J. Chem. SOC., Faraday Trans. I , 1982, 78, 3223-3234 Ion-Ion-Solvent Interactions in Solution Part 3.-Aqueous Solutions of Sodium Nitrate BY RAY L. FROST Chemistry Department, Queensland Institute of Technology, Brisbane. Australia 4001 AND DAVID W. JAMES* Chemistry Department, University of Queensland, Brisbane, Australia 4067 Received 2 1 st December, 198 I The profile of the band due to the symmetric stretching vibration in the Raman spectrum of aqueous solutions of NaNO, has been studied as a function of concentration. Analysis based on the Fourier transform indicates that there are at least three principal components in the band. Analysis gives the positions of the three components as 1047.6, 1050.0 and 1052.0 cm-I, with a fourth component appearing at 1070.0 cm-l in the most concentrated solutions.On the basis of concentration dependence and band shape these components have been assigned to the free aquated nitrate ion (1047.6), the solvent-separated ion pair (lOSO.O), the contact ion pair (1052.0) and ion aggregates (1070.0). Association quotients K, and K2 for the two equilibria K , K2 Na+(aq)+NO; (as)+ Na+-H,O.NO; (aq)eNa+'NO;.(aq) are K , = 2.7 dm3 mol-l (0.5 mol drn-,) and K , = 3.3 (6 mol drn-,). There have been a variety of spectroscopic studies of nitrate solutions having a monovalent cation and these have been extensively reviewed.' The nitrate ion has proved to be sensitive to variations in environment and has been used as a probe in studies of solids, glasses, melts and solutions4 in order to provide information about electrolyte environment.*> In an extensive study of the Raman spectra of aqueous solutions of alkali-metal nitrates it is found that even at low concentrations the antisymmetric stretching vibrational band of the NO; (v,), centred at ca.1390 cm-l, is split into two components. It is concluded that this splitting is due to the perturbation of the nitrate ion when it is aquated, and n.m.r. StudieslO have suggested that anion solvation is asymmetric, in accord with this idea. A lowering of anion symmetry from DBh to C,, would split the E' mode (D3h) into an A, and B, component.l1*l2 Similar splittings have been observed for dilute solutions of nitrates in liquid arnmonia.l2>l3 In more concentrated solutions of sodium nitrate the components of v, vary in energy and in the later report this band was separated into two pairs of components.I4 The spectral band due to the in-plane bending vibration v, was a single band at low concentrations at 720 cm-1 but at high concentrations, > 7 mol dm-3, a second component was resolved at 740 cm-l in H2015 and 728 cm-I in D20.14 The appearance of this second component was attributed to the existence of ion pairs at high concentrations.The band due to the symmetric stretching vibration (vl) was reported as a symmetrical band sh<,wing a small concentration dependent shift.l4,I5 In a later report the band was shown to develop asymmetry at high c0ncentrations.l The contour of the v1 vibration was extensively studied16-18 and values for the 32233224 I ON-I ON-SO L V E N T INTER A C T I 0 N S vibrational relaxation time and reorientional relaxation time were calculated. Both the relaxation times showed strong concentration dependence which was interpreted loosely in terms of ion association.It was pointed out that the analysis was uncertain due to the asymmetry of the band at higher concentration^.^^ We have made a systematic study of the Raman spectra of aqueous solutions of metal nitrates which will be reported in this and following papers. This paper develops the techniques which are used to analyse the spectra and applies them to the spectra of solutions of sodium nitrate. The results obtained 'are rationalised with previous spectroscopic and transport studies for this system. Subsequent papers will examine the influence of cation size, temperature, deuteration of solvent, changing anion species, cation charge and presence of partially filled valence shells on the cation.EXPERIMENTAL The sodium nitrate was laboratory reagent grade which was recrystallised twice from