86 Bulletin of Magnetic Resonance

Coupled methyl groups in dimethyl sulphide

M.R. Johnson, S. Clough, A.J. Horsewill and I.B.I. Tomsah

Department of Physics, University of Nottingham, Nottingham. NG7 2RD.

AbstractLow field methyl tunnelling spectra of dimethyl sulphidehave been measured using field cycling NMR and indicatethe existence of two distinct methyl groups with tunnel.frequencies of 100kHz and 750kHz. Spectra show a sig-nificant broadening of the Larmor peak at those fields atwhich the Larmor and tunnel frequencies are equal. Theseare resonances between the rotational and spin dynamicsof the methyl groups. An associated" change in the inten-sity and position of the 100kHz sidebands suggests thatmethyl group coupling may be responsible for these ef-fects. Narrow 100kHz sidebands are restored by irradiat-ing with an external RF field of this frequency which wesuggest is due to decoupling of the rotor pairs. Measure-ments on partially deuterated dimethyl suphide show thatthe coupling cannot be intra-molecular.

1 IntroductionThe methyl group tunnel frequency wt depends on theheight of the potential barrier hindering rotation due tothe molecular environment. Three stationary states aredistributed equally in three potential wells and form anenergy singlet and doublet split by ftwt. Excitations con-sist of a superposition of a pair of eigenfunctions to forma partially localised wavepacket which rotates in a defi-nite sense at a frequency given by the energy splitting,ie ±wt or 0. With the aid of external fields the rotationfrequency of a wavepacket can be changed by exerting arotational impulse her. The rotation frequency is then de-termined by the difference between two of the three val-ues (2w where i , y and z are the spin states, a or /?, at ,,proton sites which are defined by the hindering P°ten.*|[1]. The protons themselves are each equally ditbufr

Vol. 14, No. 1-4 87

between the three sites satisfying proton indistinguisha-bilitj. In this represenoation the matrix elements cf thetunnelling interaction reflect the balance of clockwise andanti-clockwise rotation of an undriven methyl group.

< xyz\HR\zxy >=< zxy\HR\xyz >= A (2)

A is the overlap integral between states localised in neigh-bouring wells of the three-fold hindering potential.

Away from the anti-crossings the methyl group eigen-states are linear combinations of the localised states andare the delocalised representations of the Cz symmetrygroup,

1 [\xyz> + exp(t2irn/3)\zxy (3)

(4)

where n = 0 for an A-state and n = ±1 for Ea and £&states. Temporarily ignoring the dipole-dipole interaction,these symmetrised states have energies

E{\, m) = u>Lm - 2A cos(2;rn/3) (5)

where OIL is the Larmor frequency and m is the spin com-ponent of \xyz > in the direction of the magnetic field.Mixtures of these eigenstates are partially localised, ro-tating wavepackets which have energies resulting from thedifferences between the rotational and magnetic energiesof the component states E(Xi,rm) — E(Xj ,mj). Magneticand rotational wavepacket energies add when the Larmorprecession and the rotation have the same sense and theysubtract when these senses are opposite.

The exact eigenstates and eigenvalues of the methyl' group in the magnetic field are calculated numerically by;:"'diagonalising H. The field dependence of the energy levelsMis shown in figure 1. The level anti-crossings can be seen^ . 1.2 and 2.4mT for the 100kHz methl group and 8.8 and|17.6mT for the .750kHz rotor, where the A and E sym-

metry states reflect off each other and exchange symme-due to the finite non-secular parts of the intra-methyl

1 dipole-dipole interaction.a energy levels diagram of figure 1 can be transformed1 diagram of energy differences, or wavepacket ener-

|..as shown in figure 2 from which frequency spectra atmagnetic fields can be predicted by taking hor-

sections. In this way the level anti-crossings aremanifest themselves as resonant motional broad-

M the Larmor peak. Symmetry mixing at thesings results in stationary wavepackets with en-

Pjroportional to u>£ evolving into rotating wavepackets~"Tgy Proportional to wfc (x to y in figure 2). This

he ability of the non-secular parts of the dipole-raction for converting spin angular momentum

•tional angular momentum of the methyl group.

