J . Phys. Chem. 1990, 94, 2237-2239 a conservative estimate of the error in our computed intensities would be the fL-fv differences. From Table 11 and Figure 2, where we have plotted the absorptions between 3 and 6 eV, we may conclude the following: ( I ) It is very unlikely that UV spectra of the lowest energy isomer ClOOCl will have any absorptions at wavelengths longer than 200 nm. (2) The spectra of the two other low-energy isomers are sufficiently different so that it should be possible to distinguish between CICIOz and ClOClO based on their UV spectra. (3) The strong transition of ClC102 at 243 nm is most likely the absorption seen by Basco and Hunt3 and by Schell-Sorokin et aLr9 (4) It is unlikely that any of the absorptions measured by Molina and Molina' are due to UV transitions in CI2O2 isomers. Let us consider points 3 and 4 a little further. Basco and Hunt3 reported a broad absorption in the region 232-292 nm with extinction coefficients monotomically decreasing from 2900 to 400 L mol-' cm-I, which could be interpreted as the tail absorption of a < 232 nm. Considering the inaccuracies in transition with ,,A our calculations, that may very well be the onset of the transition that we find at 243 nm. Schell-Sorokin et aI.l9 also observe a broad band originating at -290 nm and extending beyond 230 nm. Considering the energetics of the ClZO2i ~ o m e r sit, ~is in fact very likely that also some CICIOz was present during the two experiments. Molina and Molina' observed a strong transition at 270 nm and a weaker one at 220 nm in their study of gas-phase spectra of chlorine atoms with various CIO precursors. Even though the calculated spectrum of ClOClO shows some resemblance with that observed by Molina and Molina, both the relative instability of ClOClO and the intensity ratios of the two spectral lines seem to indicate that Molina and Molina did not measure the UV spectrum of a CI2O2species. This also agrees with the analysis of their IR spectrum where MCRHS showed that part of the IR (19) Schell-Sorokin, A. J.; Bethune, D. S.;Lankard, J. R.;Loy, M. M. T.; Sorokin, P. P. J . Phys. Chem. 1982, 86, 4653.
2237
frequencies measured by Molina and Molina were due to ClOOCl (which does not have observable UV absorption in the present spectral range) and the rest were due to modes of CIOz functionality such as ClC102 or CIOC102. A comparison of the UV spectra seems to rule out the former alternative. Conclusions From a study of some alternative structures of CIO dimer the present investigation has corroborated the conclusions of MCRHS that the lowest energy isomers are ClOOCl and ClC102 (Figure l a and Figure Ib), with ClOOCl being slightly lower in energy at the highest level of theory. We have demonstrated that the three lowest energy isomers, Figure la-c, have little biradical character, and we thus may use the RPA method to calculate UV absorptions. We have investigated the thermodynamical stability of ClOOCl and shown that the only exothermic reaction product is Cl, and 0, (singlet or triplet). The calculated UV spectra are quite different for the three lowest energy isomers. The peroxide structure has only very weak absorptions above 220 nm. The CICIOz isomer has one, and ClOClO has two medium absorptions. Probably the UV spectra measured previously by Basco and Hunt3 and by Schell-Sorokin et aI.l9 were due to the CICIOz isomer. Note Added in Proof. Recently, Burkholder et aLzoreported a UV absorption at 245 nm. They assigned it to a transition in the ClOOCl isomer. However, in view of the present results we believe it must be the strong transition of the CICIO, isomer that we find at 243 nm. Acknowledgment. This work was supported by grants from the Danish Natural Science Research Council (Grants 11-6844 and 1 1-6966). (20) Burkholder, J. B.; Orlando, J. J.; Howard, C. J. J . Phys. Chem. 1990, 94, 687.
