J. CHEM. SOC. FARADAY TRANS., 1994, 90(2), 315-320 Spectrochernistry of Solutions Part 26.-tAlkaIi=metal and Alkaline-earth-metal Thiocyanates in Dimethylformamide and Acetonitrile Solutions :Hot Bands, Stability Constants and Thermicity for the Formation of Inner- and Outer-sphere Ion Pairs Peter Gans,* J. Bernard Gill* and Peter J. Longdon School of Chemistry, The University of Leeds, Leeds, UK LS2 9JT The IR spectra of solutions of the thiocyanates of (CH,),N+, (C2H5),N+, (C4HJ4N+, Li+, Na+, K+, Cs+, Mg2+, Ca2+, Sr2+ and Ba2+ in acetonitrile and dimethylformamide have been recorded at various temperatures in the range 278-348 K. Peaks ascribed to ion pairs shift with temperature. This shift is explained in terms of the existence of hot bands. Equilibrium constant calculations have been attempted using the IR data and where possible AH has been estimated.[SrNCS]+ forms both inner- and outer-sphere complexes with an additional thiocyanate ion in acetonitrile. The IR spectrum of the species ([SrNCSl'NCS-}, in which one thiocyanate is in the inner- and one thiocyanate is in the outercoordination sphere of the strontium cation, has been deduced with the aid of an equilibrium calculation. The separation of the absorbance maximum of this species from that of [SrNCS]+ is one sixth of the half-width of the bands. Experimental observed spectra of solutions at a range of total salt concen- IR spectra were measured on a Philips HP9545 Ratio trations by means of the Beer-Lambert law (l), Recording spectrophotometer controlled by a BBC micro- AA, s = L(&NCS, ACNCS-ls + &WNCS, ACMNCS1s) (I)computer.Each spectrum is the average of at least nine scans. CaF, windows were used for the 2050 cm-' region and ZnSe where the subscript 2 refers to a wavelength and the subscript windows for the 750 cm-' region. A medium band-pass s refers to a solution. The concentrations [NCS-] and multidielectric filter was placed between the cell and the IR [MNCS] were obtained at each total salt concentration by source to minimize heat gain in the sample. The cells were solving the equations of mass-balance with the calculated thermostatted to fO.l "C by means of water circulating value of the equilibrium constant. The equilibrium constant through the cell jacket.Spectra of the solutes were obtained calculation was deemed to have failed if the calculated by digital subtraction of a solvent spectrum, obtained at the spectra contained unacceptable features such as excessive relevant temperature, from a spectrum of the solution. The asymmetry or negative values. The free thiocyanate ion has solvent and solution spectra were recorded using the same vibrations at cu. 2055 and 735 cm-'. Ion-pair vibrations cell, with air as reference. The salt concentrations used are occur at higher wavenumbers with the exception of the given in Table 1. species Sr(NCS), and Ba(NCS), whose v(C-N) vibrations Equilibrium constant calculations were attempted by occur in the region 2030-2035 cm-'. means of the new program HYPERQUAD.2 The calcu- Resultslations were based on absorbance data at about 12 selected wavelengths along the whole spectrum.Effect of Changing Temperature Where possible AH was calculated by using the expression As the temperature is increased the v(C-N) band due to the In K x -AH/RT with the assumption that AH is indepen- ion pairs shifts to lower wavenumber, as illustrated in Fig. 1dent of temperature: the slope of the least-squares line of for LiNCS in dimethylformamide (DMF). In all our previous In K as a function of 1/T was taken as equal to -AH/R. work a shift of peak position has been taken to indicate the Molar absorbances at each wavelength, cNa, A and cMNCS,A, presence of bands, due to two or more species, whose inten- were calculated, by the method of least-squares, from the sity varies with changes in equilibrium composition; when the bands are close together this results in an apparent move- t Part 25: ref.1. ment of the peak. In this work the presence of many species Table 1 Concentrations (mmol dm-3) of solutions examined ~ ~~ 5 10 25 100 300 ~~ ~ 25 50 100 200 400 800 25 75 350 700 lo00 30 75 150 400 500 