5254
J. Phys. Chem. 1993,97, 5254-5259
Theoretical Simulation and Experimental Determination of OH and OD Stretching Bands of Isotopically Diluted HDO Molecules in Aqueous Electrolyte Solutions Jan Lindgren' and Kersti H e r m a n Institute of Chemistry, University of Uppsala, Box 531, S-751 21 Uppsala, Sweden
Marek J. W6jcik Faculty of Chemistry, Jagiellonian University, 30-060 Krakbw, Ingardena 3, Poland Received: February 19, 1993
A combined theoretical and experimental study of the hydration of ions in aqueous electrolyte solutions is presented. Theoretical simulations of O H and OD stretching bands of isotopically diluted HDO molecules in a 0.44 m lithium formate solution have been performed. The positions of the atoms of the water molecules and the ions were taken from the trajectory file of a rigid-molecule room-temperature molecular dynamics simulation. V(rOH)potential energy functions were constructed as a sum of intra- and intermolecular energies and used in a variational calculation of the vibrational energy levels. Vibrational transition densities of states were calculated for HDO molecules in the first and second hydration shells of the ions. Infrared spectra of isotopically isolated HDO molecules in aqueous solutions of NaHCOO, LiC104, NaC104, Ca(C104)2, and Sr(C10& have been registered. The spectra were evaluated using an earlier developed double-difference method, where the number of ion-affected water molecules enters as a parameter in the analysis. In the present work, this number is obtained from the theoretical calculations, both for the Li+ and the HCOO- ion hydration. We find that OH/OD groups of water molecules in the second hydration shell of Li+, hydrogen-bonded to the first hydration shell, are affected by the ion. The earlier observed division of IR stretching frequencies for HDO molecules around cations into two distinct groups can now be explained by the presence or absence of such second-hydration-shell water molecules. For HDO molecules hydrogen-bonded to the HCOO-ions, the OH/ OD frequency is lowered, compared to bulk water, for the OH/OD group involved in H-bonding to the ion, whereas the frequency is increased for the other OD/OH group, pointing away from the ion. The frequencies of HDO molecules surrounding the CH end of the formate ion are not influenced by the ion.
Introduction Infrared and Raman studies of ionic solutionsand solid hydrates were recently reviewed in refs 1 and 2. Calculations of band shapes of OH stretching vibrations for water and electrolyte solutions have been performed by several groups using different techniques. Spectral density calculations based on Fourier transformsof thevelocity autocorrelationfunctions obtained from classical molecular dynamics (MD) simulations have been one a p p r ~ a c h . ~Quantum -~ vibrational analyses of water configurations from Monte Carlo calculations have also been used for some aqueous In the above studies, the band shapes were calculated for H20 molecules, and problems with the intramolecular coupling between the two OH oscillators and couplings between oscillators on different water molecules make the comparison with experimental spectra difficult. The technique of using isotopically diluted HDO molecules in infrared spectrscopical studies has been used on solid hydrates for a long time (for reviews, see refs 9 and 10). The interpretation of such spectra is greatly simplified because measured frequencies are free from intra- and intermolecular vibrational couplings as well as from Fermi resonances between the stretching vibrations and the first bending overtone. This technique has recently been applied to aqueous electrolyte solutions at the Institute of Chemistry in Uppsala.' '-I6 Each chemically different OH (or OD) bond, i.e., with different molecular environment, here gives rise toone absorptionband. Even so, thevarious bands are broad, and band overlaps frequently occur. We have thereforerecently17performed theoretical simulations of OH and OD stretching frequencies of isotopically isolated HDO molecules in aqueous solution. We investigated the stretching frequencies of HDO molecules in bulk water and in the first coordinationspheresof lithium and formate ions. In the 0022-3654/93/2091-5254$04.00/0
present work, the hydration situation around the lithium and formate ions will be examined in more detail. Results from both theoretical calculations and experimental measurementsof spectra will be presented and compared. Spectra from a series of alkali metal and alkaline-earth salt solutions will be discussed in light of the theoretical results on the lithium ion hydration. Methods