purified water, oven dried at 380 K for 48 h and stored over P,O,. The water was triply distilled, the final distillation being from alkaline permanganate. Spectra were run on a Cary 82 spectro- photometer using 90' scattering geometry with a restricted collection angle and constant energy band pass slits of < 0.8 cm-l. As reported elsewherelG it was established through an examination of bandwidth as a function of slitwidth that a correction for slit function was not necessary in this study. Radiation (514.5 nm) from a Coherent Radiation CR3 laser (400-800 mW at sample) was passed through a Glan-Thompson prism to ensure a high degree of polarization.The two polarized components of the spectra were recorded using a Polaroid sheet and quartz wedge scrambler and the system was checked using the v1 band of CD,CN which gave a value p = 0.002, in good agreement with published values.zo The sample was held in a 1 cm glass curvette which had all edges masked and which was held in a temperature-controlled assembly. The laser was weakly focussed and passed once through the solution. Spectra were recorded on both chart and paper tape. The digitised spectra were recorded at a 0.2 cm-l interval and several recordings of each spectrum were made and averaged. The spectra for two polarizations of the v1 symmetrical stretching band of the nitrate ion were combined to give the isotropic and anisotropic profiles21 for the band.These profiles, which were the average of several experimental determinations, were smoothed using a Savitsky-Golay smoothing routine and were then Fourier transformed using standard routines. The Raman spectrum peaked near 1050 cm-l. The Fourier transform was made about 1050.445 cm-l as origin with the band being analysed to ca. 50cm-' on each side of the origin. This was the effective limit as beyond this the band due to the nitrate ion antisymmetric stretch starts to make appreciable contribution and at lower energies the scattering due to water becomes significant. This truncation of the spectrum causes a slight curvature to appear at short times in the transformed spectrum.2z Band-component analysis was performed interactively using a suite of programsz3, 24 including a non-linear least-squares routine.25 The bands were described by a Lorentzian- Gaussian product function of the form I , e x p [ - - ~ ( ~ - ~ , ) ~ ] 1 + G(v - 9,)2 r ( q = where I, is the band intensity, vo is the position of the band maximum and X , and X , are half-width parameters for Lorentzian and Gaussian bands.Band fitting was carried out interactively with X , and X , allowed to vary. The criteria for the selection of starting values for band parameters and the number of bands will be described later.R. L. FROST A N D D. W. JAMES 3225 RESULTS A N D DISCUSSION B A N D MOMENTS A N D MODULATION TIMES In a stochastic line-shape theoryz6 which has been applied to the vibrational correlation function G(v)(t) may be determined by the measurement of the vibrational second moment [M,(a)] and the modulation time t, which characterises the correlation decay of the stochastic perturbation Hamiltorian.For slow modulation the perturbation remains for a long time; the initial phase coherence of individual oscillators is rapidly lost. Conversely for fast modulation the original phase persists and the band contour is narrow. The vibrational correlation function may be expressed as d&) = exp (- <[q(O)I*) N exp [ - ( t / z c - 1 >I + r,, t>). For short times ( t <. z,) this reduces to which is valid at all times in the slow modulation limit z,(o*)~ % 1.This expression is independent of modulation time and describes the rigid lattice approximation of vibrational dephasing. For long times, t 9 z,, we have which corresponds to extreme motional narrowing (z, (O")f < 1). The modulation times are calculated by using [ml(O)l2 from the experimentally measured second moment and adjusting T, to give agreement between theoretical and experimental correlation functions. The second moments which we calculated are much smaller than those previously reportedla and this reflects