Raman Spectrum of Water: Transverse and Longitudinal Acoustic Modes below ~ 3 0 0 cm-' and Optic Modes above ~ 3 0 cm-l 0 G . E. Walrafen Chemistry Department, Howard University, Washington, D. C. 20059 (Received: December 15, 1989)
Liquid water behaves like a moderately rigid, isotropic, elastic solid at terahertz (10l2 Hz) frequencies. The nominal 60and 175-cm-I Raman peaks, ~ 1 . and 8 ~ 5 . THz, 3 correspond to transverse spherical acoustic shear, S, and longitudinal spherical acoustic dilatational, P, waves, respectively, and involve H 2 0center-of-massmotions. The 28-9 A shear wavelength corresponds to the high-distance tail of the 0-third-0 (or 0-fourth-0) X-ray RDF peak-the structural correlation length (SCL), where G(r) = 1 . The 4 - A dilatational wavelength corresponds approximately to the density-related 0-second-0 distance. Optic and multiphonon modes above -330 cm-l mainly involve proton motion. This acoustic-optic division correlates with amorphous and crystalline ice; e.g., the TA and LA, zone-edge phonon frequency range, respectively, is 65-70 cm-I and 164-181 cm-I, for ice I, and I,,.
Introduction The 175-cm-I Raman band from liquid water was discovered by Segr6' in 1931, and the 60-cm-l Raman band by &Ala2 in 1932. Since then, this low-frequency Raman region from liquid water has been examined by several tens of workers.' However, the acoustic nature of these two modes has been clearly recognized
only very recently,4vSalmost 60 years after their discovery. In contrast, the zone-edge, TA, 65-70 cm-l, and LA, 164-181 cm-I, phonon frequencies from ice I, (cubic) and Ih (hexagonal) were identified in 1967.6 Evidence for the transverse spherical shear nature of the 60-cm-l acoustic mode, and for the longitudinal spherical dilatational
(1) Segr6, E. Rend. Lincei 1931, 13, 929. (2) Bolla, G.Nuovo Cimento 1932, 9, 290; 1933, 10, 101; 1935, 12, 243. (3) Walrafen, G. E.; Fisher, M. R. In Biomembranes, A Volume of Methods of Enzymology; Packer, L., Ed.; Academic: New York, 1986.
(4) Rousset, J. L.; Duval, E.: Boukenter, A. J . Chem. Phys., in press. ( 5 ) Walrafen, G . E. In Hydrogen-Bonded Liquids; Dore, J. C . , Teixeira, .I.Eds.; , Kluwer Academic: Dordrecht, 1990. (6) Bertie, .I.E.; Whalley, E. J . Chem. Phys. 1967, 46, 1271.
0022-3654/90/2094-2237$02.50/0
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2238 The Journal of Physical Chemistry, Vol. 94, No. 6, 1990
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Figure 1. (Top) Depolarization ratio spectrum, I [ X ( Z x ) Y l / I [ X ( Z Z ) Y l , liquid water, room temperature, ISA U-1000 (and HGZS). Arrow, first minimum, locates P-wave tail. Dashed line, p-, appears exceeded where Raman scattering absent. (Bottom)X(ZZ)Y, ISA U-1000, polaroid plus
polarization scrambler, Bose-Einstein (BE) corrected. Measured intensity multiplied by [ I - exp(-hcw/kl")] for BE correction; w, wavenumber, cm-I. S and P positions, indicated, =50-55 and 175 cm-I. Acousticoptic separation, vertical line. Horizontal axis, top and bottom, cm-'. nature of the 175-cm-I acoustic mode, is now presented. The spherical shear mode is henceforth described as the S (secondary) mode and the spherical dilatational mode as the P (primary) mode. These acoustic modes almost certainly have small coherence volumes, and it is also probable that their group velocities are small (=O), but their phase velocities, calculated from the high-frequency limiting (HFL) shear, G,, and longitudinal, M,, moduli, are used to approximate phonon wavelengths. (The HFL bulk modulus is K,.) Acoustic and optic modes are described here as phonons, but this does not imply long-range periodicity or order. Also, the Raman spectrum from water represents a weighted, vibrational density of states, all modes of which appear to be Raman and infrared active. Spectra A criterion has recently been found for locating the P mode for glasses,' namely, the P-mode position is close to the first significant minimum, just above the S mode, in the Raman depolarization ratio spectrum. The situation is only slightly different for liquid water. A depolarization ratio spectrum is presented in Figure 1 (top). The arrow, at the first significant minimum, locates the lowfrequency P-mode tail position, rather than the actual P-mode intensity maximum. This first minimum in the depolarization ratio spectrum from water is extremely weak, occurring near = I 15-120 cm-l, where p ~ 0 . 7 to 2 ~ 0 . 7 (pman 3 = 3/4). Also the spectrum from =5 to 200 cm-I is almost completely depolarized. See spectrum, bottom, Figure I . HFL Shear and Longitudinal Moduli The terahertz sound velocities (phase velocities) required to calculate the S- and P-mode wavelengths from Raman peak positions are often unavailable. Ordinary sound velocities are not usable because they show no significant dispersion from very low to gigahertz freq~encies,~ and the corresponding moduli under(7) Walrafen, G. E.; Chu, Y. C.; Hokmabadi, M. S. Raman Spectroscopic Investigation of Irreversibly-Compacted Fused Silica. J . Chem. Phys., in press.
