Chemical Physics 67 (1982) 275-285 North-HoSand Publishing Company
MUONlUM SUBSTITUTED MUON-ELECTRON Emil RODUNER,
HYT’ERFTNE COUPLING CONSTANTS Walter
OF ALKYL AND ALLYL RADICALS
Paul W. PERCIVAL
**: Harms FISCHER Pi?yJi;-alisch-Cllemisc~~~s Institut der U~i~-em’r~r,CH-8057 Ztinkh. Switzerhnd and Maria RAMOS and Brian C. WEBSTER Chemistry Depar:ment,
Universityof Gias:ow. GIZ SQQ, UK
Received 16 November
hluonium substituted free ndicals 31e observed by muon spin rotation when posiiive muons are stopped in liquid olefms and dienes. From muon precession frequencies in high external magnetic fields the isotropic muon-electron hypeifine coupling constants have been determined for 44 rndiuls end anclyzcd to yield the radical structures. Primary, secondary znd tertiary ahkylmdicah tise from mono+,!efm, and mainly cllylic rcdiuls from conju,oated d&es. They 318 fwmed by addition of the light hydrogen isotope muoraum (Mu = i;+e7 to ?he parent molecules. It is shown that the relations between coupling constants nod radical structures hollow the principles known for the snalogous H substituted radials. Further, the re:ioselectivity of milonium addition is similar to that of H atoms.
The time evolution of the spin po!ariiation of positive muons observed by muon spin rotation ($SR) is used extensively to probe the structure of matter 2nd magnetic interactions [ 1,2]. Chemical applications [3-71 have centered so far around muonium (Mu = p+e-), 2 hydrogen isotope with a mass of l/9 of H, its formation in gases, liquids, and solid insulators, nnd the rate constants
of its reactions
Recently, the prospects of the field have been extended by the direct observation of muon containing paramagnetic molecules in unsaturated liquids and solids [S-IO] _For such free radicals the Zeeman interaction of the unpaired electron, the muon and of additional nuclei and the electron-muon and electron* Present eddress: E!ekrrowstt AG, CH 8005 Ziirich, Switierlsnd. ** Tresent address: Chemistry Department, Simon Fraser University, Burr&y, BC, WA 1.56, Canada.
02.75 0 1982 North-Hohand
nuclear hyperfine interactions lead to time evolutions containing many frequencies, in general. In high transverse magnetic fields where the electron Zeeman interaction is much larger than the hyperfie interactions a degeneracy to two frequencies only occurs, from which the muon-electron hyperfme coupling constant extracted. In previof the radical can be conveniently ous publications [8,10-131 we have presented the theory for the analysis of fiR frequency spectra of muon containing radicals 2nd have reported coupiing constants obtained from high field spectra. From these the radical srructures were deduced with the assumptions (1) that the radicals arise by formal addition of muonium to the unsaturated moleculesl 2nd (2) that the variation of the muon-electron coupling consmnts with radical structures is similar to that of the ulalogous known proton-electron coupling constants [ 131. Several assignments were confirmed in zero 2nd intermediate field experiments where the frequency spectra reveal additional nuclei in the structures [ 131. In general, it was found that the muon coupling constants
E. Roduner et al. jMuonium
exceeded those expected from analogous proton couplings and the ratio of ma;_netic moments ~JJ+_ This isotope effect was ascribed to different dynamic averaging of the muon and protcn containing species. It should be noted that the identificatior! of radica!s from muon coupling constants alone, as obtained in hia field experiments, may not lead to unambiguous results. in particular, if several radicals with similar couplings are possible. On the other handl low or intermediate field esperiments are feasible for favocrab!e cases. only . It was felt that the ambiguity in tile assignment