J . Chem. SOC., Faraday Trans. I , 1984, 80, 255-265 Muon Spin Rotation Spectra for Muonium Isotopically Substituted Ethyl Radicals BY MARIA JOXO RAMOS,? DANIEL MCKENNA AND BRIAN c. WEBSTER* Chemistry Department, University of Glasgow, Glasgow G12 8QQ, Scotland AND EMIL RODUNER Physikalisch Chemisches Institut der Universitat, CH-8057 Zurich, Switzerland Received 24th June, 1983 The temperature dependence of the B-hyperfine coupling constant is reported for muonic radicals formed in ethene CH,=CH,, [,H,]ethene CH,=CHD, [,H,]ethene CHD=CD, and [ZHJethene CD,=CD,. These studies are complemented by e.p.r. observations upon the radical CH,D~H,. The barrier to internal rotation for the radical CHD,cD, is discussed. Muonium-substituted organic radicals are formed in liquid unsaturated hydrocar- bons upon which is incident a beam of p+-mesons.Although the primary events yet have to be elucidated, one of the possible precursors is the muonium atom Mu, created as the bound state of a p+-meson with an excess electron. Radicals are generated by the addition of muonium to the unsaturated molecule.' The theory for the analysis of muon spin rotation spectra @.s.r.) has been extended recently by Roduner and Fischer to muonium-substituted radicals.,. Elsewhere muon-electron hyperfine coupling constants have been reported for muonium- substituted alkyl and ally1 radical^.^ The temperature dependence of the /3-hyperfine coupling constant for the radical CD,MucD, produced in deuterated [,H,] ethene has revealed the existence of a substantial barrier to internal rotation of the CD,Mu group about the C,-C, single bond.The height of the barrier is of the order of 2710 J mol-l.5 Here we report p.s.r. spectra for radicals created in the deuterated ethenes CH,CHD and CHDCD,. These substrates, together with C2H4 and C,D,, have been selected in order that the interactions which could give rise to the barrier can be discerned. The analysis is given in the following paper.s FOURIER-TRANSFORM p.S.R. SPECTRA Observations upon the deuterated ethenes were made at the muon channel of the Swiss Institute for Nuclear Research (SIN), Villigen. The gases, having been obtained from MSD isotopes, were used without further purification. Following liquefaction, oxygen together with other dissolved gases was removed on a vacuum line by a sequence of freeze-pumpthaw cycles.The samples contained in spherical glass ampoules of 25 and 35 mm diameter were maintained at liquid-nitrogen temperature before insertion into the cryostat of the ,u.s.r. spectrometer. t Present address: Departamento de Quimica, Faculdade de Cizncias, 4000 Porto, Portugal. 255256 MUON SPIN ROTATION SPECTRA OF ETHYL RADICALS After removal of background events and the natural decay of muonium, histograms representative of 107-108 events were subjected to Fourier transformation, procedures for apodisation having been im~lemented.~ Fig. 1 and 2 show the Fourier-transform p.s.r. spectra for the species formed in ethene and perdeuterated ethene, together with the effect of temperature upon the line position and the line width.In diamagnetic environments bare muons precess at a Larmor frequency equal to 1.355 x 1 O8 Hz T-l. Under a transverse applied magnetic field of 0.16 T a diamagnetic fraction should appear in each spectrum at 21.68 MHz. Such signals have been observed but are excluded here for the purpose of clarity. Each spectrum consists of a pair of lines at all of the temperatures studied, although for ethene at 1 1 1 K broadening of the lines is evident. The signals are attributed in fig. 1 to the muonic ethyl radical CH,Mu CH,, and in fig. 2 to the perdeuterated radical CD,MuCD,. Fig. 3 and 4 in contrast show the presence of two radicals formed in monodeuterated ethene and trideuterated ethene, respectively. For reasons to be stated later, the signals denoted by A,, A, in fig.3 are ascribed to the radical CHDMucH,, with the radical CH,MucHD being represented by the pair of lines labelled B,, B,. Similarly, in fig. 4 the signals denoted by A,, A, are attributed to the radical CHDMucD,, with the pair of lines B,, B, being assigned to the radical CD,MuCHD. Note that in both