J. Phys. Chem. 1996, 100, 1381-1391
1381
Raman OD-Stretching Overtone Spectra from Liquid D2O between 22 and 152 °C G. E. Walrafen,* W.-H. Yang, Y. C. Chu, and M. S. Hokmabadi Chemistry Department, Howard UniVersity, Washington, D.C. 20059 ReceiVed: July 26, 1995; In Final Form: September 8, 1995X
Raman OD-stretching (first) overtone spectra, X(Z,X+Z)Y, X(ZZ)Y, and X(ZX)Y, from pure D2O between 22 and 98 °C yield an isosbestic frequency near 5130 cm-1. This value corresponds to the X(ZX)Y fundamental isosbestic observed near 2624 cm-1, but not to the X(ZZ)Y fundamental isosbestic near 2429 cm-1, because the fundamental 2375 cm-1 correlated deuteron OD stretch, ν1, and its overtone, 2ν1, are weak in the X(ZX)Y spectra, compared to the three higher-frequency fundamentals, ν2, ν3, and ν4, and their overtones. The 2375 and 2475 cm-1 fundamentals and their overtones probably engage in coupling with a ≈175 cm-1 LA phonon which is supported by H-bonded aggregates or patches, whereas the corresponding data for H2O provide clear and unequivocal evidence for this LA coupling. Deconvolution of the X(Z,X+Z)Y overtone spectra, 22-152 °C, plus van’t Hoff treatment yields an enthalpy for H bond, O-D‚‚‚O, rupture of 2.8 ( 0.2 kcal/ mol O-D‚‚‚O, in good agreement with present values of 2.6 ( 0.2 and 2.8 ( 0.2 kcal/mol O-D‚‚‚O, obtained from the fundamental X(ZZ)Y and X(ZX)Y spectra. Raman overtone measurements are important because the spacing between the four-Gaussian components is large in the overtone OD- and OH-stretching contours compared to the fundamentals.
Introduction Raman spectra in the first overtone OD- and OH-stretching region of D2O and H2O are important because the inter-Gaussian component separation is large compared to the corresponding substructure of the fundamentals. This arises from interintramolecular coupling and anharmonicity effects which produce changes in the relative separations and intensities of the overtone Gaussian subcomponents. The first overtone Raman spectra thus yield new information, despite the considerable experimental difficulties involved, and the increased component separation of the first overtone spectra evokes the tantalizing possibility of even better definition in the second Raman overtone. The Raman intensity of the first OD-stretching overtone from liquid D2O (or H2O) is smaller, by about 4 orders of magnitude, than that of the fundamental. Hence, only a few investigations of the Raman overtone region from water have been conducted; see ref 1 and references therein. Nevertheless, much important information can be obtained from such overtone studies because the anharmonicity varies markedly among the four Gaussian components comprising the overtone contour, thus allowing for enhanced resolution and clarification of the component substructure, as well as for the obtaining of accurate H-bond enthalpies (this work and ref 1). A signal-to-noise ratio of ≈10 may be obtained at the peak of the first OD-stretching overtone using 6-7 W of 488 nm argon ion radiation (single pass), at the sample, with slit widths corresponding to about 15-16 cm-1. Such a signal-to-noise ratio is sufficient to obtain an accurate shape for the ODstretching contour, as well as isosbestic frequencies and reliable H-bond enthalpy values (this work). Some indications of the second Raman OH-stretching overtone from pure H2O, which is 7 or 8 orders of magnitude weaker than the OH-stretching fundamental, have been obtained with pulsed 248 nm KrF excimer laser excitation and boxcar detection.2 Moreover, some evidence of the second Raman ODstretching overtone from pure D2O was obtained in the present work using a Hamamatsu R758-10 photomultiplier tube with X
Abstract published in AdVance ACS Abstracts, December 1, 1995.
0022-3654/96/20100-1381$12.00/0
high red quantum efficiency, and further measurements with improved detection and higher laser powers are planned. Raman spectra from the OD-stretching overtone are shown in the Raman Overtone Spectra section for three polarization configurations: X(Z,X+Z)Y, 22-150 °C, and X(ZZ)Y and X(ZX)Y, 23-98 °C. Isosbestic points displayed by the Raman spectra are also shown. Raman spectra from the fundamental OD-stretching region for the 22-95 °C temperature range and for the X(ZZ)Y and X(ZX)Y polarization configurations are shown in the Raman Fundamental Spectra section, again with the corresponding isosbestic points. Results of Gaussian digital computer deconvolution for the fundamental and overtone Raman spectra, as well as direct physical evidence for the existence of the Gaussian components from stimulated Raman scattering and IR hole burning, are presented in the Interpretation section. Detailed assignments of the four Gaussian components which comprise the OD-stretching fundamental and overtone contours, ν1, ν2, ν3, and ν4, are given as well. This section also contains tables listing anharmonicities of the Gaussian components, as well as van’t Hoff plots which relate to the H-bond enthalpies. The article concludes with a discussion of the inter-intramolecular coupling between ν1 ) 2375 cm-1, D2O (3212 cm-1, H2O); ν2 ) 2475 cm-1, D2O (3383 cm-1, H2O); and νP ) ≈175 cm-1 (both liquids), invoked for D2O and H2O. The νP mode involved in this coupling refers to a longitudinal acoustic (LA) phonon which occurs as a standing wave in H-bonded aggregates or patches in H2O and D2O.3-5 An Appendix is included which defines the X(ZZ)Y, X(ZX)Y, and X(Z,X+Z)Y terminology used here as well as the depolarization ratio. References dealing with the corresponding measurements, as well as with general experimental aspects of Raman spectroscopy, are provided for readers not totally conversant with Raman spectroscopy. The Appendix also contains a figure which depicts the four-Gaussian decompositions used for the fundamental Raman spectra so that interested readers may make comparisons with the corresponding overtone decompositions, shown in the main text. The Experimental Procedures section to follow includes descriptions of the analog and digital computer deconvolution of the Raman spectra, as well as details related to the Raman spectrometer, laser, polarization configurations, etc. © 1996 American Chemical Society
1382 J. Phys. Chem., Vol. 100, No. 4, 1996
Walrafen et al.