of radical structures from high field data could be removed if more were known on the validity of the ahove mentioned assumptions, on the regioselectivity of muonium addition, the relations between muon coupling constants and radical structures and the isotope effects. To this purpose we have generated a large variety of muonium substituted radicals in liquids and have studied their muon coupling constants in hi& fields at various temperatures. This paper presents results on alkyl and ally1 radicals obtained from monoolefms and dienes. The coupling constants form a selfconsistent set which leads to unambiguous assignments and will be of future diagnostic value. More inior-mation on the origin of the isotope effects and on the regioselectivity of muonium addition is obtained. A related study of cyciohexadieny! radicals will be published
The olefins and dienes were used in commercial purities and purchased mostly from Fluka, Buchs. They were degassed by three freeze-pump-thaw cycles and then sealed in thin walled spherical glass bulbs of either 25 or 35 mm diameter. The uSRexperiments were carried cut a? the .muon beam lines oi r!le SV%S Institute for Nuclear Research. SIN, Villigcn. A dctai!ed descrip!ion of the experimental procedures has been given previously [ 131. In this work transverse magneric fields of 1 kG or larger were applied. The gSR-histograms contained 10’ to IO8 events and were Fourier transfomled to obtain the USR-frequencies. As in the previous studies [8,10,13] 211samples revealed the presence of muons in diamagneric environments, i.e. the muon Larmor frequency :,~ = 13.55 kI-IzjC. In addition one or two pairs of
or,cnnicfree mdicak in liquids
frequencies appeared which were ascribed to muoniurn substituted radicals. From tile two frequencies vh (for higher) and up (for lower) of the pairs, the absolute values of the muon-electron hyperfiie coupling constants IA,1 are deduced. It is easily derived fro-m formuiae given in ref. [ 131 that Vh is given by “h=-f(“e-Y~3f[~~;(ve+~~2]1/2+~IALL(,
where Y, = 2.50247 (g/g,) MIz/G is the electron Larmor frequency,g the radical g-factor and g, the free electron value. Further, one has ]A,] = Vh ’ Vc ,
where the sum/difference ‘h
has to be taken if
_ 2 X 206.?7g/g, - 206.77(g/ge)-1
For the carbon centered radicals studied here g should be very close to ge, i.e. the rhs ofeq. (3) should be very close to 2. Thus, an analysis of multiradical spectra convenienrly starts from the hi$iest frequency z#, and a rough calculation of IALl tia eq. (1) assuming g =g,. The corresponding lower frequency ui is then identified via eq. (2) with the proper choice of sign dictated by (3). Utilizing (2) @es then the exact IAil. The process is repeated unti! all line pairs are assigned. In practice we found it useful to abbreviate the procedure by comparing observed frequencies with values calculated for g =g, and tabulated for various IA,1 and field strengths. As an experimental example fig. 1 shows a pSR frequency spectrum obtained for 2,4_hexadiene at room temperature. Line II is due to muons in diamagnetic environments, Cr is the SIN cyclotron frequency, and R,, R2 denote pairs of radical frequencies. In principle, the radical g-factor can also be obtained from the radical frequencies, for instance via
the proper sign again dictated by eq. (3). Since I+, and vQ represent nuclear transitions they depend only weakly on g. Correspondingly, g-factors cannot be measured accurately by PSR. For instance, application of eq. (4) to the frequencies of (CH$~IM&(CH& (table 5 of ref. ) gaveg = 2.01 f 0.04. On the other hand,g-factors of alkyl radicals without hetero-
F&.. 1. Muon precession frequencies in &+hcxadiene. D: rnu~n~ in diamegetic environment, Cy: cyclotron frequency, RI and RI : pairs of radical irequencics.
