2210
J . Phys. Chem. 1989, 93, 2210-2218
Infrared Intensities of Liquids. 5. Optical and Dielectric Constants, Integrated Intensities, and Dipole Moment Derivatives of H20 and D20 at 22 O C John E. Bertie,* M. Khalique Ahmed, Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada T6G 2G2
and Hans H. Eysel Anorganisch-Chemisches Institut der Universitat, Im Neuenheimer Feld 270, 0 - 6 9 0 0 Heidelberg, Federal Republic of Germany (Received: February 17, 1988; In Final Form: September 1 , 1988)
We have recorded multiple attenuated total reflection spectra of liquid H 2 0 and D20, using the Spectra-Tech CIRCLE cell, and calculated from them the infrared optical and dielectric constants and molar conductivities from 9000 to 1250 cm-l for H 2 0 and from 8500 to 700 cm-’ for D20. Our results agree well with the literature for H20, while our results for D 2 0 are the most extensive reported to date. We have calculated the dipole moment derivatives with respect to stretching and bending internal coordinates from the areas under the bands in our molar conductivity spectra. For lack of information, we have used the assumptions of the simple bond-moment model, a diagonal force field, and neglect of stretch-bend interaction. We found &/dr for the stretching vibrations to be 3.02 D/A f l % and 3.04 D/A &OS% for H 2 0 and D20, respectively, and &/dB for the bending vibration to be 0.73 D f 3 % for H 2 0 and 0.63 D f5% for D20. The two values for the stretching vibrations are indistinguishable, but this is not true for the bend. The disagreement for the bending vibration is probably due, at least in part, to our simulation of the absorption by three distinct bands of mixed Gauss-Lorentzian character, in order to try to separate the bending mode from the background absorption. It is probable that no such separation exists precisely. The bond moments for H 2 0 and D 2 0 agree with those calculated by the same approximations from literature data for HDO to about the extent allowed by the approximations. The intensities for liquid H 2 0 are compared with those for water in the gas phase, in Ba(CIO,),.H,O, in ice I, and in lithium @-aluminate.The intensity of the bending mode, v2(H20), is essentially independent of the strength of the hydrogen bonds. That of the OH stretching modes increases with hydrogen bond strength in Ba(C103)2.H20,liquid water, ice I, and lithium P-aluminate being 20, 17.5, 25, and 40, respectively, times more intense than in the gas. Explanations for this are briefly summarized.
Introduction
We have reported a simple method for measuring the infrared absorption intensities of liquids.’ Specifically, multiple-attenuated total-reflectance spectra are measured of liquids held in the Spectra-Tech CIRCLE cell,l,*which is a cylindrical multiple-ATR cell designed for the circular aperture of FT-IR spectrometers. The ATR spectra are converted to pATR spectra,’ where pATR means -loglo of ATR. Qualitatively, the pATR spectra resemble absorbance spectra.l,2 After the cell is calibrated to determine the effective number of reflections,’,2 the pATR spectra are processed iteratively’s2 to yield the real, n(v), and imaginary, k ( v ) , infrared optical constants of the liquid, given the real refractive indexes of the ATR rod throughout the infrared and the real refractive index of the sample at very high infrared wavenumbers (about 9000 cm-]). The optical constants then yield the real, d ( v ) , and imaginary, t”(v), dielectric constants throughout the infrared. As is discussed in Appendix 1 , for a fundamental vibration the area under a band in the molar conductivity spectrum, Le. in the spectrum of the conductivity, v t ” ( v ) , divided by molar concentration, is related via a numerical constant to the square of the effective dipole moment derivative with respect to the normal coordinate of the vibration, (ap/dQ),f:, from which the square of the molecular dipole moment derivative in the liquid, (~9p/eQ)~, is calculated via the Lorentz local field.* Recent refinement of the method has been described2 and the accuracy has been explored2 via a partial account of our recent measurements of H20(1) and D20(I). In this paper we present a detailed account of our measurements on these two isotopomers of water. Our wavenumber range is between 9000 and 1200 cm-’ for H 2 0 and 8500 to 700 cm-’ for D 2 0 , the lower limit being determined by the onset of the intense band due to the rotational vibrations of the water molecules and the absence of an ATR rod material that permits measurements to low-wavenumber of the intense absorption. (1) Bertie, J . E.; Eysel, H. H. Appl. Specfrosc. 1985, 39, 392. (2) Bertie, J . E.; Harke, H.; Ahmed, M. K.; Eysel, H. H . Croat. Chem. Acta 1988, 61, 39 1 .