lo00 25 50 75 100 150 200 25 50 100 200 500 lo00 18.5 40 50 100 150 300 240 480 240 120 240 240 75 5 10 15 20 25 30 50 60 90 120 21 43 85 170 395 6 12 37.5 75 180 360 130 160 320 400 25 30 35 40 45 50 37.5 75 in equilibrium seemed unlikely. We will therefore first estab- lish that the shifts in peak position with temperature are not due to changes in chemical equilibria. The argument is a long one and has three parts.It is necessary to demonstrate that the phenomenon is independent of both the cation and of the solvent and to provide a plausible mechanism for it. The shift of the ion-pair v(C-N) band to lower wavenum- ber with increasing temperature is shown by the following ion pairs: LiNCS, NaNCS, KNCS, CsNCS, [MgNCS]', [CaNCS] +,[SrNCS] +,[BaNCS]', Sr(NCS), and Ba(NCS), but is not observed in spectra of solutions containing only the free thiocyanate ion such as solutions of R4N NCS (R = CH,, C,H,, C4H,). When bands due to both an ion pair and free thiocyanate can be seen separately resolved in the spectra (e.g.[MgNCS]' and NCS- in DMF) only the band due to the ion pairs shifts with temperature. This establishes the fact that the phenomenon is independent of cation. A comparable temperature shift was found with solutions in acetonitrile (AN), DMF and tetrahydrofuran (THF). This shows that the phenomenon is independent of solvent. Since the temperature shift is independent of both cation and solvent and is observed only in bands assigned to ion pairs, it must be an intrinsic property of molecules containing the coordinated thiocyanate ion. We propose that the mechanism underlying the tem-perature shift involves the population of a low-frequency vibrational state of the ion pair [(solvent),M(NCS),]"' , giving rise to hot bands as previously identified in the cyanate ion: in that case for those molecules which are in the excited state where the low-frequency 6(NCO) vibration is populated the v(C-N) vibration occurs at lower wavenum- ber than that of the molecules in the ground state.3 The ratio of the number of molecules in an excited state, with quantum number n, to the number in the ground state (n= 0) is given by eqn.(2h4 N -= exp(-nV/0.6925T) (2)No where V is the wavenumber cm- and T is the temperature in K. It follows that the number of molecules in each excited state, expressed as a fraction of the total number of mol- ecules, is given by the expression (3). 1 -exp(-iJ/0,6925T) exp( -niJ/0.6925T);'= exp(-V/0.6925T) n = 0, 1, 2, ... (3) For the free thiocyanate ion the G(NCS) vibration at ca. 475 cm-' has, at 293 K, about 92% of the molecules in the ground state, (n = 0), giving rise to an absorption band at CQ.J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 2055 cm-' and 7% in the first excited state (n = l), giving rise to the hot band at ca. 2040 cm-': the hot band appears at lower wavenumber because of the effects of anharmonicity. As the temperature is raised, so the relative population of the excited state increases, as demonstrated in Fig. 2 by the increase in intensity at ca. 2040 cm-'. It may also be noted that the fundamental band broadens slightly with increasing temperature, as shown by the increasing intensity at ca. 2070 cm-': its maximum intensity decreases as a result of three effects; the broadening of the band, the reduced ground-state population and the thermal expansion of the solution.Now, if we postulate that the ion pair has a very low fre- quency vibration then many excited states are populated, as illustrated for V = 100 cm-l, in Fig. 3. Because of the effects of anharmonicity the first hot band is at lower ,wavenumber than the fundamental in the free thiocyanate ion. So, if a very low frequency vibrational state is populated there may be a progression of hot bands to ever lower wavenumbers. The calculated molar absorbances of LiNCS at 288 K and 338 K are shown in Fig. 4. The progression in the hot bands may be seen as resulting in an asymmetric band with a long tail on the low-frequency side.There are a number of possible candidates for the low- frequency vibration(s) that are responsible for the progression in hot bands. The Li-N stretching