Experimental Procedures The D2O used in this work was obtained from the Aldrich Chemical Co., Milwaukee, WI (catalog no. 34,716-7; 99.9 atom % D, density 1.107 g/cm3, bp 101.4 °C). This grade of D2O is excellent for Raman overtone work. It produced an extremely small amount of fluorescence in the first OD-stretching overtone region. However, even this small fluorescence was virtually eliminated (in recent work with the second Raman overtone at room temperature) by passing a stream of very concentrated O3 through the D2O for about 30 min. Raman spectra were obtained with an Instruments S.A. HG2S holographic concave grating double monochromator. Scanning of the monochromator and detection were accomplished with Jobin-Yvon Prism software using an IBM compatible 286 computer. Slit widths corresponding to 15-16 cm-1 were used when obtaining the first OD-stretching overtone spectra. A Coherent argon ion laser was employed for excitation of the Raman spectra. This laser was designed specifically for the present work. It can produce powers as large as 10 W at 488.0 nm, but power levels of about 6-7 W were more commonly used at the sample, in single-pass configuration. However, a double pass was employed in a few cases with an input power of 8 W at the sample. Such high powers were used to measure the position of the weak, first overtone feature at ≈4600 cm-1, directly, i.e., without computer deconvolution. Polarized spectra were obtained by precise and reproducible 90° rotation of a high-quality polarizer. The electric vector of the laser beam was maintained in a vertical position in all cases. A polarization scrambler was used in front of the exit slit of the spectrometer for the X(ZZ)Y and X(ZX)Y spectra only. Heating of the sample was accomplished as indicated in ref 6. The D2O sample was usually contained in a sealed glass tube, as described in ref 6. However, a few spectra were obtained with the use of high-pressure, high-temperature Raman cells made of Inconel or Monel. These cells employed either three sapphire windows or three fused silica windows, 2.54 cm in thickness and 2.54 cm in diameter. Deconvolution of the Raman spectra with Gaussian components was accomplished first with a du Pont 310 analog computer. The resulting analog component parameters were then used as the initial input for digital deconvolution. The digital deconvolution was accomplished with Galactic, Lab Calc software, and with a Compudyne Pentium 100 MHz, 20 MB computer. The du Pont 310 analog computer was found to yield Gaussian fits much more rapidly than the Compudyne Pentium 100 MHz computer. However, the digital fits were better with regard to accurate values of component positions, half-widths, and especially integrated component intensities. Moreover, statistical tests of the digital fits were also provided, e.g., chi squared. Nevertheless, the digital fits still had to be evaluated, visually, to ensure that detailed features, such as the sharp minimum and maximum observed near 5300 cm-1 at 150 °C, were adequately fit within the signal-to-noise ratio of the data. All digital computer results listed in the tables involved 2000 iterations with the Compudyne Pentium computer. Raman Overtone Spectra Raman OD-stretching (first) overtone spectra, X(Z,X+Z)Y, obtained under identical excitation and detection conditions between 22 and 95 °C are shown for the 4000-6000 cm-1 region in Figure 1. The spectra of Figure 1 show three visually obvious features: (1) a foot at roughly ≈4600 cm-1; (2) a peak which moves upward by ≈75 cm-1, from ≈5030 to ≈5105 cm-1 with temperature rise from 22 to 95 °C; and (3) a shoulder at about
Figure 1. X(Z,X+Z)Y overtone Raman spectra from pure D2O. Intensities are quantitatively intercomparable. Base lines were determined by methods described in the text. Note the foot near 4600 cm-1, and shoulder near 5300 cm-1, which is especially evident at high temperature (A). Lines of equal height at 5130 ( 5 cm-1 depict isosbestic frequency.
Raman OD-Stretching Overtone Spectra from Liquid D2O
J. Phys. Chem., Vol. 100, No. 4, 1996 1383
Figure 2. X(Z,X+Z)Y overtone Raman spectra from pure D2O at elevated temperatures. Intensities are not quantitatively intercomparable. Note minimum and maximum near 5300 cm-1 which indicate a component which is more prominent at 150 °C (A).
5300 cm-1, which is more prominent at high temperatures, e.g., 125-150 °C (Figure 2). After many trials, base lines were determined for the Figure 1 and Figure 2 spectra, by the following procedure. A nonlinear base line lower limit was determined, as a first approximation, by fitting, and connecting, the regions between 4000 and ≈4300 cm-1 and between ≈5500 and 6000 cm-1 with a spline. This procedure yielded a nonlinear base line between ≈4300 and ≈5500 cm-1, but the upward concavity of this base line was a little too constant, and it tended to be somewhat too low near ≈5000 cm-1. Then using this first base line as a guide, a linear region from 4900 to 6000 cm-1 was determined which passed through the center of the noise from ≈5500 to 6000 cm-1. The center of the noise was next fitted by least squares from 4000 to ≈4300 cm-1 by the function ln I ) a + bw + cw2 (w ) Raman frequency, cm-1). This least-squares fit and its slope were made to match the linear fit and its slope at about 4900 cm-1. The resulting analytical functions were used to transfer the spectra (digitally) to horizontal base lines for computer analysis, determination of an isosbestic frequency, etc. The transferred spectra (not shown) indicated a good isosbestic point at 5130 ( 5 cm-1. This isosbestic frequency is shown in Figure 1, 22-95 °C, by vertical lines of equal height. On the basis of previous work with OH-stretching overtone spectra from pure H2O1 and from much other Raman work with H2O/D2O and H2O/T2O mixtures,7-10 it is expected that
Gaussian component centers, related to broken hydrogen bonds, should lie above the isosbestic frequency and Gaussian component centers, related to intact hydrogen bonds, namely, deuteron correlated and deuteron uncorrelated H-bonded components,1,5,11 should lie below the isosbestic frequency. These expectations are confirmed by subsequent analysis, which also clearly indicates that the ≈75 cm-1 upward shift, mentioned above for the OD-stretching peak position, is the result of intensity changes of two Gaussian components at constant frequency, not a true shift of components. Raman OD-stretching overtone spectra for the X(ZZ)Y and X(ZX)Y polarization configurations are shown in Figures 3 and 4, respectively. Base lines were determined, and the spectra were transferred to horizontal base lines. Isosbestic points resulted at 5130 ( 5 and ≈5100 ( 10 cm-1, as shown in the figures. The intensities and signal-to-noise ratios (Figures 3 and 4) are lower than those of Figure 1, because of the loss due to the polarizer and polarization scrambler and also from the polarization of the Raman components. The experimental uncertainty of the isosbestic frequency from Figure 4 is much larger than that from Figures 1 and 3. Because of such experimental uncertainties, we regard the X(Z,X+Z)Y, X(ZZ)Y, and X(ZX)Y overtone isosbestic frequencies to be essentially the same, i.e., about 5130 cm-1.
1384 J. Phys. Chem., Vol. 100, No. 4, 1996
Walrafen et al.