substituents are expected [ 141 to lie in the narrow range of 2.0027 k 0.0003. The value obtained by PSR is compatible with expectation. It is too inaccura?e to be of diagnostic help, however. Therefore,g-factors are not given in the following sections
3. Assignments of muonium substituted radicals 3. I. General comideratiom
3.2. Radicals from erhene, propme and Z-methyl propme For Each of these basic olefins of type CH7 = CR1R2 (RI, R2 = 1-lor CH3) only one muonium substituted radical war observed. Table 1 presents rhe muon-electron coupling constants at various temperatures, the structures of the radicals assigned and the proton coupling constants of the H-analogous radicals. To facilitate the comparison of coupling constants the muon values are given in reduced form
A; = I-4,l(fl,/LQ
As previously [BJO--131 we assume that the radicals are formed by formal addition of muonium. For the alkenes and conjugated dienes studied here, this places Mu in RIRzMuC-groups (RI, R? = H, olkyl or allyl) attached to radical centres or conjugated systems at C,. The coupling constants of protons in analogous fi positions in alkyl and ally1 radicals in liquids are known to obey the relation A=Ao+5kosW,
A approaches-40 + ;B. As the temperature is lowered, ri will increase for radicals with equilibrium conforma‘tions having 00 < 45”, and decrease for 45 < 8, < 90”. For the three protons bia methyl group,A is normslly nearly temperature independent and corresponds at not too low temperatures to the free rotation value [14,15] due to the threefold symmetry of the group. In a classic study of internal rotation ti alkyl radi. cals  Fessertden has shown that eq. (5) is equally valid for deuterons in &positions, and that the constants A,, and B are equal for protons and deuterons if the ratio of magnetic moments is taken into account properly. We thus may expect eq. (5) to hold for our radicals with p.muons also and to be applicab!e in the assignment procedures.
where A, and B are constants (B >_4,) and 0 < 0 < 90” is the dihedral angle between the axis of the porbital at C, and the Cp-H-bond [Is]. The observed coupiing is a statistically weighted average over conformations with different 0. It depends on the synmetry and the height of the potential barrier to internal rotation about the C,-Cp-bond, on the reduced moment of inertia, and on temperature. In the high temperature limit, where rotation is essentially free,
For ethene the radical must be the muonium substiiuted ethyl radical, of course. We note from table 1 that, in contrast to A,: the muon coupling decreases markedly with increasing temperature and exceeds A, substantially at al! temperatures. In terms of eq. (5) this behaviour is qualitatively explained by assuming BO(hlu) = 0”: i.e. equilibria with the C+u-bond eclipsing the ztis of the p-orbital at C, and by a rather large barrier to internal rotation. An excellent fit of the temperature dependence to the empirica! relation AI(T)[email protected]
x [I - exp(-&/XT)]
was found withA;(T= -) set equal to the value ofAp. It converged atA’C,(T= 0) = 153.5 MHz and E, = 270 c%!/mol. From eq. (5) one \vould expect A:,(T = 0) x 2 A;(T= m) = 150 MHz. lXs agreement indicates that the constants d,, and B of eq. (5) do, in facr,
Table 1 Radicals from erhene, pmpene and 2-methY propeW --Olafin
A; (MHz) b, _----
111 120 140 162 182 298 9i 119 163 298 134 156 190 215 247
i30.8 128.7 124.2 120.0 116.7 104.1 d)
119.4 110.1 93.5 d, 116.9 111.8 105.4 100.6 96.0 93.3 91.7
Ap (MHz) =I
a) -2 1;.
b, +O.l hlHz. ‘1 Nearly rcmpcnture independent.
d, Evtrapohted via cq. (7), see test.
change with isotopic substitution only through the change of magnetic moments. From ref.  we note that the deutetium substituted ethyl radkal CH2DCH2 has Be(D) = 90’ and that CHD2eD2 .sbows On(H) = 0” and a decrease of A, with increasmg temperature. This tendency ofH to avoid the plane of substituenis at C, has been attributed to a higher cffectivc (van der Waals) radius of H compared with D and caused by larger amplitudes of mclecular vibrations of the C,-H-bond. Thus, the lighter isotope experiences a higher and the heavier a lower degree of steric hindrance ivhen it eclipses the substituents. The muon coupling constant of with these findings and Ci-1~Mu~H2 is in agreement supports the previous esplanarions j16]. Further, ihe lnrge ?emperature dependence points to Ixger \i.brationa! effects of muonium on the rotational barrier. A fuil analysis of the temperature dependencies of coupling constants of various isotopica!ly substituted ethyl radicals along the lines of refs. [16,19] is in progress. Preliminary results support the interpretation and lead to quantitative barrier parameters. At comparable temperatures the muon coupling constants of the radicals found fWethcne, propene and 2-methylpropene hecrease in this order (table !>.
