21 08
J. R. Scherer, M. K. Go, and S.Kint
Raman Spectra and Structure of Water in Dimethyl Sulfoxide James R. Scherer,* M a n K. Go, and Saima Kint Western Regional Reseafch Laboratory, Agricultural Research Service, (Received April 26, 1973)
U.S. Department of Agriculture, Berkeley, California 94710
Publication costs assisted by Agricultural Research Service
A simple model is proposed for the structure of liquid water that explains the concentration and temperature dependence of the Raman spectra of water in water-dimethyl sulfoxide (DMSO) mixtures. The model proposes two states for a hydrogen-bonded water molecule. One state involves a symmetrically hydrogen-bonded species and the other state an asymmetrically hydrogen-bonded species. The symmetric species exhibits a symmetric OH stretching vibration, Ydsym, that is infrared and Raman active and an antisymmetric OH stretching vibration, vda5, that is active in the infrared and anisotropic Raman spectra but forbidden in the isotropic Raman spectrum. The asymmetric species has two OH stretching vibrations, one of which, I+, involves the hydrogen-bonded OH, and the other, v w , the weakly hydrogenbonded OH. Fermi resonance with the overtone of the bending vibration is shown to affect the spectra of VdsYrn and Vb. The values of the resonance constant for liquid HzO and Dz0 agree with vapor-phase results. A questionable third state involving two weak hydrogen bonds is proposed to account for weak scattering in the high-frequency region that is not explained by the two state model. The change in depolarization ratio across the OH stretching region is readily understood in terms of this model and is in good agreement with corresponding data for HOD.
I. Introduction The structure of liquid water is very complex and has been the subject of many investigati0ns.l-3 The most obvious feature in the infrared and Raman spectra of liquid HzO i s a vaguely featured broad band in the 3300-cm-1 region. This band is associated with OH stretching vibrations of HzO and various conflicting models of water structure have been proposed to explain its observed band shape. These models may be grouped into two categories. The mixture model4-11 considers the liquid to be a mixture of a small number of distinct molecular species with different numbers of hydrogen bonds per molecule, while the continuum modeP2-19 considers the liquid to be completely hydrogen bonded, but having a distribution of molecular geometries and hydrogen bond strengths. Fermi resonance between the “symmetric stretch,” u1, and the first overtone of the bending vibration, ~ V Z is, also in considerable dispute. On the continuum side, Shiffer and Hornig favor strong Fermi resonance with 2uz and Cunningham20 questions its primary importance. On the mixture side, Murphy and Bernsteinzl argue for strong Fermi resonance and Choppin and Violante6 deny its significance. The solubility of dimethyl sulfoxide (DMSO) in water and the similarity of the DMSO-water and water-water hydrogen bondsz2 prompted our Raman investigation of the water-DMSO system. The formation of water-DMSO complexes has been verified by several authors23-26 and Fermi resonance of the U I and 2uz modes of complexed water is quite apparent in the infrared spectra of tertiary systems of water, hexamethylphosphoric triamide (HMPT), and CC14,26 and to a lesser degree in the waterDMSO-CC14 and water-DMSO s y ~ t e m s . ~ 7 In the following we present a simple model for liquid water that includes features of the mixture and continuum models and is consistent with the Raman spectra of The Journal of Physical Chemistry, Vol. 77, No. 17, 1973
the water-DMSO system. The large change in the depolarization ratio across the OH stretching bandz0 can also be explained. The application of this model to pure HzO and D20 at various temperatures will be given in a later paper. 11. Experimental Section
DMSO-water mixtures of known concentrations were prepared by mixing measured volumes of dry DMSO and triply distilled water. DzO (99.84%) was obtained from Bio Rad and used without further purification.28 DMSO was dried by standing over Linde type 3A molecular sieve and finely divided particulate matter from the sieve was removed by distilling, in a closed system, small amounts of the mixture in the apparatus shown in Figure 1. The transfer of the mixture from A to B was done under vacuum using liquid Nz to cool the receiver. Capillary Raman cellszga of 0.25 mm inside diameter were used in order to facilitate the high- and low-temperature measurements. The cells were filled by dropping the open end of the capillary below the liquid surface and breaking the vacuum with dry air. The capillaries, attached to a small iron nail with teflon tubing, were manipulated by means of an external magnet. The filled capillaries were sealed by fusing the ends with an oxy-acetylene micro torch. The samples were rapidly cooled or heated with a specially constructed laminar air-flow apparatus shown in Figure 2. For low-temperature experiments (not reported here) dry air, cooled with an alcohol-dry ice slurry, was introduced a t inlet A with inlet B closed. For heating, inlet A was closed and dry air was passed through inlet B over a 15 ohm nichrome wire heater, D, connected to a 12-V transformer. E is a short section of steel wool used to even out local temperature gradients. Dry air a t room temperature was introduced a t inlet C to prevent fogging of the capillary cells. The diameters of the outer and inner
2109
Raman Spectra amd Structure of Water in Dimethyl Sulfoxide
c
VACUUM
I
Figure 2. Laminar flow cooler-heater. The capillary size has been exaggerated by a factor of 4.