Figure 3. X(ZZ)Y overtone Raman spectra from pure D2O. Intensities are quantitatively intercomparable. The (A), (B), and (C) spectra were transferred to horizontal base lines. Note the isosbestic frequency at 5130 ( 5 cm-1, shown in the lower right panel.
Figure 4. X(ZX)Y, i.e., pure anisotropic, overtone Raman spectra from pure D2O. Intensities are quantitatively intercomparable. The (A), (B), and (C) spectra were transferred to horizontal base lines. Note the isosbestic frequency near 5100 ( 10 cm-1, shown in the lower right panel.
Raman Fundamental Spectra Raman fundamental OD-stretching spectra obtained between ≈22 and 95 °C for the region from 1900 to 3000 cm-1, and with the X(ZZ)Y and X(ZX)Y polarization configurations, are shown in Figures 5 and 6, respectively. The X(ZZ)Y spectra indicate an isosbestic point near 2429 ( 5 cm-1 (Figure 5), whereas the X(ZX)Y spectra show an isosbestic point near 2624 ( 5 cm-1 (Figure 6). The X(ZZ)Y isosbestic point of 2429 cm-1 cannot relate to the overtone isosbestic frequencies observed here, i.e., 5130 ( 5, 5130 ( 5, and ≈5100 ( 10 cm-1 from Figures 1, 3, and 4, respectively, because such a correspondence would lead to negatiVe anharmonicity, which is impossible. However, the 2624 cm-1 isosbestic frequency is related to the present overtone isosbestic frequencies, as seen from the anharmonicity given by [(2 × 2624/5130) - 1] × 100 ≈ 2%. This 2% anharmonicity is not far from that reported for H2O,1 but it is smaller, as expected. The X(ZZ)Y isosbestic frequency of 2429 cm-1 may be a new type of isosbestic point. This point separates the 2375 cm-1
deuteron correlated OD-stretching Gaussian component1,5,11 from the 2475 cm-1 uncorrelated deuteron OD-stretching Gaussian,1,5,11 as detailed subsequently in the Interpretation section. Both of these components refer to H-bonded water molecules, as opposed to the more common isosbestic point which separates H-bonded and non-H-bonded components. See discussion in Interpretation section. The X(ZX)Y isosbestic frequency of 2624 cm-1 is of the common type recognized previously.7-9,12 It separates Hbonded Gaussian components, whose centers lie below it, from non-H-bonded Gaussian components, whose centers lie above it. The 2624 cm-1 X(ZX)Y isosbestic frequency occurs about midway between the fundamental Gaussian components 3, ≈2560 cm-1, and 4, ≈2670 cm-1, and the ≈5100 cm-1 X(ZX)Y isosbestic frequency is also about midway between the overtone Gaussian components 3, ≈5080 cm-1, and 4, ≈5280 cm-1; see ref 11 and subsequent discussion. Component 3 has previously been designated NHB because the corresponding, weakened H bond involves a deuteron on a
Raman OD-Stretching Overtone Spectra from Liquid D2O
J. Phys. Chem., Vol. 100, No. 4, 1996 1385
Figure 5. X(ZZ)Y fundamental Raman spectra from pure D2O. Intensities are quantitatively intercomparable. Note the isosbestic frequency at 2429 ( 5 cm-1. (No transferral from one base line type to another was involved here.) A, B, C, D, and E ) 95, 81, 61, 41, and 22 °C, respectively.
Figure 6. X(ZX)Y, i.e., pure anisotropic, fundamental Raman spectra from pure D2O. Intensities are quantitatively intercomparable. Note the shoulder near 2650 cm-1 which becomes increasingly more pronounced from 24 to 95 °C. The isosbestic frequency occurs at 2624 ( 5 cm-1. (No base line transferral was involved.) A, B, C, D, and E ) 95, 80, 63, 45, and 22 °C, respectively.
D2O molecule whose second deuteron is dangling or free (an analogous situation occurs for H2O).1,5,11 The X(ZX)Y fundamental and overtone isosbestic points for D2O [and for H2O1,12] correctly separate H-bonded versus dangling or free OD (and OH) interactions. Nevertheless, we will retain the NHB designation for component 3 for consistency with prior work, and because both components 3 and 4 increase in intensity at elevated temperatures (relative to components 1 and 2) and also engage in stimulated Raman scattering as a pair, etc. Interpretation A. Direct Physical Evidence for Inhomogeneously Broadened Gaussian OD- and OH-Stretching Contour Substructure. i. Picosecond Stimulated Raman Scattering. Stimulated Raman scattering (SRS) is a two-photon interaction involving a laser quantum, hνL, and (n) Stokes quanta, hνs, in which the sample is excited by an amount, h(νL - νS), and (n + 1) Stokes quanta, hνS, are emitted. Interaction between the laser quanta and the spontaneous Stokes quanta gives rise to a coherent stimulated Stokes wave which grows exponentially from the spontaneous noise level and is observed in the forward direction.
SRS from water and aqueous mixtures has been reported.13-15 The 5300 Å picosecond pulses at ≈200 MW were focused to yield the required power density threshold of about 25 GW/ cm2. High-power SRS from pure H2O and D2O yields two peaks which lie in the H-bonded (HB) region of the spectrum, but two stimulated peaks in the non-H-bonded (NHB) region of the spectrum are produced when the concentration of the H2O (or D2O) is reduced by isotopic dilution to below about 40 mol %.13-15 Stimulation of the HB pair of peaks or the NHB pair of peaks occurs in a mutually exclusiVe manner.13-15 The above-described high-power SRS process in water and aqueous mixtures definitely Violates simple SRS theory, which requires the most intense spontaneous peak to stimulate according to IS(l) ) IS(0) exp(glI0). IS(l) and IS(0) are the stimulated and spontaneous scattering intensities at l and l ) 0, I0 is the laser intensity, l is the excited sample length, and g is proportional to the spontaneous differential scattering cross section and inversely proportional to the spontaneous full width at half-height (fwhh).14 Colles16 has presented a parametric coupling theory, using
1386 J. Phys. Chem., Vol. 100, No. 4, 1996
Walrafen et al.