the uncertainty in the previous measurement owing to the use of excessively large The second moments and modulation times are listed in table 1. The quantity M, z,/271c gives a measure of modulation in the correlation function. The values for sodium nitrate solutions lie between 0.9 and 1.26, which are intermediate between the values in CHCl, (0.2) where modulation is fast and D,O in H,O ( 5 ) where modulation is This intermediate modulation reflects the influence of hydrogen bonding between the nitrate ion and water.TIME CORRELATION FUNCTIONS The time correlation functions (t.c.f.) obtained by Fourier transforming the energy spectra are given in fig. 1. They are all curved with the slope increasing with increasing concentration. The slope at the exp (- I ) point gives a measure of the relaxation time which for a pure Lorentzian band will correspond to the value obtained from the band half-width.16 These values are both listed in table 1 and are seen to be appreciably different but to follow the same trends. The shape and slope of the t.c.f.are dependent on the nature of the spectroscopic band. If a band is composed of two components of the same half-width the t.c.f. will display minima, the positions of which are related to the separation of the components. If there are two components of different half- width the slope of the t.c.f. will change as the relative intensity of the two components change and minima will appear at times corresponding to the peak separation.22 For sodium nitrate solutions the band is close to Lorentzian in shape for dilute solutions and hence the curvature reflects the presence of a minimum outside the range of the time scale shown (the t.c.f. becomes very noisy at long times). This will correspondw N N o\ v 7 /PS /PS 0 TABLE 1 .-BAND PARAMETERS FOR AQUEOUS SOLUTIONS OF NaNO, I - 0 concentration v, vs M2 (a) MZ (D) z, z,, * zv(w9 z&lj rf: v, /mol dm-3 /cm-l /cm-l /(cm-1)2 /(cm-l j2 (b/c) /PS /2nc ~~ 1 .o 1048.4 1048.4 56.0 144.0 - 1.8 0.94 0.94 1.36 1.07 2.0 1049.1 1049.1 64.0 144.0 - 3.8 0.98 1.04 1.31 0.89 4.0 1049.9 1050.5 64.0 152.0 + 3.7 1.14 1.21 1.15 0.77 6.0 1050.8 1051.2 69.0 169.0 + 3.2 1.07 1.18 1.12 0.78 8.0 1051.1 1051.2 72.0 176.0 + 6.5 1.03 1.16 0.98 0.8 1 M,(a), second moment of the isotropic band; M,(J?), second moment of the anisotropic band; C(h/cr), band asymmetry parameter; T~,, modulation ime; z,, vibrational/relaxation time.I 0 zR. L. FROST AND D. W. J A M E S 3227 FIG. 1.- t i p s -Time correlation functions from the A ; symmetric stretching vibration band of NO; in solutions of NaNO,.Concentration/mol dmp3: (a) 0.05; ( b ) 1 ; (c) 2; (d) 4; ( e ) 6; (f) 8. aqueous to a peak separation between two components of < 2 cm-l. The change in slope as the concentration increases indicates that the half-width of the components which grow at higher concentrations is greater than those dominant at low concentrations. The above discussion of the t.c.f. refers to the modulus of the Fourier transform. A single Lorentzian profile which is transformed about an origin different from the band maximum, or any band consisting of more than two components, has both real and imaginary parts to the Fourier transform. If la1 is the magnitude of the real part of the transform and (bl that of the imaginary part, tan-' Ib/al describes an angle 8 which is time dependent.For a single Lorentzian band, a plot of 8 against t gives a straight line, the slope of which depends on the separation between the transformation origin and the band maximum. For a band having two components, a plot of B against t gives a curve which oscillates about the straight line describing the major component. The curve crosses the straight line at a time t, which depends on the separation of the two components. The magnitude of 8 for the curve and straight line at a time tn/2 gives a measure of the relative intensity of the two peaks.28 The development described previously28 used synthetic bands which were noise free. The application to experimental bands will be influenced by the signal-to-noise ratio of the spectrum.For solutions