J. CHEM. SOC. FARADAY TRANS., 1994, 90(18), 2697-2701 ATR-FTIR Studies of Ion-Solvent and Ion-Ion Interactions in Divalent-metal Perchlorate-Acetonitrile Solutions W. Ronald Fawcett," Guojun Liut and Alla A. Kloss Department of Chemistry, University of California Davis CA 95616,USA ~ ~ ~~~~ The effect of divalent-metal ions on the IR spectrum of acetonitrile has been examined by studying the depen- dence of the spectral features on concentration for seven divalent-metal-ion perchlorates. Data are reported for both the frequency shifts and molar absorption coefficients of the major bands in acetonitrile which are affected by the presence of a cation in solution. It is shown that ion association plays a major role in determining the magnitude of the frequency shift.Other features discussed include the effect of the combination band in proto-nated acetonitrile, and the role of metal-ion softness in cation-acetonitrile interactions. Vibrational spectroscopy is a powerful tool for examining the solvation of electrolytes in acetonitrile.'-' By examining changes in the frequency and intensity of important solvent bands, such as the CEN stretching frequency (v,), one can assess the strength of cation-solvent interaction and deter- mine solvation numbers and the extent of ion pairing. An important goal of our work has been to assess changes in cation-solvent interaction with changes in cation size and charge. These can be determined, to a first approximation, by measuring the shift in the v, band when the electrolyte is added to the s~lvent.~*~ However, in protonated acetonitrile, this shift is affected by the nearby combination band (v3 + v,) with which the v, band is in Fermi In order to avoid this interaction, studies have been carried out in deu- teriated acetonitrile in which the shifts in the CEN band give a true measure of the strength of the interaction of cations with the electronegative end of the solvent molecule without the complication of a nearby combination In order to compare values of Av, for different cations one must also know how the extent of ion pairing changes with cation nature.Ion pairing is conveniently studied by examining the changes in intensity of bands resulting from cation-solvent interaction with cation c~ncentration.~ The solvation numbers for divalent cations in acetonitrile have been assumed to equal six, on the basis of previous work.' In a recent paper,3 a detailed examination of FTIR spectra obtained for Mg(ClO,), solutions in acetonitrile showed that the average solvation number for Mg2 + is much less, i.e.3.4. Evidence was presented that the predominant cationic species in solution were the Mg2+ cation solvated by four acetonitrile molecules, and a species surrounded by three acetonitrile molecules and one perchlorate anion. We have extended this study to six other divalent ions, namely, the alkaline-earth-metal cations Ca2+, Sr2 + and Ba2+, the transition-metal ions ZnZ+ and Cd2+, and the post-transition-metal ion, Pb2 +.Estimates of the average solva- tion numbers are presented and the roles of ion size, ion pairing, and metal-ion softness assessed in determining the strength of cation-solvent interactions.Experimental Mid-IR spectra were obtained using an IBM Instruments IR-98 FTIR spectrometer equipped with a liquid-nitrogen cooled HgCdTe detector and a SpectraTech variable-angle ATR attachment. Details of the method of data acquisition t Present address : Center of Advanced Technology Development, Institute of Physical Research and Technology, Iowa State Uni-versity, Ames, IA 50011, USA. were given earlier4 except that resolution was increased to 2 cm-'. Band peak maxima were found by fitting a Lorentzian curve to the band using Spectro Calc software (Galactic Industries). Band positions were reproducible to better than 1 cm-'.Acetonitrile (Fisher, HPLC grade) and deuteriated acetoni- trile (Aldrich, 99.5% deuteriated) were used as received. The perchlorate salts were obtained as hydrates either from Johnson-Matthey [Ca(ClO,), and Cd(CIO,),] or from Strem [Sr(ClO,), , Ba(C10,), , Zn(ClO,), and Pb(ClO,),]. They