Experiment. Stock solutions of analytical grade salts were prepared and the concentrationsdetermined by passing solutions through a cation exchanger and titrating the eluate using a standard base. D20 (99.98%) from StudsvikAB was used in the preparation of the isotopically diluted HDO solutions. The HDO solutions were prepared by adding a weighed amount of D20 to a weighed amount of stock solution. The reference H2O solutions were prepared by adding an equivalent amount of H20 to the stock solutions. Spectra were recorded on a Perkin-Elmer 500B spectrometer on line with a Perkin-Elmer Data Station 3500. The resolutionselectedwas 10cm-l to minimize thenoise. Sixteen scans (60 min) were made in the region 1800-2400 cm-I, and the average was taken. The solutionswere contained in a cell equipped with CaFz windows and a Teflon spacer, with a path length of 0.050 mm, as determined interferometrically. The temperature was kept at 20.0 OC by circulating thermostated water through the mounting plates of the cell. Evaluation of the Spectra. The double-difference technique used in this study has previously been described in detail.'' Therefore, only a brief outline of the method is given here. The spectra of the decoupled OD oscillators in the hydration spheres of an Meq+ ion and an X- ion in a Me9+Xb(q/b)-(aq)solution were obtained by recording the spectra of the following four solutions: (A) x M Me4+Xb(db)-and 8.00 mol % HDO in H2O; (B) x M 0 1993 American Chemical Society
The Journal of Physical Chemistry, Vol. 97, No. 20, 1993 5255
Determination of OH and OD Stretching Bands
H20; (C) 8.00 mol 9% HDO in H20; and (D) H20. Here Meq+ is Na+, Li+, Ca2+,or Sr2+and X is C104- or HCOO-. The difference spectrum is then calculated as Meq+Xb(q/b)-in
where Aobs,Bobs, Cobs, and D0b are the spectra corresponding to the solutions A, B, C, and D, respectively. The scale factors kl and k2 were determined from
(3) where C H ~ O are ( ) the HzO concentrations in the different solutions. The scale factor k3 was determined from the relation
where C(s) is the salt concentration and m and n are the number of cation- and anion-affected water molecules. The scale factor k3and hence the number of ion-affected water moleculesper ion may in some cases be determined by a band-shape analysis.” Conversely, if the numbers m and n can be determined from other sources,thedifferencespectra can beobtainedusing relations 4 and 1. Calculatiom. Our method of calculating vibrational frequencies of isotopically isolated HDO molecules in solution will be reviewed briefly here. The reader is referred to ref 17 for more details. The H2O molecules were placed at positions and orientations generated in a molecular dynamics (MD) simulationlaof a 0.44 m lithium formate aqueous solution at 300 K. From configurations obtained at regular intervals in the 20-ps MD calculation, OH/OD vibrators were selected accordingto certain geometrical criteria specified below under Results and Discussion. In the calculations, all vibrational couplings have been neglected and only one-dimensionalOH/OD anharmonicvibrators were treated. The OH/OD frequency for a given bond was calculated in the following way. A sum of intra- and intermolecular energies for the selected HDO molecule was calculated with one OH/OD bond fixed at 0.957 A and the other varied between 0.900 and 1.035 A at intervals of 0.015 A. The intermolecular energies were calculated using the same atom-atom potentials as were used in the MD simulation, i.e., the water-water interaction potential was that of Matsuoka, Clementi, and Yoshimine (MCY),l9 the Li+-H20 potential was taken from Kistenmacher et al.20 (refitted by Hermansson et a1.I8),and the HCOO--HzO potential was taken from ref 21; all interaction potentials were derived fromab initio calculations. In addition, calculationshave been made using two other water-water potentials, viz., the one by Jargensen (TIPS222)and the one by Reimers et al. (RWK223). The intramolecular potential chosen was the quartic potential of Hoy et for the free water molecule, expressed in p coordinates as used by Carney et al.25 (p = &/r, 6r = r - re).The energies obtained were fitted to a polynomial. The vibrational eigenstates were obtained by solving the one-dimensional Schr6 dinger equation in a variational calculation. Density-of-states histograms were constructed and are presented in the figures. The justification for using different potentials from those used to generate the configurationswas discussed in ref 17. For bulk water, we calculated spectra using the MCY potential for configurations generated with the modified CF2 central force potential by Bopp et al.3 The positions of the OH and OD bands were the same as with configurations generated with the MCY potential. A comparison with infrared spectra should take into consideration the variation of the transition dipole moments with frequency; therefore, the density-of-states bands were weighed according to linear relationships of intensity vs frequency found
experimentally for water molecules in different ~ o l v e n t s .Band ~~.~~ parameters for thedensity-of-statesbands and the weighed spectra are given in Table I. The uncertaintiesof the frequencies reported are 1 5 cm-I. The calculations performed with the RWK2 potential give rise to some spurious,very high frequencies which would give rise to negative IR intensities-therefore, we do not include IR intensity data for the RWK2 potential in Table I.