above 1 mol dm-, concentration the SINratio for individual bands was at least 100 : 1, and since up to 10 spectra were averaged to give the profile to be analysed the ratio was better than this. In fig. 3 the experimental curve is shown together with the composite curve so the noise level can be gauged. The time resolution of the t.c.f. and 8 functions is 0.3 ps and the time range is tens of picoseconds. This makes use of the 8 function method feasible for the solution spectra recorded. The variation of 8 with time for solutions of sodium nitrate are shown in fig. 2. The straight line represents the 8 function for a curve which we have identified in dilute solutions (0.01 mol dm-,) of KNO,, LiNO, and Mg(NO,),. This band, having a peak position of 1047.6cm-l, a half-width (h.w.h.h.) of 3.395cm-l and a shape ratio [x3/(.x3+x4)] of 0.85, we identify with the nitrate ion aquated by water in an environment where interaction with the cation can be ignored.As the concentration3228 I 0 N-I 0 N-S 0 L V E N T I N T E R A C T I 0 N S -1.34 -2.04 1.6 3 . 2 4.8 t i p s (4 4; (el 6 ; (1) 8. FIG. 2.-Theta functions for transforms in fig. 1. Concentration/mol dm-3: (u) 0.05; (6) 1 ; (c) 2; of NO; is increased the slope of the 0 function becomes more positive. There is evidence, particularly in the 1 mol dm-3 solution spectrum, of an intersection between 7 and 8 ps. The 0 function becomes noisy in this region and this prevents accurate estimation of the cross-over point. An intersection at 7-8 ps would correspond to a second band at ca.2cm-' higher energy than 1047.6, i.e. 1049.6cm-l. The 2 and 4 mol dm-3 solution 0 functions appear to oscillate about the position of this second band, indicating that it is the dominant component. The functions for the highest concentrations appear to oscillate about a line of more positive slope and have inflections at times corresponding to separations of 2 and 4.5 cm-l. The curves are consistent with an initial peak at 1047.6 cm-l, a second peak growing in intensity at ca. 1050 cm-l and at high concentrations a third component at ca. 1052 cm-l. In the band-component analysis to be described below the plots of 8 against t for the original and synthetic bands were compared to give a goodness-of-fit criterion. It was found that this comparison was a much more sensitive measure of the fit than the more common e.m.s.value. However, in the curves presented the e.m.s. curve is presented as being a familiar criterion. The isotropic band profiles for the symmetrical stretching frequency of the nitrate ion were analysed for component bands using a non-linear least-squares routine in an interactive mode. Three band components having initial peak energies of 1047.6, 1049.6 and 1052 cm-l were used to fit the band. For each band the four parameters of peak energy, peak height, X3 and X , were allowed to vary. There must be a question of the uniqueness-of-fit in a procedure of this sort. Since there are a total of twelve parameters it is not surprising that excellent fitting was attained. However, there are a number of criteria by which the validity of the results can be assessed.The e.m.s. between the experimental and calculated spectrum must be small, the 0 function for the composite spectrum must agree with that for the experimental band at least toR. L. FROST A N D D . W. JAMES 3229 4 ps, the position of the bands and the concentration variation of the band intensity must make chemical sense, agreement with previous work must be examined, and the band parameters for the component bands must be reasonable. In this analysis a band component at 1047 6 cm-I identified with the aquated nitrate was fixed (peak position, X , and X,) with only its peak height allowed to vary. Two additional peaks having initial peak positions of 1049.6 and 1052 cm-I with X3 and X , the same as the initial peak were allowed to vary in all four parameters (peak position, X3, X , and peak height).At the highest concentrations Lhere was a persistent residual at appreciably higher energy so an addition band was permitted. The results for the