The same order is observed for the CH3-coupling constants of ethyl, 7--propyl and tert-butyl radicals and is ascribed to increasing hyperconjugative delocahzation of the unpaired electron onto the methyl goups [lS]. Consequently, we identify the radicals from propene and 2.msthyl propene as muonium substituted 2propyl and tert-butyl radicals, respectively. This is supported by excellent tits of the temperature dependencies ofA; to eq. (7) obtained when A;(T= mj wasset equal to the values of.49. Furthermore, the alternative choice of muonium addition would lead to the primary radicals tH3CHMuCH3 and ~H;Chiu(CH3)2, the p&n counterparts of which having coupling constants of the P-protons larger than those of the CH3-proteus of ethyl [ 131. Fig. 2 shows the temperature dependencies ofdk for three isotopically substituted tert.butyl radicals CH,XC(CH,),, X = Mu, H, D. Whereas An is near!y temperature independent  kt; decreases strongly and Ai increases weakly [2 11 with increasing temperature. As discussed for the ethyl radicals the equilibrium conformations have 6,(Mu) = 0’ and 0,(D) = 9Oa, ?he large isotope effect and temperature dependence of.4; again calling for a large rotational barrier for the CHZMu.group. Finally, we note from the data in table 1 that at
E. Roduner et a1. / Muonium subrh’tu;ed orgmic free rcdicols i)~lipids
room temperature the ratio AL/A, is 1.38 for ethyl and isopropyl
and 1.44 for tert-butyl.
3.3. Frcr#zer radicals from temzirralo!efi,u
Fig 2. Temperature
Table 2 presents muon coupling constantsd; for radicals obtained from a variety of terminal olefins CH2 = CR, R2 at roo,n temperature arid the radicals assigned to then. For the compounds of the first three goups the formation of primary (CH2ClTMuR) and of secondary (CH2hiukHR) radicals is possible. However, only for allylpropyl and diallyl ether two different radicais were observed, the more abundant radicals hating the lower muon coupling constants. A comparison of
the va!ues with the coupling constarits of ethyl and 2.
extrapolated to room temperature (table 1) immediately suggests the identification of the less abundant radicals 2s primary (.CH2CeuR) and the more abundant as secondary (CH2MuCHR) species. propyl
T’cble 2 Radicals
Okfm allylpropylether allylpropvlether diz!Uylether diallylerher
Ai, (4!Hz) CH2=CHCH,0CH2CHZCH3 CH2=CHCH20CH~CH1CH~ CH2=CHCH2C’CH2CH=CH, CH,=CHCH,C?CHtCH=CH2
105.7 99.2 102.S 97.4
c) c) e) e)
r[:;; z d)
99.7 h) 86.6 83.5 57.0
69.7 67.2 64.4 iO.l
1251 WI [7,271
CH2=C(CH3)C3H5 CH2=C(CH3)C00CH2CH3 CH~=C(CHJ)COWH~CH~
CH2=CHCOOCH2CH3 CHI=CHOCOF13 CH2=CHCN CH5=CHC6H5
91.4 96.7 97.5
CI12=CHCH20CH2CH3 CH2=CH(CH2)$H=CH2 CH2=CHC(CH&
69.5 71.2 69.5
allylshylather heptadiene-1,6 3,3dimethylbutene-1 butene-14 01 bu tene-l-3 01
vinylacetate acryloaitrile styrene
a) (293 i 5) K unless noted otherwise. d)A D is @W-I for the r+red CH2CH2CH20H. h) (33 z 2) K. c) AL ti given for CHjCHCH2CH,CH=_. ‘) Ap k given for CH3k(CH3)COa’Hs. k) (570 * 2) K.