vibration has been found' to lie at 390 cm-', which is too high to account for the phenomenon in LiNCS, but with other metals the M-N 1.o 0.8 a) 6 0.6 f! 0.4 0.2 2080 2070 2060 2050 2040 2030 2020 wave n urnber/c m -' Fig. 2 IR spectra in the v(C-N) stretching region of a solution of (C2H5),N NCS in DMF (0.24 mol dm-') at temperatures between 278 and 348 K in steps of 10 K. The arrows indicate increasing tem- perature. h $ 30-v > C $ 20-0 ' 0 280 300 O 320 340 360I I 1 I 2090 2080 2070 2060 2050 2040 2030 wavenumber/cm-' TIK Fig. 1 IR spectra in the v(C-N) stretching region of a solution of Fig.3 Occupancy (Yo)of vibrational levels with quantum number n LiNCS in DMF (0.8 mol dm-3) at temperatures between 278 and of a vibration with fundamental wavenumber of 100 cm-'. (0) 348 K in steps of 10 K. The arrows indicate increasing temperature. n = O;(A)n= l;(+)n= 2;( x)n= 3;(0)n = 4. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 wavenumber/crn-' Fig. 4 Molar absorbances calculated from spectra of solutions of LiNCS in DMF. (-) NCS-at 288 K; (-.-.-) NCS-at 338 K; (---) LiNCS at 288 K; (-. ...) LiNCS at 338 K. stretching frequency is much lower (estimates vary in the range 100-200 cm-'). The most likely vibration in the (solvent),LiNCS case is the M-(NCS) wagging mode, S(MNC). This has been found in the region 98-105 cm-' in a number of octahedral thiocyanato complexes6 though a normal coordinate analysis performed on [Zn(NCS)J2 -led to the suggestion that G(MNC) is thoroughly mixed with S(NMN) which occurs at lower frequencies.' Excitation of either G(MNC) and/or v(M-N) may be expected to weaken the metal-thiocyanate interaction and therefore give rise to absorption maxima at lower wavenumbers, an effect to be added to the effects of anharmonicity.We have searched the region from ca. 2800 cm-' to ca. 1600 cm-' for both sum and difference bands of v(C-N) with the low-frequency vibration, without success, so that the actual value(s) remains unknown. The intensity of the transition u, -+u,+ will be propor- tional to the population of the u, level and will show the same tendencies as the populations illustrated in Fig.3. The effect of increasing temperature is to reduce the population of the ground state whilst the populations of the excited states increase. The decrease in ground-state population is more rapid than the increase of any single excited state. Thus, assuming that the fundamental and hot bands are extensively overlapped, the spectrum will show a decrease in intensity at the high-frequency side of the absorption band, and a general increase in intensity at the positions of all the hot bands. This will result in a band which appears to be shifted to lower frequency, is broader and has a more pronounced tail on the low-frequency side.The calculated spectrum at 338 K shown in Fig. 4 displays precisely these characteristics. Note, the small change in intensity at ca. 2040 cm-' is due to the pro- portion of the hot band of the free thiocyanate ion increasing with temperature. Having established that band shifts with temperature are not due to changes in equilibria it becomes possible to analyse the effect of changing temperature on the ion-pairing equilibria. In other words, the band intensities can be used to estimate equilibrium constants notwithstanding the fact that the peak positions change with temperature. DMF Solutions Lithium Thiocyanate There are only two species in equilibrium, the free ion and the contact ion pair. The stability constants for the 1 : 1 ion Table 2 Stability constants for LiNCS in DMF at various tem- peratures 278 0.94 (6) 288 0.97 (6) 298 0.93 (6) 308 0.94 (6) 316 0.79 (8) 328 0.80 (9) 338 0.70 (9) pair are given in Table 2 and calculated molar absorbances are shown in Fig.4.Log /3 appears to decrease slightly with temperature which indicates that the formation of this ion pair is weakly exothermic: AH = -7 & 2 kJ mol-'. In the v(C-S) region there is a band due to DMF coordinated to Li which overlies the coordinated thiocyanate band, making + the latter difficult to observe. Sodium Thiocyanate Representative spectra obtained in the region of