were purified by recrystallizing them twice from nanopure water. Considerable effort was made to obtain well dried salts. This was achieved by heating them under vacuum in the presence of P205in a drying pistol. The temperature of the drying operation was controlled by surrounding the pistol by a refluxing organic solvent. Salts such as Ca(ClO,),, Cd(C10,), and Sr(C10,), which have low melting points were dried in three steps: (a) under vacuum for two days at room temperature; (b)heated at 56 "C (acetone vapour) for 1 day and (c) heated for several days at 140°C (xylene vapour) for Ca(ClO,), and Sr(ClO,), , or at 80 "C (benzene vapour) for Cd(C10,), .Zn(C10,), was dried at 80 "C for five days and then for a week at 110°C (toluene vapour). Pb(ClO,), was dried at 56°C for 2 days, and then at 80°C for 4 days. During the drying operation, the P,05 was replaced when it showed signs of being wet. Drying was stopped when there was no visible sign of wetness on the P,05. A test solution of the dried salt was then made and monitored by IR spectros- copy in the region of the water bands. The salt was only con- sidered dry when no evidence of water contamination was obtained in this manner.All solutions were prepared in a dry environment, exposure of salts and solvent to the open atmo- sphere being kept to a minimum. Results IR spectra were collected in protonated acetonitrile solutions containing the six different metal-ion perchlorates in the con- centration range 0.02 to 1.0 moll-'. The difference spectra of CH3CN in the presence of Sr(C10,), are shown as a typical example in Fig. 1 and 2. The intensities of the CH, symmetric stretching band (vl, 2943 cm-') and the asymmetric stretch- ing band (v5, 3003 cm- ') increase significantly with electro- lyte concentration [Fig. l(a)], but their positions are essentially the same as in the pure solvent.These changes are attributed to interaction between the methyl group at the positive end of the molecular solvent dipole and the perchlor- ate anion., Three bands are seen in the CSN stretching region [Fig. l(b)], one of them increasing in the negative direction. This latter band is due to the C=N stretching fre- I 3080 2900 2i80 2 0 wavenumber/cm-' Fig. 1 IR difference spectra for acetonitrile solutions containing various concentrations of Sr(ClO,), in (a)the CH, stretching region and (b)the C'N stretching region. The concentration of Sr(ClO,), increases from bottom to top. quency in unassociated acetonitrile (v2, 2253 cm-') whose concentration decreases with increase in electrolyte concen- tration. The band at 2288 cm-' is attributed to the CEN stretching frequency for the solvent when it is associated with the Sr2+ cation, whereas that at 2316 cm-' is due to the combination band (v3 + v4).Bands observed at lower fre- quencies are shown in Fig. 2. There are two bands which increase in the negative direction corresponding to the free C-C stretching mode (v4, 918 cm-') and the overtone due to the C-CEN deformation mode (2v8, 746 cm-l) for unas- sociated solvent molecules. The two bands increasing in the J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 1 Frequency shifts (cm-')of the major IR bands of CH,CN in the presence of divalent-metal cations band metal cation v1 v2 v3+4 v4 2% ~~ ~~ ~ Mg2+ -1 36 24 -21 Ca2+ -2 22 13 12 28 Sr2+ -2 36 24 21 46 Ba2+ -1 11 7 6 17 Zn2+ -2 34 23 19 39 Cd2+ -3 28 18 16 29 Pb2+ -2 12 6 6 17 pure solvent' 0 (2945) 0 (2253) 0 (2293) 0 (918) 0 (748) 'The frequency of the band in the pure solvent is given in brackets.positive direction at 939 and 795 cm-' are clearly attribut- able to CH3CN molecules associated with the electrolyte. The band at 746 cm-' is due to the 2v, mode. The absorp- tion intensity observed in the region from 914 to 939 cm-' is partially due to the C-C stretching mode in the associated molecule, and also to the symmetrical stretching modes of the perchlorate anion which fall in this range. The frequency of the v2 band varies significantly with the nature of the cation when acetonitrile is associated with a cation.Significant frequency shifts are also seen