Infrared intensities of liquids. Part XXIII. Infrared optical constants and integrated intensities of liquid benzene-d 1 at 25 C

Journal of Molecular Structure 550 551 (2000) 135 165 www.elsevier.nl/locate/molstruc Infrared intensities of liquids. Part XXIII. Infrared optical constants and integrated intensities of liquid benzene-d 1 at 25 C J.E. Bertie*, Y. Apelblat, C.D. Keefe 1 Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada, T6G 2G2 Received 28 July 1; accepted 22 September 1 Abstract This paper presents the first absolute infrared absorption intensities of liquid benzene-d 1,C 6 H 5 D, at 25 C. It also presents what, surprisingly, seems to be the first complete assignment of an infrared spectrum of liquid benzene-d 1 recorded with post- 150 instrumentation. The spectra of the real and imaginary refractive indices are given as graphs and tables between 6200 and 500 cm 1, and a table is given of the peak wavenumbers, absolute integrated intensities and vibrational assignments between 4800 and 500 cm 1. Errors in the imaginary refractive index, k, values are estimated to be 5 7% for peaks and 5 20% for the baseline between 6200 and 4700 cm 1, 0.3 2.0% for both peaks and baseline between 4700 and 825 cm 1, 3 4% for both peaks and baseline between 825 and 620 cm 1, and 40 50% between 620 and 500 cm 1 where the very strong peak near 600 cm 1 was too intense for us to measure accurately. Errors in the real refractive indices, n, are estimated to be 0.25% at 8000 cm 1 increasing to 0.5% near 800 cm 1 and, due to the uncertain intensity of the peak near 600 cm 1, to range up to 10% between 710 and 500 cm 1. The refractive index spectra were converted to spectra of the real and imaginary dielectric constants, e 0 and e 00, the molar absorption coefficient, E m, and the real and imaginary molar polarizabilities under the Lorentz local field, a 0 m and a 00 m. The peak heights and wavenumbers in the spectra of the different absorption quantities are compared for the most intense bands. Integrated intensities were determined as C j, the area under bands in the ~na 00 m spectrum, for all bands between 4800 and 500 cm 1. The contributions from the different bands were separated by fitting the spectrum with classical damped harmonic oscillator bands. The estimated errors in the integrated intensities range from 2 to 10% for most bands, although they may reach 100% for very weak bands and shoulders. The integrated intensities of the fundamentals and the corresponding transition dipole moments are summarized and compared with literature values for the gas. Crawford s F-sum rule shows that the measured integrated intensities of C 6 H 5 D are nicely consistent with those reported recently for C 6 H 6 and C 6 D 6. The total integrated intensity of the first overtone of the CH stretches is 20 times smaller than that of the fundamentals. 2000 Elsevier Science B.V. All rights reserved. Keywords: Benzene-d 1 ; Infrared intensities; Optical constants; Refractive indices; Dielectric constants Dedicated to Professor James R. Durig on the occasion of his 65th birthday. * Corresponding author. Tel.: 1-780-42-3560; fax: 1-780-42-8231. E-mail address: john.bertie@ualberta.ca (J.E. Bertie). 1 Current address: Department of Physical and Applied Sciences, University College of Cape Breton, Sydney, Nova Scotia, Canada B1P 6L2. 0022-2860/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S0022-2860(00)00518-4