the v(C-N) bands are shown in Fig. 5. There is extensive overlap between the bands due to the contact ion pair and the free ion.Because of this, the spectrum shows a single asymmetric peak which appears to narrow and move to higher wavenumber with increasing temperature, a trend which is difficult to interpret unambiguously. In the v(C-S) region, Fig. 6, the band at 765 cm- ',which has been assigned to the N-bonded ion pair NaNCS,* shows evidence of being a multiplet and although the peak 1.4 1.2 $ 1.0 C 0.8' 0.60, 0.4 0.2 I 1 2090 2080 2070 2060 2050 2040 2030 wavenurnber/crn-' Fig. 5 IR spectra in the v(C-N) stretching region of a solution of NaNCS in DMF (0.4 mol dm-3) at temperatures between 278 and 348 K in steps of 10 K. The arrows indicate increasing temperature. 1.2 Q) g 1.0 (0 0.84 0.6 0.4 0.2 I 800 790 780 770 760 750 740 730 720 710 wavenurnber/cm -' Fig.6 IR spectra in the v(C-S) stretching region of a solution of NaNCS in DMF (2.0 mol dm-3) at temperatures between 278 and 338 K in steps of 10 K. The arrows indicate increasing temperature. maximum does not shift with temperature the band shape changes. At the same time the band due to the free ion moves to slightly lower wavenumber, and broadens considerably. It is noteworthy that, in contrast with the v(C-N) region, there is a general decrease in intensity with increasing temperature. Potassium Thiocyanate Representative spectra in the v(C-S) region are shown in Fig. 7. The potassium and sodium thiocyanate systems are qualitatively similar with the intensities suggesting that pot- assium forms a weaker ion-pair than does sodium.Caesium T hiocyanate There is evidence for ion pairing, but the bands due to the two species are extensively overlapped. Magnesium Thiocyanate Representative spectra are shown in Fig. 8. This salt has limited solubility in DMF but nevertheless an approximate stability constant of log fi = 1.7 at 293 K was obtained. The intensity of the ion-pair band increases with temperature showing that the formation of this species is endothermic. Calcium Thiocyanate Representative spectra are shown in Fig. 9. Log fi for this ion pair is ca. 0.9. The small decrease in maximum intensity of the ion-pair band, taken together with the fact that the inten- sity of the free ion band usually decreases indicates that the ion-pairing process is approximately athermic.".s 1.2'11 .o 0.8' I1 4 0.6 0.4 o.20.0I- I 760 750 740 730 720 710 700 wavenumber/crn-' Fig. 7 IR spectra in the v(C-S) stretching region of a solution of KNCS in DMF (1.0 mol dm-3) at temperatures between 278 and 338 K in steps of 10 K. The arrows indicate increasing temperature. I I 2120 2100 2080 2060 2040 2020 waven umber/crn -' Fig. 8 IR spectra in the v(C-N) stretching region of a solution of Mg(NCS), in DMF (0.09 mol dm-3) at temperatures between 298 and 348 K in steps of 10 K. The arrows indicate increasing tem- perature. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 1.4 1.21 Q, 1 .o 0.8e2 0.6 rn 0.4 o.2I 2090 2080 2070 2060 2050 2040 2030 waven urn ber/cm -' Fig.9 IR spectra in the v(C-N) stretching region of a solution of Ca(NCS), in DMF (0.395 mol dm-3) at temperatures between 278 and 338 K in steps of 10 K. The arrows indicate increasing tem- perature. Strontium Thiocyanate and Barium Thiocyanate The spectra of solutions of these salts are qualitatively similar to those of Ca(NCS), but with more extensive overlap between the free ion and ion-pair bands. AN Solutions Lithium Thiocyanate We have reported previously details concerning solutions of LiNCS in AN at 293 K.' We postulated the existence of both inner-and outer-sphere ion pairs. Representative spectra showing the effects of changing temperature are given in Fig.10. Since the band due to the inner-sphere ion pair decreases in intensity whilst the composite band representing the free ion and the outer-sphere ion pair remains approximately constant we conclude that the ion-pairing process is exother- mic, and that the proportion of inner- and outer-sphere coni- plexes remains constant. Unfortunately all attempts to compute the equilibrium constants using HYPERQUAD failed. Sodium Thiocyanate Representative spectra are shown in Fig. 11. Extensive band overlap precludes an unambiguous interpretation. Potassium Thiocyanate The spectra of solutions of this salt are similar to those of sodium thiocyanate solutions, but band overlap is more extensive. 