0022-3654/89/2093-2210$01.50/0
The optical constants of H20(1) have been reported several times over the entire infrared region (ref 3-15 and citations therein). There is currently good agreement between the values of the two groups most recently active in the midinfrared region, those of william^^-^ and Z ~ l o t a r e v . ” - ~The ~ literature data are partly from specular reflection and transmission spectra, so they cover a wider wavenumber range than our measurements and are the preferred data against which our measurements of H20(1) can be compared. Small-scale graphs of the optical constants of samples of D20(l) of varying isotopic purity have been p ~ b l i s h e d , ~sometimes ,~~J~ with a table of extrema of the optical constants, but numerical data has been tabulated” only for the range 2900-2100 cm-I. Values of the integrated absorption intensity of the O H stretching and HOH bending vibrations of H20(1) have been
(3) Downing, H. D.; Williams, D. J . Geophys. Res. 1975, 80, 1656. (4) Rusk, A. N.; Williams, D.; Querry, M. R. J . Opt. SOC.Am. 1971, 61, 895. ( 5 ) Robertson, C. W.; Williams, D. J . Opt. SOC.Am. 1971, 61, 1316. (6) Hale, G . M.; Querry, M. R.; Rusk, A. N.; Williams, D. J . Opt. SOC. Am. 1972, 62, 1103. (7) Robertson, C. W.; Curnutte, B.; Williams, D. Mol. Phys. 1973, 26, 183. (8) Palmer, K. F.; Williams, D. J . Opt. SOC.Am. 1974, 64, 1107. (9) Pinkley, L. W.; Sethna, P. P.; Williams, D. J . Opt. SOC.Am. 1977, 67, 494. ( I O ) Hale, G. M.; Querry, M . R. Appl. Opf. 1973, 12, 5 5 5 . (1 1) Zolotarev, V. M.; Demin, A. V . Opt. Spectrosc. 1977, 43, 157 (Opt. Spektrosk. 1977, 43, 271). (12) Zolotarev, V. M.; Mikhailov, B. A,; Alperovich, L. I.; Popov, S. I. Opt. Spectrosc. 1969, 27, 430 (Opt. Spektrosk. 1969, 27, 790). (1 3) Zolotarev, V. M.; Mikhailov, B. A.; Alperovich, L. I.; Popova, S. 1. Opt. Commun. 1970, 1, 301. (14) Hasted, J. B.; Husain, S. K.; Frescura, F. A. M.; Birch, J. R. Infrared Phvs. 1987. 27. 11-15. ‘(1s) Hasted; J. B.; Husain, S. K.; Frescura, F. A. M.; Birch, J. R. Chem. Phys. Lett. 1985, 118, 622. (16) Sethna, P. P.; Palmer, K . F.; Williams. D. J . Opt. SOC.Am. 1978, 68, 815.
( I 7) Zolotarev, V. M. Opt. Spectrosc. 1967, 23, 442
0 1989 American Chemical Society
The Journal of Physical Chemistry, Vol. 93, No. 6, 1989 2211
Infrared Intensities of Liquids
0.2
0.3
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Ll
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i
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Figure 1. pATR spectra of liquid H20(top) and Dz0.
measured from transmission spectra'* and calculated'* from previous3*'*optical constants. Again these measurements serve to check the accuracy of our results for H20(1). No integrated intensities of D20(1) have been reported.