136 J.E. Bertie et al. / Journal of Molecular Structure 550 551 (2000) 135 165 1. Introduction This paper continues our report of absolute infrared absorption intensities of liquids measured by transmission spectroscopy, by presenting quantitative infrared intensities of liquid benzene-d 1,C 6 H 5 D, at 25 C. Similar measurements of the intensities of liquid benzene [1], toluene [2], chlorobenzene [3], dichloromethane [4] and benzene-d 6 [5] have been published recently and the first four of these have formed the basis of intensity standards [6]. This paper also presents the assignment of most of the features in the infrared spectrum of liquid C 6 H 5 D. A number of studies of the vibrations of C 6 H 5 D have been reported in the literature. In 146 Bailey et al. [7] reported and fully assigned the complete infrared spectrum of the gas between 3400 and 380 cm 1, as well as the Raman spectrum, presumably of the liquid, over the same range. Since then, the majority of the reports have presented only complete [8 13] or partial [14,15] assignments of the 30 fundamental vibrations, and only three reports [10,14,16] have contained assignments of some combination and overtone bands. In particular, the complete assignment of spectra obtained with post-150 instrumentation has not been reported previously. There are no previous reports of the quantitative infrared intensities of liquid C 6 H 5 D. Three groups [17 1] have reported quantitative infrared intensities of gaseous benzene-d 1. In the present work experimental absorbance spectra [1] of liquid benzene-d 1 at 25 C were measured. From these spectra, spectra of the optical constants, i.e. of the real, n, and imaginary, k, refractive indices, were calculated by methods described previously [1,20]. The refractive index spectra were converted to spectra of the real and imaginary dielectric constants, the molar absorption coefficient and, under the Lorentz local field, the molar polarizability, as described elsewhere [21]. To the extent that the Lorentz local field is valid, molecular properties and behavior are more directly reflected in the spectrum of the imaginary molar polarizability, am, 00 than in the spectra of the imaginary refractive index, the imaginary dielectric constant, or the molar absorption coefficient [21]. Thus, the imaginary molar polarizability spectrum is the absorption quantity of greatest interest in the study of liquid-phase molecules. Correspondingly, the integrated intensity of band j, C j, is defined as the area under the band in the spectrum of ~na 00 m [21] Z C j ˆ ~na 00 m ~n d ~n 1 Under the assumption that all of the hot transitions of the fundamental contribute to the fundamental band, C j is related to the dipole transition moment, R j, through Eq. (2) [21 24] C j ˆ NAp 3hc 0 g j ~n j R j 2 2 Under the assumptions of mechanical and electrical harmonicity, C j can also be related to the square of the dipole moment derivative with respect to the jth normal coordinate, m 2 j ˆ 2m=2Q j 2 ; through [21] C j ˆ NA 24pc 2 g j m 2 j 0 3 In these equations, N A is the Avogadro constant, h is Planck s constant, c 0 is the velocity of light in vacuum, and g j is the degeneracy of the jth vibration. For C 6 H 5 D, g j ˆ 1 for all vibrations. In order to calculate the integrated intensities, the am 00 spectrum must be separated into contributions from the different bands. This is not trivial when the spectrum contains adjacent or overlapping bands. However, Eqs. (2) and (3) result from both quantum theory and the classical damped harmonic oscillator (CDHO) model [21 24], so the separation can be attempted by fitting the am 00 spectrum with CDHO bands. When this is successful, as for benzene-d 6 [5], methanol [25] and benzene-d 1, the integrated intensity C j may be obtained directly from the parameters of the CDHO band without numerical integration, as is described elsewhere [5,25]. 2. Experimental Benzene-d 1, labeled 8%, was purchased from