for the v4, 2v8 and the v3+4 combination band. These frequency shifts for the six cations in the present study, together with those for Mg2+ obtained ear lie^,^ are summarized in Table 1. As one would expect the largest frequency shift is observed for Mg2+ which is the smallest cation and therefore expected to have the largest polarizing effect on the electron density at the electronegative end of the acetonitrile molecule. At the same time, the smallest shift is seen for the largest ions, Ba2+ and Pb2+. However, the shift for each of the modes con- sidered does not follow the change in cationic size in a regular manner. This is most clearly seen in the alkaline- earth-metal series where the frequency shifts in v2, v4 and the v3+4 combination band are the same for Mg2+ and Sr2+.Thus, some other factor must play a role in determining the extent of interaction between the cation and the solvent mol- ecule. This question is examined in more detail below. The concentration dependence of the integrated band intensities for the major solvent bands was examined in order to determine molar absorption coefficients and to assess the extent of ion pairing. The data obtained in the case of Sr(ClO,), are shown in Fig. 3. Very good linear relations between integrated intensity and electrolyte concentration are 15.0 1000 900 800 700 .oo 0.32 0.64 wavenum ber/cm -[Sr (CIO4) 2] /mol 1 -' Fig. 2 IR difference spectra for acetonitrile solutions containing various concentrations of Sr(ClO,), in the C-C stretching and Fig.3 Integrated intensity us. concentrationof Sr(ClO,), for 0,the C-C=N deformation regions. The concentration of Sr(ClO,), v2 band in free acetonitrile and for the A, v,; A, v3+,; +,v1 and 0, increases from bottom to top. v5 bands in coordinated acetonitrile J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 2 Molar absorption coefficients (intensity units 1 mol-') for the major IR bands of CH,CN in the presence of divalent-metal cations band ~ ~ ~~ ~~ metal cation v1 v2 (coord) v2 (free) v3+4 v5 Mg2+ 3.75 10.2 -2.41 9.6 2.48 Ca2+ 2.7 1 13.5 -3.52 5.4 2.01 +Sr2 4.1 1 11.7 -4.25 11.1 2.87 Ba2 2.50 14.6 -3.49 4.3 2.17+ Zn2+ 4.50 11.7 -4.11 13.8 3.35 Cd2+ 3.99 11.9 -3.88 8.4 3.03 Pb2+ 1.68 12.5 -3.61 3.5 1.64 obtained for the v2, v~+~,v1 and v5bands for coordinated acetonitrile.The intensity data for the v2 band of free aceto- nitrile are also linear in electrolyte concentration, the inten- sity at zero concentration corresponding to that for pure acetonitrile. Similar data were obtained for the other five electrolytes studied here. A summary of the molar absorption coefficients for these bands is given in Table 2. These data may be used to calculate an average coordination number, S, for acetonitrile with a given metal ion. The analysis used here makes use of the molar absorption coefficient for acetonitrile measured in carbon tetrachloride solutions, namely, 0.718 intensity units per mole., The intensity of the v2 band in pure acetonitrile is 13.3 intensity units corresponding to a molar concentration of 18.5 mol 1-'.On the basis of the density of acetonitrile (0.776 g ml-'), the molar concentration of ace- tonitrile in the pure liquid is 18.9 mol I-'. Thus, the experi- mental results obtained in the CCl, solutions can be used to determine an approximate coordination number, S, in the electrolyte solutions. The molar absorption coefficient for the v2 band of free acetonitrile measured with respect to electro- lyte concentration is related to the number of acetonitrile molecules coordinated to the electrolyte on the basis of its molar concentration. By dividing this number by the molar absorption coefficient for acetonitrile in CCl, one obtaips the average coordination number of acetonitrile with the metal cation of the electrolyte.In the case of Sr2+, the result is 5.92. The result is approximate because the value of S is expected to vary with electrolyte concentration owing to changes in solution density and the extent of ion pairing. However, this variation is not expected to be large as can be seen from the quality of the linear fit for the