Study of Molecular Motion in Liquids by Measurement ofNuclear RelaxationBY R. A. DWEK AND R. E. RICHARDSPhysical Chemistry Laboratory, OxfordReceived 23rd January, 1967Nuclear magnetic relaxation times depend on the strengths of the magnetic components of randommolecular motion at nuclear or electron resonance frequencies. The methods by which these spectraldensities can be obtained are outlined. Measurements of correlation times for different types ofmolecular motion and their dependence on temperature are reviewed.Magnetic resonance methods may be used to study molecular motion in liquidsand in suitable cases can provide detailed information about specific interactionsbetween molecules in the liquid phase. In this paper the principles involved in suchstudies are set out in an attempt to illustrate the scope and limitations of the method.Molecular motion in liquids directly affects the nuclear relaxation times TI andT2.The spin lattice relaxation time TI is a measure of the time taken for the nucleito achieve an equilibrium population among the allowed energy levels in the appliedmagnetic field HO ; it is sometimes referred to as the longitudinal relaxation time as it isconcerned with the relaxation of the nuclear magnetization along the direction of theapplied field Ho, usually called the z direction. TI is a measure of the time requiredfor the nuclei to exchange energy with their surroundings. The spin-spin relaxationtime T2 measures the time taken for nuclei to exchange energy among themselves byan adiabatic process ; it is sometimes referred to as the transverse relaxation timebecause it is concerned with the relaxation of the nuclear magnetization in thetransverse (xu) plane at right angles to Ho.In liquids, TI and T2 are usually nearlyequal, but in some special cases their differences can give valuable information.It is convenient to consider first the mechanism of spin lattice relaxation for asystem of nuclei of spin 3. In an applied magnetic field HO these nuclei are distributedbetween two energy levels, which by convention we label + (lower) and - (higher),and which correspond to the two allowed orientations of the nuclear magnets in Ho.When radiation of angular frequency mn is applied to the system in the appropriateway, transitions are induced among the energy levels ; the probability of a quantumof radiation inducing an upward transition is the same as for a downward transition,so a net exchange of energy between the nuclear spins and the radiation can onlyoccur if the populations of the two nuclear energy levels are unequal.If the lowerenergy level has an excess population (as it would have at thermal equilibrium) thenenergy is absorbed from the radiation, but if the upper energy level were more highlypopulated for some reason, then an emission spectrum would be induced.The angular frequency 0% is equal to YnHO, where yn is the nuclear magnetogyricratio, and HO is the magnetic field actually experienced by the nucleus. For magneticfields of the order of 104 gauss, 0% is near lo7 c/sec.The prcbability that a nucleuswill make a spontaneous jump from one energy level to another is vanishingly small,19R. A . DWEK AND R . E. RICHARDS 197and for nuclei of spin +, there is no mechanism other than the oscillating field at confor the particular applied field Ho, which can cause transitions.When a sample of nuclei of spin + is placed suddenly in Ho, the initial populationof the two nuclear energy levels must be equal because the nuclei have randomorientations in zero field. The nuclei then relax to the populations correspondingto thermal equilibrium with the characteristic time TI. The oscillating magneticfields at con, needed to induce the transitions, are derived from the random motion ofthe molecules in the liquid.The magnetic moments of the nuclei in the liquid set up local fields in theirenvironment which are proportional to ,u/d3, where p is the nuclear magnetic momentand d is the distance from it to the point at which the field is measured. The pro-portionality constant depends on the angle between HO and the vector joining thenucleus to the point considered.These local magnetic fields fluctuate according to the molecular motion.Rotationof a molecule will cause the local field at one nucleus due to another in the same mole-cule to fluctuate at the rotational frequency. Relative