liquids a radical is formed having a chiral centre created by the hydrogen isotopes, muonium, protium and deuterium. In all of the p.s.r. spectra the frequencies at which the signals for a particular muonic radical appear to decrease with increasing temperature ; consequently there is a decrease of the /I-hyperfine muon-electron coupling constant with increasing tem- perature. Values for these coupling constants are collated in table 1. To allow a comparison to be made with proton-electron hyperfine coupling constants for the analogous protium-substituted radical, the muon-electron coupling constants are cited in the reduced form A; defined by where p p and pp are the magnetic moments for the proton and the muon, respectively, the ratio pp/pp being equal to 0.3141.Fig. 5 shows the variation of the /I-hyperfine muon-electron coupling constants with temperature for six muonium-substituted ethenes. E.P.R. SPECTRA FOR THE RADICAL CH,DcH, The radical CH,DcH, was generated following the procedure outlined by Itzel and Fischer and Burkhard and Fischer.87g Ethyl oxirane solutions containing 0.8 vol % monodeuterated ethyl bromide, 17 vol % di-t-butylperoxide and 10 vol % triethylsilane were photolysed in the cavity of a Varian E-4 spectrometer.Reaction of silyl radicals with deuterated ethyl bromide results in production of the radical CH,DcH,. The hyperfine interaction was measured in the temperature range 163-273 K. The first-derivative e.p.r. spectrum observed at 180 K is shown in fig. 6. Only the outer lines have been used to measure the coupling constant. Of the lines numbered 1-27 in fig. 6, lines 1-4 and 24-27 were scanned accurately with a frequency counter at each temperature. The relationshipsM. J. RAMOS, D. MCKENNA, B. C. WEBSTER AND E. RODUNER 257 120 K 1 . . . 1 . . . 1 . , . . 1 . . . 1 . . . 1 . . . 1 . . . 1 . . . 1 . . . 1 I b O 120 140 160 I60 200 220 240 260 280 300 frequency /MHz Fig. 1. Fourier-transform p.s.r. spectra for the muonic ethyl radical at five temperatures and applied transverse field of 0.16 T.258 MUON SPIN ROTATION SPECTRA OF ETHYL RADICALS frequency /MHz Fig.2. Fourier-transform p.s.r. spectra for the muonic radical formed in tetradeuteroethene at five temperatures and applied transverse field of 0.16 T.M. J. RAMOS, D. MCKENNA, B. C. WEBSTER AND E. RODUNER 259 I I80 K L ~ . . . ~ l l . l . I l l l l . l l l . l l . I 1 . . . I 140 160 180 200 220 240 260 280 frequency /MHz Fig. 3. Fourier-transform p.s.r. spectra for the muonic radicals formed in monodeuteroethene at five temperatures and applied transverse field of 0.16 T. A,, A, are frequencies for CHDMucH, and B,, B, are frequencies for CH,MueHD. were adopted to specify values for the a-protium A g , #?-protiurn A? and #?-deuterium A; hyperfine coupling constants.These values are listed in table 2. For the #?-deuterium coupling constant a reduced value A;, defined by A6 = IAFl(pp/PD) (3) where pD is the magnetic moment of the deuteron, is given also to facilitate comparison with the p.s.r. results. Fig. 7 contrasts the behaviour of the temperature dependence for the #?-proton4ectron coupling constant with the #?-deuteron coupling constant. It is to be seen that A; decreases with increasing temperature, ranging from 77.88 MHz at 163 K to 76.54 MHz at 273 K. The #?-deuteron reduced interaction A;, increases from 70.8 to 72.6 MHz over the same temperature range. The mean of the coupling constants equal to 1/3 (2AF+Ab) shows only a slight variation with temperature, decreasing by 0.29 MHz from a value of 75.52 MHz at 163 K to 75.23 MHz at 273 K.260 MUON SPIN ROTATION SPECTRA OF ETHYL RADICALS 129 K I 144 K # I 164 K I 184K 1 1 l .. ~ ~ 140 160 180 200 220 240 260 280 frequency /MHz Fig. 4. Fourier-transform ,u.s.r. spectra for the muonic radicals formed in trideuteroethene at hur temperatures and applied transverse field of 0.16 T. A,, A, are frequencies for CHDMueD, and B,, B, are frequencies for CD,MueHD. HYPERFINE INTERACTIONS AND RADICAL CONFORMATION The hyperfine interaction originates from electron spin density at the nuclear site under observation. For the isotopically substituted ethyl radicals the major component of the