C~-M~U~(CH~)C~H~ CH2MuC(CH3)COOCH2CHj cis + tram isomers
,we~ for CH$HCH20H. i) Ap is given for CHJCHCOOCH3.
This assignment is supporkd further by the ordering of the corresponding proton coupling constants (table 2). Uskg the same reasoning we identify the radicals found for the second group of cornpounds ir? table 2 as being of type CH2MukHR with R = alhyl. Their muon couplings are all in the narrow ranSe of 96.5-9’7.5 MHz. The radicals found for the compounds
of the third group are also identified as secondary species CH2MuCHR, but here R is not an alkyl group. -4s the proton coupling constants of the ana!ogous hydrogen radicals, Al decreases in this group in accord with an increasing deiocalization of the unpdred.electron spin onto the substituents. The values ofA; ru!e out other rsdical structures expected for muonium addition to carbon-heteroatom bonds or to the benzene ring of styrene since they are not compatible with known values for correspondinS species [S,10,12,13]. Comparison ofq; and Ap for all secondary radicals of type CH2MuCHR of table 2 reveals the rather narrow range 1.30
Table 3 Radicals
okfins ___. -_-
CE,CH=CHCH2CH3 CEjCH=CHCH$X3 CE$X=CHCH20H C!+CH=CHCH20H
butcnc-2401 butane-2-l butene.?-l,3
2.3-dimcthylbutcna-2 2,4,4-trimethy1pentene-Z. 2-methylbutene-2
‘) (293 + 5)
3.4. Radicals from nontemzinnI
95.9 90.4 96.4
’ Dr. A.
Hill, CERN, Ger,ex~, has kindly informed the observaiion of the radiul from styrene md
MHz which we believe CH2hIu~(CH3)COOCH3.
to be the cis- and trans-isomers
CH3kHCH!+KH2CH3 CH;CHMuCHCH2’& CH3CHCH+CH20H CHjCHVuCHCH20H
(CHs)2~Cbtu(CHa)2 (CHs)sCSfukHC(CHa)a ‘) (CH3)ZCCHhIoCH3
d, (2SB k 2) K.
of two radiuls from methylmethncrylate with AL = 84.8 and 87.0
‘) AssiSnmcnt tentative, see test.
The first group of entries in table 3 refers to radicals from olefms of type R1CH=CHR2 with RI, R, f H. -4s expected, only one radical appeared for the symmetric diol, R, =R7=CH,0H, and two radicals with similar abundancies were found for each ofthe unsymmetric compounds. The assignments of the latter are based on the order of the proton coupling constants of the H-analogous species. The radical formed from 2,3dimethyl-butene-2 has
cis- and trans-isomers of the radical formed by addition to the CHl-group *. This is noteworthy since radicals of type (CH3)2CCOOR have been reported to show magnetically equivalent CH3-groups at room temperature [ 141. However, the previous ESR results were obkined with low resolution. Therefore, we have remeasured *lhe ESR-proton coupling constants of (CH3),CCOOCH2CH3 and now fuld the CH3-groups inequivalent by 2.5 MHz, which confirms the assignment ofA;. INDO-calculations further suggest that the larger coupling is due to the CH2Mu-group trans to the carbonyl oxygen, as in alkanoyl radicals 1301. The isotope effect A; jA, of the tertiary radicals of table . 3_ is 1.43 f 0.03.