Results and Discussion OH and OD Spectra of the Hydrated Li+Ion. Experiment. As described in the Experimental Section above, the evaluation of the difference spectra requires knowledge of the scale factor k3. Due to severe band overlap in the spectra discussed here, no bandshape analyses giving k3 were possible. We have therefore taken the numbers m and n (the number of water molecules affected by the cation and anion, respectively) from other sources. For the Clod-ion, n has been determined to be 4.6(5) by diffraction28 and 3.8(3) by infrared spectroscopic technique^;^^ the latter has been used in the present cases. In the case of LiC104(aq), we have used m = 6 for the Li+ ion, which is the coordinationnumber determined experimentally by neutron diffraction30 and theoretically from MD simulations (ref 18 and references therein). The resulting differencespectrum is given in Figure 1, and shows one band maximum at 2630 cm-I with two shoulders at lower frequencies. A difference spectrum of a 0.52 M Ni(C10d2(aq) solution,Il evaluated in exactly the same manner using m = 6, is shown in the insert in Figure 1; two well-defined bands at 2630 and 2420 cm-1 are seen. The bands at 2630 cm-I are common to the two spectra and originate from OD oscillators hydrogenbonded to the Clod- ions. The band at 2420 cm-I for Ni(C104)2(aq) has been assigned to OD oscillators in the hydration shell of the Ni2+ ion.” One possible explanation for the two shoulders corresponding to the hydrated Li+ ion is that too large a bulk water contribution was subtracted in the spectral evaluation procedure, Le., the assumed value of 6 for m is too low (cf. eqs 1 and 4). A series of theoretical calculations were therefore undertaken to investigate the possibility of a larger effective hydration number around Li+. Calculations. In the MD simulation,18it was found that an exchangeof water molecules takes place around the Li+ ions and that, during rather long periods of time, the ions were surrounded by seven water molecules instead of six. We have calculated densities of states for OD and OH vibrations of HDO molecules separately for cases with six and seven coordination (see Figure 2). No difference between the two groups is observed; Le., all first-shell water molecules are equally much affected by the Li+ ion. Due to the relatively small number of seven-coordinated configurations, however, the increase in effective hydration number originating from this effect is less than 0.1. Next, the second hydration shell of the Li+ ion was considered. The analysis of our MD configurationsshows that in many cases a water molecule outside the first coordination sphere donates one hydrogen bond to a water molecule within the first sphere. This hydrogen atom is rather close to the Li+ ion, and we have calculated densities of states for such OH/OD bonds, as well as for the other OD/OH bond on the same water molecule, Le., the one pointing away from the Li+ ion out into the bulk. The following classification for hydrogen bonding has been used: an 0-H.-0 contact is considered a hydrogen bond when the angle between the 0-H and 0-0 directions is smaller than 20° and the distance R ( 0 - 0 ) less than 3.5 A. Oscillators of types 1 and 3 (see Figure 3 for the definition of the types) result in densityof-state bands very close to those for bulk water.17 Oscillators of type 2, however, give rise to density-of-state bands shifted to higher wavenumbers; the shifts relative to bulk water of the OH stretching frequencies for the three potentials (MCY, TIPS2, RWK2) are 8, 47, and 79 cm-1. A decrease in the half-widths relative to bulk water is also seen. We conclude that these oscillators (type 2) are significantly affected by the Li+ ions.