t3 fcz
3800
3700
3600
3500
3400
3300
3200
3100
cm-1
Figure 1. Apparatius for distilling water-DMSO mixtures. tubes at the delivery end of the cooler are 16 and 12 mm, respectively. A 0.15-mm diameter thermocouple, F, positioned next to the capillary, was used to measure the temperature of the air at the capillary position. The small mass of the capillary ensures rapid temperature equilibration of the sample and our temperature control over several hours was found to be within f l " .The Raman scattering was imeasured from a 2 mm length of capillary, G , just below the lower surface of the capillary lens. We used a Spex 1401 double monochromater and the spectral resolution was 5 cm-I (0.35 mm slit width and 10 mm slit height). A Coherent Radiation 52B argon ion laser operating at 5145 A at power levels ranging from 40 to 500 mW was used for excitation. The detector was an RCA C31034 gallium-arsenide photomultiplier tube operating at 1400 V. The photon pulses were amplified and shaped with a SSR Instruments 1120 amplifier-discriminator, integrated on an RC network, and the output displayed on a strip chart recorder. The recorder pen output is encoded with a 1050 count encoder. The details of the data acquisition system and procedure for correcting photomultiplier and optical efficiency may be found elsewhere .29b We observe Raman scattering at 90" to the incident beam. The observed intensity using an analyzer is proportional to (4562 4p2) for a Y ( Z Z ) X experiment30 and (3p2) for a Y(Z'Y)X experiment; d is the mean polarizability derivative and p is the anisotropy derivative with respect to normal coordinate. These spectra are transformed into isotropic (I,) and anisotropic (Io)spectra31
+
I o b , ( y ( z Z ) x ) = 1, where
+ Io
I
i
r-/ 2700
\I. 2600
2500
2400
2300
cm-1
Figure 3. Isotropic and anisotropic spectra of pure DMSO from 3100 to 3800 cm-' and from 2250 to 2750 cm-'. The intensity scale for I g is reversed.
v is the vibrational frequency, and V L is the exciting frequency. This separation has the advantage that antisymmetric vibrations (depolarized lines) are forbidden in the I , spectrum and the interpretation of the Raman spectrum is simplified. The I, spectrum is frequency dependent and it is necessary to transform I, to 45G in order to consider Fermi resonances in detail. At temperatures near 300 K and higher, the factor (1 - e - h ' / R T ) is essentially unity; however, the term ( V L - u ) ~ / leads v to a 24% increase in intensity at 3600 cm-1 relative to the intensity at 3200 cm-l in the 45&2 spectrum compared to the intensities in the I , spectrum. We note that all previous work on the Raman spectra of liquid water has ignored this frequency correction. DMSO bands have been subtracted from the spectra shown in the following sections. The I , and ID spectra of dry DMSO at 23" in the region 3100-3800 cm-I and 2250-2750 cm-I are shown in Figure 3. The IB spectra The Journal of Physical Chemistry, Vol. 77, No. 17, 1973
2110
J . R. Scherer, M. K . Go,and S.Kint
and DMSO in 5 mol % water solutions. In the following sections, only the mean polarizability derivative difference spectra, 45C2, of water are shown and for simplicity we shall refer to this as the spectrum. Similarly the 4p2 spectrum will be called the 6 spectrum.
: v)
Z w c
z
3800
3700
3400
3500
3400
3300
3200
3100
cm-1
cm-1
Figure
Isotropic spectra of 5 mol YO H20-DMS0 mixture ( u p p e r ) and D20-DMSO (lower). 4.
have been plotted with a reversed intensity scale to avoid overlapping baselines. We note that the I , spectrum of dry DMSO is relatively free of bands in the region 3100-3800 cm-I. However, the intense band at 3225 cm-1 in the Io spectrum leads to baseline error in the DMSO I , spectra in this region. The baselines for the H20-DMSO I , spectra were taken to be appropriately scaled I , spectra of dry DMSO. The amount of scaling was determined by graphic comparison on a computer driven cathode ray tube (crt) of the amount of Io spectrum of dry DMSO required to match out the DMSO bands in the Io spectrum of the water-DMSO mixture in the 3100-3350-~m-~ region. The Ia spectrum of pure DMSO is relatively free of scattering from 2250 to 2550 cm-1 and it is easy to obtain accurate I , difference spectra of water in this region. However, the two DMSO bands above 2500 cm-1 undergo frequency shifts of up to 14 cm-1 with increasing water concentration. We found it possible to approximate this “solvent shift” by shifting the dry DMSO I , spectrum up by 1-cm-1 increments. The band at 2575 cm-1 also exhibited some decrease in intensity with respect to the 2625cm-1 band a t high water concentrations, but this was ignored because of the low intensity of these bands relative to the water spectrum. The I, backgrounds for the D2ODMSO mixtures were determined by graphic comparison of the intensities of the DMSO bands in the 3200-cm-l region of the IDspectra. Difficulty was experienced with dynamic error on scanning over the sharp bands a t 2600 cm-1. We therefore scanned this region a t very slow speeds (0.4 cm-l/sec) with 0.1 sec time constant. In all, these difficulties lead to inaccuracies estimated to be no more than 5% of full scale in the region above 2550 cm-l a t low water concentrations. At high water concentrations these errors become insignificant. In Figure 4 we show the relative intensities of the I , bands of water The Journal of Physical Chemistry, Vol. 77, No. 17, 1973
111. Fermi Resonance Figure 5 shows the & spectrum of 25 mol ’%o*HzOin DMSO and the OH stretching region of HOD in DMSO (25 mol % total water with a mixture ratio of D20 to H20 of 6 : l or a [HOD]/[HzO] = 11).The low-frequency shoulder a t 3300 cm-1 in the H2O spectrum we attribute to a Fermi resonance32 of the symmetric stretch and the first overtone of the HOH bend. We attribute the absence of this shoulder in the HOD spectrum to a reduction in resonance due to lowering of the HOD bending frequency from 1640 to 1440 cm-1. We should like to classify this resonance by its occurrence in three situations. The first situation is well known and occurs between two narrow spectral lines: one usually associated with a fundamental and the other with an overtone having small or zero intrinsic intensity.33 334 This perturbation leads to two separate spectral peaks, one of which can be associated principally with the fundamental and the other the overtone which “borrows intensity” from the fundamental. The second situation, which we would like to name “The Evans hole,” is the situation where a broad distribution of active fundamental levels (resulting from many molecules) are perturbed by a narrow level involving a low-intensity transition of the same symmetry.35.36 The resonance in this instance leads to sharp “transmission holes” in the absorption spectra. The last situation is one that we feel exists in liquid water and this involves a resonance between a broad OH stretching fundamental and a broad distribution of overtone levels. The result of this interaction is a broad “Evans hole” in the observed Raman spectrum. The observed separation of two transitions of a Fermi diad,37 X, is given by where A is the separation between the unperturbed levels and W is the Fermi interaction constant. The ratio of intensities of upper to lower levels in the & spectrum is34
+ A)”’(aJaI) F ( X - A Y ] (2) -II1, = [ (X *(X + + (X - A > 1 / 2 ( ~ u / ~ J 2
where au/a1is the ratio of the matrix elements of the polarizability for the transitions from the ground state to the upper and lower unperturbed levels of the Fermi diad. If the matrix element for the overtone is assumed to be zero, eq 2 simplifies to
+
I,/I1 (X - A)/(X A) (3) The anharmonic force constants for gaseous H20 and D20 have been calculated by Smith and Overend.38 The Fermi interaction constant is given by W < ~ 1 , ~ 2 , ~ g l H ‘ /-h cl ,lv~z ~ 2 , ~ 3>
+
(h,z2/2)((v1/2)(vz + l)(uz + 2 ) Y (4) where VI, u2, and u 3 are the vibrational quantum numbers for the fundamentals, H’/hc i s the anharmonic term of the Hamiltonian, and h l 2 2 is an anharmonic force con-
2111
Raman Spectra and Structure of Water in Dimethyl Sulfoxide -------
3E100 Figure 5. d spectra in H 2 0 in DMSO (upper) mol YO DMSO) (lower).