band-component analyses are presented in table 2, the fitted spectra at two representative concentrations are shown in fig. 3 and the variation of band area of the component bands with concentration change is shown in fig. 4. Although the band parameters were not fixed it is evident that a band component at I050 cm-1 has essentially constant parameters at all concentrations and bands at 1052 and 1070 cm-1 have reasonably constant parameters for all concentrations in which they appear with reasonably intensity.The e.m.s. values at all concentrations are excellent. It might be expected that the band parameters for a given component will be concentration dependent. Indeed the half-width and band shape do show appreciable variation. In a study of solutions of perchlorate saltsz9 it has been found that the band position may also change. This is more extensively discussed el~ewhere.~~ ION ASSOCIATION IN NaNO, SOLUTIONS The conclusions which can be drawn from the analysis presented above are clearly different from those which have been previously made. On the basis of analysis of the Raman bands due to the antisymmetric stretching vibration and the appearance of a component in the plane bending vibration at ca. 730 cm-I it was suggested that contact ion pairs were formed at 8 mol dm-, concentration.It was also suggested that although solvent-separated ion pairs might contribute to a shift in the symmetrical stretching vibration, their presence could not be positively identified. Although ion association will vary with concentration in a continuous manner our results are consistent with the series of equilibria K , K2 K : , Na+(aq)+NO;(aq) + Na+-H,O*NO;(aq) eNa+-NO;(aq)e (Na+*NO;), (as) where (aq) denotes species existing as aquated species. The band centred at 1047.6 cm-' we associate with NO; (aq), the band at 1050.0 cm-I with Na+-H,O*NO; (aq), the band at 1052.0 cm-I with Na+-NO; (as) and the band at 1070.0 cm-I with the ion aggregate (Na+*NO,), (aq). If it assumed that the molar intensity for each species is the same, the association quotients for the various association equilibria can be calculated.Kl in a 0.5 mol dm3 solution of NaNO, is 2.7 dm3 mol-I. The second equilibrium is always in competition either with the first or third equilibria and is also undoubtedly dependent on the water concentration. However on the simple assumption that "a+ NO;(aq)] I (band 3 ) - [Na+-H,O*NO;(aq)] - I (band 2) _____ - K - where I is a measure of band area, values of K , of 1.1 at 4 rnol dm-3 and 3.3 at 6 mol dm-, were calculated and these may be compared with the value of 2.98 estimated previously.' For NaNO, in D,O the K , value for 4 mol dm-, solution is 0.8, which compares with a value of 0.6 reported previously.14 However, since the basis for the band analysis is quite different in the two studies the correspondence must be regarded as fortuitous.w w w 0 TABLE Z.-cOMPONENT-BAND ANALYSIS FOR THE ISOTROPIC BAND OF NaNO, SOLUTIONS aquated NO; solvent-separated ion-pair band contact ion-pair band ion aggregate band concentration V", 04 shape V , wi shape vm w: shape 'm 4 shape /mol dm-3 /cm 1 /cm 1 ratio area /cm-l /cm-' ratio area /cm-l /cm-1 ratio area /cm-l /cm-' ratio area K , K2 ___ - 0.001 2.74 - 0.5 1047.6 3.395 0.851 0.560 1050.0 3.61 0.851 0.43 1052.0 3.98 0.72 0.01 1070.0 - 1 .o 1047.6 3.395 0.851 0.420 - 3.5 0.850 0.58 1052.0 3.98 0.72 0.01 1070.0 - - 0.001 3.3 - 6.0 1047.6 3.395 0.851 0.098 ~- 3.50 0.840 0.202 1052.0 5.07 0.655 0.660 1070.0 9.38 0.790 0.028 - 3.3 8.0 1047.6 3.395 0.851 0.05 ~- 3.50 0.840 0.168 1052.0 5.13 0.613 0.731 1070.0 5.13 0.790 0.040 ~ 4.3 2.0 1047.6 3.395 0.851 0.375 - 3.627 0.842 0.475 1052.0 4.00 0.723 0.128 1070.0 8.52 0.689 0.013 1.7 .27 4.0 1047.6 3.395 0.851 0.250 - 3.488 0.840 0.342 1052.0 4.40 0.696 0.384 1070.0 9.14 0.757 0.021 1.34 1.12 In each section: v, is the band maximum (cm-I); (dm3 mol-I); K , is the second equilibrium constant.is the band half-width (h.w.h.h.) (cm-'); shape ratio is x3/(x,+x4); area is the integrated band area; K , is the first equilibrium constant U 0 7 U 7 0 m 0 r c m z rl z 4 m w 9 cl rl e( c( 0 z mR. L. FROST AND D. W. JAMES 323 1 7. 