E. Rodurrer et 01. /diuonium subrti;u:ed orgmic free rudicclr ir?liquids
been assigned unambiguously in a previous publication [ 13]_ Both A; and Ap increase with increasing temperature [19,31]. This suE*ests that Bu(H. Mu) = 90’. However, the temperature dependence of.4; (x1.2 MHz/l00 K) is considerably smaller than that afAp (~5.6 XiHz/lOO R). Further, the value ofAL is closer. to the high temperature limit, estimated from (CH,),C as ~63.7 MHz, thanAp. These fmdings both suggest that the barrier to internal rotation is smaller for the muonium substituteli radica! than for the H-analogue and reflects the larger effective radius of Mu mentioned before. From 2,4,4-trimethylpentene-2 a radical with a low A; and a positive temperature dependence (-2.7 MHz/ 100 K) was observed pointing to 0,(Mu) > 45”. This is compatible,with the structures (CH&MuCCHC(CH3); and (CH3)2CCHM~C(CH;)3 for w_hich O. = SO” and 8,, = 60’ are cxpected.Although an unambiguous assignment cannot be given we prefer the former structure since Al is very sir-nilar to the value for . (CH,)#CMu(CH,), 2Jvlethylbutene2 leads to a radical with a rather large A; which eliminates a structure like (CH3)21$rCeHCH3 and suggests the identification as (CH&CCHMuCH;. At 253 K Al was found to be 52.3 MHz. Both the values of_4;, which are larger than the esrimated high temperature limit (63.7 MHz) and the negative temperature dependence of A; require !YO(Mu)< 45”. In contrast,Aip is smaller than 63.7 MHz and increases with increasing temperature [24,32]. This indicates Bu(H) = 60” for the H-analogous radical. Obviously, the locations of the barrier minima change for this case on substituting H by Mu. With respect to steric repulsions Mu seems to be more like a CH,- than 2 H-substituent, in keeping with the larger effective radius. 3.5. Rudicak from dienes Nine butadienes with different methyl substitutions were studied. As table 4 shoivs, one radical w2s observed for each of the compounds butadiene, 4-methylpentadiene-!,3 and 2,3_dimethylbutadiene whereas two radicals were found for each of the remaining six compounds. The coupling constants of most of the radicals are within the range 49.9
temperature, and two radicals have high values of A; and 79.0 MHz) with negative temperature ccefficients. To assign the radicals we note that for each diene several possibilities exist: Muonium can add in principle both at the end and the central carbon atoms of the diene system. The first process leads to ally! type radicals with muonium in CH~Mu-, CH3CHMu~ or (CH&Mu-substituents: either in endo- or eso-positions. Addition at the central carbon atoms gives alkcl radicals, and inspection of the dienes reveals that of these eight would be primary (RI R2CMubH2), three secondary (RCYMu~HCH3) and three tertiary [RCHMU~(CH;), I. Using the resuits of the previous sections we first consider the formation of alkyl type radicals. As tables 1 and 2 show primary species have A; > 100 MHz at 300 K. None of the values of table 4 is in that range. This excludes the fom?ation of ptiaary alkyl radicals. Secondary radicals of type RCHMuCHCH3 should have A; = 93 MHz near room temperature (tab!e 3). This leads to the immediate identification of the radical from hexadiene-2,4 with A; = 0 1.7 &lHz (R1 in fig. 1). Further, a tertiary species of type RCHMUL’(CH~)~ hasAL = 79.C MHz at 285 K (table 3). One radical found for 2,5dimethylhexadiene-2,4 has this same value at 300 K and is assigned correspondingly. Thus, of the 14 alkyl type radicals expected only two are observed, and the remaining radicals of table 4 must be allylic species. This is in general agreement with the order of ma_gnitude of the coupling constants Al: Proton coupling constants of CH,,groups at the terminal allylic carbons are known to be about 33.6-42 MHz and to represent free rotation values. CHahlu-groups in the same position are expected for allylic radicals from the first seven compounds of table 4. As in the previous sections AI should not represent free rotation, should exceed A, by about 30-40% at 300 K and approach.4P with increasing temperature. Thus, muon coupling constants of 43 6_41< 59 MHz are expected which decrease with increasing temperature, as is observed. The same ranges hold for the radicals with CH3CHMugroups. The allylic radical expected from 2,5dimethylhexadiene-2,4 has a (CH,),Mu C-group for which 0,,(Mu) = 90’ is probable. Consequently, AL should be low and increase with temperature. Again, this is as observed. Consequently, the ally1 radicals must have the structures given in table 4. However, we still have to (PI,7
Table 4 Radkals from conjugated -~--
et al. /M~oniuumslrbrtitutcd
dienes at room temperature --___
~~ Ap (MAz)
A; (MHz) 3
to.1 MHz. ‘) The asteris); dL’rlotcs the c) .-Ip not known. ‘I) Skewed s-tnns and s-cis ‘1 A clCn for the ESR observ;ltion and for a non-plarur f) Ap is more typical for nn endoCH3 group [do].