5256 The Journal of Physical Chemistry, Vol. 97, No. 20, 1993
Lindgren et al.
TABLE I: Band Parameters of the OD and OH Stretching Vibrations of Isotopically Dilute HDO Molecules Calculated with Different Water-Water Intermolecular Potentials (in cm-9’ density of states position
0
IR intensity half-width
potential
v(OD)
v(OH)
v(OD)
MCY TIPS2 RWKZ
2569 2556 2587
3489 3467 3514
119 187 228
MCY TIPS2 RWKZ
2554 2478 2470
MCY TIPS2 RWK2
position
dOH) Bulk Water 166 248 31 1
half-width
v(OD)
v(OH)
dOD)
v(OH)
2553 2526
3464 3421
113 172
156 236
3469 3359 3353
First Shell of Lit with Six Waters 115 162 2540 178 257 2456 235 326
3441 3326
113 180
151 249
2555 2494 2487
3470 3382 3375
First Shell of Li+ with Seven Waters 116 155 2540 177 247 2472 23 1 262
3447 3349
99 176
145 256
MCY TIPS2 RWKZ
2560 2542 2559
3477 3447 3474
Second Shell of Lit, Type 1 109 149 2546 186 253 2515 229 318
3455 3407
107 170
145 230
MCY TIPS2 RWKZ
2575 2591 2646
3497 3514 3593
Second Shell of Lit, Type 2 84 118 2562 125 177 2569 170 226
3478 3480
82 123
132 157
MCY TIPS2 RWKZ
2564 2537 2558
3483 3440 3474
Second Shell of Lit, Type 3 115 144 2549 139 189 2511 218 280
3460 3401
116 128
133 209
MCY TIPS2 RWKZ
2571 2561 2585
349 1 3474 3510
First Shell of HCOO-, around C-H 131 182 2554 161 223 2532 220 309
3466 3430
121 148
163 205
The definition of three different types of second-shell O H (OD) groups is given in. Figure 3.
0.08 1
I
wol
0.4 M IiCIO,
0.52 M Ni(CIO&
0
2900
2500
2 100 Wavenumbers lcm-1)
Figure 1. Infrared difference spectrum in the OD stretching region of 0.4 M LiC104(aq). Crosses indicate the measured spectrum, and the solid line is a band-shape-fitted spectrum. The inset, showing the OD stretching spectrum of 0.52 M Ni(ClO&(aq), is taken from ref 11. C(HD0) = 8 mol %, T = 20.0 OC, path length = 0.050 mm.
Spectra of Different Mono-, Di-, and Trivalent Hydrated Cations. In the evaluation of the experimentaldifference spectra, we assumed six cation-affected water molecules in eq 1. If, as is suggested by the calculations, more than six molecules are affected, the experimental spectra have to be reevaluated. The number m in eq 4 equals [2m( 1st) + m(2nd)]/2, since only one OH/OD oscillator per second-shell water molecule is involved in hydrogen-bond donation to a first-shell water molecule. We do not know how many second-shell water molecules are involved in hydrogen bonding to the first shell in real solutions; here we have chosen to use the maximum number of affected water molecules, Le., 9 (6 + 3 = 9). The resulting spectrum for the LiC104(aq) solution is presented in Figure 4, where also the
2200 23W 2402 25W 26W 27W 28W 2 K) (“1)
Figure 2. Calculated densities of states for the first hydration shell of Lit. The solid line refers to configurations with six water molecules and the dashed to seven water molecules in the shell. Here and in Figures 3 and 6 the spectra to the left are for O H and those to the right for OD.
experimentaldifference spectra for Na+,Ca2+,and Sr2+are given. The maximum number of affected water molecules for these ions would be 6 + 3,9 + 4.5, and 11 + 5.5, respectively, based on the first-shell coordination numbers given in ref 5 . It is now seen that, for this maximum number of affected water molecules, one broad band results, besides the 2630-cm-1 band from the C1O4---affectedmolecules. The peakmaxima and the half-widths (full widths at half-maximum) obtained from a band fit to the bands, as described in ref 11, are 25 19 and 180cm-l ,respectively, for Li+, 2528 and 138 cm-1 for Na+, 25 18 and 173 cm-1 for Ca2+, and 2529 and 156 cm-1 for SrZ+. The estimated standard deviations of the peak maxima and half-widths are 10 cm-I.