3100
the OH stretching region of 25 mol % and HOD in DMSO (6:l D 2 0 : H p O ; 75
stant of the potential function in normal coordinate space. For the case considered here UI = 1, u2 = U Q = 0, and W = k 1 4 2 . The values of W calculated from Smith and Overend are 36 cm-I for H2O and 25 cm-1 for DzO. The effect of different values of W on our Fermi resonance calculations will be illustrated later. To calculate the effect of Fermi resonance on the spectra of liquid water we assume an unperturbed intensity distribution for VI, in the form of a product of Gaussian and Lorentzian functions.39
Figure 6. Fermi resonance calculation involving a broad symmetrical distribution of fundamental transitions centered at vo ( L = 142 cm-l, G = 240 cm-', and half-width, 118 cm-l) with a broad symmetrical distribution of overtone states centered at v o 140 cm-1 ( L = 300 cm-l, G = 115 cmJ1, band half-width, 105 cm-'). The dashed line represents the overtone distribution. i
-
I
I
I
I
1
7 -
I
A *i
(5) where G and L are the half-width parameters and vo and IO are the central frequency and intensity. Band halfwidths, Av1/2, are not related, in a simple manner, to L and G and were determined by computer search of the value of v - vo for which I ( v ) = I0/2. A similar distribution is chosen for the overtone 2v2, but, because we assume the overtone to have zero intrinsic intensity, the parameter I ( v ) in this distribution is taken to represent the probability of finding the overtone level at frequency v. We consider these distributions as resulting from summation of a large number of levels (1 cm-I wide), and eq 1 and 3 are applied. The resulting spectrum is then normalized so that the area of the 2vz distribution is unity. A similar calculation of Fermi resonance of a single level with a broad distribution of states has been given by Evans.36 Figure 6 shows the result of a calculation of Fermi resonance ( W = 36 cm-l) between a hypothetical fundamental centered at Y O and an overtone a t vo - 140 cm-1. It is obvious that Fermi resonance distorts the symmetric band shape and creates a shoulder at the overtone frequency. In Figure 7A-C we show observed and calculated d spectra for a 5 mol % solution of DzO in DMSO with W = 20, 25, and 30 cm-I. Because of difference spectra errors mentioned in the last section, we focus on the region to the low-frequency side of the central peak. The 282 distribution half-width parameters, L and G, are 200 and 79 cm-I (mostly Gaussian) and the L and G parameters for the fundamental distribution are 64 and 170 cm-1 (mostly Lorentzian). It is evident from this figure that the intensity in the 2400-c1n-~region is matched best by a value of W = 25 cm-l. The curvature and intensity of the calculated profile in this region is sensitive to the shape and
I
2750
I
1
1
1
I
2250
Calculated and observed d spectra for a 5 mol % solution of D20-DMSO with W = 20 ( A ) , 25 (E), and 30 cm-l
Figure 7.
(C).
position of the overtone distribution as well as the value of W. We found that a predominantly Lorentzian shape for 2 v ~was not as successful as a Gaussian one in matching the observed band shape. For a given value of W, the intensity of the scattering in the overtone region is determined by the separation of the fundamental and overtone distributions. Our justification of the 2vz bandwidth parameters rests on their closeness to those observed for v2 in pure liquid water. Because of the agreement of the observed and calculated spectra we further constrain our fitting by assuming that Smith and Overend's values of W determined for the gas phase are also applicable to liquid water. Our assumption of symmetrical distribution functions, eq 5, may not be exact (ref 2, p 239); however, for dilute solutions of water in DMSO at room temperatures, it seems to be reasonable. This point will be discussed further in the next section. The Journal of Physical Chemistry, Voi. 77, No. 17, 1973
2112
J. R. Scherer, M. K. Go,
Calculated spectra were generated by a program written for the CDC 6600 computer with teletype and 250 Vista (cathode ray tube) terminals. The program is interactive and options and parameters are entered and modified through the teletype. Input to the program consists of spectral data, fundamental and overtone positions, peak intensities, half-width parameters, and W. Calculation of the resonance perturbation for four bands took of the order of 2 sec and the resulting bands, their sum curve, the observed spectrum, and the difference curve between observed spectrum and sum curve were displayed on the crt. The parameters were adjusted along directions that were judged to improve the goodness of fit and the resonance calculation was repeated. This process was continued until the error curve was judged acceptable. We note that this procedure is not a least-squares fitting process but we believe that it is sufficiently good to explore the validity of a model for the structure of water. The figures that follow were made from 35-mm film or microfiche generated by the computer.