A(3/2)

^(-3/2)

A(-3/2)

18 B(mT)

Figure 1: Energy levels of dimethyl sulphide in a magneticfield showing resonances between tunnelling motion andspin dynamics as level anti-crossings at 1.2, 2.4 ,8.8 and17.6mT

15-; '1:-.

10-

Reld(mT)

5 - • .?• .:•?" ,v*

0 S~=r200 400 600 800

Frequency(kHz)1000

Figure 2: Field/frequency plane of dimethyl sulphideshowing resonant broadening of the Larmor peak at thelevel anti-crossings, notably at 9mT and 18mT

88 Bulletin of Magnetic Resonance

3 Low field, field cycling experi-ments

Measuring magnetisation at low field using a Faraday lawdetector results in poor signal to noise. Thus in order tomeasure a low field frequency spectrum either a differenttype of detector [5] or a different technique such as fieldcycling must be employed. Field cycling has been usedin this investigation. Each cycle of the experiment be-gins with the preparation of a standard magnetisation bydestroying all magnetisation with a train of 90° pulses fol-lowed by the preparation period of 20 seconds in a fieldof 0.6T, The field is then switched rapidly in about 2 sec-onds to the chosen magnetic field where the initial mag-netisation is destroyed by spin-lattice relaxation by anamount proportional to the relaxation, rate T{~ and thetime at low field, 15 seconds. Anomalously rapid relax-ation can be stimulated by an external RF field of scan-ning frequency / if this frequency matches the character-istic wavepacket frequencies in figure 2 and can thereforeexcite these wavepackets. The remnant magnetisation ismeasured by a single 90° pulse after a rapid field switchto 0.6T. The cycle is repeated increasing / each time, pro-ducing a frequency spectrum which is a flat plateau inwhich holes are drilled where f is equal to the frequenciespredicted in figure 2. These spectra are inverted to givepeaks for presentation.

A slightly more complicated experiment entails the ap-plication of a second RF field of fixed frequency fsU atlow field , which is applied on the same coils as the scan-ning field in an alternating sequence of short bursts of 0.5seconds of each field. This is a stirring experiment whichmay affect the intensity of spectral peaks by depopulatingenergy levels and enhancing transitions which would oth-erwise become suppressed as the populations of the initialand final states become equal [6].

4 Sample preparationDimethyl sulphide was obtained from the Aldrich Chem-ical Company and was used in an unsealed sample tube.The deuterated sample was prepared in the Chemistry De-partment by mixing aqueous solutions of CHzS~ No. andCD2I as outlined in [7]. It was also used in an unsealedsample tube.

5 Low field frequency spectra ofdimethyl sulphide

A typical low field spectrum of dimethyl sulphide, mea-sured at 3.5rnT, is shown in figure 3 and it is in excellentagreement with the corresponding slice through figure 2,indicated by the broken line. The Larmor peak occurs at175kHz indicating a true magnetic field of 4.1mT and theAm = 2 version of this peak occurs at 350kHz. These are

250 BOO 750 1000Frequency [kHz]

1250

Figure 3: Frequency spectrum of dimethyl sulphidemesaured at 3.5mT

labelled 1 and 2 respectively. They are each flanked by apair of 100kHz sidebands (labelled 1± and 2±) and alsoby a pair of 750kHz sidebands (labelled 1± and 2±). Sincethe Larmor frequency is much smaller than the larger tun-nel frequency, the reflected low frequency sidebands giverise to a 750kHz spectrum which appears as a Am = 0peak split into five peaks, each separated by the Larmorfrequency.