J.E. Bertie et al. / Journal of Molecular Structure 550 551 (2000) 135 165 137 Cambridge Isotope Laboratory and was used as is except that it was kept over molecular sieve to ensure dryness. The samples were checked by gas chromatography and by infrared spectroscopy of the liquid. Non-benzene impurities were determined to be less than 0.06%. The samples were also analyzed by mass spectrometry and were found to contain C 6 H 6, 13 CC 5 H 5 D and 0.45% C 6 D 6. The intensity of the n 4 band of C 6 H 6 at 67 cm 1 in the infrared 2 spectrum of the liquid benzene-d 1 indicated 3.5% of C 6 H 6. We were unable to distinguish between 12 C 6 H 5 D and 13 CC 5 H 5 D in the infrared spectrum of liquid benzene-d 1, although its natural abundance suggests the presence of about 6% of 13 CC 5 H 5 D. The experimental and instrumental details of this work have been described [1,20] and are summarized briefly here. The infrared spectra were measured with a Bruker IFS 113 V spectrometer. A Globar source, a 10 mm aperture, and deuterated triglycine sulfate (DTGS) detector were used. The interferograms were recorded with 0.665 cm s 1 optical retardation velocity and 1 cm 1 nominal resolution. Trapezoidal apodization, multiplicative phase correction, and one level of zero-filling were used in the Fourier transform. Experimental absorbance spectra of liquid benzene-d 1 were measured in fixed path length cells with KBr windows and path lengths between 11 and 1500 mm. To determine the linear absorption coefficients at the anchor points [1,20], spectra were also measured in KBr cells with fixed path lengths of 500 and 1500 mm, and in a NaCl cell with variable path lengths up to 3.7 mm. The path lengths of the cells were determined as described previously [1 5]. To assist in the assignment of the bands in the spectrum of the liquid, an infrared spectrum of gaseous benzene-d 1 was recorded on the Bruker IFS 113 V in order to observed the band contours, and Raman spectra were measured to observe the wavenumber shifts and polarizations. Accurate Raman wavenumber shifts were obtained from an unpolarized spectrum recorded at 2 cm 1 nominal resolution on a Bruker FT-Raman spectrometer with Nd : YAG 2 The n 4 band is at 673 cm 1 in the absorbance spectrum of neat C 6 H 6 (l) but shifts to 67 cm 1 on dilution. excitation. In the software, the HeNe wavenumber was set to its vacuum value, 1578.002 cm 1, and that of Nd:YAG was set to 34.2 cm 1. Measurement of both Stokes and anti-stokes Raman shifts of four bands of chlorobenzene and one of dichloromethane showed that the Stokes wavenumber shifts are accurate to ^0.1 cm 1. Parallel- and perpendicular- polarized Raman spectra were recorded with 0 excitation on a dispersive SPEX spectrometer with laser excitation at 514.5 nm, 380 mw power, slit width of 2 cm 1 and step size 0.5 cm 1. The intense parallel-polarized bands allowed wavenumber calibration by comparison with the accurate though unpolarized FT spectra. 3. Infrared intensities 3.1. Imaginary refractive index spectrum The k spectrum was determined by the procedures described in previous papers [1 5], and the presentation in this section follows the logic described in those papers. The values of the linear absorption coefficient, K, required to correct the baseline at the anchor points [1,20] are given in Table 1 with the cell pathlengths used, the corresponding k values, the 5% confidence limits of the values of K and k and the approximate value of the real refractive index, n, used at each anchor point. The baseline absorption is extremely weak above 4500 cm -1 and could be determined to only t10% precision with the available path lengths up to 3.7 mm. The approximate n values were determined from a preliminary calculation of n and k by program RNJ46A from an uncorrected spectrum recorded through an 11 mm cell. The experimental absorbance, EA, spectra from cells of many thicknesses were converted to imaginary refractive index spectra by program RNJ46A, using the anchor point information. The k spectra were only used in regions where the corresponding EA peak maxima were between 0.2 and 2.0 absorbance units. These regions, the path lengths used, and the number of spectra averaged to give the average k spectrum for the region, are given in Table 2. The average k spectra for the different regions were merged to give the k spectrum from 6200 to 620 cm 1.