diffusion of molecules causesthe local fields at the nuclei of one molecule, due to those of another, to change. Thefrequency of the molecular motion is usually characterized by a correlation time, 7,.for rotation and zd for diffusion.For any random motion there is the whole spectrumof frequencies and the variation of the intensity of the fluctuations with frequencymust depend on the type of motion concerned. However in all cases, the variationof the “spectral density” J(co) with CL) has a similar form which is roughly representedin fig. 1. J ( o ) is independent of co until wz approaches unity, when the intensity fallsto zero as (o increases. W-hen T is small, J(co) is low and extends to high values of01 ; when z is large, J(w) is greater but falls to zero at a lower frequency.The relaxation times are therefore dependent on the values of J(m) at the particularvalue of con. J ( u ) may be writteng(z) exp (- icoz) dz, (1)where g(z) is the correlation function.The form of this function must be known ifcorrelation times are to be calculated from relaxation data. It is common to use anexponential function, which is physically reasonable for some types of motion and forwhich the Fourier transform is particularly simple. If we writej(o) = J(co)/J(O) thenand in several cases, this has been shown to be a good approximation.However, more precise correlation functions can only be calculated on the assump-tion of a suitable molecular model, and Abragam 1 has dealt with several cases insome detail. Two further examples, however, are given to illustrate the type ofprogress that is being made towards our understanding of molecular motion. Thefirst is that of Hubbard 2 who has considered the dipolar interactions between spinspositioned off the centre of spheres.He assumed that both relative translation androtation of the spheres could be described by a diffusion equation and has shown thatto a first approximation, it is valid to neglect the contribution of the rotational motionto the relaxation rates, and to treat the spins as being at the centre of the spheres.jd(co) is then given bywhereandj(0) = 1/(1 +02z2) (2).id@) = (WWW,u = ~oz/*, z = d2/D,I(U) = ~ - ~ ( ~ ~ - 2 + e - ~ [ ( ~ ~ - - 2 ) sin u+(u2+4u+2) cos u ] ] 198 MEASUREMENT OF NUCLEAR RELAXATIONd is the distance of closest approach of the two spins, and D is the diffusion coefficientin the equation describing the translational diffusion of the spheres.Although theform ofj(w) appears to be quite different from eqn. (2), it still has a shape similar tothose of fig. 1.The second example is simpler, and invokes the concept of a distribution ofcorrelation times. It is often found that discrepancies between theory and experimentcan be removed by such a postulate. A recent paper concerned with the hydrationof keratin 3 shows this well. It is assumed that the water molecules can exist in arange of different environments, each characterized by its own correlation time, andproton exchange occurs between these sites in a time short compared with T2. Alog-normal distribution of correlation times was used in this case, implying that forrotation of the water molecules, there is a Gaussian distribution of free energies ofactivation, and the experimental measurements could be reproduced well.On theother hand, there may be a quite different correlation function with a single value ofzc. A recent paper by Waugh4 is concerned with the nature of the correlationI II 1I II III1IA ! In 3%vIIIIII! I \FIG. 1. 0A, large T ; B, small T.function for rotation in liquids and gases, and points out how in certain special casesadditional information about the form of the correlation function may be obtained.For most liquids, zc is near 10-10 sec, and con usually lies near 107 sec-1. wnzc istherefore much less than 1 (fig. 1) and we are well back on the flat part of the correla-tion spectrum, in the so-called “white spectrum”.The relaxation time is thereforeindependent ofmn and hence of Ho. In special cases, such as rotationally relaxednuclei in molecules at infinite dilution in a non-magnetic solvent, the theory ofrelaxation allows T~ to be obtained from measurements of T1.5 Usually, however,we are not able to do this, but the effect of changing conditions on z can often befollowed directly by measuring the change of TI. For example, when the temperatureis changed, z changes