-position of muonium. confwrstions. structure of this radial [38,39] was revised . g) Ap given for (CH3)2CHCH=CHeH2.
E. Roduungr dt al. /Aiuonium mbriiiured
consider their configurations. Unless severe steric hindrance interferes, as is the case for heavily tert-butyl substituted species , the central skeleton of ally1 radicals is planar. Further, the isomerization rate of lmethylallyl is less than lo2 s-l for T< 273 , so ‘&at the muonium substituted radicals should be configurationally stable during the muon lifetime (2.2 gs). This leads to wo possibilities for the configuration of each of the ally1 radicals expected from the dienes: The muonium containing group can be either exe- or endo with respect to the allylic skeleton. The proton coupling const~ants of corresponding exo- and endo-groups are quite different. For instance, for 1 -methyl ally1 A ,(CH,,exo) = 46 .O MHz and A,(CH3, endo) = 39.2 MHz . Therefore, we expect a similar difference in Al for exo- and endoCH7Mu- or other groups. For most of the parent dienes of table 4, with the exception of 2,4&nethylpentadiene-I ,3, the planar trar;sconfiguration is thermodynamically favoured and dominant at room temperature [42-441. if this configuration is conserved during muonium addition the muonium substituted groups become exo-substituenls for most of the dienes. 2,SdimethylpentadieneI :3 has been claimed [@I to exist in two skewed conformations resembling cis- and transforms. Thus, for this compound muonium may be found incorporated in eso- and endo-groups. Although muoniurn addition is highly exothermic and configurational scrambling may seem reasonable, we believe that it does not take place because of the following reasons: For the symmetric dienes butadiene, 2,3dimethylbutadiene, hexadiene-2,4 and 2,5dimethylhexadiene-2,4 only one allylic rype radical was observed. If scrambling had occurred one would have found two isomers, in particular fo,r 2,3-dimathylbutadiene where they must be nearly isoenergetic. ?herefore, we base the coniigurationa! assignments given in table 4 on the configurations of the starting materials. This is supported further by a variety of trends. (1) As the values ofAp for exoCH3-protons of table 4 reveal introduction of methyl groups at either ends of the allylic system decreases A p by about (2.4 5 0.7) MHz on the average. On the other hand, methyl substitution at the central carbon causes a smaller increase. Since for all casesAp corresponds to the free rotation value these effects are due to changes of spin populations by delocalization onto the methyl groups,
or2mic free rcdicrls 81 l&ids
the relative _ma_titudes reflecting the distribution of spin populations in ally1 radicals , The muon coupling constants of CHZMu-groups do not represent free rotation values. Nevertheless, we still except a decrease ofAL with methyl substitution at the remote carbon atom since this should not alter the, rotation barrier and since the raiioAljAp for CH?Mu-groups was found to vary only little with radical structure (sections 3.2 and 3.3). In fact, the assigned coupling constantsAL of ally1 radicals show the espected trends: Methyl substitution at the remote carbon decreasesAl by (2.2 i 0.S) MHz on the average. Further, likeAP, the muon coupling decreases on methyl substitution at the adjacent carbon by (1.9 + 0.9) MHz On the other hand: methyl substitution at the central carbon causes an increase. This increase is larger than expected on the basis of the values ofA,. However. molecular models show that exo-methyl or e:hyl groups suffer steric I;indrance from a methyl group at the central carbon whereas there is little interaction with a seminal methyl group. Therefore, we ettribute the large increase to effects on the internal