0.181 0.161 Q, 0.14 0.12 e 0.10 0.08 g.06 0.04 0.02 2100 2090 2080 2070 2060 2050 2040 wavenumber/crn-' Fig.10 1R spectra in the v(C-N) stretching region of a solution of LiNCS in AN (0.010 mol dm-3) at temperatures between 288 and 338 K in steps of 10 K. The arrows indicate increasing temperature. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 0.35 r A/ I 0.30 0.25 0.20 0.15 0.10 0.05 2090 2080 2070 2060 2050 2040 2030 wavenumber/crn-Fig. 11 IR spectra in the v(C-N) stretching region of a solution of NaNCS in acetonitrile (0.025 mol dm-3) at temperatures between 288 and 338 K in steps of 10 K. The arrows indicate increasing tem- perature. Strontium Thiocyanate Representative spectra are shown in Fig. 12. The equilibria appear to be as follows : [Sr2+] + 2NCS-GSr(NCS), [Sr2'] + 2NCS-e([SrNCS'lNCS-) (1) The formula {[SrNCS'INCS-} represents a 1 : 1 outer-sphere ion pair between [SrNCS] and NCS- ; it could also + be called an inner-and-outer-sphere complex.In these spectra there is no evidence for the presence of free thiocyanate. This implies that log is so large that the free thiocyanate con- centration is undetectable, i.e. log PI > ca. 5. The calculated equilibrium constants for the reaction (11) are given in Table 3. [SrNCS'] + NCS-eSr(NCS), + {[SrNCS']NCS-} (11) The decrease with temperature appears to be within the experimental errors, but if this fact is ignored the value of AH z -3.6 f0.5 kJ mol-' may be obtained, showing that the reaction may be weakly exothermic. Calculated molar absorbances are shown in Fig.13. The two bands belonging 1.4 1.2 $ 1.0 C 0.8 02 0.6 m 0.4 0.2 2080 2070 2060 2050 2040 2030 2020 wavenurnber/crn-' Fig. 12 IR spectra in the v(C-N) stretching region of a solution of Sr(NCS), in AN (0.36 mol dm-3) at temperatures between 278 and 328 K in steps of 10 K. The arrows indicate increasing temperature. Table 3 Stepwise formation constants for the formation of Sr(NCS), from [SrNCS]+ and NCS- in AN at various temperatures T/K log K 278 0.88 (6) 288 0.85 (6) 298 0.84 (6) 308 0.81 (6) 319 0 21 40 2100 2060 2020 ' waven u rnber/crn-Fig. 13 Molar absorbances calculated from spectra of solutions of Sr(NCS), in acetonitrile. (-) {[SrNCS'INCS-1 (ca.2065 cm-') and Sr(NCS), (ca. 2035 cm-'); (---) [SrNCS]+. to the species of 1 : 2 stoichiometry are well separated; the inner-and-outer-sphere complex band is on the high wave- number side of the 1 : 1 ion-pair band, whilst the inner-sphere complex has a band at much lower wavenumber. It should be noted that both bands shift with temperature. Barium Thiocyanate The spectra shown in Fig. 14 resemble those of the strontium system. Log K z 0.7 at 298 K. This reaction is approximately athermic. THF Solutions We have confirmed the temperature shift of LiNCS in THF illustrated in Fig. 1 of the paper by Goralski and Chabanel." Discussion For the most part we agree with the assignments of the vibra- tional bands given in the literature, except that a triple ion has been suggested for magnesium and calcium thiocyanates in DMF," for which we find no evidence.No data for stron- tium and barium thiocyanates in AN have been previously published. The strontium thiocyanate-AN system has provided the first instance in which the spectrum of an outer-sphere complex has been resolved from the experimental data. Nor- mally the band due to an outer-sphere complex is very close to the band due to the free ion, and its presence has been I 2080 2070 2060 2050 2040 2030 2020 waven u mber/crn-' Fig. 14 IR spectra of the v(C-N) stretching regon of a solution of Ba(NCS), in AN (0.045 mol dm-3) at temperatures between 278 and 338 K in steps of 10 K. The arrows indicate increasing temperature.3 20 inferred from the asymmetry of the second derivative of the latter.12 In this case the bands are 'resolved' by means of an equilibrium constant calculation. It can be seen in Fig. 13 that the outer-sphere complex of [SrNCS]+ has a band at slightly higher wavenumber than that of the [SrNCS] + ion itself: the separation is approximately one sixth of the half- width which means that the two bands could not be separat- ed either by curve resolution' or numerical differentiati~n.'