicals 2a, 2b, and 2c between 260 and 320 K are −4.89(4), −4.65(3), and −5.3(1) MHz, respectively, and do not change significantly with temperature. Two weak Δ0 resonances were observed at 2.483(1) and 2.645(4) T (300 K). The first peak is due to the methylene proton of 2a and the second peak is due to the ortho CH2 protons of 2a. 7770



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smallest. The surprising result from the ALC-μSR spectra is the considerable yield of 2b, which was not expected given the much larger barrier to addition at the endo position. Radical Formation in the Solid State. The ALC-μSR measurements on 1 and 2 have shown that the relative yields of radicals produced by the addition of a radical to strained and unstrained aromatic molecules has very little relationship with the activation barriers calculated for isolated molecules. Perhaps this is not surprising. The interactions with neighboring molecules must be taken into account if we wish to determine the true activation barriers for radical addition in the solid state, although this is too computationally expensive for us at present. At this stage we can only draw qualitative conclusions by examination of the crystal structures. We propose that when Mu adds to the secondary carbons of 1, there are unfavorable steric interactions between Mu or the H at the site of addition and the methyl group of a neighboring molecule, which is at a distance of 2.99 Å. This should effectively block off two of the four addition sites that produce 1a. Mu addition at the tertiary carbon is relatively favored as the formation of a roughly tetrahedral geometry at the ipso carbon moves the methyl group in a way that decreases the steric interactions with neighbors (Figure 10).

Both the muon hfccs of the 2a and 2c decrease approximately linearly with increasing temperature (dAμ/dT = −0.013(1) MHz K−1 for 2a and dAμ/dT = −0.041(2) MHz K−1 for 2c) whereas the muon hfcc of 2b decreases with increasing temperature, although there is considerable scatter in the data points (Figure 9). Yu et al. measured the temperature

Figure 9. Temperature dependence of the muon hyperfine coupling constants of the Mu adducts of [2.2]paracyclophane. Top = exo adduct; middle = bridge adduct; bottom = endo adduct.

dependence of the muon hfcc of the muoniated cyclohexadienyl radical (C6H6Mu) in benzene by TF-μSR and found the muon hfcc decreased linearly with increasing temperature, with a slope of −0.0781(5) MHz K−1. The decrease of the muon hfcc of the C6H6Mu with increasing temperature is due to the increasing amplitude of the scissor vibration of the methylene group. The temperature dependence of the muon hfccs of the Mu adduct of paracyclophane are much smaller than that of the cyclohexadienyl radical. The relative yields of each radical of each radical (P0z ) were determined from the amplitudes of the Δ1 resonances in the ALC-μSR spectra (Table 7). The major product is 2a, which is in line with predicted barrier to addition at the exo site being

Figure 10. Crystal structure of p-xylene viewed along the a axis. The arrows indicate close (2.99 Å) interactions with neighboring molecules.

Addition of Mu to the exterior positions of 2 appears to be destabilized with respect to addition at the endo sites. We propose that this is due to the steric interaction with neighboring molecules, which is similar to the case of endo addition where the activation barrier is increased because of the steric interaction between Mu and a proton on the second phenyl ring of 2. Examination of the crystal structure of 2 shows that there are likely unfavorable interactions for Mu at the exo transition state geometry with the molecules located on the a and b crystallographic axes. The distance between the secondary unsaturated carbon and the proton of a neighboring molecule is 3.37 Å, which means that the separation between Mu and this proton in the transition state could be as little as ∼1.6 Å, which is comparable to the separation between Mu and the proton on the opposite ring of 2 at the endo transition state (Figure 11). For addition at the bridging site there are

Table 7. Relative Yields of the Mu Adducts of [2.2]Paracyclophane Determined from the Amplitudes of the Δ1 Resonances in the ALC-μSR Spectra position

relative yield/%

exo endo bridge

0.671(1) 0.218(1) 0.111(1) 7771



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ASSOCIATED CONTENT

S Supporting Information *

Optimized structures of all molecules described in this paper. This material is available free of charge via the Internet at http://pubs.acs.org/.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 604-222-7386. Fax: 604-222-1074. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Support from the staff at the Laboratory for Muon Spin Spectroscopy at the Paul Scherrer Institute is gratefully acknowledged. This research project has been supported by the European Commission under the seventh Framework Programme through the “Research Infrastructures” action of the “Capacities” Programme, Contract No. CP-CSA_INFRA2008-1.1.1 Number 226507-NMI3. Computing resources were provided by STFC’s e-Science facility, WestGrid, and Compute/Calcul Canada. Prof. P. W. Percival is thanked for useful discussions.

Figure 11. Crystal structure of [2.2]paracyclophane viewed along the c axis. The methylene protons have been removed for clarity. The arrows indicate close (3.37 Å) interactions with neighboring molecules.