IV. Results and Discussion A. Model for Liquid Water. In the following we develop a simple model with which the high- and low-temperature Raman spectra of H20, D20, and HOD in DMSO can be explained. In addition, we can extend the model to account for the observed spectra of pure water and also show its relationship to the spectrum of ice. Saumagne and Josien40 and Gentric27 have shown that water at high dilution in nonelectrolytes occurs in two complexed forms. If we designate the hydrogen acceptor as base B, the two hydrogen-bonding states of water are B...HOH for the 1:l complex and B..-HOH...B for the 1:2 dibonded complex. Normal coordinate calculations by Burneau and Corset4I show that the symmetric and antisymmetric coordinates are decoupled when one of the OH stretching force constants is changed by hydrogen bonding and the other remains a t its “free” value. Consequently, two vibrational frequencies should be observed for the 1:l complex: Vb and v f for bonded and free OH stretching vibrations. Their graphs of normal coordinate L matrix elements as a function of the difference in force constants between the two OH bonds indicate that, for the type of bonding considered in the 1:l complex, the high-frequency mode still retains significant antisymmetric character and the low-frequency mode symmetric character. Therefore, in the B spectrum, the high-frequency mode is less intense than the low-frequency mode. In the case of the dibonded complex, a water molecule will have symmetric and antisymmetric OH stretching vibrations. In infrared studies of very small amounts of water in DMS0(5%)-CCl4(95%) solution, Gentric27 has observed a sharp band a t 3682 cm-1 which he assigns to the “free OH stretch” for the 1:l complex. He also observes a broad intense band at 3450 cm-1 which he assigns to the bonded (vb) OH stretching vibration. In the case of the dibonded complex (0.2 mol % H2O in DMSO) two strong peaks are seen in the infrared spectrum and have been assigned to the symmetric (3446 cm-1) and antisymmetric (3496 cm-1) OH stretching vibrations of water. Investigation of the OH bending region27 of this mixture shows that the 1:2 complex (bending vibration at 1663 cm-l) predominates but that the 1: 1 complex (bending vibration a t 1627 cm-1) is still present. However, the 3682The Journal of Physical Chemistry, Vol. 77, No. 7 7, 7973
A
3
2
.
and S.Kint
C
3
4
5
2
4
U -
3800
3100
3800
3100
Calculated and observed iE spectra for 5, 10, 25, 50, 66, and 75 mol % H20 in DMSO at 23 (A-F) and 80” (G-L). Figure 8.
cm-1 band has disappeared from the spectrum. We conclude that the 1:l complex in the binary mixture of water and DMSO cannot have an OH bond that is completely “free.” Antisymmetric vibrational modes are forbidden in isotropic Raman spectra and we see from Figure 4 that the 3496-cm-1 mode is absent from this spectrum and that only the symmetric OH stretch appears. We believe that the absence of the antisymmetric OH stretch is strong evidence that the hydrogen bonding in the 1:2 complex is symmetric. The absence of a sharp band near 3682 cm-1 and the observation of a weak band near 3650 cm-1 in the difference spectrum (see Figure 8A) lead us to question the existence of a “free OH stretch” in this mixture. Gentric also observes a sharp intense infrared band a t 3683 cm-1 in the tertiary mixture water-HMPTCC14 that persists, although more weakly, in the dilute binary mixture water-HMPT. We have obtained Raman spectra of 5 mol % H2O in HMPT and have observed a sharp, weak band a t 3680 cm-1 and a weaker shoulder in the 3650-cm-l region. The 3680-cm-l band can be assigned to a free OH stretching vibration of a 1:l complex where the H is shielded from interaction with other base molecules by the bulky side groups on the base molecule. We feel that the absence of this band in the Raman spectra of dilute H20 in DMSO indicates that all H atoms in DMSO solutions must be hydrogen bonded to some extent. We propose that the shoulder near 3650 cm-1 is due to weakly hydrogen bonded OH stretching vibrations.