The Journal of Physical Chemistry, Vol. 97, No. 20, 1993 5257
Determination of OH and OD Stretching Bands
I
2600
"C"
h'
7E
U
2200 2300 2400 2500 2600 2700 2800 2
Figure 3. Calculated densities of states for the different types of waterion geometries found in the second hydration shell of Li+.
2500
t
Figure 5. Band positions (YOD) for a number of hydrated cations as a function of the ion charge/radius ratio. The figure is taken from ref 13.
for CaZ+,for example, is twice that of Na+; one might therefore have expected a shift to lower wavenumbers for the hydration band of CaZ+relative that of Na+. In order to rationalize the experimental and theoretical observations concerning this similarity between the spectra for different cations, we make use of the potential energy curves presented in ref 17. There the variation of the interaction energy between a vibrating water molecule and its surroundings was calculated for a water dimer and a Li+.HZO--H20complex when the H-bond-donating OH bond was being stretched. In both complexes, the O-.O distancewas fiied and only the0-H distance varied. The interaction energy becomes more negative (attractive) as the 0-H bond is stretched. The total (intra + inter) potential energy curve for bonded HDO molecules thus gives a larger equilibrium OH distance and a lower OH/OD vibrational frequency than the free HDO molecule. This explains why the frequency of the water molecules in the first hydration shell of Li+ is downshifted. If, however, the direction of the water 0-H bond relative to Li+ is reversed, as is the case for the type 2 oscillators discussed above, the slope of the almost linear Coulombic contributionto the intermolecular interaction between H and Li+ becomes positive instead of negative. The slope of the total intermolecular interaction energy with respect to OH bond stretching for a type 2 oscillator is still negative, due to the interaction with the other water neighbors, but now less so. The result is a smaller increase in &H distance (with respect to the free water molecule) and a smaller frequency downshgt for the type 2 oscillators compared to the lithium-coordinated water molecules. The difference in the frequency shift for these two types of OH oscillator (cation-coordinated and type 2) would clearly be a function of the charge/radius ratio of the cation; a small ratio gives a small difference and a larger ratio a larger difference. The cation hydration bands for Li+, Ca2+, and Sr2+ are broader than that of Na+. Each of these bands is a nonresolved superposition of the two types of OD oscillators just considered; it is only in the half-widths of the bands that the difference in charge/radius ratios of the cations is observed. When the infrared band positions (YOD) for a number of hydrated cations are plotted as a function of the ion charge/ radius ratio, a division into two distinct groups is noticed (see Figure 5; see also ref 13). One group of cations (group I) produccs absorption bands around 2525 cm-' and the other (group 11) around 2420 cm-I. As discussed in ref 13, the group I ions differ from group I1 not only with respect to the frequency shifts but in several other respects as well, such as solvent dynami~s.3~ The residence lifetimes for inner-shell water molecules of group I cations are small (TM 10-11 s) compared with those of group I1 cations (TM > 10-8 s).32 Another difference is observed in the formationof crystalline hydrates. Group I1cationsare frequently found to crystallizewith their solution coordination spheres intact.
0"4K NaCI04
02 900
0.10
2 500
"
"
"
2100
"
"
LiCIO,
a,
u C
0
n
l z L L l J
0 2900
2 500
2 loo
L
0 In
n
a
Ca (C IO&
0 02900 .
0 2900
2500 1
42100
2500
2100
E
Wavenumbers (cm-l)
Figure 4. Infrared difference spectra in the OD stretching region for the different solutions indicated in the figure. C(HD0) = 8 mol 8,T = 20.0 OC, path length = 0.050 mm.