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REFERENCES

(1) Rigden, J. S. Hydrogen, The Essential Element; Harvard University Press: Boston, MA, 2003. (2) Heller, H. C.; Schlick, S.; Cole, T. J. Phys. Chem. 1967, 71, 97− 102. (3) McKenzie, I.; Roduner, E. Naturwissenschaften 2009, 96, 873− 887. (4) McKenzie, I.; Brodovitch, J.-C.; Percival, P. W.; Ramnial, T.; Clyburne, J. A. C. J. Am. Chem. Soc. 2003, 123, 11565−11570. (5) Percival, P. W.; Addison-Jones, B.; Brodovitch, J.-C.; Ghandi, K.; Schüth, J. Can. J. Chem. 1999, 77, 326−331. (6) Brodovitch, J.-C.; Ghandi, K.; McKenzie, I.; Percival, P. W.; Schüth, J. Physica B 2006, 374−375, 310−313. (7) Brodovitch, J.-C.; Addison-Jones, B.; Ghandi, K.; McKenzie, I.; Percival, P. W.; Schüth, J. Can. J. Chem. 2003, 81, 1−6. (8) Percival, P. W.; Addison-Jones, B.; Brodovitch, J.-C.; Ji, F.; Horoyski, P. J.; Thewalt, M. L. W.; Anthony, T. R. Chem. Phys. Lett. 1995, 245, 90−94. (9) Tumanskii, B. L. Russ. Chem. Bull. 1996, 45, 2267−2278. (10) Cram, D. J.; Steinberg, H. J. Am. Chem. Soc. 1951, 73, 5691− 5704. (11) Cram, D. J.; Cram, J. M. Acc. Chem. Res. 1971, 4, 204−213. (12) Ishitani, A.; Nagakura, S. Mol. Phys. 1967, 12, 1−12. (13) Gerson, F.; Martin, W. B. J. Am. Chem. Soc. 1969, 91, 1883− 1891. (14) Roduner, E. Hyperfine Interact. 1990, 65, 857−872. (15) Heming, M.; Roduner, E.; Patterson, B. D.; Odermatt, W.; Schneider, J.; Baumeler, H.; Keller, H.; Savic, I. M. Chem. Phys. Lett. 1986, 128, 100−106. (16) Frisch, M. J. et al. Gaussian 09, Revision B.01; Gaussian Inc.: Wallingford, CT, 2009. (17) Improta, R.; Barone, V. Chem. Rev. 2004, 104, 1231−1253. (18) Roduner, E.; Reid, I. D. Isr. J. Chem. 1989, 29, 3−11. (19) van Koningsveld, H.; van Den Berg, A. J.; Jansen, J. C.; de Goede, R. Acta Crystallogr. 1986, B42, 491−497. (20) Hope, H.; Bernstein, J.; Trueblood, K. N. Acta Crystallogr. 1972, B28, 1733−1743. (21) Chipman, D. M. J. Phys. Chem. 1992, 96, 3294−3298. (22) Roduner, E.; Brinkman, G. A.; Louwrier, P. W. F. Chem. Phys. 1982, 73, 117−130. (23) Reid, I. D.; Roduner, E. Struct. Chem. 1990, 2, 419−431.

unfavorable steric interactions between Mu and the methylene protons of neighboring molecules. The observed distribution of products can be obtained if the calculated barriers to addition at both the exo and bridging sites are increased by ∼28 kJ mol−1. Reid and Roduner studied the Mu adducts of naphthalene in solution and in a single crystal using TF-μSR, where they observed only addition at the secondary carbons and found that the relative yield of the muoniated β-hydronaphthyl isomer did not differ substantially in solution (40%) or in the crystal (∼41%).23 Reid and Roduner note that there are several neighboring atoms less the 3 Å away, but rationalizing the relative yields of the Mu adducts of naphthalene will require a detailed study of all the interactions with neighboring molecules. When these interactions are taken into account, our expectation is that Reid and Roduner’s findings and ours will agree with each other. More experimental and computational work is required to rationalize and better predict how H and Mu react with aromatic molecules in the solid state.

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CONCLUSIONS Mu adds to both the secondary and tertiary unsaturated carbons of both strained and unstrained aromatic molecules in the solid state. The resulting radicals were identified by comparing the experimental hfccs with values calculated for the possible structures. The relative yield of each radical product was determined from the amplitude of the ALC resonances and does not appear to be strongly related to the gas phase addition barriers obtained from the DFT calculations. The calculations indicate that the partial release of the strain in 2 upon Mu addition should increase the relative yield of the Mu adduct to the tertiary unsaturated carbons compared with 1, but in the solid state the steric interactions with neighboring molecules are of approximately equal importance in determining the product yield. 7772


How Do Strain and Steric Interactions Affect the Reactions of Aromatic

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