rotarion. On the average, the isotope ratio for ally1 radicals with CHzMugroups isA;/Ap = Z.34 f 0.05, i.e. identical to that found for a!kyl radica!s (sections 3.2 and 3.3). (2) INDO-calculations were performed for Ap of exo$-protons of ally1 radicals using a standard program and standard geometries . The proton COUpling constants of the CHS-protons of l-methyl a!lyl were calculated Lo fol!ow the co$B-law [eq. (j)] nearly exactly (m&mum deviation 0.5% at 9 = 30’). Tlierefore,A40 andB for b-protons of other ally1 radicals were obtained from calculations for two orienrations only assuming the co&-law to be vslid. Table 5 shows that A0 is small compared to B for al! radicals. For ethyl protons negative vaiues were fouad. The variations in B with radical structures are more significant and reveal the trends in the experimental values ofAL andAp (table 4). Table 5 also displays (cos’0) values [email protected] the muonium substituted radicals calculated from AL, A0 and B via eq. (5). We expect the values to bt rather similar for all radicals with similar environments of the muonium location which appears to be the case. Finally, as expected, radic& with negative temperature dependence ofAj, have (COSTS}> 0.5, and the radical with the positive temperature dependence [(CH&MuC-group] has (cos20) < 0.5.
Table 5 INDO results for allylic radicals
=)~COS’20) = (.4;l -
(2) For non-terminal olefms (table 3) muoniu,m addition occurs preferentially at the less substituted carbon of the double bond. (3) For dienes, addition. to end carbons to yield the thermodynamically more stable ally1 type radicals is normally preferred compared to addition at the central carbon leading to alkyl species. The latter process occurs if the end carbon atoms both carry methyl substituents and the center carbons do not (hexadiene-2,4; 2Sdimethylhexadiene-2,4, fig. 1). Interestingly, for 2,4-dimethylpentadiene-1,3 we find a dominance of the radical with the lower coupling constant (table 4). This radical should be formed frcm the skewed cisisomer of the parent compound. In fact, it has been found experimentally that this isomer is slightly more stable than the trans compound  whereas calculations suggest the opposite [a]. The trends found for muonium addition follow those for addition of thermal hydrogen atoms  _ Thus, these may be used as auxiliary guidelines in the identification of muonium substituted radicals. However, we do no: infer that the precursor of the radicals observed is necessarily thermal muonium. For the case of 2,3-dimethylbutene-7 this was demonstrated previously [ 13] but it may not hold for al! compounds studied here. Furthermore, even hot hydrogen atoms add to about 70% at the terminal carbon of butene-1 [49 1. Future studies of asymmetries on the radical frequencies and their field dependencies  should distinguish between the various possible pathways for radical formation: Addition of thermal or epithermal muonium or of muons with subsequent rapid neutralizarion of the primary carbocation.
Acknowledgement 4. Selectivity of muonium addition The radicals identified in the previous sections are 311formed by formal addiiion of muonium to double bonds. The following trends can be stated: (1) For terminal oletins of type CH,=CR, R, (Rz + H) muonium addition occurs exclusively, or at least predominantly (allylethcrs’), at the unsubstituted carbon atom. This also holds for styrenc where addition to the aromatic ring could have been expecTed since radicals formed by muonium addition to benzene rinks have been identified [8,1O,i3].
This work is supported by the Swiss Nationa: Foundation for Scientific Research and the Swiss Institute for Nuclear Research (SIN).
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