Letters estimate the rigidity of the hydrogen-bonded network. This problem can be surmounted, however, by use of HFL moduli, determined from extrapolations of low-temperature data, Slie et a1.* The HFL longitudinal modulus, M,, is calculated from the HFL shear and bulk moduli* by using M , = K , + (4/3)G,. M , ~7.X 2 IO'O dyn c d at 25 "C. Accordingly, the HFL longitudinal P-wave phase velocity, Vp, is ~ 2 . 7X IO5 cm s-l. Vp increases slightly to ~ 2 . 8X IO5 cm s-I at 0 oC.8 It is interesting to observe that the HFL shear, bulk, and longitudinal moduli all increase with decreasing temperature* and that the P-wave Raman peak position also increases markedly with decreasing temperat~re.~ This is reasonable because it was shown recently' that S- and P-mode Raman peak frequencies follow variations in the shear and bulk moduli. The P-mode peak position, after correction for the collisioninduced background, is ~ 1 7 ~5 m - l .(The ~ extremely broad and featureless collision-induced backgroundlo is not discussed here. The main acoustic phonon contributions lie above it.) The P-mode wavelength is given by Vp/cwp,where c is the velocity of light, and wp is the P-mode peak position in cm-I. The P-mode wavelength is thus 4 . 1 A. ( A similar relation, Vs/cws yields the S-mode wavelength.) The second-nearest-neighbor (0-second-0) peak in the X-ray RDF from liquid water occurs near 4.5 at 20 "C.I1 This is sufficiently close to 5.1 A to identify the P-mode peak with this 0-second-0 distance. Note that the acoustic waves involve the motions of entire H 2 0 molecules and probably describe irregular paths in the hydrogen-bonded network, whereas the X-ray RDF involves direct 0 to 0 distance averages. The 60-cm-I S-mode wavelength may be calculated from the Vs2 = G,/p. HFL shear modulus, G, = 1.7 X 1OIo dyn Hence, Vs ~ 1 . X3 lo5cm s-'. The S-mode wavelength at the peak, 55 is thus ~ 7 . A. 9 The X-ray RDF from liquid water (20 "C) indicates that the last major peak wanes on the high-distance side near 7.8 A.I' The calculated S-mode wavelength of ~ 7 . A 9 is thus almost identical with the 7.8-A X-ray value; 7.8 A is roughly the structural correlation length (SCL) for liquid water, and the shear mode wavelength has been shown, for a series of glasses, to correspond to the SCL value.' [A calculated wavelength of 8.7 A results for 50 cm-], Figure 2, which more nearly corresponds to the 0fourth-0 distance-weak ripples in the RDF."] The shear motion of H 2 0 molecules involves a coherence volume, which refers approximately to some correlation length. Because the shear wavelength is larger than the dilatational wavelength, it is the largest phonon wavelength and corresponds to the largest correlation length, namely, the SCL, which is essentially the 0-third-0 (or 0-fourth-0) neighbor distance for liquid water at ambient temperature. The dilatational wave must change the density, momentarily, and thus it involves some density-related distance. This distance cannot reasonably be the nearest-neighbor 0-0distance, because such a distance cannot sustain a full wave involving H 2 0 particle motions. Instead, the 0-second-0 distance is involved, in rough analogy to the second-neighbor distance associated with the Brillouin zone edge in crystals. The shear mode, of course, involves only rotation, no dilatation. The order of the acoustic modes, that is, the spherical harmonic, is related to the depolarization ratio,' which is nearly 3/4 for the and higher, low-frequency region, Figure 1. S-mode orders of and P-mode orders of uPo,oand higher, help explain the observed depolarization. For example, large numbers of neighboring 0-0 restricted translations of 0-0-0units are out of phase with each (8) Slie, W. M.; Danfor, A. R.; Litovitz, T. A. J . Chem. Phys. 1966, 44, 3712. (9) Walrafen, G. E.; Fisher, M. R.; Hokmabadi, M . S.; Yang, W.-H. J . Chem. Phys. 1986, 85, 6970. (10) Walrafen, G. E.; Hokmabadi, M. S . ; Yang, W.-H.; Chu, Y. C . ; Monosmith, B.J . Phys. Chem. 1989, 93, 2909. ( 1 1) Narten, A. H.; Levy, H. A. In Water, A Comprehensive Treatise, Vol. I . The Physics and Physical Chemistry of Water; Franks, F., Ed.; Plenum: New York, 1972.