and this is reflected by a corresponding change of T I . Fromsuch measurements, activation energies for molecular motions can be obtaineddirectly. For example, in benzene, the nuclear relaxation rate is determined bymodulation of the dipole-dipole interactions. These may be either inter- or intra-molecular, and we may writef/Ti intrs depends only on the rotation of the molecules while l/T1 inter dependsTI = 1/Tl inter+ l/T1 intraR .A . DWEK AND R . E. RICHARDS 199primarily on translation. By measuring the proton TI for mixtures of benzene witha non-magnetic diluent such as carbon disulphide, or better, with fully deuteratedbenzene, and extrapolation to zero proton concentration, these two contributionscan be separated.6 The activation energies obtained from relaxation measurementsfor these processes have been compared with those corresponding to various physicalproperties 6 and are listed in table 1.TABLE AP APPARENT ACTIVATION ENERGIES FOR LIQUID BENZENE IN kcal mole-1 AT ROOMTEMPERATUREself diffusion 3.1 kcal mole-1viscosity/absolute temperature 3.2TI inter 3.0Rayleigh light scattering 1.35deuteron TI 1-86TI intra 1.2TI intra(4 1.86One might expect agreement between the activation energies of TI inter and thoseof self-diffusion and viscosity, as all three depend mainly on translational motion.Similarly, those of Rayleigh light-scattering, deuteron T I , and TI intra agree reasonablywell, since all depend principally on rotation.The rotation of a group or molecule may give rise to a group or molecular magneticmoment, and interaction of the nuclear magnetic moment with this may provide anadditional relaxation mechanism.This interaction is termed the spin-rotationinteraction and contributes to l/Tl intra. By considering the two contributions toTI intra the dipolar one, TI intra (d) and the spin rotation TlSR, we can writel/Tl intra = l/Tl intra ( d ) + l/TISR,The apparent activation energy for TI intra ( d ) is then found to be 1-86 kcal/mole-1in excellent agreement with that found from the deuteron T1.6 It may be that aredetermination from Rayleigh light-scattering is desirable.The nuclear relaxation times in a diamagnetic liquid are often reduced remarkedlywhen very small concentrations of paramagnetic solutes are added.The presence ofdissolved oxygen, for example, in benzene, reduces the proton relaxation time by afactor of 5. The reason for this is that the magnetic moments of unpaired electronsare about three orders of magnitude greater than nuclear moments, so that the localfields generated by them are correspondingly greater ; the increased intensity of thefluctuating fields induce more efficient nuclear spin relaxation. The situation is morecomplicated than this, however, and can lead to more important information aboutmolecular motion in the liquid.In a dilute solution of a paramagnetic solute, the nuclear relaxation is often entirelydominated by pairwise interactions between an unpaired electron, S, and nucleus, I ;the rapid diffusion of the solute through the solvent ensures that all the nuclei areequntry affected so that the relaxation is shared among them all.The strong localfields ?rodwed by the electron can be coupled to the nuclei by simple dipole-dipoleinterat :tion, or sometimes by a scalar coupling transmitted through a chemical bond,which may be transient, by the same mechanism which is responsible for the hyperfinestructure of e.s.r.spectra or the spin-spin multiplets in n.m.r. spectra.For purely dipole-dipole coupling, the pairwise interaction of a nucleus and anelectron can induce three types of transition involving the nuclei, which are illustratedin fig. 2. There are four energy levels, corresponding to the combinations of th200 MEASUREMENT OF NUCLEAR RELAXATIONS and I spin quantum numbers. The lowest nuclear energy level is by conventionlabelled+, and because the magnetic moment of the electron has the opposite signto that of the proton, we label the lower electronic energy levels negative. Therandom magnetic field fluctuations can induce nuclear transitions which may bedenoted conveniently by the shorthand I- and I+, which represent nuclear transitionsfrom the-and from the + levels respectively, As well as these transitions, thedipolar coupling can introduce the coupled transitions S+Z+(S-Z-) and S+I-(S-Z+)(fig.2) in which the electron and nucleus make