TABLE 1: Comparisons of Stimulated Raman and IR Hole-Burning, Double-Resonance Component Frequencies (cm-1) with Spontaneous Raman Gaussian Component Frequencies (cm-1) from Water-Heavy Water Mixtures (Component Numbers in Parentheses) spontaneous Raman Gaussian analysisa
HB Components 3250-3290b 3275c 3380-3450b 3450c
(1) 3212-3218 (2) 3380-3393
NHB Components 3525b 3550c 3650b
(3) 3480-3520 (4) 3616-3620 a
e
stimulated Raman
b
c
infrared hole burning, double resonanced 3345 3422
3520 3650e d
Reference 11. Reference 13. Reference 15. Reference 17. NHB OH induced absorption poly(vinyl butyral).
an inter-intramolecular coupling mechanism, νU - νC ) νP, described below, to explain the mutually exclusive SRS observed for aqueous mixtures. The SRS HB and NHB peak frequency positions are compared in Table 1 with the central frequency positions of the spontaneous Raman Gaussian OH-stretching stretching components used in previous contour deconvolutions. ii. Picosecond Infrared Hole-Burning and Infrared DoubleResonance Spectroscopy. Picosecond infrared hole-burning spectroscopy (IR-HBS) is a process in which pump pulses of high power density, ≈10 GW/cm2, at an IR frequency ν1, are used to saturate vibrations in an inhomogeneously broadened medium. The saturated medium is then simultaneously probed by weaker monochromatic laser pulses whose frequency can be varied over the spectral contour, which, under these saturation conditions, exhibits a hole around the frequency ν1.17 Infrared double-resonance spectroscopy (IR-DRS) is a refinement of IR-HBS in which additional information is obtained from parallel (||) and perpendicular (⊥) polarizations of the probe pulse, e.g., the induced dichroism δR(D) ) [δR(||) - δR(⊥)]/ δR(RF), may be measured, where δR(||)LS ) ln[T(||)/T°) ) A, δR(⊥)LS ) ln[T(⊥)/T°) ) B, and δR(RF)LS ) [δR(||) + 2δR(⊥)]LS/3 ) (A + 2B)/3, where LS is a sample length, D refers to induced dichroism, RF refers to rotation-free transmission, T° is the unpolarized probe pulse transmission, and T(||) and T(⊥) are the parallel and perpendicular transmissions, respectively.17 [A simplified form for the induced dichroism is thus δR(D) ) 3(A - B)/(A + 2B).] Laubereau and Graener (LG)17 have recently reported the results of an IR-DRS study of 0.5 and 1.0 mol/L solutions of HDO in D2O. They find that the OH-stretching contour involves three distinct, broad components whose central frequencies are listed and compared in Table 1. Examination of Table 1 indicates that the agreement between spontaneous Raman OH-stretching Gaussian component central frequencies and the SRS peak positions for H2O and H2O/D2O mixtures is very good. The agreement between the spontaneous component frequencies and the IR-DRS frequencies is good for three out of the four IR-DRS values listed. Only the IR-DRS value of 3345 cm-1 is too high. Also, the 3620 cm-1 component from dilute HDO in D2O is known to be extremely weak (almost inactive) in the infrared spectrum,18,19 and thus a hole was not uncovered at this position. However, an IR-DRS hole was observed at about the correct position from broken H bonds in poly(vinyl butyrate),17 and thus this value is included in Table 1. LG17 concluded that spectral substructure is clearly present in the OH-stretching contour from HDO in D2O and that the contour is unquestionably broadened, inhomogeneously. They
TABLE 2: Fundamental and Overtone Raman Component Frequencies (cm-1) and Anharmonicity Parameters for D2O j
ω1j
ω2j
xj
Aj(2)
ω0j
∆j(2)
1 2 3 4
2375 2475 2560 2666
4616 4917 5077 5280
0.0267 0.0065 0.0083 0.0095
0.0290 0.0067 0.0085 0.0098
2509 2508 2603 2718
134 33 43 52
TABLE 3: Fundamental and Overtone Raman Component Frequencies (cm-1) and Anharmonicity Parameters for H2O j
ω1j
ω2j
xj
Aj(2)
ω0j
∆j(2)
1 2 3 4
3214 3393 3505 3616
6160 6665 6850 7030
0.038 0.017 0.022 0.026
0.044 0.018 0.023 0.029
3482 3514 3665 3818
268 121 160 202
TABLE 4: Four-Gaussian Frequencies and fwhh Values for the Raman X(Z,X+Z)Y Overtone Contours from D2O at the Extremes of the Temperature Range Examined in This Worka 22 °C
150 °C
Gaussian center
fwhh
Gaussian center
fwhh
(1) 4604 (2) 4917 (3) 5077 (4) 5280
332 277 266 164
(1) 4606 (2) 4949 (3) 5129 (4) 5324
328 305 231 180
a All Gaussian center and fwhh values are in cm-1. The uncertainties of the fwhh values vary from about (10 cm-1 for the strongest components to about (15 cm-1 for the weak, broad components. The uncertainty of the weak, broad component (1) Gaussian center frequency values is (15 cm-1. The component (1) central frequency in Table 3 differs by 12 cm-1 from the above 22 °C value because a different deconvolution run was employed.
also state that, “Our analysis of the measured transient spectra suggests that the band structure is not due to a smooth, singly peaked frequency distribution but displays several maxima corresponding to preferred environments of the OH group. The spectra can be explained by a discrete set of at least three subcomponents of the OH band...”. In addition, LG17 show three Gaussian OH-stretching subcomponents (at the three frequencies listed in Table 1); see their Figure 6. B. Gaussian Deconvolution of Spontaneous OD-Stretching Raman Spectra. i. General Procedure. Raman overtone and fundamental OD-stretching spectra of this work were deconvoluted by using four corresponding Gaussian components. The term corresponding Gaussian components means that component 1 of the fundamental OD-stretching contour at 2375 cm-1 corresponds to component 1 of the overtone contour at about 4600 cm-1, and so forth, for components 2, 3, and 4. (See Tables 1, 2, and 3 for frequencies of components 1, 2, 3, and 4.) Fixed central frequencies and full widths at half-height (fwhh) were used for the four Gaussian components in the fundamental contour deconvolutions, but variable central frequencies were used for the four-Gaussian deconvolutions of the overtone Raman spectra. Some systematic frequency shifts for the four Gaussian components of the X(Z,X+Z)Y overtone spectra were observed, but the fwhh values were essentially constant (see Table 4). The integrated Gaussian component intensities changed, of course, within the present 130 °C temperature range because of (1) decreasing deuteron correlation and (2) breakage of hydrogen bonds, both with temperature rise. These integrated Gaussian component intensity changes were exploited to obtain H-bond enthalpies from ln(Ii/Ij) versus 1/T plots, where, for example, i and j refer to broken (NHB) and to intact (HB) H-bonds, respectively.
Raman OD-Stretching Overtone Spectra from Liquid D2O
J. Phys. Chem., Vol. 100, No. 4, 1996 1387
Figure 8. van’t Hoff plot of the natural logarithm of the 4 to 2 integrated Gaussian component intensity ratio versus 1/T using the Figure 1 data. The slope of this plot corresponds to an enthalpy change for H-bond breakage of 2.8 ( 0.2 kcal/mol O-D‚‚‚O.