electron spin density drives from the 2pz orbital centred at the a-carbon nucleus. If 0 defines the dihedral angle for rotation of the C, - X axis involving the substituent X to eclipse this 2p, orbital centred at C,, an equilibrium conformation for the radical is specified by 0, where 0, is the value of 0 at the minimum of a two-fold barrier taken to replicate the potential hindering internzl rotation about the C,-C, axis.A potential barrier is of the form defined by This barrier can be discerned to be derived by truncation of a Fourier series for V(0) with only the two-fold term being retained. Furthermore, assuming that the internal rotation of a CH,X group about the CB-C, internuclear axis can be treated indepndently of vibrational motion, molecular rotation and solvent interaction, the torsional Hamiltonian H(0) given byM. J. RAMOS, D. MCKENNA, B. C. WEBSTER AND E.RODUNER 26 1 Table 1. Muon+lectron hyperfine coupling constants for muonic radicals formed in ethene, monodeuterated ethene, trideuterated ethene and tetradeuterated ethene measured at an applied transverse magnetic field of 0.16 T olefin radical T/Ka AJMHz ALjMHzf A,/MHz ref. ethene CH,MueH, CH,=CH, [,H,]ethene CH,MucHD CHD=CH, CHDMucH, [,H,]ethene CD,M&HD CHD=CD, CHDMU~D, E2H,]ethene CD,MueD, CD,=CD, 111 120 140 162 182 110 122 139 160 180 110 122 139 160 180 129 144 164 184 129 1 44 164 184 113 120 141 161 183 416.3b 409.6 395.5 381.9 371.4 420.4b 410.6 397.8 384.3 373.9 423.4b 414.0 401.7 388.3 377.9 425.4d 412.6 396.8 383.2 428Sd 416.1 401.0 386.7 438.5b 431.7 416.0 401 .O 387.8 130.8b 75.3" (1 1) and (12) 128.7 124.2 120.0 116.7 132.1b this work 129.0 125.0 120.7 117.4 130.0 126.2 122.0 118.7 133.6d 129.6 124.6 120.4 1 34.6d 130.7 126.0 121.5 135.6 130.7 126.0 121.8 133.0b B (11) and (12) 1 37.7b e (11) and (12) a +2 K; kO.1 MHz; nearly temperature independent; k0.2 MHz; temperature dependent; at 98 K, for example, its value is 83.4 MHz; f Ah = lAplpp/pp; g temperature dependent; at 97 K, for example, its value is 79.1 MHz.can be employed to calculate the torsional energy 1evels.lO In eqn ( 5 ) I, the reduced moment of inertia. is defined as in terms of the moments of inertia Il and I, for the two groups rotating about the CB-C, axis evaluated at the equilibrium molecular geometry. If there exists a Boltzman population of the torsional energy levels Ei, the temperature dependence of the /I-hyperfine coupling constant will follow262 MUON SPIN ROTATION SPECTRA OF ETHYL RADICALS 1 1 I 1 1 1 I 1 120 140 160 180 TIK Fig.5. Temperature dependence of the reduced muon hyperfine coupling constants for CH,MuCH, (@), CHDMucH, (0), CH,MucHD (O), CD,MuCHD (a), CHDMU~D, ( X ) and CD,MuCD, (0) at an applied transverse field of 0.16 T. 12 14 16 1 2 3 25 26 27 Fig. 6. First-derivative e.p.r. spectrum for the CH,DcH, radical at 180 K. where y = O+O, and is the expectation value of the P-hyperfine coupling constant for the molecule in the ith torsional level. Often the angu!ar dependence of the P-proton-electron hyperfine interaction and P-deuteron-electron interaction is (8) represented in the form of = + cos2 where the leading constant L represents a contribution to the hypefine interaction arising from a spin polarisation mechanism and the second constant A4 describes the variation with torsion angle of the electron spin density at the Q-nucleus. In the following paper we demonstrate that such a relationship can be extended toM.J. RAMOS, D. MCKENNA, B. C. WEBSTER AND E. RODUNER 263 Table 2. a-proton (A:), 8-proton (Ap), 8-deuteron (A?) and /?-deuteron (Ah) reduced hyperfine coupling constants for the CH,DcH, radical measured at 180 K. T/K A,H/MHz AF/MHz A'IMHz" AF/MHz AL/MHz 163 173 183 193 203 213 223 233 243 253 273 62.38 f 0.03 62.30 f 0.06 62.35 f 0.03 62.33 f 0.03 62.33 f 0.03 62.30 f 0.01 62.33 f 0.03 62.33 f 0.03 62.24 f 0.03 62.27 f 0.03 62.27 f 0.03 77.88 & 0.03 77.77 f 0.03 77.63 f 0.03 77.49 f 0.03 77.35 f 0.03 77.2 1 f 0.03 77.07 f 0.03 76.93 f 0.03 76.93 f 0.03 76.76 f 0.03 76.54 & 0.03 75.52 75.51 75.49 75.49 75.47 75.44 75.41 75.32 75.39 75.34 75.23 10.76 & 0.03 10.79 f 0.03 10.8 17 f 0.008 10.87 0.01 10.90 f 0.03 10.93 fO.01 10.958 4 0.008 10.96 f 0.03 10.98 & 0.03 1 1.01 f 0.03 1 1.04 0.06 70.8 f 0.2 71 .Of 0.2 71.2 f0.2 71.520.2 71.7f0.2 71.9f0.2 72.1 f 0.2 72.1 f 0.2 72.3 & 0.2 72.5 f0.2 72.6 f 0.2 a A' = &(2A,H+Ai).I I I I I I 160 180 200 220 240 260 280 TIK Fig. 7. Temperature dependence of the (a) 8-proton and (b) Bdeuteron reduced hyperfine coupling constants for CH,DcH radical. /3-muon+lectron hyperfine interactions. For occupancy of the ith torsional level the expectation value can be evaluated from <A&))i = L + M ( ilcos2 yli) (9) adopting the wavefunction defined by 1 v / .