6 x c G .3 4 . 0 * .- X 1.00 1.02 1.04 1.06 1.08 1.1 0 wavenumber/ 1 O3 cm-' l b l wavenumber/103 cm-' FIG. 3.-Band-component analysis of the A ; symmetric stretching vibration band of NO; in aqueous solutions of NaNO,: ( a ) 2 mol dmP3 solution, (6) 4 mol dm-3 solution.The differences in the parameters for the component bands we assign to the four solution species may be rationalised in terms of possible solution interactions. The band at 1047.6cm-' is highly Lorentzian with a halfwidth of 3.4 cm-I. This corresponds to a value of z, of 1.56 ps. In liquids where the relaxation is controlled by collisional interactions the value of z, lies between 2 and 4.5 ps.21q27 It could be suggested that the measured bandwidth is instrument limited. In solutions of NaNO, in [2H,]DMS0 we have measured the width of this band as 1.65 cm-l (z, = 3.2 ps).3232 I 0 N-ION-SO L VENT INTERACT IONS 0.8 i 0.2 \ 1050.0 I \ I I 1070.0 1047.6 1 2 3 1 5 6 7 8 cation concentration/mol ~ i r n - ~ FIG. 4.-Variation in component-band intensities with concentration.It is this latter value which we feel is an indication of the relaxation in which hydrogen-bonded interactions play little part, i.e. the collisions are essentially elastic. In aqueous solution the anion is hydrated through a hydrogen-bonding mechanism and this will change the nature of the ‘collisions’. The reduction in the relaxation time in aqueous solution means that the dephasing process is more efficient and this may occur through a symmetry perturbation when the nitrate ion is aquated. This suggestion supports the previous observation that even in dilute aqueous solution the antisymmetric stretching vibration gives rise to a band showing loss of degeneracy. Because solution in [2H,]DMS0 yields a very different bandwidth it is probable that in the hydration process the symmetry of the nitrate ion is perturbed either through a solvent cage of different symmetry or through preferential solvation at one or more of the oxygen atoms on the nitrate ion.The band positions for all associated species in the solutions studied are at higher energy than the band for the dilute solution species. This shift reflects an increasing coulombic perturbation of the nitrate ion by the cation. There appear to be two mechanisms contributing to the change in energy of the v , band. A symmetrical polarization (space and time averaged) increases the energy whereas an unsymmetrical polarization decreases the energy. This can be understood in terms of changes in the electron distribution and is discussed in detail el~ewhere.~” 32 The position of the band maximum attributed to the contact ion pair species is close to that observed in molten NaN03,6 while the position of the highest energy component assigned to the ion aggregate is close to the value observed for the anhydrous The band attributed to the solvent-separated ion pair has a shape ratio essentially the same, and a half-width only marginally greater than the dilute solution species.This indicates that the relaxation processes are similar for the the two species and so although the formation of the species increases the coulombic field on the nitrate ion it does not lead to an increased symmetry perturbation. This requires that the cation exchanges rapidly and the coulombic influence is averaged over the whole of the hydration shell of the anion.R.L. FROST AND D. W. JAMES 3233 The band attributed to the contact ion pair species shows both a significant increase in Gaussian character and a considerable increase in half-width. The shorter relaxation (z, = 1.18 ps) which this indicates will arise from the greater symmetry perturbation caused by the directional nature of the close approach of the cation. The Gaussian character of the band reflects that the interactions in the associated com- plex are increasingly solid-like (Gaussian). The band associated with the ion aggregate shows all the characteristics expected of a vibrating disordered solid. The linewidth is broad (z, = 0.55 ps), indicating a high