simultaneous flips, and these termshave larger coefficients than the I+ or I- terms. The frequency involved in the I+, I-transitions is con, but the coupled transitions involve frequencies (638 -0,) and (me +con)which, bccause me is so much larger than@%, can both be taken to be me, the electronicLarmor frequency. The expression for the effect of the paramagnetic solute on theS Ii-+ +1nuclear relaxation time therefore contains two terms, one invoving an and the otherWe.If there is also a scalar interaction between the nuclei and electrons, this will adda further term, and since scalar coupling can induce only the coupled transitionsS+L(S-Z+), it also will involve me. The resulting equation may be written :where Ne and Nn are the molar concentrations of unpaired electrons and of nucleirespectively, p is the number of nuclei affected at each encounter, s is the electron <pinquantum number, g is the electronic g factor, B the Bohr magneton, A the scalarcoupling constant and r e is the correlation time for the modulation of the scalarcoupling.Whereas co,2z,2 in liquids is usually much smaller than 1, this is not necessarily sofor co:z,2.For example, if zc is 10-10 sec, then at 104 gauss, oe is about 1.8 x 1010sec-1 and co,2~,2 is 3-24. It therefore follows that an important term in eqn. (4) willbe magnetic-field-dependent, and a study of the variation of TI with magnetic fieldcan allow zc to be measured if the scalar contribution to TI is unimportant. Thisvalue of zc will be the correlation time for relative motion of nuclei and electrons;it may be a measure of the rate of rotation of a weak complex of solvent and solutemolecules or it may be the diffusional correlation time of solute molecules with respectto solvent molecules. An example of the former would be the relaxation of nucleiin a large ligand bound to a paramagnetic metal atom ; the latter situation arises whenthere is no significant binding between solute and solvent as in the case of a free radicaldissolved in an inert solvent.Several measurements of molecular correlation times in liquids by this methodhave been performed.Hausser, Kruger and Noack 7 have measured the frequencyand temperature dependence of the relaxation times of several protonic systemR. A . DWEK AND R. E. RICHARDS 201containing various free radicals. The experimental results agree with the theoreticalpredictions based on the translational diffusion of spheres with only dipole-dipoleinteractions between radical and solvent molecules. The correlation times werefound to depend on the diffusion constant of the solvent and on the temperature.However, for solutions of free radicals in toluene, discrepancies between this theoryand experiment were apparent at low temperatures.7 Reinvestigation of toluenesolutions over an extended temperature and frequericy range* showed that theexperimental results could be interpreted in terms of purely dipolar interactions, thetime dependence of which arises from the relative translational motions and also therotational tumbling of an associated complex.The activation energies for theseprocesses were found to be 3.1 and 7.8 kcal mole-1 respectively. The activationenergy calculated in previous work 7 assuming only translational motion to be contri-buting to TI, was 4.4 kcal mole-1. Thus it is essential to analyze relaxation data insome detail, if meaningful activation energies for molecular motions are to be calculated.Kramer, Muller-Warmuth and Schindler 9 have also investigated the temperaturedependence of the correlation times of several protonic systems containing free radicals.Since translational diffusion had been shown to be the main mechanism of relaxation,the activation energies for viscosity should be similar to those of the correlation times,and indeed this was the case.On the other hand, the activation energies fromdielectric relaxation measurements would be expected to be different, since the molecu-lar motion in this case is rotation. This has been illustrated for diethyl ether, for whichthe activation energies for the viscosity and those of the translational correlation timesare about 1.8 kcal mole-1. This value can be contrasted with that of 1.3 kcal mole-1obtained from dielectric relaxation.If scalar interaction makes an important contribution to the nuclear relaxation,there are two correlation times to contend with and it