2113
Raman Spectra and Structure of Water in Dimethyl Sulfoxide Our model for liquid water assumes the presence of two types of hydrogen bonded species, both of which are dihydrogen bonded. In the first type, the two hydrogen bond strengths are equal and the isotropic Raman spectrum contains only the symmetric OH stretch vd. In the second type, water molecules have one strong and one weak hydrogen bond. The asymmetry in hydrogen bond strength uncouples the symmetric and antisymmetric vibrations and the isotropic spectrum contains the “bonded,” vb, and “weakly bonded,” vw, frequencies. Evidence will be presented in the next section for inclusion of a third type of water molecule in which both hydrogens are weakly hydrogen bonded. The intensities lead us to believe that only a very small fraction of water exists in this form at 23”. The breadth of the observed bands arises from a distribution of hydrogen bond strengths. It is interesting to note that configurations of the B- .HOH. .B complex, in which the water molecule is translated out of the plane of symmetry bisecting the BOB angle, are asymmetric. Conversely, configurations in which the water molecule is rotated slightly are still symmetric with respect to the strength of hydrogen bonding and the symmetry of symmetric and antisymmetric vibrations is preserved. Therefore, we can realistically consider the existence of a distribution of symmetric and antisymmetric vibrations for a 1:2 complex. I[ntermolecular coupling may also be responsible for the breadth of the observed bands but we feel that is not the primary mechanism since the uncoupled OH stretch of HOD in DzO is not appreciably narrower than the HzO band (Figure 5). In applying this model to the water-DMSO system we have made the further assumption that a t any given concentration the hydrogen bond between water and DMSO is the same as that between water and water. Rigorously, differences between DMSO. .HO and HzO. .HO bonding are expected to modify the distribution parameters (half-width1 and Vd and vb) and Fermi resonances involving the bending modes of water for the 1:2 and 1 : l water-DMSO complexes and water-water complexes further complicate the picture. Therefore, we have assumed a single distribution for the B..-HOH...B complex and a Fermi resonarce with a single 2vz distribution a t a compromise frequency (which is concentration dependent). A similar simplification was made for the B-..HOH....-.13 complex. We expect these assumptions to be very good for very dilute water concentrations and for pure water, but less appropriate for the intermediate concentrations. On the basis of the positions of v 2 observed by Gentric,Z’ ZVZ for the B...HOH...B complex should be at higher frequencies than 2v2 for the B.-.HOH-.-...B complex. We have observed that the shape of the vz band in the Raman spectrum of pure water is not as asymmetric as the vz infrared band of water in DMSO observed by Gentric. This suggests that the bending modes of the 1 : l and 1:2 complexes may be closer in pure water than they are for water in DMSO. For pure liquid water, we have found it impossible to fit the observed spectrum with W = 36 cm-I when the same overtone value is used for the symmetric and asymmetric complexes. However, when the overtone of the asymmetric complex is raisled above that for the symmetric complex by about 20 cm-1, the observed spectrum can be matched. Because of concentration problems and solvent
-
e
3
2750 Figure 9.
5
2
4
2250
2750
2250
Calculated and observed 6 spectra for 5, 10, 25, 50, 66, and 75 mol % D20 in DMSO at 23 (A-F) and 80” (G-L). interferences we could not observe the bending vibration in the Raman spectra of water-DMSO mixtures. Finally, our model postulates that hydrogen bonding (weakening of the OH valence bond) is enhanced by involvement of the lone pair electrons of the oxygen atom. It is generally accepted that the intense Raman band of hexagonal ice at 308642 (77°K) or 3152 cm-I 43 (269°K) is due to coupled symmetric stretching vibrations of four-coordinated water molecules
.. . .
0... H ~ H .-. 0 The ice frequency is an end point representing complete conversion of asymmetrically bonded molecules to symmetric four-coordinated molecules. Liquid water has a strong peak near 3200 cm-1 whose intensity grows as the temperature approaches the freezing point and this feature has been associated with the four-coordinated form of waterW2 We therefore associate the vd distribution with the symmetric stretch of a four-coordinated water molecule in ice. Calculations of hydrogen bond stabilization energies44 show that cooperative effects in cyclic or polymeric water can lead to an increase in the strength of hydrogen bonding and these effects may be responsible for the continuous shifting of the Vd distribution to lower frequencies. B. Application t o the Water-DMSO System. Except for pure Hz0, we have not attempted an analysis of the 8 spectra for the following reasons: antisymmetric OH stretching bands overlap the anisotropic bands of symmetric vibrations and separation is difficult and arbitrary; The Journal of Physical Chemistry, Vol. 77, No. 17, 1973
2114
TABLE I :
J. R . Scherer, M. K . Go, and S.Kint
Spectroscopic Parameters for 5 Mol % Water in DMSO at 23 and 80"
Overtone, cm
Fundamental, c m - ' Assignment
H20,23"
(Figure 8) H20,80°
(Figure 8) D20, 23" (Figure 9)
D20,80" (Figure 9)
Y
L
G
A V i 12
3432 3448 3640
102 138 137
514 240 121
99 116 87
3300 3240 3240
300 300 300
110 110 110
101 101 101
36 36 36
3454 3460 3665 3590 2513 2521 2690
129 140 137 189 74 62 100
293 315 60 104 140 138 210
115 125 54 88 63 55 88
3290 3248 3248 3248 2425 2395 2395
300 300 300 300 199 199 199
140 140 140 140 74 74 74
123 123 123 123 68 68 68
36 36 36 36 25 25 25
2520 2535 2694 2605
97 68 100 100
148 103 260 110
78
241 1 2397 2397 2397
199 199 199 199
100 100 100 100
87 87 87 87
25 25 25 25
TABLE II: Spectroscopic Parameters for
55 91 71
G
L
Y
H 2 0 , 23" (Figure I O )
HzO, 90"
(Figure IO) D20, 23"
(Figure 10) DzO, 90" (Figure 10)
Au7/2
W
Band no.
4l 2 3
4 2/ 3 5 4 21 3 4 21
3 5
Relative area
-
1.oo 0.04 1.00
0.05 0.04 1 .oo 0.03 1.oo
0.08 0.08
Pure Water at 23 and 90"
-
Fundamental, cm -I Assignment
-'
Overtone, cm
u
L
G
4~112
U
L
G
AUI/Z
W
3241 341 1 3627 3551 3318 3447 361 2 3535 2388 2476 2665 2567 2435 251 3 2675 2588
329 450 117
426 345 156 170 444 341 141 120 320 300 200 115 320 205 210 110
250 262 90 108 300 252 94 98 125 130 105 97 166 153 107 83
3300 3319 331 9 331 9 3279 3289 3289 3289 2440 2450 2450 2450 2426 241 5 241 5 241 5
300 300 300 300 300 300 300
140 140 140 140 140 140 140 140 115 115 115 115 125 125 125 125
123 123 123 123 123 123 123 123 96 96 96 96 102 102 102 102
36 36 36 36 36 36 36 36 25 25 25 25 25 25 25 25
150 443 414 137 190 140 150 130 205 205 257 130 139
the intensity of fl for water is very weak and solvent scattering tends to obscure any separation of bands. In Figure 8 we show 6 spectra and band separations for H2O in DMSO at 23 and 80" and for water concentrations of 5, 10, 25, 50, 66, and 75 mol 70. Band 4 is the dibonded symmetric OH stretch, vd, and bands 2 and 3 are the uncoupled v b and vw of asymmetrically bonded H20. For water concentrations up to 25 mol % it is possible to combine 2 and 4 into a single symmetric band with an insignificant sacrifice in fit. This is because Vd and v b are very close, uiz. 3446 and 3450 cm-1, respecti~ely.~7Consequently, the relative intensity of v b and vd is ambiguous a t these concentrations but the combined intensity and the effect of Fermi resonance is well defined. The analogous D20-DMSO spectra are shown in Figure 9. Corresponding 6 spectra and band separations for pure HzO and D2O a t 23 (A and C) and 90" (B and D) are shown in Figure 10. A more detailed investigation of the effect of temperature on these bands will be given in a later paper. Band parameters and assignments for 5 mol 70 water in DMSO and pure water are given in Tables I and 11,respectively. The Journal of Physical Chemistry, Vol. 77, No. 7 7, 7973
300 200 200 200 200 200 200 200 200
Band no.