~ It is also interesting to note that [SrNCS]+ forms both inner- and outer-sphere complexes with thiocyanate in AN that appear to have comparable stability in so far as they are both present in equilibrium with the core ion. This behaviour is an exact parallel to what we have proposed, on the basis of less direct evidence, for the Li + ~ation.~ The enthalpy of the ion-pairing interaction can, in prin- ciple, be calculated from the variation of the equilibrium con- stant with temperature.However it is well known that this method requires equilibrium constants to be known with great precision and we have not yet been able to achieve a precision high enough to enable enthalpies to be calculated in all cases. Nevertheless, ion-pairing processes can be classed as exothermic, athermic or endothermic on the basis of the qualitative changes in spectra with changes of temperature. A summary of the available information is shown in Table 4. The formation of a contact ion pair is a complex process involving the desolvation of both cation and anion as well as the formation of a cation-anion link and reorganization of the solvent.It must therefore be seen as fortuitous and so many of the reactions studied have proved to be athermic, endothermic or, at best, weakly ex other mi^.'^ However, if ion-pairing is athermic or endothermic (or weakly exothermic with a large equilibrium constant) it follows that the entropy change that accompanies the process must be positive, that is, Table 4 Thermicity of ion-pair information in DMF and AN ion-pair DMF AN LiNCS exothermic exothermic MgNCS endothermic -[CaNCS] athermic -+ Sr(NCS), -athermic" Ba(NCS) -athermic Both inner- and outer-sphere complexes are formed. J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 that there must be an overall increase in disorder in the solu- tion. This may appear to be paradoxical as the formation of the ion pair is accompanied by a loss of some of the trans- lational entropy of the separated ions. The paradox is re- solved by noting that the entropy change is determined by the same set of factors as the enthalpy change. In addition, when two solvated ions come together to form a contact ion pair one or more solvent molecules will presumably be liberated to the bulk solvent with a concomitant gain of translational entropy. It may be noted that the electrostatic potential of the monopolar ions in solution operates over a much longer range than that of the dipolar ion pairs.The increase in dis- order can be interpreted as due to a loss of local order around the cations and anions. Whether this amounts to evidence for a pseudo-lattice structure in solutions of fully dissociated salts may well be a matter for debate. References 1 P. Gans, J. B. Gill and L. H. Johnson, J. Chem. SOC., Dalton Trans., 1993, 345. 2 A. Sabatini, A. Vacca and P. Gans, Coord. Chem. Rev., 1992, 120, 389. 3 J. Rannou and M. Chabanel, J. Chim. Phys., 1980,77,201. 4 P. Gans, Vibrating Molecules, Chapman and Hall, London, 1971. 5 D. Paoli, M. Luqon and M. Chabanel, Spectrochim. Acta, Part A, 1978,34, 1087. 6 R. J. H. Clark and A. D. J. Goodwin, Spectrochim. Acta, Part A, 1970,26, 323. 7 D. Forster and W. D. Horrocks, lnorg. Chem., 1967,6,339. 8 D. Paoli, M. Luqon and M. Chabanel, Spectrochim. Acta, Part A, 1978,34,1087. 9 P. Gans, J. B. Gill and P. J. Longdon, J. Chem. SOC.,Faraday Trans., 1989,85, 1835. 10 P. Goralski and M. Chabanel, Znorg. Chem., 1987,26,2169. 11 I. S. Perelygin, V. S. Osipov and S. I. Gryaznoz, Russ. J. Phys. Chem., 1985,59, 1462. 12 P. Gans, J. B. Gill and J. N. Towning, Z. Phys. Chem., 1982, 133, 159. 13 P. Gans and J. B. Gill, Anal. Chem., 1980,52,351. 14 P. Gans and J. B. Gill, Appl. Specrrosc., 1983,37, 515. 15 D. D. K. Chingakule, P. Gans and J. B. Gill, Monatsh. Chem., 1992,123,521. Paper 3/05194C; Received 31st August, 1993