v2 band for free acetonitrile seen in Fig. 4. Moreover, the precision of the present data is not sufficiently high to warrant a more detailed analysis. Similar analyses were carried out for the other cations con- sidered in this study. The average coordination number, S, varies from a low of 3.35 for Mg2+ to a high of 5.92 for Sr2+ (see Table 3).The fact that good linear relationships were obtained between the integrated intensity and electrolyte con- centration (r > 0.96) demonstrates that S is approximately constant over the concentration range used in the present 50 40 r' 305-..520 10 0 0 5 10 15 20 25 z, r-'/nm -' Fig. 4 Frequency shift of the v2 band in deuteriated acetonitrile us. the effective field ze/r for seven divalent-metal cations. The straight line was drawn using a one-parameter least-squares fit. studies. The large variation in the coordination number with the nature of the cation is due to the effects of ionic size and extent of ion association. The larger cations would clearly have a coordination number of six in the absence of ion association.The extent of ion association also reflects the strength of the metal-solvent bond which is clearly stronger for a transition-metal ion such as Cd2+ than for a main- group element such as Ca2+, in spite of the fact that these ions are approximately the same size. When one examines the data for the alkaline-earth-metal ions only, the value of S does not change smoothly with increase in ionic radius. Thus, other factors come into play and they are considered in more detail below. On the basis of the data summarized in Table 2, it is clear that the v2 and v,+~bands are considerably enhanced when the acetonitrile molecule is coordinated to a metal cation.Quite large variations in this enhancement are seen for the combination band v,+4. The observed enhancement is attrib- uted to the fact that the dipole moment change in the coordi- nated species is more sensitive to the CSN stretching than in the isolated molecule. Molar absorption coefficients for the CH, stretching bands v1 and v5 also depend on the nature of the cation. The observed enhancement is attributed to interaction of per- chlorate anions with the positive end of the molecular dipole which is located at this group. The variation with the nature of the cation is because the concentration of free perchlorate anions depends on the cation owing to varying degrees of ion association. On the basis of these results, ion association is strongest in the presence of Pb2+ and very strong in the presence of Cat+ and Ba2+.The least amount of ion associ- ation occurs in solutions containing the Zn2+ ion. Discussion One of the most interesting features of the present study is that the frequency shift for the signature band in acetonitrile, namely, the CEN stretching frequency, does not follow Table 3 Other relevant parameters for divalent-metal-ion perchlorates in acetonitrile Pauling radius, effective solvent coordination effective cationic frequency shift for the v2 band Marcus softness ion r/Pm number, S charge, z, in CD3CN, AvJcm-' parameter, Mg2+ 65 3.35 1.35 42 -0.37 Ca2+ 99 4.90 0.90 24 -0.67 Sr2+ 113 5.92 1.92 42 -0.59 Ba2+ 135 4.85 0.85 12 -0.60 Zn2+ 74 5.72 1.72 41 0.37 Cd2+ 97 5.40 1.60 32 0.59 Pb2+ 121 5.03 0.97 11 0.58 2700 changes in ionic size.This can be partly attributed to the effects of ion association which lower the effective charge on the cation. If a maximum of one anion is associated with a given cation, then the fraction,f; which are paired is given by f=N-S (1) where N is the maximum number of solvent ligands around a given cation. For the present group of ions, N is assumed to be six for all cations except Mg2+ for which it is four. The average effective charge on the cation is then Z, = 2 -N + S (2) The simplest explanation of the variation in Av, with cation nature is that is follows the variation in the field due to cation charge, ze/r, where r is the cation radius taken as the Pauling value (see Table 3).In order to test this proposal, values of Av, determined for CD,CN were chosen since these are not affected by