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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
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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
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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
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Vol. 14, No. 1-4 89
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4: Field dependence of the Larmor peak and the
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
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90
Bulletin of Magnetic Resonance
G)z-100"FREQUENCY/kHz
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
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Vol. 14, No. 1-4 91
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FREQUENCY/kHz7: Field dependence of the Larmor peak and the
z sidebands in partially deuterated dimethyl sul-
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