0.0
Figure 2. Imaginary refractive index, k(u), spectra of liquid HzO(top) and DzO.The curves marked X10 are offset by 0.1 and have ordinates expanded 10 times. 1.6 1.5
Experimental Section Spectra were recorded with a Bruker IFS 113V FT-IR spectrometer which was kept evacuated. DTGS detectors were used to keep the phase corrections small. A 10" aperture, no gain switching, and an optical retardation velocity of 0.4 cm s-I were used with two sources, globar and tungsten, and two beam splitters, Ge-on-KBr and Si-on-CaF,. 512 interferograms each of 0.25 cm (or 0.50 cm) optical retardation were averaged and Fourier transformed with 4-point (trapezoidal) apodization and one level of zero-filling to give spectra of 4 cm-' (or 2 cm-I) resolution, digitized a t 1.92 cm-' (or 0.96 cm-I) intervals. The trapezoidal function is formed by the ramp through the zero-path position, a straight line at unity to 0.85 of maximum path difference, and a straight line to zero a t maximum path difference. Phase correction used 512 points centered on the zero-path position, zero-filled to a 2048-point interferogram. No optical filtering was used and the electronic filters were set sufficiently far apart to avoid distortion of the i n t e r f e r ~ g r a m . ' ~The instrument chose its own gain to use the full range of the analogue-to-digital converter and was wavenumber-calibrated with the standard gases to a t least 0.2 cm-I. CIRCLE rods of zinc selenide were used with home made, flow-through CIRCLE cells mounted in the optics from Spectra-Tech. The liquids contact only the rod, glass, and Teflon in our cell, which is left permanently mounted in the vacuum chamber of the instrument and is filled and emptied via Teflon tubes and a hypodermic syringe or a water-free suction pump. The H20(1) was building distilled water passed through a Millipore SUPER-Q water system consisting of a SUPER-C carbon filter, two ION-EX ion-exchange cartridges, and an ORGANEX-Q carbon filter. It was kept in a closed polyethylene bottle and was used within a few weeks of purification. The D20(l) was "99.8 atom % D" grade, either from Aldrich Chemical Co., Gold Label quality, or from General Intermediates of Canada; it was used as supplied because no hydrogen or other impurities were detected. The benzene used for calibration of the cell was either Aldrich spectrophotometric grade or met ACS reagent grade (18) Motojima, T.; Ikawa, S.-I.;Kimura, M. J . Quant. Spedrosc. Radiot. Trans. 1981, 25, 29. ( 1 9 ) Bertie, J . E. Vibrational Spectra and Strurrure; Durig, J . R., Ed.; Elsevier: New York, 1985; Vol. 14, Chapter 4, p 221.
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Figure 3. Real refractive index, n(u), spectra of liquid HzO(top) and
D20. specifications and was used as supplied apart from being dried over 4A molecular sieve. Background spectra were recorded, with the cell containing nitrogen gas at atmospheric pressure, before and after the spectra of the liquid samples.
Results The CIRCLE cell was calibrated with spectra of benzene recorded at 2 cm-' resolution, as described in detail elsewhere.2 The calibration was found to be independent of beam splitter and of source, as is expected under ideal conditions. pATR spectra of each water sample were measured at a resolution of 4 cm-' with a globar source and both beam splitters, Ge on KBr and Si on CaF,, and also with a tungsten source, red filter, and the Si on CaF, beam splitter. These spectra coincided where their wavenumbers overlapped and were merged to a single pATR spectrum for each sample, between 9000 and 1250 cm-l for H 2 0 and 8500 and 700 cm-' for D 2 0 . The pATR spectra below 4500 cm-' are in Figure 1.
The Journal of Physical Chemistry, Vol. 93, No. 6, 1989
2212
Bertie et al. 0.6
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Figure 4. Imaginary dielectric constant, (top) and D 2 0 .
~ " ( u ) , spectra
of liquid H20
2.3 2.1
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by Kramers-Kronig transformation, so the reproducibilities of the two spectra are related, changes in [n(v) - 11 following from changes in k(u). The k ( v ) spectrum of DzO(l) (Figure 2) is the average of individual spectra which agreed with it to better than 1% a t the two strong bands, to f 2 % near 1600 and 1000 cm-l, and to 15% in the region of very weak absorption ( k 0.002) near 2000 cm-l. The n ( v ) spectrum (Figure 3) is the Kramers-Kronig transform of the average k spectrum and agreed with the individual n spectra to 0.1%. The molar conductivity spectra in Figure 6 are Vmvt"(v) vs v, where V ,is 18.02 mL/mol for H 2 0 and 18.09 mL/mol for D 2 0 . The areas under the OH and O D stretching bands in Figure 6 are (Table 111) 194 km/molf2% and 104 km/mol f l % , where the integration was from 4000 to 2500 cm-' for H z O and from 2950 to 1850 cm-] for DzO. W e have followed Motojima et al.l* by fitting, several times, the spectral region about the bending vibration, vz, to three bands. W e used bands of mixed Gaussian-Lorentzian character, and the area under the strongest, sharpest band was 13.0 km/mol f - 6 % for H 2 0 and 5.2 km/mol &-lo% for DzO. The rather large errors reflect the various assumptions that were made about the band shapes, in different attempts to fit the spectrum that each gave a reasonable, but not exact, fit.