is also of interest to be able tomeasure the value of the scalar coupling constant. For this purpose, additionalinformation can be obtained from the field and temperature dependence of the nuclearT2.Any mechanism of interaction between nucleus and electron which can affect TImust also affect T2, but scalar coupling can also shorten T2 by a mechanism whichcannot affect T I . T2 measures the time taken for the nuclear magnetization in the xyplane to decay by a gradual loss of phase of the precessing nuclei. This phase losscan be induced by any static component of a local field which can cause some nuclei toprecess at different frequencies from others ; scalar interaction produces such acomponent which does not vary as the complex rotates.The longer the componentis applied the more the nuclei lose phase, so the effect will be proportional to ze, thelifetime of the scalar coupling. The expression for T2 is therefore similar to that forTI but contains an additional term in Te in the scalar part :Note that Tl/T2 = 1 except when scalar coupling becomes important, when Tl>T2.The importance of the scalar term for relaxation depends not only on A but also onze and we and hence on temperature and applied field strength. The detailed studyof systems to evaluate all these parameters has been carried out only in a few cases ;a recent paper by Pfeifer et al.10 describes some interesting examples and gives manyreferences.Further information about molecular correlation times for diffusion may beobtained from nuclear electron double resonance experiments.If the electronresonance of the free radical dissolved at low concentration in a diamagnetic liqui202 MEASUREMENT OF NUCLEAR RELAXATIONis saturated, remarkable changes in the nuclear resonance intensities often occur. Thisphenomenon depends on the spin-lattice relaxation processes already described.When the electron resonance of the radical is strongly irradiated, the populationsof the electron energy levels (+ - and - +) may be equalized ; the resonance issaturated.The spin-lattice relaxation processes attempt to restore the populationsof the energy levels to the thermal equilibrium values in which more spins are in thelower two levels than in the upper two (fig. 2). For dipolar coupling, the processesare S+I+ and &I-, but the first has the greater importance. The electronic transitionis from the (- +) to the (+ +) level, and from the (- -) to the (+ -) levels (fig. 2).The dominant relaxation is from (+ +) to (- -) by the S+I+ process, so that nucleiinitially in the lowest (- +) energy level are transferred to the (- -) upper nuclearlevel. Under optimum conditions the populations of the two nuclear levels can bechanged by a fraction +ye/yn, which for protons is - 330 ; the population of the uppernuclear level becomes 330 times greater than that of the lower level is greater in theupper at thermal equilibrium.The nuclear resonance becomes an emission insteadof an absorption spectrum and is greatly increased in intensity.The theory of the effect is well understood2 and depends entirely on the spin-lattice relaxation of the nuclei and of the electrons. Since this mechanism dependson the spectral density of the thermal motion in the liquid at we as described above, sothe enhancement of the nuclear resonance must also depend on this spectral density ;when coe is small enough to lie on the flat part of the correlation spectrum (fig. l), themaximum enhancement (of - 330 for protons) may be obtained, but at higher valuesof we the spectral density decreases and the nuclear resonance enhancement becomessmaller.Measurements of the enhancement of the nuclear resonance at differentmagnetic field strengths (and hence of we) can often be satisfactorily interpreted by amodel of diffusing spheres with a single translation correlation time 99 1 1 s 12If there is also scalar coupling between the electrons and the nuclei, there is anadditional relaxation mechanism of the S+L type (see above). If this relaxationmechanism is stronger than the dipolar mechanism? saturation of the electron reson-ance equalizes the population of the two electronic energy levels, and the S+I-relaxation returns nuclei to the lower (- +) nuclear energy level. Under optimumconditions the population of the lower level is increased by a fraction -ye/yn,whichis about + 660 for protons ; the nuclear