the proximity of a combination band. A reasonable linear correlation is found between Av, and ze/r, the resulting relationship on the basis of a one-parameter fit being Av, = 2.0ze/r (3) The correlation coefficient, r, is equal to 0.937 indicating that approximately 88% of the observed variation in Av, can be attributed to the change in the effective field of the coordi- nating cation. The outlying points involve the hard cations + +Ca2+ and Sr2 and the soft cations Pb2 and Zn2 + . Some improvement in the understanding of the factors affecting Av2 can be made if one considers the role of cation softness.A parameter quantifying this factor was developed by Marcus8 in order to assess the tendency of cations to undergo covalent bonding. The softness parameter, 0, is determined from the difference between the ionization poten- tial of the gaseous atom to form the cation and the enthalpy of hydration of the latter. From the values listed in Table 3, o varies from -0.67 for hard cations such as Ca2+ to 0.59 for soft cations such as Cd2+. When this is included in the description of the variation of Av2 with cation, the resulting relationship from a two parameter fit is Av, = 2.Oze/r-6.20 (4) with a correlation coefficient equal to 0.973. As a result, 95% of the observed variation in Av, is explained, with 79% of the explained variation being attributed to the effective cation field through changes in ze/r, and 21% to changes in cation softness.The resulting fit is illustrated in Fig. 5. The values of the coordination number, S, determined from the change in intensity of the v2 band for free acetonitrile 50 I 1 -40 r -' 30 zj--. 20-jot 7Ba2+ I OO" 10 20 30 40 50 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 3' h* +? m\? 2. > v \ a 1-0' I -2 0 2 4 6 8 A(Av2)/cm-' Fig. 6 Ratio of molar absorption coefficients for the v2 and v3+4 bands. RI(v2/v3+J, us. the difference in frequency shifts for the v2 band in deuteriated and protonated acetonitrile, A(Av2).The straight line was fitted by least squares. vary significantly with the nature of the cation. In the case of Mg2+, for which the maximum value of S is assumed to be 4, the result obtained indicates that CQ. 65% of the Mg2+ ions are paired with a C104 anion., In the case of Sr2+ and Zn2+, the extent of ion pairing is small, amounting to 8% and 28% of the ions, respectively. The solvation numbers for Ca2+ and Ba2+ are less than 5. These results are taken as evidence that ion triplets are formed in these solutions. Supporting evi- dence for this conclusion is obtained by analysing the per- chlorate bands observed in acetonitrile solutions containing these electrolytes.' Finally, it should be noted that the degree of ionic association reflected in the value of S is consistent with the observed changes in intensity of the CH, stretching modes, v1 and v5.As pointed out above, the intensity and position of the v2 band for the coordinated acetonitrile is effected by the fact that it is in Fermi resonance with the nearby combination band v3+4 for the same species. This effect was assessed by comparing the ratio of the molar absorption coefficients for these bands RI(v2/v3+J with the difference in the CzN stretching frequency shifts between the deuteriated molecule and the protonated molecule, A(Av,). The latter difference is ca. 0 for the Ba2+ and Pb2+ ions and increases to 7 cm-' for the Zn2+ ion (see Tables 1-3). A plot of RI(~2/~3+4)against A(Av,) shown in Fig.6 demonstrates that there is a linear relationship between these quantities. This result can be interpreted on the basis of the following argument. The pres- ence of Fermi coupling between the v2 and v3+4 bands in acetonitrile results in their frequencies being shifted apart, the v2 band moving in the red direction and the v3+4 band in the blue direction. When a cation is added to the system both of these bands are blue-shifted for a coordinated acetonitrile molecule, the shift for the combination band being about two thirds of that for the v2 band. Thus, the frequency separation between this pair of bands is smaller for the coordinated mol- ecule, and