-
1.7
1.1
Figure 6. Molar conductivity, V,,,ud'(u), spectra of liquid H 2 0 (top) and D20. The ordinate scale has the units lo5 cm2/mol.
1
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Figure 5. Real dielectric constant, ~ ' ( u ) spectra , of liquid H 2 0 (top) and
D20.
Discussion Refractive Indexes. Our values of the imaginary refractive
to real and imaginary The pATR spectra were optical constant spectra, n(v) and k ( v ) , using the value2 1.325 for 49000 cm-') of H20(1) and also 1.325 for n(8500 cm-') of D20(l). The real and imaginary dielectric constant spectra were calculated from the optical constants.'S2 The optical constant spectra are in Figures 2 and 3. Numerical values are in Table I for HzO and Table I1 for D 2 0 ,with those of the dielectric constants. The dielectric constant spectra are in Figures 4 and 5 and the molar conductivity spectra are in Figure 6. The imaginary optical constant, k ( v ) , spectrum of H20(1)2 (Figure 2) is the average of spectra obtained in 1984l and 1987. The precision (reproducibility) is within f l % of the value given below 3300 cm-I, A3.5% at the peak of the O H stretching band, which is notoriously nonreproducible?" and --f5-10% for k ( v ) values between 0.002 and 0.009 in the region above 3700 cm-'. The high-wavenumber noise was -0.0004 in k ( v ) , so k values less than 0.001 are only qualitative. The real refractive index, n ( v ) , spectrum (Figure 3) was obtained from the k ( v ) spectrum
index of HzO(l) must be compared with those in the literature. Both Williams3 and Zolotarev" have summarized the work of their groups, and both have published two major sets of optical constants for water in the periods 196912to 19715and 19753to 1977." The two major sets published by william^^,^ agreed to within 3% and had estimated accuracies of 5%. The two sets of Zolotarev11,12 have estimated accuracies of 3-5% but differ significantly. In particular, the OH stretching band in the more recent data" differs in shape from the earlierI2 one, has a 3% lower peak value, and is shifted some 20 cm-I to low wavenumber which causes gross changes in the k ( v ) values at wavenumbers on its sides. Further, the more recent data differs by between -15% and +3% between 1640 and 1050 cm-'. Between 2800 and 1640 cm-', Zolotarev's two sets agree to better than 1%, and it is only in this region, and a t the peak of the OH stretching band, that we consider his data further. Within these limitations, the data of Williams and Zolotarev agree on average to 5%. The k(v) values in Table I and Figure 2 are, on average, higher than those of Williams3 and Zolotarev"
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Infrared Intensities of Liquids TABLE I: Infrared Optical and Dielectric Constants of H20(1) vlcm-" k(v)b n(v) €"(V)b CYV) 0 1.325 0 1.756 9000 8500 0 0 1.322 1.749 0 0 1.320 1.742 8000 1.317 1.734 0 0 7500 1.314 1.726 0 0 7000 1.310 1.717 0 0 6500 1.306 1.705 0 0 6000 1.303 0 0 5750 1.698 1.300 0 0 1.690 5500 1.298 0 0 5400 1.686 1.297 1.683 0 0.0004 5350 1.296 1.680 0.0006 0.0016 5300 1.296 1.678 0.001 1 0.0028 5275 1.295 1.678 0.0016 0.0042 5250 1.295 1.678 0.0020 0.005 1 5200 1.295 1.677 0.0020 0.005 1 5150 0.0017 1.295 1.676 0.0045 5100 1.294 1.675 0.0015 0.0038 5050 1.293 1.672 0.0012 0.003 1 5000 1.289 1.661 0.0006 0.0017 4800 1.283 1.646 0.0004 0.001 1 4600 4400 1.275 1.626 0.0003 0.0009 1.264 1.597 0.0007 4200 0.00 16 1.245 1.551 0.0019 4000 0.0047 1.206 1.454 0.0034 3800 0.0083 1.191 1.418 0.0047 3760 0.0113 1.167 1.362 0.0083 3720 0.0194 1.130 0.0267 1.276 3680 0.0603 1.107 0.0722 1.220 3640 0.160 1.103 1.203 0.118 0.261 3600 1.104 1.198 0.144 3580 0.3 18 1.108 1.199 0.169 3560 0.374 1.116 1.207 0.195 3540 0.435 1.131 1.229 0.223 3520 0.505 1.149 1.259 0.246 3500 0.566 1.171 1.300 0.267 3480 0.625 0.287 1.199 1.356 3460 0.687 1.230 0.300 3440 0.738 1.423 1.266 1.509 0.305 3420 0.772 1.281 0.306 3410 0.783 1.547 0.306 0.792 1.297 1.588 3400 1.632 0.303 3390 0.797 1.313 1.675 0.299 3380 0.793 1.328 1.757 0.284 3360 0.771 1.356 0.272 0.747 1.818 3340 1.375 1.874 0.258 0.7 18 3320 1.393 0.243 0.684 1.409 1.925 3300 1.969 0.230 3280 0.654 1.422 2.016 0.2 15 3260 0.618 1.436 2.059 0.200 3240 0.581 1.449 0.183 3220 1.460 2.099 0.534 2.115 0.173 3210 0.508 1.465 2.149 0.141 3180 0.416 1.473 0.122 2.155 3160 0.360 1.473 0.103 3140 0.304 1.470 2.151 2.126 0.0736 3100 0.215 1.460 2.091 0.0528 3060 0.153 1.447 0.0439 2.070 3040 0.126 1.439 0.0314 3000 0.0895 1.426 2.033 "Accuracy f l cm-'.