Relative area
4 2 3 5 4 2 3 5 4 2 3
1.oo 0.98 0.08 0.06 0.87 1.00 0.10 0.10 1 .oo 0.84 0.13 0.16 0.80 1 .oo 0.12 0.12
5 4 2 3 5
We should like to call attention to the steep rise in intensity on the high-frequency side of the 3650-cm-l band, 3 in the 80" spectra (Figure 8). The shape of the band in this region dictates its half-width characteristics with the result that there is not enough intensity to match the observed intensity in the overlap region 3500-3600 cm-I. A similar problem exists, to a lesser degree, in the 23" data. These difficulties can be alleviated by introducing a fourth band in the region of 3580 cm-1. Thus far, we have considered two species for liquid water: a symmetric species having two strong hydrogen bonds and an asymmetric species having one strong and one weak hydrogen bond. At high temperatures we might expect a third species having two weak (symmetric) hydrogen bonds. This species would have a symmetric OH stretch below vw and an antisymmetric stretch above v w . The antisymmetric and symmetric stretches of water in CC14 have been observed a t 3705 and 3614 cm-1, r e ~ p e c t i v e l y , and ~ ~ ? it ~~ seems reasonable to attribute band 5 in Figures 8-10 to the symmetric stretch, v w w , of such a weakly dibonded species. Walrafen46 has found strong bands appearing a t
2115
Raman Spectra isnd Structure of Water in Dimethyl Sulfoxide
3
u 3000
Figure 10. Calculated D 2 0 at 23 and 90".
2000
and
l
i
i
i
l
2900 observed 6 spectra for
l
pure
l
l
l
'2100 H 2 0 and
3640 and 3590 cm-1 in 5.3 M solutions of NaPFa in H20. When the salt concentration is lowered to 2.6 M , only the 3640-cm-1 band remains. We have made depolarization measurements that indicate that the band a t 3590 cm-I is highly polarized. Therefore, we feel it reasonable to associate this band with the symmetric stretch of a weakly dibonded species and are encouraged by its similarity to band 5 in our spectra. The intensity of band 5 is weak and we do not consider it as very strong evidence for a third species. Figure 11 shows a two-band fit of the OH stretching region of & spectrum of HOD in DMSO ( 6 : l D2O:H2O, 75 mol % DMSO) at 23". In this spectrum the OH and OD stretching vibrations are uncoupled and we can no longer distinguish between v b and vd. It is apparent that the band shape is symmetrical and that there is no Fermi resonance shoulder. It has been argued2 that the steep increase in repulsive energy for short O...O distances should produce fewer molecules having short 0..S O distances relative to the most probable O.-.O distance. This effect would produce a skew distribution of states which could lead to asymmetric band shapes. The symmetry of the band shapes in the HOD spectrum leads us to conclude that, for the type of hydrogen bonding observed in liquid water, skew distributions are unimportant. The parameters for the component bands are as follows: 3463 cm-l, L = 185 cm-l, G = 330 cm-l; 3637 cm-1, L = 107, G = 151 cm-l, area 3/area 2 = 0.055. Before proceeding we should like to emphasize the differences between the continuum model and the present model. The continuum model assumes that symmetrically hydrogen-bonded molecules can only occur when the hydrogen bonding on one OH of a water molecule randomly matches the hydrogen bonding of the second OH. The extent of this symmetrical bonding is determined by the probability of randomly selecting pairs of equivalent vOH'S from a gaussian profile of uncoupled OH frequencies. As one might expect, this analysis leads Shiffer and Hornigl3 to conclude that most of the molecules in liquid water are greatly distorted and that the OH stretching vibrations are essentially those of individual OH bonds. The infrared spectra of HOD and H2O are very similar and the continuum model seems to offer an explanation of this. However, the Raman data for water-DMSO mixtures indicate that symmetrically dibonded water molecules are present in large quantiities and that these molecules have antisymmetric vibrations that do not appear in the isotropic Raman spectra. On the other hand our asymmetrically bonded species corresponds closely to the distorted H2O molecule of the, continuum model.