Frequency spectra of dimethyl sulphide have been mea-sured at many magnetic fields up to 35mT and a selectionof these are shown in figure 4. The spectra are aligned bytheir Larmor peaks and only the frequency range incorpo-rating the 100kHz sidebands is covered. Away from thelevel anti-crossings of the 750kHz rotor, that is below 7mT,between 10 and 14mT, and above 20mT, the Larmor peakand sidebands are well defined and reasonably symmet-rical. However in the vicinity of the level anti-crossings,between 7 and lOmT and between 14 and 20mT, this dis-crete structure is lost as the Larmor peak broadens, thelow frequency sideband virtually disappears and the highfrequency sideband is poorly defined. Where a frequencyseparation of the Larmor peak and a sideband can be de-termined it is apparent that rotation frequency of thesewavepackets is less 100kHz and is sometimes as small a?70kHz. . 1

Although these effects occur at the level anti-crossingof the 750kHz rotor, the field range over which they occ^and the extent of the frequency broadening are too grêfor them to be explained by dipolar broadening alone. Fulthermore the the dramatic change in the sideband mteisity and frequency is not predicted by the dipole-dipole"teraction. That it is the 100kHz spectrum which is so pr'foundly affected by the level anti-crossings of the 750Krotor suggests that these spectra may be evidence of sp

Vol. 14, No. 1-4 89

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coupling between the 100kHz and 750kHz rotors.The 100kHz sidebands can be restored in a stirring ex-

periment with an external RF field with a stirring fre-quency of 100kHz, as shown in the spectra in figure 5. Itappears that stirring at 100kHz drives rotation of methylwavepackets at this frequency and therefore prevents cou-pling which has been seen to modify this frequency, asshown in figure 4.

In order to probe the methyl group coupling a par-tially deuterated sample of dimethyl sulphide, in whichone methyl group per molecule is fully deuterated, wasinvestigated. Figure 6 shows a low field spectrum of thedeuterated sample measured at 4mT which is very similarto the spectrum of the fully protonated sample shown infigure 3, one difference being the increase in the large tun-nel frequency from 750kHz to 780kHz. Field dependentspectra of the deuterated sample covering the frequencyrange which incorporates the Larmor peak and the 100kHzsidebands are shown in figure 7 and they too are almostidentical to the spectra from the fully protonated sam-ple of figure 4. It therefore appears that the coupling ofprotonated rotors persists in the deuterated sample, sug-gesting that the packing of the molecules in the solid re-garding the relative positions of protonated and deuter-ated methyl groups is random. Deuteration reduces thenumber of coupled protonated rotors and slightly distortsthe packing of the molecules, decreasing the magnitudeof the hindering potential of the 750kHz rotor which be-comes 780kHz rotor. These spectra indicate clearly thatthe anti-crossing effects cannot arise from intra-molecularmethyl group coupling since each molecule has a proto-nated and a deuterated methyl group. One new feature ofthese spectra which may arise from coupling of protonatedand deuterated rotors is a small, sharp, field independentpeak at 200kHz which is indicated by a V in figure 7.

6 Discussion - Coupled rotatingwavepackets

Tunnelling of small molecular rotors like CH3, CH4 andNHf is generally single particle in character. Few exam-ples exist,of coupled tunnelling of rotors (see [8] and refer-ences therein) perhaps the most notable example being ofcoupled methyl groups in lithium acetate [9]. In both ofthese papers the coupling of methyl groups is mechanical,being propagated by the modulation of the hindering po-tential which has the three-fold symmetry of the individ-ual methyl groups. The coupled states of the system are adirect product of the symmetrised eigenstates of each ro-tor. Lithium acetate has weakly hindered methyl groups,the tunnelling spectrum of the coupled system has beenobserved using neutron scattering, and it is thought thatsuch a coupling is unlikely to be observable in strongly hin-dered methyl groups, although the computational methodin [8] has been extended to consider such systems.