Figure 7. Digital four-Gaussian deconvolution of Figure 1 spectra, A and E. The raw digital intensities are shown as points. The sum of the four Gaussians is shown by the heavy line through the digital points. The Gaussian components are shown by thin lines. The deconvolutions involved 2000 iterations with a 100 MHz computer. Gaussians components from left to right in the figure are numbered 1, 2, 3, and 4. See text and tables.
Gaussian deconvolution of fundamental OH- and ODstretching contours has been used extensively in the past.1,5,7-11 Moreover, the same Gaussian OD-stretching component (central) frequencies obtained previously11 were used here. Numerous examples also exist in which the spontaneous Raman and SRS spectra from aqueous electrolyte solutions clearly provide direct physical evidence for the broad Gaussian OH- and ODstretching substructure.1,5,7-11,19 The four corresponding Gaussian components employed here for the OD-stretching contour deconvolution, fundamental and overtone, may be further classified according to two pairs: the HB pair, 1 and 2, and the NHB pair, 3 and 4, as illustrated by frequency assignments used in previous fundamental contour deconvolutions.11 In the case of the fundamental Raman OD-stretching contour, component 1 of the H-bonded pair refers to (C) correlated, 2375 cm-1, whereas component 2 of this pair refers to (U), the uncorrelated, 2475 cm-1, H-bonded deuteron component; see also refs 1, 5, and 11. The other OD-stretching pair refers to D2O molecules having one deuteron not H-bonded, 2665 cm-1, component 4, whereas the second deuteron of the same molecule, when H-bonded, refers to component 3 at 2565 cm-1; see also refs 1, 5, and 11. Raman intensities of members of these two pairs show opposite temperature dependences, as demonstrated subsequently by quantitative data; see also refs 7, 8, and 19. We begin with four-Gaussian contour deconvolutions of the X(Z,X+Z)Y OD-stretching overtone spectra, shown in Figure 1. ii. Gaussian OD-Stretching OVertone DeconVolution. Digital OD-stretching overtone deconvolution was accomplished for the X(Z,X+Z)Y spectra using four Gaussian components for temperatures from 22 to 152 °C. Typical Gaussian fits for temperatures of 22 and 95 °C are shown in Figure 7. This figure
shows the fwhh values by means of the Gaussian components, which are displayed in the figure. Values of the enthalpy change corresponding to H-bond breakage were obtained from ln(Ii/Ij) versus 1/T plots (subscripts defined in subsection i). Numerous ∆H values were obtained from individual component intensity ratios and from ratios of sums of component intensities, e.g., 1 and 2, 2 and 3, 3 and 4, 1 and 4, 1 and 3, 1 + 2, and 3 + 4, etc. However, we finally proceeded with the following joint criteria: we only used (1) components whose central frequencies are separated by the greatest amount and (2) components having the largest integrated intensities over the temperature range examined. Overtone components 2 and 4, for example, fit criteria 1 and 2 jointly, but components 1 and 4 did not, nor did components 1 and 3. A plot of ln(I4/I2) versus 1/T (henceforth called a van’t Hoff plot) obtained from the X(Z,X+Z)Y overtone spectra is shown in Figure 8. The least-squares slope from the Figure 8 data corresponds to an H-bond breakage enthalpy change of 2.8 ( 0.2 kcal/mol ODO ((0.2 is a conservative error estimate). iii. Gaussian OD-Stretching Fundamental DeconVolution. Digital four-Gaussian OD-stretching contour deconvolution was also conducted for the fundamental X(ZZ)Y and X(ZX)Y spectra, using fixed frequencies and fwhh values (see Figure 10). van’t Hoff plots (not shown) were constructed from the component intensity data obtained from the OD-stretching contour fits. Least-squares fits of the data led to an H-bond breakage ∆H value of 2.6 ( 0.2 kcal/mol ODO, X(ZZ)Y, and of 2.8 ( 0.2 kcal/mol ODO, X(ZX)Y. The scatter of the data comprising the van’t Hoff plots was the same as that shown in Figure 8. iV. Further Aspects of the Data. ∆H values for H-bond breakage from pure D2O (sections ii and iii) are 2.8 ( 0.2, 2.6 ( 0.2, and 2.8 ( 0.2 kcal/mol ODO. (The extreme error limits of these enthalpy values produce a range from 2.4 to 3.0 kcal/ mol ODO.) The H-bond breakage ∆H value obtained from intermolecular Raman intensities of pure H2O is 2.6 ( 0.1 kcal/ mol OHO, and thus the agreement with the above three values is very good.20 Nevertheless, one might make a case to the effect that the ODO hydrogen bond is slightly stronger, roughly 8% stronger, than the OHO hydrogen bond. This case is strengthened when a recent nonspectroscopic value of 2.43 kcal/ mol OHO is compared to the extreme range of 2.4-3.0 kcal/ mol ODO given above; i.e., the probability that the ODO values lie well above the 2.43 kcal/mol OHO value, say ≈15% above, is large. An alternative analysis of the difference between the ODO and OHO hydrogen-bond energies may be more instructive. This involves comparisons only between Raman enthalpy values. Let