2
M 3800 3'100 Figure 11. Calculated and observed (Y spectra of HOD in DMSO (6.1D 2 0 : H 2 0 , 75 mol % DMSO) in the OH stretching region. Band 2 parameters are v = 3463 cm-l, L = 185 cm-l, G = 330 cm-I; band 3 parameters are v = 3637 cm-l, L = 107 cm-', G =: 151 cm-l. We agree with Schiffer and Hornig regarding the presence of Fermi resonance. But, at high water concentrations we regard the 3250-cm-l band as originating from symmetric stretches of symmetrical 1:2 complexes with a minor perturbation from Fermi resonance, whereas they regard the intensity in this region as resulting from strong Fermi resonance of 212 with stretching vibrations of distorted molecules. Examination of Figures 8-10 reveals that our proposed model can adequately account for the variation of the observed cu spectra as a function of concentration. Figure 12 shows the variation in unperturbed band centers as a function of concentration. We note that vw and v b do not vary greatly with concentration but that vb shows a significant shift to lower frequencies with increasing concentration. We also see that an increase in temperature shifts the fundamentals to higher frequencies and that this is consistent with ideas of H...O bond weakening associated with volume expansion. Figure 13 shows the dependence of band half-widths on concentration and Figure 14 shows the variation of 2vz as a function of concentration. As mentioned earlier, we see that 2 v 2 for the 1 : 2 complex is always higher than 2uz for the 1:l complex (except for HzO) and that this is consistent with the observations of Gentric.27 We should note that an increase in temperature causes a decrease in the position of 2v2 and that this is in agreement with a weakening of hydrogen bonding. The distribution of overtone states was taken to be essentially gaussian with half-widths slightly larger than those observed for the fundamentals and with a linear concentration dependence. The variation in half-widths for 2vZ from low water concentration to pure water was 101-123 cm-1 for H2O and 68-102 cm-1 for DzO. Figure 15A shows the 6 spectrum of H20, vb, V d , and vw before Fermi resonance and the sum of these distributions. Figure 15B shows the resulting spectrum after Fermi resonance. If we ignore the shoulders produced by Fermi resonance, Figure 15B is very similar to one shown by Murphy and Bernstein21 using a symmetric four-band decomposition. The two major features of their spectra correspond to our bands 2 and 4. They interpret these bands as a Fermi doublet. If we use their integrated areas and eq 1 and 3 ( I u / I , = 0.76, X = 185 cm-1, A = 24.8 cm-l) we obtain a value for W of 93 cm-1 which would lead to a deep Evans hole at the overtone position. Clearly, the Fermi resonance interaction cannot be approximated by the sum of two broad symmetric overlapping bands. Murphy and Bernstein note that their model leads to widely different values of the depolarization ratio for their two Fermi components. Our model gives an explanaThe Journal of Physical Chemistry, Vol. 77, NO. 17, 1973
J. R. Scherer, M. K. Go, and S. Kint
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c
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MOLE % H20 IN DMSO 2440 I
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e4 2600 2400
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MOLE % OF D2O IN DMSQ
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Figure 14. Variation of 2v2 for symmetric and asymmetric species of water as a function of concentration and temperature.
0
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MOLE % D20 IN DMSO Figure 12. Variation of V b , vd, and vW in H20 and D2O as a function of concentration and temperature. The data for H20 corresponds to Figures 8 and 15 and for D20, to Figures 9 and 10.
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ziI
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Figure 15. (A) Calculated 15 spectrum of H20 at 23" without Fermi resonance interaction; (6)calculated I5 spectrum of H20 at 23" with Fermi resonance interaction; and ( C ) calculated @ spectrum of H20 at 23" assuming identical band parameters
100
D20as a function of concentration and temperature.
and frequencies for vb, vd, and vf and introducing a new distribution for antisymmetric vibrations of symmetrically bonded states at 3480 c m - ' (L = 400 c m - ' and G = 250 c m - ' ) . The intensities in C must be divided by 2.55 to compare with 6.
tion of the difference in depolarization ratio across these bands. Figure 15C shows the 6 spectrum of H20at 23". The ordinate scale of the 6 spectrum is 2.55 times smaller than that of the 6 spectrum. The spectrum parameters (frequency, half-width, and resonance parameters) were
transferred to the 6 spectrum and varying only the peak intensity. A new band corresponding to a distribution of antisymmetric vibrations of dibonded states was introduced at 5 (3480 cm-1) and its position, half-width ( L = 400 cm-1, G = 250 cm-I), and intensity were varied to fit
MOLE % OF WATER IN DMSO Figure 13. Variation of half-band widths of vb and vd in
The Journal of Physical Chemistry, Vol. 77, No. 17, 1973
ti20
and
Raman Spectra and Structure of Water in Dimethyl Sulfoxide the spectrum. Fermi resonance is not permitted for these states. The resulting fit of the p spectrum is remarkable considering the constraints imposed on the system. The resultant calculated depolarization ratio for these bands are as follows: VdsYm (4) 0.033, Vb (2) 0.16, Vdas (5) 3/4, vW (3) 0.21. Because of decoupling, 2, 4,and 5 collapse into a single band in HOD and the measured depolarization ratio for this band varies from 0.16 a t 3300 cm-1 to 0.17 at 3550 cm-1. We note with satisfaction, the close agreement of this depolarization ratio with the V b component of HzO. We should caution the reader that our band decompositions for water-DMSO at high water concentrations and for pure water may not be unique. We may conclude from Figure 15 tha.t three distributions and Fermi resonance can explain the observed band shape of the fi and p spectra however 1,he relative intensities of the distributions may be varied within limits and still achieve a reasonable fit; Le., in Figure 15A we note that a fair fit might be achieved by using two asymmetric distributions (one for band 3 and one for bands 2 and 4). However, from arguments given in the previous section, our model requires that band 2 (Yb) accompany band 3 ( v W ) . We might then expect that the relative intensities of bands 2 (vb) and 4 ( V d ) may not be unique. Further work on the temperature variation of the spectra of H20, DzO, and HOD is in progress which may help to improve the uniqueness of the fitting procedure and provide a more strenuous test of our proposed model. Summary
We have proposed a simple model for liquid water and water in DMSO. This model assumes that water can be separated into two major species: one is symmetrically hydrogen bonded and the other asymmetrically hydrogen bonded. The symmetrically bonded species contributes a distribution of totally symmetric vibrations to the a! spectrum and a second distribution of antisymmetric vibrations to the fi spectrum. In the asymmetrically bonded species the OH oscillators decouple due to differences in hydrogen bond strengths and produce a bonded OH stretch and a more-or-less free OH stretch. Fermi resonance of the OH stretching bands (excluding the antisymmetric distribution) with the overtone of the bending vibration is an important factor in understanding the band shape and can be quantitatively approximated. At high temperatures a weak band is required in the region of 3580 cm-1 and we tentatively attribute this band to the symmetric stretch of a species of water having two weak hydrogen bands. The model also is successful in explaining the observed depolarization ratio of H2O and is consistent with the HOD spectrum. Acknowledgment. One of us (M.K.G.) wishes to acknowledge fin(ancia1assistance through the NSF Presidential Intern program. We should also like to thank Dr. K.