It is seen from Figure 4 that the difference spectra for the different cations are very similar, indicating similar hydration situations. This similarity may appear surprising, considering the differencesin charge/radius ratio among the ions. The ratio
-
5258 The Journal of Physical Chemistry, Vol. 97, No. 20, 1993
The more labile hydration spheres for group I cations in solution often result in the formation of lower hydrates or anhydrous salts. In the present investigation, we have found the approximately similar frequency of the hydration bands for group I cations to result from the combined absorption from first-shell water molecules and second-shell molecules hydrogen-bonding to the first shell (type 2). Group I1 (see Figure 5) consists of divalent first-row transition-metal ions and trivalent rare-earth ions. The charge/radius ratios are larger than those in group I. Secondshell water molecules of type 2 for group I1 ions would therefore be expected to absorb at higher frequencies than for group I. No such absorption band or shoulder has been observed, however] (cf. also the insert of Figure l), and we conclude that no water molecules of type 2 geometry exist in the second shell for group I1 ions. This situation is possible if the water molecules in the first shell are oriented approximately trigonally, e.g., with the bisector of the water angle closely parallel to the cation-oxygen vector (we denote the angle between these vectors as 8). Such a coordination geometry is in contrast to the bonding situation found for Li+(aq) above, where the first-shell water molecules are "tetrahedrally" coordinated, with a Li+ contact and a secondshell hydrogen-bonded water contact in the two oxygen lone-pair directions. For the ideal trigonal and tetrahedral cases, 8 equals 0 and 55O, respectively. Neutron diffraction studies of Dy3+(aq) and Nd3+(aq)34have reported 8 values of 17 f 3 O and 24 f 4O, respectively. 8 values obtained from neutron diffraction are evaluated from the difference in the aaerage metal-oxygen and metal-hydrogen distances and represent the average absolute deviation of 8 from zero. A non-zero value of 8 does not necessarily indicate that the equilibrium geometry differs from a trigonal configuration, however; it can also arise from librationaltype motion of the water molecule around an average trigonal geometry. We have estimated the 8 value for a D 2 0 molecule executing a wagging libration at 400 cm-l and 300 K to 10'. Other types of motion, such as rotational diffusion, can further increase the 8 value. We thus conclude that the observed 8 values for Dy3+(aq) and Nd3+(aq) (17 and 24O) are consistent with trigonal coordinations. We also suggest that the group I1 ions all have closely trigonal first-shell water coordinations, with no (or few) type 2 water molecules present. OHandODSpectraoftheHydratedHCCKkIon. Calculations. The water molecules surrounding the formate ion in the 0.44 m lithium formate solution have been divided into two categories: those hydrogen-bonded to the formate oxygen atoms and those which are close to, but not hydrogen-bonded to, the ion. The latter category consists of water molecules surrounding the CH end of the ion. The geometric criterion for hydrogen bonding was the one given above. The results for the hydrogen-bonded water molecules were presented in ref 17, where the densities of states for the OH/OD groups hydrogen-bonded to the formate 0 atoms were given, as well as densities of states for the other OD/OH groups of the same water molecule but pointing away from the ion. The density-of-state bands of the hydrogen-bonding OH/OD groups are shifted to lower wavenumbers and the other group to higher wavenumbers, compared to the bulk water band. The two bands were drawn separately, and the peak values were scaled to the same height. In Figure 6 of the present work, no such scaling has been made; Le., the band areas represent the number of oscillators and can be directly compared with experimental spectra (when converted from densities of states to intensities). For the TIPS2 and RWK2 potentials, the two componentsare so far apart that a clear high-frequency shoulder is seen. Thedensity-of-statebands for the water molecules around the W e n d is given in Figure 7 and are seen to be exactly similar to those for bulk water given in ref 17. A similar conclusion was drawn from infrared spectroscopic studies on CF$O3- and CF3COO- ion^;^^.^^ the absorption from water molecules sur-
Lindgren et al.