1388 J. Phys. Chem., Vol. 100, No. 4, 1996 us assume that the value of 2.6 kcal/mol OHO obtained from intermolecular Raman intensities and the value of 2.8 kcal/mol ODO obtained from the present X(Z,X+Z)Y overtone intensities are precisely correct. These two values differ by 0.2 kcal/mol H-bond. Let us further assume that a rotational process constitutes part of the H-bond rupture process. Then following an interesting suggestion of Agmon,21 we would expect the rotational differences between protons and deuterons to lead to an enthalpy difference of roughly RT ln(1.38), where 1.38 is the square root of the ratios of the moments of inertia, [I(D2O)/ I(H2O)]1/2. The average T value for the present measurements is 360 K. Hence, we obtain an enthalpy difference of 230 cal/ mol, or about 0.2 kcal/mol, in agreement with the above Raman enthalpy difference. (This agreement should not be treated as proof of any, e.g., rotational, mechanism.) Many physical properties of D2O, of course, suggest that its ODO bonds are slightly stronger than the OHO bonds of H2O.22-24 However, there is no question, whatever, that the anharmonicities of the OD-stretching components are significantly smaller than those of the OH-stretching components, as demonstrated quantitatively below. C. Detailed Features of the Gaussian Components. i. Inter-Intramolecular Coupling, C, U, and LA Components. The correlated, C, component, namely, component 1, has a number of properties which put it in a separate class from components 2, 3, and 4. The anharmonicity of component 1, for example, is shown below in (iii) to be larger than that of components 2, 3, and 4. Component 1 is also very intense in the fundamental X(ZZ)Y and isotropic OD- and OH-stretching Raman spectrum from the pure liquids, in contrast to its overtone intensity, and it also displays very low depolarization ratios, namely, 0.042 for D2O and 0.037 for H2O.11 Such low depolarization ratios are a major reason for assigning this component to correlated deuteron and correlated proton motions.1,5,11 Component 1 is designated C for correlated, and component 2 is designated U for uncorrelated in ref 5. The frequency difference between components 2 and 1 in the fundamental OH-stretching region, i.e., the U - C frequency difference, is about 175 cm-1 for pure H2O. This 175 cm-1 value also corresponds to the central position of the longitudinal acoustic (LA) phonon (P-wave) from pure H2O which arises from O-O stretching along the H-bond, O-H‚‚‚O direction.3,5,20 The LA phonon occurs as a standing wave with zero group velocity and is supported by H-bonded patches or aggregates in water whose size is related to the structural correlation length (SCL).3-5 The U - C frequency difference for pure D2O is about 100 cm-1, and hence it is not in exact resonance with the central frequency of the LA phonon (roughly 175 cm-1 for D2O). However, the width of the LA phonon is so large that sizable contributions from the LA phonon density of states must still result in the same general type of inter-intramolecular coupling described for H2O. This is even more apparent when it is realized that the central position of the TA phonon (S-wave), with which the LA phonon overlaps, is about 55 cm-1.3,4 See discussion in section iii to follow. ii. Raman EVidence for Pure (Two-Phonon) OVertone Modes. Component 1, the C mode, is very strongly polarized.11 In contrast, the LA phonon for pure H2O, νP, has a depolarization ratio of 3/4; i.e., it is completely depolarized.4 Moreover, zero isotropic intensity is observed between about 0 and 300 cm-1.25 A pure overtone of the type 2ν1 is polarized. Inter-intramolecular coupling does not change the polarization from polarized to depolarized. The only way in which complete
Walrafen et al.
Figure 9. Dispersion of the depolarization ratio throughout the first OD-stretching overtone contour from pure D2O at three temperatures. No region of complete depolarization, 0.75, is indicated. Note that all three curves display a minimum near 5350 cm-1. The shapes shown are qualitatively the same as that obtained in the fundamental Raman region for pure D2O at room temperature.
depolarization could occur would be through a direct threephonon interaction such as 2ν1 - νP, but such an interaction is not involved here. The inter-intramolecular coupling involves fundamentals and overtones which are coupled with νP, but the coupling occurs between one-phonon (fundamental) or twophonon (first overtone) modes. Depolarization ratios observed for the OD-stretching overtone contour are shown in Figure 9 for three temperatures. The depolarization ratios shown in Figure 9 display varying degrees of polarization. There is no evidence for complete depolarization, 0.75, over the principal part of overtone contour. Moreover, the shapes of the curves shown in Figure 9 correspond qualitatively to the shape of the depolarization ratio curve reported for the fundamental from pure D2O.11 An analogous comparison may be made for pure H2O.1,11
Raman OD-Stretching Overtone Spectra from Liquid D2O
J. Phys. Chem., Vol. 100, No. 4, 1996 1389
Figure 9 clearly indicates that all of the main components observed between roughly 4400 and 5600 cm-1 are two-phonon interactions, i.e., pure first overtones. However, the minimum displayed just below 5350 cm-1, near component 4, is also interesting and may be inferred from direct visual examination of the Raman spectra. Figures 3 and 4 provide clear visual evidence of polarization for component 4. An overt shoulder at the component 4 position, about 5300 cm-1, is evident in the X(ZZ)Y spectrum, but this feature is absent from the X(ZX)Y spectrum. This observation agrees with Figure 9, and it also clearly agrees with the pure overtone assignment of component 4. The depolarization ratio of fundamental component 4 is 0.32 for pure D2O and 0.27 for pure H2O.11 Component 4 arises from free or dangling OH and OD units, i.e., OH and OD units which are non-H-bonded (NHB). Such dangling OH and OD units on H2O and D2O molecules whose other protons or deuterons are H-bonded give rise to Cs symmetry due to the proton and deuteron inequivalence. This means that the dangling or free OH and OD stretches are of the A′ vibrational species and must be polarized in the fundamental spectrum, as observed.11 iii. Anharmonicity Constants and Predictions of the Second OVertone Component Frequencies. Use of the Morse potential, V(q) ) DE[1 - exp(-βq)]2, in the Schroedinger equation yields vibrational energy eigenvalues in units of cm-1 given by