138 J.E. Bertie et al. / Journal of Molecular Structure 550 551 (2000) 135 165 Table 1 (Decadic) linear absorption coefficients for benzene-d 1 at 25 C ~n (cm 1 ) Path length (mm) n ~n a K ~n (cm 1 ) b k ~n c 6350.4 0.00( 5) d 0.0000000( 15) 6055.3 2.7 3.7 1.477 0.42(43) 0.0000130(13) 5747.3 2.7 3.7 1.477 0.224(20) 0.0000071(6) 5416.1 2.7 3.7 1.477 0.177(14) 0.000005(47) 5106.5 2.7 3.7 1.477 0.146(12) 0.00000524(43) 4878.0 2.7 3.7 1.477 0.218(11) 0.0000081(41) 4547.3 1.5 3.7 1.477 2.100(25) 0.0000846(10) 42.6 2.7 3.7 1.477 0.816(10) 0.0000348(4) 4117.3 1.5 3.7 1.476 3.812(30) 0.000166(13) 347.5 1.5 3.7 1.477 2.336(13) 0.0001084(6) 3727.7 2.7 3.7 1.476 1.266(5) 0.0000622(2) 356.5 2.7 3.7 1.476 0.870(4) 0.0000447(2) 330.2 2.7 3.7 1.475 1.207(4) 0.0000668(2) 3228.8 1.7 3.7 1.474 2.268(6) 0.0001287(3) 234.1 0.5 1.5 1.480 7.625(51) 0.0004762(32) 282.5 1.5 3.7 1.478 1.777() 0.0001151(6) 270.5 2.7 3.7 1.477 0.755(3) 0.0000511(2) 2534. 2.7 3.7 1.477 1.440(3) 0.0001041(2) 2438.0 2.7 3.7 1.476 1.83(3) 0.0001423(2) 223. 0.5 1.5 1.474 7.516(27) 0.0006004(22) 2217.3 1.5 3.7 1.477 3.601(8) 0.000276(7) 2120.4 2.7 3.7 1.475 0.753(3) 0.0000651(3) 2043.7 2.7 3.7 1.474 1.24(3) 0.0001160(3) 128.5 0.5 1.474.876(28) 0.000384(27) 1858.5 1.5 3.7 1.474 4.347() 0.0004286() 172.5 0.5 1.474.542(24) 0.000754(25) 1728. 0.5 2.7 1.474 5.347(17) 0.0005667(18) 1653.1 1.5 3.7 1.473 4.038(20) 0.0004476(22) 1514.3 1.5 3.2 1.466 5.36(16) 0.000647(1) 1415.0 0.5 1.7 1.481 7.12(34) 0.001025(4) 1341.3 1.5 3.2 1.476 5.356(18) 0.0007317(25) 126.4 1.5 3.7 1.473 3.616(15) 0.0005220(21) 1122.3 0.5 1.5 1.468 7.16(24) 0.00122(4) 1055.3 0.5 1.465 13.1(8) 0.002415(1) 8.5 0.5 1.470 20.20(11) 0.003707(20) 48.8 0.5 1.5 1.464 12.87(5) 0.002485(10) 01.5 0.5 1.5 1.462.513(83) 0.00134(17) 827.8 0.5 1.44 14.42() 0.00312(20) 736.6 0.5 1.45 13.80(7) 0.003433(17) 65.0 0.5 1.456 28.46(16) 0.00713(44) 500. 1.5 1.512 1.41(37) 0.00051(13) a This column gives the approximate value of n used to calculate the reflection from the cell windows during the calculation of K from experimental absorbance spectra. b K values with their 5% confidence limit in the last digit (given in parentheses), are given to the precision used in further computations. c k values and Dk, their 5% confidence limits in the last digit (given in parentheses) were calculated from k ˆ 2:303K= 4p ~n : d This value was set to zero because the experimental absorbance was less than 0.02 when measured through 3.7 mm path, the longest cell used. The 5% confidence limit was estimated from the maximum possible error in the absorbance (0.02) in these cells.