A
P.;; A
RW2
0 2300 2400 25W 26CC 27W 28W 2
x)
(")
Figure 6. Calculated densities of states for the first hydration shell surrounding the COO- end of HCOO-, for the different potentials used here.
j
,
I
I
I
I
I
I
I
I
I
I
3 0 3200 3300 3400 3500 3600 3700 3 00 (cm-')
Figure 7. Calculated densities of states for water molecules surrounding the CH end of the HCOO- ion and for bulk water.
rounding the nonpolar CF3 ends could not be distinguished from the bulk water absorption. Experiment. The evaluation of the experimental difference spectra of OD vibrations of isotopically isolated HDO molecules around the HCOO- ion requires several steps. Solutions of NaC104and NaHCOO were studied. The band from the water molecules affected by the C104- ion taken from ref 11. This enabled us to derive the band from the Na+ ion-affected water molecules from the spectra of the NaC104 solutions. This Na+(as) band was then used in the difference procedure for the NaHCOO solutions. Unlike the other s p t r a given in this work, the final difference spectrum for HCOO- (Figure 8) is thus one where the cation-affected water band has been subtracted. The evaluation also requires the knowledge of the number of water molecules affected by the HCOO- ion. We have used the results from the M D simulation,I8 where it was found that on average 4.5 water molecules were hydrogen-bonded to the formate 0
Determination of OH and OD Stretching Bands
The Journal of Physical Chemistry, Vol. 97, No. 20, 1993 5259 into two groups,consisting of molecules around the nonpolar CH and around the polar COO- ends. The calculated OH/OD stretchingbands for the former group coincide with thecalculated bulk water bands, while the COO- end water molecules give rise to two bands, one on either side of the bulk band, in agreement with experiment.
n L
0
ro
Acknowledgment. This work has been supported with grants from the Swedish Natural Science Research Council which is gratefully acknowledged. A travel grant from Uppsala University for M.J.W. is also gratefully acknowledged, as is the support from the Polish Committee on Research (No. 2 2690 92 03).
n 4
2900
2 500
2100
W a v e n u m ber s (cm-1)
Figure 8. Infrared difference spectrum in the OD stretching region for HCOO-. C(HD0) = 8 mol %, T = 20.0 OC, path length = 0.050 mm.
atoms. In eq 4, we have in this case used n = 9, since, as we have seen from the calculationsthat both OH groups of the hydrogenbonding water molecules were found to be affected by the presence of the HCOO- ion. The resulting band maximum in Figure 8 is found at 2480 cm-I, and in addition, a high-frequency shoulder is present. The resemblance with the theoretical result for the TIPS2 potential (Figure 6) is evident. A high-frequency component, observed here both experimentally and theoretically for the formate ion, has also been found experimentallyfor the fluoride and sulfateZ9ions. Several other anions, on the other hand, such as PFc, BF4-, C104-? I-, B r , C1-, and N03-,29do not give rise to a high-frequency component. To shed further light on the origin of this component in the HCOOcase, we have calculated the OH/OD frequencies for an isolated HC00-.-H20 dimer with an 0-0 distance of 2.75 A. The hydrogen-bonded OH group lowered its frequency by -400 cm-I compared to a free HDO molecule, whereas the frequency of the non-hydrogen-bonded group increased by 8Ocm-I. Theanalogy with the discussion aboveconcerning second-shell water molecules around Li+ is obvious. In both cases, it is the Coulombic term in the interaction potential which governs the OH stretching frequency shift. In the case of the positive Li+ ion, those secondshell OH groups pointing toward the ion show a frequency increase as compared to an average bulk water molecule, while for the HCOO- ion the opposite is true.