This kind of coupling is in stark contrast to that seen

90

Bulletin of Magnetic Resonance

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Figure 5: Stirred spectra of dimethyl sulphide showing 'restoration of the 100kHz sidebands

O 250 BOO 7S0 1000 1250Frequency (kHz]

Figure 6: Frequency spectrum of partially deuterateddimethyl sulphide mesaured at 4mT

in dimethyl sulphide. An analysis in terms of uncoupledrotors was pursued in previous sections because first, thecoupling only occurs at those magnetic fields correspond-ing to level anti-crossings and secondly, the form of thespectra indicate that the coupled states are not simpleproducts, with three-fold symmetry, of the eigenstates ofthe individual rotors. Furthermore, these methyl groupsare very strongly hindered in comparison with the methylgroups in lithium acetate.

It is noted from figure 2 that at the level anti-crossingsthere is a matching of the frequencies associated withthe rotational and magnetic evolution of the states ofthe 100kHz and 750kHz rotors. If the stable states ofthe methyl groups at these magnetic fields are rotatingwavepackets then the frequency of evolution of the spinson each proton site is modulated by the rotation in a waythat depends upon the composition bf the wavepacket.For example a coherent mixture of A and Ea states withthe same spin quantum number is a partially localisedwavepacket, which precesses clockwise at the tunnel fre-quency and consequently modulates the longitudinal com-ponent of the spins at this frequency. A similar mixedsymmetry state, but composed of states with spin quan-

n e turn numbers differing by unity modulates the transversecomponent of the spin states at each proton site at a fre-quency equal to the Larmor frequency plus or minus thetunnel frequency, depending on whether the rotation andLarmor precession have the same or opposite senses. Thus,providing the proton sites of the two methyl groups arftclose enough together, the rotational motions may bepled by the spin dynamics and angular momentum maytransferred between the groups. This results in an imbance of clockwise and anti-clockwise rotation, the uniclu

Vol. 14, No. 1-4 91

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tunnel frequency being replaced by a pair of discrete rota-tion frequencies. A reduced rotation frequency is clearlyobserved in figure 4.

Taken as evidence not only of coupled methyl groupsbut also for rotating wavepackets at 4K, these results arevery significant. The wavepackets do not have three-foldsymmetry which throughout the history of methyl dynam-ics has wrongly been regarded as an essential prerequisitefor satisfying the indistinguishabilty of the methyl protons(e.g. [10]). Each basis function \xyz > accomodates pro-ton indistinguishability since each proton has an equal am-plitude at each proton site and therefore any combinationsof these functions, ranging from delocalised states whichressemble spin symmetry species to completely localisedfunctions, satisfy proton indistinguishability requirements.

7 AcknowledgementsThe authors are grateful to the B.P. Venture ResearchUnit for supporting this work. I.B.I.T. would like to ex-press his gratitude to the Sudanese government for hisfellowship. We would also like to thank Dr D.K. Knightof the Chemistry Department for preparing the deuteratedsample.

References[1] S. Clough, A.J. Horsewill, M.R.Johnson and

I.B.I.Tomsah (1992) submitted to Molec. Phys.

[2] P.J. McDonald, G.J. Barker, S. Clough, R.M. Greenand A.J. Horsewill (1986) Molec. Phys. 57,901

[3] S. Clough, A. Heidemann, A.J. Horsewill, A.J. Lewisand M.N.J. Paley (1982)J. Phys. C 15,2495

[4] S. Clough, A.J. Horsewill, P.J. McDonald and F.O.Zelaya (1985)Phys.Rev. Lett. 55,1794

[5] C. Connor, A. Chang and A. Pines (1986)Rev. Sci.Instrum. 61,1059

[6] M.J. Barlow, S. Clough, P.A. Debenham and A.J.Horsewill (1992)J. Phys. C 4,4165

[7] L.Pierce and M. Hayashi (1960)J. Chem. Phys. 35,479

[8] W. Hausler and A. Huller (1985) Z. Phys. B 59,177

[9] S. Clough, A. Heidemann, A.J. Horsewill and M.N.J.Paley (1984) Z. Phys. B 55,1

[10] J.H. Freed (1965)J. Chem. Phys. 43,1710