Fermi coupling is stronger. As a result the net blue shift of the v2 band is reduced in magnitude by a red shift due to Fermi coupling.Since Fermi resonance is not present in the CD,CN spectrum in this region, the shift in the v, band measured in this solvent gives a measure of the influence of the cation alone. Thus, the quantity A(Av2) gives a measure of the influence of Fermi resonance on the position of the v2 band in the protonated solvent. Another effect of Fermi coupling is that the combination band borrows intensity 2.02,r-l -6.20 from the v2 band to an extent which depends on their fre- quency separation. Thus, the ratio RI(v,/v, +4) also reflects Fig. 5 Frequency shift of the v2 band in deuteriated acetonitrile us. the function 2.02, r--6.20. The constants were determined by a the strength of Fermi coupling in the presence of a given two-parameter least-squares fit, and the straight line drawn with a cation. It follows that there is a linear relationship between slope of unity.RI(v2/v3+4) and J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 One other feature of the spectra merits comment. Because must be considered in order to understand the frequency of Fermi resonance, the shift of the combination band Av~+~shifts and intensity changes observed in the spectra. By con- should be greater than the sum of the shifts Av3 and Av4. The shift Av, for the symmetric deformation band is zero for all systems studied. Examination of that data in Table 1 reveals that Av, +4 is always greater than Av4. However, the differ- ence between these frequency shifts should be approximately equal to the net shifts in the v2 band due to Fermi resonance, namely, A(Av2). However, A(Av2) is clearly greater, that is A(Av2) > Av3+4 -Av, -Av, This observation is attributed to the effects of vibrational anharmonicity when the acetonitrile molecule is coordinated to a metal ion.In pure protonated acetonitrile, the com-bination band is at 2293 cm-' which is the exact sum of the frequencies of the v3 band (1375 cm-') and the v4 band (918 cm-I). This signifies that the blue shift in the combination band due to Fermi coupling is offset by a red shift of equal magnitude due to the anharmonicity of the vibration. When acetonitrile is coordinated to a cation, its anharmonicity con- stant changes. Thus, one must consider three factors in rationalizing the frequency shifts of the combination band, namely, the effect of the cation reflected in the large blue shift of the v4 band, the small blue shift due to Fermi resonance, and the small red shift due to the anharmonicity effect.In conclusion, the effects of divalent cations on the IR spectrum of acetonitrile cannot be understood simply on the basis of the size of the cation and its polarizing effect on the electronegative end of the acetonitrile molecule. Ion associ- ation plays an important role in these systems, and its effects sidering a wide range of cations from both main group and transition elements one can assess the role of covalent bonding in the metal-acetonitrile interactions. Further infor- mation about the nature of the ion association can be obtained by examining the perchlorate region of the spectra. These results will be presented in a subsequent paper. The financial support of the Officeof Naval Research, Wash- ington, is gratefully acknowledged. References 1 D. E. Irish and M. H. Brooker, Adv. Znfiared Raman Spectrosc., 1976,2, 212. 2 I. S. Perelygin, in Ionic Soluation, ed. G. A. Krestov, Nauka, Moscow, 1987, ch. 3. 3 W. R. Fawcett and G. Liu, J. Phys. Chem., 1992, %, 4231. 4 W. R. Fawcett, G. Liu, P. W. Faguy, C. A. Foss Jr. and A. J. Motheo, J. Chem. Soc., Faraday Trans., 1993,89,811. 5 P. Gans, J. B. Gill and P. J. Longdon, J. Chem. Soc., Faruday Trans., 1989,85, 1835. 6 P. Gans, J. B. Gill and P. J. Longdon, J. Chem. Soc., Faruday Trans., 1994,90, 315. 7 Y. Marcus, Ion Solvation, Wiley-Interscience, New York, 1985, ch. 4. 8 Y. Marcus, Zon Solvation, Wiley-Interscience, New York, 1985, ch. 3. 9 Guojun Liu, Doctoral Dissertation, UC Davis, 1993. Paper 3/06779C; Received 12th November, 1993