-
Concluding Remarks The combined use of theoretical simulation and IR spectroscopic methods applied to the stretching vibrations of water molecules in the hydration shells of Li+ and HCOO- ions allows us to make the following conclusions. 1. The vibrations of water molecules in both the first and second hydration shells of the Li+ ion are influenced by the ion. 2. The division of the observed IR stretching frequencies for HDO molecules around cations into two distinct groups (Figure 5 ) can be explained by the presence or absence of second-shell water molecules donating hydrogen bonds to the first shell. 3. Water molecules around the HCOO- ion can be divided
References and Notes (1) Zundel, G.;Fritsch, J. In The Chemical Physics of Solvation, Part B Dogonadze, R. R., Kalman, E., Kornyshev, A. A.; Ulstrup, J., Eds.; Elsevier: Amsterdam, 1986; Chapters 2 and 3. (2) Brooker, M. H. In The Chemical Physics of Solvation, Part B Dogonadze, R. R., Kalman, E., Kornyshev, A. A,, Ulstrup, J., Eds.; Elsevier: Amsterdam, 1986; Chapter 4. (3) Bopp,P.; Jancso,G.;Heinzinger. K. Chem. Phys. Lett. 1983,98,129. (4) Probst, M. M.; Bopp, P.; Heinzinger, K.; Rode, B. M. Chem. Phys. Lett. 1984, 106, 317. ( 5 ) Bopp, P. Pure Appl. Chem. 1987, 59, 1071. (6) Lie, G. C.; Clementi, E. Phys. Rev. 1986, A33, 2679. (7) Reimers, J. R.; Watts, R. 0. Chem. Phys. 1984, 92, 201. (8) Mills, M. F.; Reimers, J. R.; Watts, R. 0.Mol. Phys. 1986,57,777. (9) Falk, M.; Knop, 0. In Water. A Comprehensive Treatise; Franks, F.,Ed.; Plenum: New York, 1973; Vol. 2, p 55. (10) Lutz, H. D. Struct. Bonding 1988,69,97. (1 1) Kristiansson, 0.; Lindgren, J.; de Villepin, J. J . Phys. Chem. 1988, 92, 2680. (12) Kristiansson, 0.;Lindgren, J. J . Mol. Srrucr. 1988, 177, 537. (13) Kristiansson, 0. Ph.D. Thesis, University of Uppala, 1989. (14) Kristiansson, 0.;Lindgren, J. J. Phys. Chem. 1991, 95, 1488. (15) BergstrBm, P.-A,; Lindgren, J. J. Mol. Struct. 1990, 239, 103. (16) Bergstrcm, P.-A.; Lindgren, J. J . Mol. Struct. 1991, 245, 221. (17) Wojcik, M. J.; Hermansson, K.; Lindgren, J.; OjamBe, L. Chem. Phys. 1993, 171, 189. (18) Hermansson, K.; Lie, G.C.; Clementi, E. IBM Technical Report, 1986, KGN 54, to be published. (19) Matsuoka, 0.;Clementi, E.; Yoshimine, M. J . Chem. Phys. 1976, 64, 1351. (20) Kistenmacher, H.; Popkie, H.; Clementi, E. J. Chem. Phys. 1973,59, 5892. (21) Hermansson, K.; Lie, G. C.; Clementi, E. Theor. Chem. Acta 1988, 74, 1. (22) Jsrgensen, W. L. J. Chem. Phys. 1982, 77,4156. (23) Reimers, J. R.; Watts, R. 0.;Klein, M. L. Chem. Phys. 1982, 64, 95. (24) Hoy, A. R.; Mills, I. M.; Strey, G.Mol. Phys. 1972, 24, 1265. (25) Carney, G. D.; Curtiss, L. A.; Langhoff, S.R. J . Mol. Spectrosc. 1976, 61. 371. (26) Glew, D. N.; Rath, N. S.Can. J . Chem. 1971, 49, 837. (27) Lindgren, J.; Persson, A. Infrared Absorption Intensities of OD Stretching Vibrations of HDO and D20. UUIC-B19-320, Institute of Chemistry, University of Uppala, Sweden. (28) Neilson, G. W.; Schibberg, D.; Luck, W. A. P. Chem. Phys. Lett. 1985, 122, 475. (29) BergstrBm,P.-A.; Lindgren, J.; Kristiansson, 0.J . Phys. Chem. 1991, 95, 8575. (30) Newsome, J. R.; Neilson, G. W.; Enderby, J. E. J. Phys. 1980, C13, L923. (31) Hunt, J. P.; Friedman, H. L. Proc. fnorg. Chem. 1983, 30, 359. (32) Hewish, N. A.; Enderby, J. C.; Howells, W. S. J . Phys. 1983, Cl6, 1777. (33) Annis, B. K.; Hahn, R. L.; Narten, A. H. J . Chem. Phys. 1985,82, 2086.