Ej(n)/hc ) w0j(n + 1/2)[1 - Xj(n + 1/2)]
(1)
The index j of eq 1 refers, in the instant case, to the four Gaussian OD- and OH-stretching components, j ) 1, 2, 3, and 4. w0j is the vibrational frequency in cm-1, without anharmonic coupling, and xj is the anharmonicity coefficient. [Xj ) 0 refers to a harmonic oscillator, whereas a large Xj value refers to strong anharmonicity.] The anharmonic vibration corresponding to the n ) 1 to n ) 0 fundamental transition yields w1j in units of cm-1, given by
w1j ) w0j(1 - 2Xj)
(2)
whereas the anharmonic vibration corresponding to the n ) 2 to n ) 0 first overtone transition gives w2j in cm-1 as follows:
w2j ) w0j(2 - 6Xj) ) 2w1j - ∆j(2)
(3)
In eq 3, the ∆j(2) term is given by
∆j(2) ) 2Xjw0j
(4)
∆j(2) is the first overtone frequency shift or decrement. For the general case, the (n - 1)th overtone frequency, wnj, in cm-1 is given by
wnj ) nw1j - ∆j(n)
(5)
∆j(n) in eq 5, however, is a simple function of ∆j(2), as seen from
∆j(n) ) [n(n - 1)/2]∆j(2)
(6)
It is evident from eq 6 that all higher anharmonic decrements depend upon the first overtone decrement. This conclusion, of course, is specific to the use of the Morse potential. We next define the nth anharmonicity as
Aj(n) ≡ (nw1j - wnj)/wnj ≡ ∆j(n)/wnj
(7)
TABLE 5: Predicted Second Overtone Stretching Frequency Components for D2O and H2O Compared with Luck’s IR Data26 D2O (3)
j ∆j
1 402 2 99 3 129 4 156
H2O
-1
ω3j (cm ) expt error, % 6723 7326 7551 7842
}
7250
3
7550 7750
0.1 1
∆j(3)
ω3j (cm-1)
804 363 480 606
8838 9816 10035 10242
}
expt
error
9650
3
10187 10385
1 1
Measurements, solely of the fundamental frequency and first overtone frequency, plus eqs 2 and 3, are sufficient for determining values of Xj, Aj(2), w0j, and ∆j(2) by means of
Xj ) [2(w1j/w2j) - 1]/[6(w1j/w2j) - 2]
(8)
Aj(2) ) (Xj-1 - 3)-1
(9)
w0j ) w1j/(1 - 2Xj) ) w2j/(2 - 6Xj)
(10)
and
[Note that Xj from eq 8 is necessary for use in both eqs 9 and 10.] By using eqs 5-7, we can also obtain wnj, ∆j(n), and Aj(n) for any value of n. Only the fundamental and first oVertone frequencies are important in obtaining the higher oVertone parameters in the Morse approach. See eqs 2-6. In Tables 2 and 3 we present observed fundamental and overtone frequencies for components 1-4, obtained from Gaussian deconvolution of the fundamental and overtone ODand OH-stretching contours. We also present values of Xj, Aj(2), and w0j, calculated for j ) 1-4, from the observed fundamental and first overtone frequencies. In Table 5 we compare predictions from our data for the second overtone, n ) 3, with component frequencies obtained from our Gaussian deconvolution of the IR data of Luck.26 Good agreement between our calculations and the Gaussian frequencies from Luck’s IR data is obtained. The agreement is about 1% for components 3 and 4 and about 3% for the aVerage of our components 1 and 2, compared to the corresponding single, very broad, IR component, which was not resolved into components 1 and 2. Hence, the 3% agreement tacitly assumes that the IR components 1 and 2 have equal intensities, which is very unlikely. The agreement with Luck’s data would almost certainly be much better if a four-Gaussian deconvolution of the IR data were more feasible (but the large original spectral tracings would be needed). Finally, we present a critically important development for pure H2O, which clearly illuminates the connection between the U-C coupling, i.e., the coupling between components 2 and 1, which involves the LA phonon at ≈175 cm-1. This development demonstrates the U-C coupling for both the fundamental and the first overtone. Examination of Table 3 indicates that the difference between the fundamental frequencies for components 2 and 1 is given by
w12 - w11 ) wLAH2O ) 179 cm-1
(11)
(wLA refers to the LA phonon for H2O, superscript, also designated here by νP.) Examination of Table 3 also indicates that
w22 - w21 ) 505 cm-1
(12)
Note that the frequency difference in eq 12 is neither equal to,
1390 J. Phys. Chem., Vol. 100, No. 4, 1996
Walrafen et al.
Figure 10. Four-Gaussian deconvolutions of X(ZZ)Y (upper two panels) and X(ZX)Y (lower two panels) fundamental Raman spectra from Figures 5 and 6. The residual near 2200 cm-1, evident in the two upper panels, was previously fitted (11) with a fifth Gaussian component, but this was not done here. Heavy line is the sum of the four Gaussian components. The individual Gaussian components, numbered 1-4 from left to right, are shown by thin lines. The raw digital intensities are shown as points (2000 iterations, 100 MHz computer.)
nor twice the frequency of, the LA phonon; that is, it is not any reasonable multiple of ≈175 cm-1. From eq 3 we obtain
w22 ) 2w12 - ∆2(2)
(13)
w21 ) 2w11 - ∆1(2)
(14)
and
Subtraction of eq 14 from eq 13 leads to
w22 - w21 ) 2(w12 - w11) + (∆1(2) - ∆2(2)) ) 2wLAH2O + (∆1(2) - ∆2(2))
(15)
Substitution of 2wLAH2O ) 2 × 179 cm-1 ) 358 cm-1, and from Table 3, substitution of ∆1(2) - ∆2(2) ) 268 - 121 cm-1 ) 147 cm-1 into eq 15 gives the value of 505 cm-1, which agrees with the result of eq 12. [Note that the 2νP value of 358 cm-1 is exactly twice the LA phonon frequencysnot its overtone. No 2νP anharmonicity is needed. This occurs because the difference between eqs 13 and 14 involves 2νP exactly.] The important point to be gained from the above development is that the difference between the overtone frequencies of components 2 and 1, namely, 505 cm-1, is not immediately recognizable. This difference is not equal to the LA phonon frequency, and it is not equal to twice the LA phonon frequency. But when the overtone anharmonic decrements, namely, ∆1(2) and ∆2(2) are included, it becomes immediately obvious that components 2 and 1 are coupled to the LA phonon, both in the fundamental and in the overtone.