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Cunningham, Dr. Gentric, and Professor Saumagne for communicating their work prior to publication and Dr. R. Snyder, Dr. W. Murphy, and Dr. H. Bernstein for helpful discussions. Finally, we are grateful to the Lawrence Berkeley Laboratory for making available their computer facilities. References and Notes R. A. Horne, Ed., "Water and Aqueous Solutions," Wiley, New York, N. Y., 1972. D. Eisenberg and W. Kauzman, "The Structure and Properties of Water," Oxford University Press, London, 1969. G. C. Pimentel and A. L. McCellan, "The Hydrogen Bond," W. H. Freeman, San Francisco, Calif., 1960. G. E. Walrafen, J. Chem. Phys., 47, 114 (1967). R. A. More O'Ferrali, G. W. Koeppl, and A. J. Kresge, J. Amer. Chem. SOC.,93, 1 (1971). G. R. Choppin and M. R. Violante, J. Chem. Phys., 56, 5890 (1972). E. C. W. Clarke and D. N. Glew, Can. J. Chem., 50, 1655 (1972). G. E. Wairafen and L. A. Blatz, J. Chem. Phys.. 56, 4216 (1972). G. E. Walrafen, J. Chem. Phys., 48, 244 (1968). G. Nemethy and H. A. Scheraga, J. Chem. Phys., 36,3382 (1962). G. E. Walrafen, J. Chem. Phys., 52, 4176 (1970). J. A. Pople, Proc. Roy. SOC.,Ser. A, 205, 163 (1951). J. Schiffer and D. F. Hornig, J. Chem. Phys., 49,4150 (1968). J. W. Schultz and D. F. Hornig, J. Phys. Chem., 65, 2131 (1961). T. T. Wall and D. F. Hornig, J. Chem. Phys., 43, 2079 (1965). M. FalkandT. A. Ford, Can. J. Chem., 44, 1699 (1966). 8. Curnutte and J. Bandekar, J. MOL Spectrosc., 41, 500 (1972). H. R. Wyss and M. Falk, Can J. Chem., 48,607 (1970). J. Schiffer, J. Chem. Phys., 50, 566 (1969). K. M. Cunningham, Thesis, Yale University, 1971. W. F. Murphy and H. J. Bernstein, J. Phys. Chem., 76, 1147 (1972). G. Brink and M. Faik, J. Mol. Struct., 5, 27 (1970). G. J. Safford, P. C. Schaffer, P. S. Leung, G. F. Doebbler, G. W. Brady, and E. F. X. Lyden, J. Chem. Phys., 50,2140 (1969). J. M. G. Cowie and P. M. Toporowski, Can. J. Chem., 39, 2240 (1961). A. L. Narvor, E. Gentric, and P. Saumagne, Can. J. Chem., 49, 1933 (1971). A. Burneau and J. Corset, J. Chim. Phys., 1, 142 (1972). E. Gentric, Thesis, L'Universite De Bretagne Occidentale, 1972. Reference to a company or product name does not imply approval or recommendation of the product by the U. S. Department of Agriculture to the exclusion of others that may be suitable. (a) G. F. Bailey, S. Kint, and J. R. Scherer, Anal. Chem., 39, 1040 (1967); (b) J. R. Scherer and S. Kint, Appl Opt.. 9, 1615 (1970). T. C. Damen, S. P. S. Porto, and B. Tell, Phys. Rev., Ser. 2, 142, 570 (1966). J. R. Scherer, S. Kint, and G. F. Bailey J. M o l , Spectrosc,, 39, 146 (1971). G. Placzek, Lawrence Radiation Laboratory, Report No. UCRLTrans-526(L), pp 138-145 (1962). H. R. Gordon and T. K. McCubbin, Jr., J. Mol. Spectrosc., 19, 137 (1966). H. G. Howard-Lock and B. P. Stoicheff, J. Mol. Spectrosc., 37,321 (1971). J. C. Evans and N. Wright, Spectrochim. Acta, 16, 352 (1960). J. C. Evans, Spectrochim. Acta, 16, 994 (1960). G. Herzberg, "Infrared and Raman Spectra," Van Nostrand, New York, N. Y., 1945. D. F. Smith and J. Overend, Spectrochim. Acta, Part A, 28, 471 (1972). J. Pitha and R. N. Jones, NRC Bulletin No. 12, National Research Council of Canada, Ottawa, Canada (1968). P. Saumagne and M. L. Josien, Discuss. Faraday SOC., 43, 142 (1967). A. Burneau and J. Corset, J. Chm. Phys., 1, 153 (1972). M. J. Taylor and E. Whaliey, J. Chem. Phys., 40, 1660 (1964). J. R. Scherer, unpublished data. P. A. Koliman and L. C. Alien, Chem. Revs., 72, 283 (1972). E. Greinacher, W. Luttke, and R. Mecke, Ber. Bunsenges. Phys. Chem., 59, 23 (1955). G. E. Walrafen, J. Chem. Phys., 55, 768 (1971).
The Journal of Physical Chemisfry, Vol. 77, No. 77, 1973