= ~ I= c , exp (ima ' ~ ' ( 2 ~ 1 m264 MUON SPIN ROTATION SPECTRA OF ETHYL RADICALS The result is expressed as ( ilcos2 y l i ) = 4 Z C,[C, +gC,,, (cos 28, - sin 20,) +$Cm-, (COS 28, + sin 28,)]. m (1 1) For example, if 0, = 0 then (i)cos2 yli) reduces to the simple expression The expansion coefficients C , are obtained by solution of the secular problem arising from adoption of the Hamiltonian in eqn (5). The secular determinant then has the - . n2 Hmm = -m2-/-- 21 2 elements defined in HmmI =- -v, m'=m+2,m-2 Hmml = 0, rn' # m+2, m-2. 4 , (13) Some years ago Fessenden and Schuler measured the B-proton-electron hyperfine coupling constant for the radical CHD,cD, to equal 83.43 MHz at 98 K. Fessenden suggested that the equilibrium conformation is defined by 8, = 0" with a barrier of height 384.9 J mol-l.By comparison both of the radicals CH3eH, and CD$D2 reveal no temperature dependence of the /?-hyperfine coupling, from which observation it is concluded there is no detectable barrier which hinders internal rotation in these radicals. For the radical CHD,cD, with values 8,, L = 0.0 MHz, M = 150.61 MHz, = 384.9 J mol-l and Z = 3.47 x lov4' kg m2, a solution of the secular problem in the manner outlined provides three torsional levels within the barrier. These levels are located at E, = 148.7 J mol-l, E2 = 182.1 J mol-1 and E3 = 371.6 J mol-l, as depicted in fig. 8. With such a barrier to internal rotation the /I-hyperfine constant at 98 K is calculated from eqn (7) as 83.47 MHz.The temperature dependence of the B-deuterium-electron hyperfine interaction displayed in fig. 7 is consistent with an equilibrium conformation for CDH,cH, such that 0,(D) = 90°. For the muonic ethyl and perdeuterated radicals CH2MucH2 and CMuD2cD2 the high values for the reduced B-hyperfine muon-electron interaction, t Fig. 8. Barrier Y(O))/J rno1-l to internal rotation for the deuterated ethyl radical CHD$D,; the equilibrium conformation is defined by 8, = 0".M. J . RAMOS, D. MCKENNA, B. C . WEBSTER AND E. RODUNER 265 130.8 MHz at 1 1 1 K for CH,Mu CH, and 132.1 MHz at 110 K for CD,MuCD,, are indicative of an equilibrium conformation O,(Mu) = 0' restrained by a substantial barrier. In the monodeuterated muonic radical CHDMucH, and the trideuterated radical CHDMu CD2 the C, symmetry of the CX, group is maintained.Accordingly the higher-frequency doublet of the p.s.r. spectrum has been assigned to these species in fig. 3 and 4, for it is anticipated that the barriers to internal rotation will be slightly higher than for the radicals CH,MutHD and CD,MuCHD. In the following paper we support such an assignment in a detailed study of the barriers to internal rotation for muonium-substituted ethyl radicals. We thank Dr Lung-min, who kindly assisted with the e.p.r. measurements. We also thank the Instituto Nacional de Investigaciio Cientifica, Lisbon, for the award of a research studentship to M. J. R. and the S.E.R.C. for a research studentship to D. McK. This work is supported by the Swiss Institute for Nuclear Research. E. Roduner and B. C. Webster, J. Chem. SOC., Faraday Trans. 1, 1983, 79, 1939. P. W. Percival and H. Fischer, Chem. Phys., 1976, 16, 89. E. Roduner and H. Fischer, Chem. Phys., 1981, 54, 261. E. Roduner, W. Strub, P. Burkhard, J. Hochmann, P. W. Percival, H. Fischer, M. Ramos and B. C. Webster, Chem. Phys., 1982, 67, 275. B. C. Webster, M. J. Ramos and E. Roduner, Proc. 5th Tihany Symp. (Akademiai Kiado, Budapest, 1983), pp. 135-140. M. Ramos, D. McKenna, B. C. Webster and E. Roduner, J . Chem. Soc., Faraday Trans. 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