Letters
The Journal of Physical Chemistry, Vol. 94, No. 6. 1990 2239
Figure 2. Depolarized, BE corrected, Raman spectrum, X(ZX)Y, 20 "C Horizontal scale, cm-'.
other, moving between 180 and 165 cm-', to obtain a reasonable deconvolution of the acoustic-mode region between 3 and 95 O C . I o Finally, an isotropic elastic solid can only yield one S-mode peak See Figure 2. The 70-cm-I component was not resolved in the and one P-mode peak. The S-mode peak is doubly degenerate; spectrum, and it was not observed as an isolated peak. that is, it involves two transverse particle motions, say, X and Y, The unresolved 70-cm-I feature is believed to be a new P wave whereas the longitudinal P-mode particle motion must occur along that results from the disrupted network which involves bifurcated Z , the remaining degree of freedom. The S and P peaks, therefore, hydrogen bonds, first proposed by G i g ~ & r e . ' ~The bifurcated comprise the entire acoustic spectrum. When these have been hydrogen hydrogen bond is much weaker than the linear 0-H-0 identified at 60 and 175 cm-I, it becomes obvious that higher bond. Its longitudinal, bulk, and shear moduli should be smaller. frequency modes must refer primarily to optical phonons, as If the 70-cm-I feature is the high-temperature P mode of the described next. See Caveat section. extensively broken network, there must also be a high-temperature S mode. But this high-temperature S mode, like the corresponding Optic Modes P mode, should occur at a much lower frequency, compared to Optic modes often involve the lighter atoms, which for water the S mode of the fully hydrogen bonded network, e.g., well below are the protons. The first optic modes that occur above ~ 3 0 cm-I 0 60 cm-'. It may, in fact, be the lowest frequency, roughly 5-25 are the three librations between about 330 and 1000 cm-1.12 These cm-', shoulder feature reported in ref 4. If so, its integrated three librations (as well as higher optic modes) decrease in frecomponent intensity should rise with increasing temperature, just quency by a factor of ~ 1 . 3 upon 5 deuteration, =2i/2. They are, as the integrated intensity of the 70-cm-I component rises with in decreasing order of moment of inertia (1) the libration around temperature.I0 0 (2) the in-plane, (rocking) the C2 (2-fold) H 2 0 axis, ~ 4 5 cm-I; A region of downward concavity, =14 f 10 cm-' (see brace libration, =550 cm-I; and (3) the out-of-plane libration, ~ 7 2 5 in Figure 2), may be the high-temperature S mode. This downward concavity disappears in favor of upward concavity at The OH-stretching region constitutes the high-frequency end low t e m p e r a t ~ r e s . The ~ 14-cm-l feature makes its appearance of the fundamental optic mode region, extending to ~ 3 8 0 cm-I. 0 when the filling-in between 60 and 175 cm-I, associated with the Two features of the OH-stretching contour near 3390 and 3215 70-cm-l Gaussian, increases with rising temperature. cm-l 12 are important, because they differ by 175 cm-I. The Finally, the structure of liquid water near 0 "C must be similar, 3215-cm-I optic mode was assigned to the symmetric stretches locally, to ice, and the acoustic and optic modes of water and ice of five H 2 0 molecules (in a hydrogen-bonded tetrahedral arshould be related, but the relation between the low-frequency S rangement), all in-phase with each other.13 The 3390-cm-I mode and P modes of amorphous ice and liquid water should be closer. involves loss of this phase relationship. As expected, the 3215-cm-I A Raman peak near 219 cm-I has recently been observed for mode is very highly polarized, depolarization ratio, ~ 0 . 