level of symmetry perturbation probably due to the dynamic disordered nature of the aggregate.At the same time the band shows appreciable Gaussian character indicating that the vibration is overdamped by the fluctuating field of the environment. As the concentration of salt solution increases, the dynamic continuum of states which characterises the liquid changes, and it may be appropriate to treat the system as a continuum. We feel, however, that there are probably ion-ion and ion-solvent associated species which occupy minima in the potential-energy surface. The analysis which we present is an attempt to characterise these minima and give rational description to the species associated with them. A study of this sort is only acceptable if the premises involved can be applied to a wide range of systems.To this end we present in the following papers an analysis of the Raman spectra of an extensive set of salt systems under a variety of conditions. We thank the Australian Research Grants Committee for grants enabling the purchase of Cary 82 spectrometer system. Dr R. Appleby is thanked for helpful discussions. D. E. Irish and M. H. Brooker, in Advances in Infrared and Raman Spectroscopy, ed. R. J. H. Clark and R. E. Hester (Heyden, London, 1976), vol. 2, p. 212. R. D. Tobias, in The Ramun Eflect, ed. A. Anderson (Marcel Dekker, New York, 1973), vol. 2, p. 405. R. E. Verrall, in Water, A Comprehensive Trearise, ed. F. Franks (Plenum Press, New York, 1973), C. C. Addison, N. Logan, S. C. Wallwork and C. D. Garner, Q. Rev., 1971, 25, 289.D. E. Irish, A. R. Davis and R. A. Plane, J. Chem. Phys., 1969, 50, 2262. G. J. Janz and D. W. James, J . Chem. Phys., 1961,35,739; D. W. James and W. H. Leong, J . Chem. Phys., 1968, 49, 5089. 0. Redlick, Chem. Rev., 1946, 39, 333. ti R. E. Hester, Anal. Chem., 1972, 46, 490R. W. E. L. Grossman, Anal. Chem., 1974, 48, 345R. lo H. G. Hertz, J . Solution Chem., 1973, 2, 239. D. E. Irish, in Physical Chemistry of Organic Solvent Systems, ed. A. K. Covington and T. Dickinson (Plenum Press, London, 1973), p. 433. H. Brintsinger and R. E. Hester, Znorg. Chem., 1966, 5, 980; R. E. Hester and W. E. L. Grossman, Znorg. Chem., 1966, 5, 1308. l 3 K. R. Plowman and J. J. Lagowski, J . Phys. Chem., 1974,78, 143; A. T. Lemley and J. J. Lagowski. J . Phys. Chem., 1974, 78, 708. l4 J. D. Riddell, D. J. Lockwood and D. E. Irish, Can. J . Chem., 1972, 50, 2957. l5 D. E. Irish and A. R. Davis, Can. J . Chem., 1968,46,943; D. E. Irish and G. E. Walrafen, J. Chem. vol. 3, p. 21 1. Phys., 1967, 46, 378. D. W. James and R. L. Frost, Faraday Discuss. Chem. Soc., 1978, 64, 48. M. Koubaa and M. Perrot, C . R. Acad. Sci., Ser. C, 1978 286, 99. T. Kato, J. Unemura and T. Takenaka, Mol. Phys., 1978,36,621; T. Kato and T. Takenaka, Chem. Phys. Lett., 1979, 62, 77. l9 D. E. Irish and T. Jarv, Faraday Discuss. Chem. Soc., 1978, 64, 95. 2o J. E. Griffiths, J . Chem. Phys., 1967, 47, 1836. 21 J. E. Griffiths, in Advances in Raman Spectroscopy, ed. J. P. Mathieu (Heyden, London, 1973), vol. 22 R. L. Frost, R. Appleby, M. T. Carrick and D. W. James, Can. J . Spectrosc., in press. 1, p. 444.3234 I ON-I0 N-S 0 L V E N T INTER ACT I 0 N S 23 D. Sweatman and W. Garrett, unpublished results. 24 R. L. F. Frost and R. Appleby, unpublished results. 25 P. Sampson, Program B.M.D.O7R, in Biomedical Computer Programs, ed. W. J. Dixon (University 26 R. Kubo, in Fluctuations, Relaxation and Resonance in Magnetic Systems, ed. D. T. Haas (Plenum 27 W. G. Rothschild, J . Chem. Phys., 1976, 65, 455. 28 D. W. James, M. T. Carrick and R. L. Frost, J . Raman Spectrosc., in press; D. W. James and R. L. Frost, Can. J. Spectrosc., 1978, 1, 1. 29 R. L. Frost, D. W. James, R. Appleby and R. E. Mayes, J. Phys. Chem., in press. 30 J. E. Griffiths, J . Chem. Phys., 1973, 59, 751. 31 D. W. James and R. L. Frost, Aust. J. Chern., 1982, in press. 32 M. T. Carrick, D. W. James and W. H. Leong, Aust. J. Chem., in press. 33 D. W. James and W. H. Leong, J. Chem. Phys., 1968 49, 5089. of California Press, 1974), p. 387. Press, New York, 1962), p. 27. (PAPER 1 / 1999)