resonance absorption is increased in intensity.There is thus a striking and qualititative difference in the results for dipolar and scalarcoupling.If the scalar coupling is weak and comparable with the dipolar coupling,the nuclear resonance intensity lies somewhere between - 330 and + 660.Various attempts have been made to interpret quantitative measurements of thesenuclear electron double resonance experiments in terms of simple models for thescalar coupling.ll9 l3 These studies give values for correlation times and couplingconstants which are in approximate agreement with other measurements, but un-fortunately none of them have so far proved entirely satisfactory.13~ 14 When scalarcoupling is present, therefore? double resonance experiments provide an extremelysensitive indication of its importance, although the correlation times derived may notbe accurate. On the other hand, when scalar coupling is absent, the double resonancemeasurements provide a useful addition to direct measurements of TI, and the valuesof translational correlation times and their field dependence, as obtained from boththese methods are often in excellent agreement.9For nuclei with spin quantum numbers greater than 3, the distribution of positivecharge over the nucleus may be aspherical, and this situation may be described interms of a nuclear electric-quadrupole moment.If the electron distribution aboutthe nucleus has less than cubic symmetry, the resulting electric field gradient caR. A .DWEK AND R . E. RICHARDS 203couple with the nuclear electric quadrupole moment.1 This nuclear quadrupolecoupling provides a further mechanism in addition to the nuclear magnetic momentby which the nucleus can relate its orientation to that of other particles around it.Thus fluctuation of the electric field gradient coupled to the quadrupole moment canprovide an additional mechanism for nuclear relaxation; the relaxation rate l/Tl =1/T2 is proportional to the square of the electric quadrupole coupling constant.1Because the relaxation is governed by fluctuations of the quadrupole interaction atthe nuclear resonance frequency con, the relaxation rate is also proportional to z inthe “white spectrum” approximation, where z is the correlation time for the motionwhich modulates the quadrupole interaction.The electric field gradients produced by chemical bonds are often very strong andthe electric quadrupole interaction often completely dominates the relaxation timesof the nuclei.The quadrupole relaxation is often so strong that nuclear resonancesbecome very broad and difficult to detect.In amolecule such as carbon tetrachloride, the quadrupole coupling arises from theelectric field produced by the C-C1 bond, so that relaxation is produced by rotationof the molecule. On the other hand, the electron distribution about the brominenucleus in the bromide ion in solution is symmetrical, but the symmetry is momentarilyreduced by collisions with solvent molecules or with other ions.In this case thetransient quadrupole coupling is associated mainly with a diffusional correlationtime.15The relevant correlation time may be rotational or diffusional in a liquid.TABLE 2A E expt. AE viscosity(kcal mole-1) (kcal mole-1) moleculeCC14 1-3 k0.1 2.3HCC13 1.4 f0.1 1.8ClC6H5 1.6 f0.2 2.3Tic14 1.0 f0.1 2-1ClO; (in H20) 1 a 5 f0.4 3.7If the quadrupole coupling constant is known from other measurements, theexperimental values of TI or T2 can be used to obtain a value for z. Herbison-Evansand Richards made such measurements on some nitrogen compounds 16 and foundthat their results supported the theory of Wirtz which relates the correlation time tothe microviscosity.The temperature dependence of correlation times of some chlorine compoundshave also been determined from measurements of T2 of the 35Cl resonances.17 Thistemperature dependence is quite different from that of the bulk viscosity as is evidentfrom the activation energies in table 2.In this case the motion involved is molecularrotation so the activation energies are different from those for viscosity which dependon translation. The authors suggest that the correct temperature dependence of thecorrelation time would be obtained from considerations of the microviscosity tempera-ture dependence. This would also seem to be the case for the results of Herbison-Evans and Richards. It will be interesting to