Similar conclusions can be obtained for D2O only if it is realized that part of the LA phonon density of states (DOS) is not zero at 100 cm-1, which is the U - C fundamental frequency separation. Let us consider the fact that the LA phonon DOS for pure D2O at 100 cm-1 is ≈25% as large as the LA phonon DOS at 179 cm-1.24 We might then hope, at least, that this offresonance condition would make the C and U mode coupling for D2O about 25% as strong as the corresponding coupling for H2O. However, it has been found that the C/U Raman intensity ratios from this work for D2O fall exactly on the C/U Raman intensity ratios reported very recently for H2O versus temperature; see Figure 1 of ref 5. This involves other measurements, of course, but it nevertheless suggests that strong C and U mode coupling occurs for both H2O and D2O. Acknowledgment. The help of Dr. D. A. McKeown in making a number of drawings and tables for this work is very greatly appreciated. Numerous private discussions and communications with Professor N. Agmon are gratefully acknowledged. This work was supported by a contract from the Office of Naval Research. Appendix A. Raman Polarization Terminology. An explanation of the terminology X(ZZ)Y, X(ZX)Y, and X(Z,X+Z)Y used here may be of use to workers not completely conversant with Raman spectroscopy. Consider the geometry defined by X(ZX)Y. The X before the parentheses refers to the axis of the incoming laser beam. The Y after the parentheses refers to the direction of observation, the Y axis. The first entry in the parentheses, the
Raman OD-Stretching Overtone Spectra from Liquid D2O Z, refers to the direction (axis) of the electric vector of the incoming laser beam. The laser beam, in this specific case, is linearly polarized. The second entry in the parentheses, in this instance an X, refers to the fact that the orientation of the polaroid in front of the slit allows only the X-polarized part of the Raman radiation to enter the slit. In the two other cases, X(ZZ)Y and X(Z,X+Z)Y, the polaroid allows the z-polarized part of the Raman radiation to enter the slit, or in the X+Z case, no polaroid is used; hence, both the X- and Z-polarized parts of the Raman radiation enter. A polarization scrambler also should be used just between the polaroid and the slit, so that the spectrometer always receives unpolarized radiation, since the response of the gratings to the X- and Z-polarized light is different and in fact is a different function of frequency as well. In the above three cases, it is assumed that the long direction of the slit coincides with the Z direction. The depolarization ratio, usually given the symbol F, is given by the ratio I(ZX)/I(ZZ), where I(ZX) refers to the intensity measured by the X(ZX)Y geometry and I(ZZ) refers to the intensity measured by the X(ZZ)Y geometry. The depolarization ratio may assume all values between 0 and 3/4, including precisely 0 or precisely 3/4, for linearly polarized laser (exciting) radiation. The Raman feature is described as depolarized, or sometimes as completely depolarized, if F is precisely 3/4. If F is less than 3/4, even by a small amount, the Raman feature is described as polarized. The totally symmetric stretching or breathing motion of a molecule such as CCl4, which is tetrahedral, Td, point group symmetry, should be zero according to simple theory, and the experimental depolarization ratio values even from the liquid approach zero very closely. It is very difficult to measure depolarization ratios to an accuracy of better than about 3%. Such an error is not serious, if the F value indicates complete (F ) 0) or strong polarization. However, the difference between 0.75, completely depolarized, and say, 0.73, polarized, albeit weakly, would be difficult to determine and would require very high signal-to-noise ratios, as well as meticulous experimental procedures. Other experimental pitfalls, not described here, can also make the accurate determination of extremely small F values very difficult as well. Excellent texts in which experimental Raman procedures, as well as theoretical aspects of Raman spectroscopy, are described are those of Strommen and Nakamoto27 and Long.28 B. Gaussian Deconvolution of Fundamental OD-Stretching Contours. The results of four-Gaussian (fixed frequency and fwhh) deconvolutions of X(ZZ)Y Raman spectra and of X(ZX)Y Raman spectra in the fundamental OD-stretching region of pure D2O are shown in the upper and lower sections of Figure 10, respectively. Interested readers may make comparisons between the components of this figure and the previous overtone results shown in Figure 8. Overtone and fundamental Gaussian component parameters,
J. Phys. Chem., Vol. 100, No. 4, 1996 1391 i.e., central frequencies, fwhh values, integrated component intensities, and their error limits, as well as chi-squared values, for all temperatures examined in this work may be obtained upon request. References and Notes (1) Monosmith, W. B.; Walrafen, G. E. J. Chem. Phys. 1984, 81, 669. (2) Walrafen, G. E.; Pugh, E. Doctoral dissertation of the latter, Howard University, May 1989, and unpublished work. (3) Walrafen, G. E. Chapter in Hydrogen-Bonded Liquids; Dore, J. C., Teixeira, J., Eds.; NATO ASI Series, Series C: Mathematical and Physical Sciences, Vol. 329; Kluwer Academic: Dordrecht, 1991. (4) Walrafen, G. E. J. Phys. Chem. 1990, 94, 2237. (5) Walrafen, G. E.; Chu, Y. C. J. Phys. Chem. 1995, 99, 11225. (6) Walrafen, G. E.; Yang, W.-H.; Chu, Y. C.; Hokmabadi, M. S.; Carlon, H. R. J. Phys. Chem. 1994, 98, 4169. (7) Walrafen, G. E. J. Chem. Phys. 1968, 48, 244. (8) Walrafen, G. E. J. Chem. Phys. 1969, 50, 567. (9) Walrafen, G. E.; Blatz, L. A. J. Chem. Phys. 1972, 56, 4216. (10) Walrafen, G. E. J. Solution Chem. 1973, 2, 159. (11) Walrafen, G. E. Chapter in Structure of Water and Aqueous Solutions; Luck, W. A. P., Ed.; Verlag Chemie, Verlag Physik: Weinheim, 1974. (12) Walrafen, G. E.; Hokmabadi, M. S.; Yang, W.-H. J. Chem. Phys. 1986, 85, 6964. (13) Colles, M. J.; Walrafen, G. E.; Wecht, K. Chem. Phys. Lett. 1970, 4, 621. (14) Walrafen, G. E. AdV. Mol. Relax. Processes 1972, 3, 43. (15) Walrafen, G. E. J. Chem. Phys. 1976, 64, 2700. (16) Colles, M. J. Chapter in book cited in ref 11. (17) Laubereau, A.; Graener, H. Chapter in Hydrogen Bond Networks; Bellissent-Funel, M.-C., Dore, J. C., Eds.; NATO ASI Series, Series C.: Mathematical and Physical Sciences, Vol. 435; Kluwer Academic: Dordrecht, 1994. (18) Senior, W. A.; Verrall, R. E. J. Phys. Chem. 1969, 73, 4242. (19) Walrafen, G. E. Chapter in Water, A ComprehensiVe Treatise, Vol. 1. The Physics and Physical Chemistry of Water; Franks, F., Ed.; Plenum: New York, 1972; Chapter 5. See pp 190-192. (20) Walrafen, G. E.; Fisher, M. R.; Hokmabadi, M. S.; Yang, W.-H. J. Chem. Phys. 1986, 85, 6970. (21) Agmon, N. Private communications and discussions, Aug 1995. (22) Atkins, P. W. Quanta; Oxford University Press: Oxford, 1991. See p 181. (23) Chandler, D. Introduction to Modern Statistical Mechanics; Oxford University Press: New York, 1987. See pp 194-195 for a lucid discussion of the decreased diffusiveness in the location of deuterons, compared to protons. (24) Frank, H. S. Chapter in book cited in ref 19; see especially p 527, and footnote on that page, plus references in the footnote. Frank, H. S. Chapter in book cited in ref 11; see pp 16 and 28. (25) Walrafen, G. E.; Chu, Y. C.; Carlon, H. R. Chapter in Proton Transfer in Hydrogen-Bonded Systems; Bountis, T., Ed.; NATO ASI Series, Series B: Physics, Vol. 291; Plenum: New York, 1992; see Figure 4 on p 304 of this book. (26) Luck, W. A. P. Habilitationsschrift, “Spektroskopische Bestimmungen in Naher I.R.”, University of Heidelberg, 1968. This work contains numerous important IR overtone spectra from water, heavy water, and HDO solutions. (27) Strommen, D. P.; Nakamoto, K. Laboratory Raman Spectroscopy; Wiley: New York, 1984. (28) Long, D. A. Raman Spectroscopy; McGraw-Hill: New York, 1977
JP952134I