The Journal of Physical Chemistry, Vol. 93, No. 6, 1989 2213
v/cda 2960 2920 2880 2840 2800 2750 2700 2650 2600 2550 2500 2450 2400 2350 2300 2275 2250 2225 2200 2175 2150 2125 2100 2075 2050 2025 2000 1950 1900 1850 1800 1760 1740 1720 1700 1680 1670 1660 1650 1645 1640 1630 1620 1610 1600 1590 1580 1560 1540 1500 1475 1450 1425 1400 1375 1350 1300 1275 1250
k(v)b 0.022 1 0.0157 0.01 11 0.0083 0.0062 0.0046 0.0037 0.0034 0.0035 0.0039 0.0047 0.0056 0.0067 0.008 1 0.0099 0.0110 0.0122 0.0134 0.0147 0.0158 0.0166 0.0171 0.0170 0.0164 0.0155 0.0144 0.0132 0.01 14 0.0106 0.01 11 0.0137 0.0194 0.0264 0.0384 0.0594 0.0933 0.1 10 0.124 0.134 0.136 0.134 0.123 0.105 0.0874 0.0728 0.0604 0.0535 0.0449 0.0404 0.0361 0.0350 0.0343 0.0339 0.0338 0.0339 0.0341 0.0345 0.0349 0.0344
n(v)
€"(V)b
1.413 1.402 1.392 1.383 1.375 1.366 1.359 1.352 1.346 1.341 1.336 1.332 1.328 1.324 1.321 1.319 1.318 1.317 1.316 1.316 1.316 1.316 1.316 1.316 1.315 1.314 1.313 1.308 1.301 1.293 1.281 1.268 1.258 1.247 1.238 1.242 1.252 1.267 1.288 1.303 1.318 1.340 1.354 1.359 1.359 1.354 I .350 I .342 1.336 1.327 1.323 1.320 1.316 1.314 1.311 1.308 1.301 1.295 1.295
0.0624 0.0441 0.0309 0.0228 0.0169 0.0125 0.0101 0.0092 0.0093 0.0105 0.0124 0.0148 0.0177 0.0215 0.0263 0.0291 0.032 1 0.0353 0.0386 0.04 15 0.0438 0.0449 0.0447 0.0431 0.0407 0.0378 0.0347 0.0297 0.0276 0.0288 0.0351 0.0492 0.0664 0.0957 0.147 0.232 0.275 0.315 0.345 0.354 0.353 0.329 0.285 0.238 0.198 0.164 0.144 0.121 0. I08
0.0960 0.0926 0.0904 0.0892 0.0889 0.0891 0.0891 0.0898 0.0905 0.0892
€'(V)
1.997 1.965 1.936 1.913 1.890 1.867 1.846 1.828 1.812 1.798 1.785 1.774 1.763 1.753 1.744 1.741 1.737 1.734 1.732 1.731 1.731 1.731 1.731 1.731 1.730 1.727 1.723 1.710 1.693 1.672 1.641 1.607 1.581 1.553 1.530 1.534 1.554 1.589 1.642 1.679 1.720 1.781 1.823 1.840 1.841 1.831 1.820 1.799 1.783 1.760 1.749 1.740 1.732 1.724 1.716 1.710 1.69 1 1.676 1.676
means