compare the activation energies for thequadrupole relaxation of halide ions in solutions of electrolytes, which depend ontranslational motion, with the appropriate energies for bulk viscosity.Moniz and Gutowsky 18 have studied the relaxation times of 14N in differenttypes of groups and again using known values of 14N quadrupole coupling constants,correlation times for the molecular reorientation were calculated.The temperatur204 MEASUREMENT OF NUCLEAR RELAXATIONdependence of TI was also measured for several compounds, and the range of activa-tion energies was found to lie between 1.4 and 3.2 kcal mole-1, the differences generallyreflecting the relative sizes and shapes of the molecules. The temperature dependenceof the proton and 14N spin lattice relaxation times in methyl cyanide were found tobe 1.4 kcal mole-1 and 1.9 kcal mole-1 respectively.This reflects the differenttypes of motion contributing to the 7'1 in each case ; rotation for the 14N, rotation andtranslation for protons. The relaxation time of the nitrogen nucleus is determinedmainly by rotation about the axes perpendicular to the C-CN bond, while rotationabout all axes could contribute to the relaxation rate of the protons. Zeidler 19 hasfound the rotational correlation time for the protons to be in good agreement withthat obtained by the nitrogen TI. This could be understood if rotation about theC-CN axis makes little contribution to the proton 7'1 because of very fast reorienta-tion about the C3 axis of the molecule, as would seem reasonable. Thus rotationabout this bond would have an extremely short correlation time and would not makemuch contribution to TI.In conclusion, it must be emphasized that from measurements of nuclear relaxationtimes or of the enhancement of the nuclear resonance in a nuclear electron doubleresonance experiment, we are measuring the spectral density of the molecular inter-action at particular frequencies, con or we.We can measure how these functions varywith co by making measurements at different magnetic field strengths ; their tempera-ture dependence at each frequency can also be measured. It is therefore possiblein principle to plot out the correlation spectrum at any temperature from purelyexperimental results. If a model for the molecular motion is assumed, the correlationfunction can be obtained and the experimental results expressed in terms of one ormore correlation times. These can then be compared with values measured in otherways.When there are specific intermolecular interactions during a collision betweentwo molecules in the liquid, these can often be detected in the nuclear resonancespectrum. If one of the molecules is paramagnetic, measurements of T1 and 7'2 andespecially of the enhancement of the nuclear resonance in a nuclear electron doubleresonance experiment, can give sensitive indications of scalar coupling formed byweak transient chemical binding.1 A.Abragam, The Princigles of Nuclear Magnetism, chap. VII, (Clarendon Press, Oxford, 1961)2 P. S. Hubbard, Proc. Roy. SOC. A , 1966,291, 537.3 B. §heard and J. Clifford, Biopolymers, 1966,4,1057.4 J. S. Waugh, Molecular Relaxation Processes, (Chem. SOC. Spec. Publ. no. 20), p. 113. (Academic5 see e.g., A. M. Pritchard and R. E. Richards, Trans. Faraday Soc., 1966, 62, 1388.6 J. G. Powles and R. Figgins, Mol. Physics, 1966, 10, 155.7 K. H. Hausser, G. J. Kruger and F. Noack, Z. Naturforsch, 1965, 20a, 91.8 G. J. Kruger, W. Muller-Warmuth and R. Van Steenwinkel, 2. Naturforsch. 1966,21a, 1224.9 K. D. Kramer, W. Muller-Warmuth and J. Schindler, J. Chem. Physics, 1965, 43, 31.10 H. Pfeifer, D. Michel, D. Sames and H. Spring, Mol. Physics, 1966, 11, 591.11 K. D. Kramer, W. Muller-Warmuth, and N. Roth, 2. Naturforsch., 1965, 20a, 1391.12 R. A. Dwek, J. G. Kenworthy, D. F. S. Natusch, D. J. Shields and R. E. Richards, Proc. Roy.13 W. Muller-Warmuth, 2. Naturforsch., 1966, 21, 153.14 R. A. Dwek, J. G. Kenworthy, J. A. Ladd and R. E. Richards, Mol. Physics, 1966,11, 287.15 C. Deverell, D. J. Frost and R. E. Richards, Mol. Physics, 1965,9, 565.16 D. Herbison-Evans and R. E. Richards, MoZ. Physics, 1964, 1, 515.l7 D. E. O'Reilly and G. E. Schacher, J. Chem. Physics, 1963,39, 1768.18 W. B. Moniz and H. S. Gutowsky, J. Chem. Physics, 1963,38, 1155.19 M. D. Zeidler, Ber. Bunsenges. Physik. Chem., 1965, 69, 659.Press, 1966).SOC. A , 1966,291,487