0 4 . ~ ~ 3 ' amorphous ~ ice at high pressure ( ~ 2 kbar) 6 and low-temperature The vibrational periods of the optical OH-stretching modes are This is probably the P mode. The S mode is probably ( ~ 7 K).I6 7 much shorter than the P-mode vibrational period. Nevertheless, the peak observed near 80 cm-I. it seems more than fortuitous that the optic-mode frequency Caveat difference should equal the acoustic, P mode, frequency. The TA and LA modes of ice I, were assigned at 65 or =70 cm-I, 175-cm-' mode involves 0-0 stretching, which would almost and 164 or 181 cm-I, respectively, with optic modes between 190 certainly couple very strongly with the corresponding OHand 240 cm-1.6 However, the present water model is radically stretching motion, because both motions are coaxial for a linear different and designates optic modes as those displaying an hydrogen bond. Either the 3215-c1n-~or the 3390-cm-l mode may H 2 0 / D 2 0frequency ratio of ~ 1 . 3 5Le., , >330 cm-I. Nevertheless, be a two-phonon, optic-acoustic mode; probably the former, 3390 optic 0-0stretching and 0-0-0 bending frequencies also follow cm-I - wp = 3215 cm-'. their respective bulk and shear moduli, which leads to overlap with Temperature Effects the acoustic modes. A temporal structure of H20 molecules treated as points, mass The acoustic-mode region displays an isosbestic point when it 18, and having an 4 - 9 A radius related to loss of stress wave is Bose-Einstein corrected (see Figure 1 and caption). This point phase coherence (at roughly the third [or fourth] neighbor or SCL is precise if the collision-induced background is also subtracted.I0 distance) is considered. This coherence volume can sustain only The isosbestic point indicates that one class of acoustic S and P S modes involving the orders, PI,*,, @2,i2, modes is giving way to a different class of S and P modes, with temperature rise. The transverse and longitudinal elastic moduli ..., and P modes involving the orders uPo,o, p2,0, uP2,+1,uP2,+2, ..., where the subscripts relate to I , m of the thus decrease, as the hydrogen-bonded network breaks down. spherical harmonics. These orders approximate the collective Evidence for this breakdown has been presentedi0 and is evident motions of the 17 (or 53) hydrogen-bonded mass points. They from Figure 2. differ from those of a Td or C2, model of 5 mass points, which It was necessary to employ a Gaussian component near 70 cm-I, yields optic-type 0-0stretching and 0-0-0 bending modes, but plus two other Gaussian components, one near 50 cm-' and the cannot, for example, yield high-order shear modes. The remaining motions, namely librational, H 2 0 bending, and ( 1 2) Walrafen, G. E. In Wafer,A Comprehensive Treafise, Vol. 1 . The OH stretching, are optic modes involving protons and occur above Physics and Physical Chemistry of Wafer;Franks, F., Ed.; Plenum: New -330 cm-I. York, 1972. other even in the lowest order P mode when the wavelength is ~ 4 . 5
A
+
+
( 1 3) Walrafen, G. E. In Strucfure of Waferand Aqueous Solutions;Luck,
W.. Ed.; Verlag Chemie: Weinheim, FRG, 1974.
(14) Murphy, W. F.; Bernstein, H. J. J . Phys. Chem. 1972, 76, 1147.
(15) GiguBre, P. A. J . Chem. Phys. 1987, 87, 4835 (16) Hemley, R. J., private communication.
u'l,al,