J.E. Bertie et al. / Journal of Molecular Structure 550 551 (2000) 135 165 13 Table 2 Pathlengths and number of spectra recorded for the regions processed Region (cm 1 ) Pathlength (mm) Number of spectra 6350.4 6000 1700 3700 11 6010.0 5700 500 3 5707.7 4700 2700 3700 8 4700.6 4540 500 3 4547.3 4115 1700 3700 11 4118.2 350 500 3 352.8 3725 1700 3700 23 3728.2 3570 500 1500 11 3571.0 3300 1700 3700 23 3308.7 3225 1500 2700 17 3230.1 230 11 35 7 236.0 2825 500 6 282.5 2430 500 2700 23 2435.6 2215 11 50 10 2220.6 180 1500 3700 28 185.6 1645 11 50 10 1651.2 1510 50 500 1515.7 1410 11 35 7 1413.0 1340 35 50 6 1341.2 1120 50 3 1122.3 825 11 50 10 827.7 620 11 4 622 500 11 4 The region of the most intense band, 620 500 cm 1 was not well determined, because in our thinnest cell, 11 mm, the peak EA was 2 and varied significantly between spectra. Initially the average of the four k spectra between 620 and 500 cm 1 that were calculated from these EA spectra was merged with the k spectrum for the higher-wavenumber region. The following steps were taken in an attempt to improve the reliability of the k spectrum below 620 cm 1. The n spectrum was calculated from the k spectrum, as described later, and was used with the k spectrum to calculate the spectrum of the imaginary molar polarizability, am 00 [5,21,24 26]. Three CDHO bands were then fitted to the wings of the am 00 band at 600 cm 1, two for the strong peak near 610 cm 1 and one for the weak shoulder near 625 cm 1. The need for two bands to fit the strong peak is obvious in the original spectra. The fit was very good. The sum of the CDHO bands was then converted back to a k spectrum and merged with the k spectrum for the higher wavenumber region to give the final k spectrum of liquid benzene-d 1 from 6200 to 500 cm 1. The Fig. 1. The 605 cm 1 band of liquid C 6 H 5 Dat25 C. Top: The original average imaginary refractive index, k, band and the final k band obtained as described in the text. Bottom: The bands in the dielectric loss, e 00, and imaginary molar polarizability, a 00 m, spectra. The e 00 band has been multiplied by 3 for clarity. The units of a 00 m are cm 3 mol 1. improved k spectrum near 600 cm 1 is compared with the average of the original four k spectra in the top box of Fig. 1. The k spectrum of C 6 H 5 Dat25 Cis shown in Fig. 2, and is tabulated in Table 3 in the Compact Table format [27]. 3.2. Precision and accuracy of k The accuracy of a k value is described by the absolute error in the value. This error cannot be known exactly, so can only be estimated. Here the error is estimated [1 5] as the sum of the precision of the k value, expressed by its 5% confidence limit (5% CL), and the systematic error that arises from fixing the baseline at the anchor points. This systematic error

140 J.E. Bertie et al. / Journal of Molecular Structure 550 551 (2000) 135 165 reproducibility. Between 620 and 500 cm 1 the error is 40%, which is the 5% CL of the peak value; as discussed above, this large error results from our inability to measure precisely the very intense band near 600 cm 1. 3.3. Real refractive index spectrum Fig. 2. Imaginary refractive index spectrum, k ~n ; of liquid C 6 H 5 D at 25 C. Top box, 6200 4000 cm 1 ; middle box 4000 2100 cm 1 ; bottom box, 2400 500 cm 1. Divide the ordinate scale labels in the top, middle and bottom boxes by 10, 20 and 60, respectively, for the upper curve in the box. is taken to be the average of the 5% CLs of the anchor points (Table 1) at the two ends of the region. Previous studies have shown [1 4] that this method of estimating the accuracy of intensities measured by the Bruker FT spectrometer in this laboratory is supported by measurements on other instruments in other laboratories. The errors in the 6200 4700 cm 1 region, where the absorption is very weak, come mainly from the anchor points. Thus, the errors in the peak and baseline k values are 5 7% and 5 20%, respectively. Below 4700 cm 1 the absorption is much stronger and the errors from the two sources are about equal. The errors in k are 0.3 2.0% between 4700 and 825 cm 1, for both the peaks and the baseline absorption. Between 825 and 620 cm 1, the errors are larger, 3 4%, mainly due to unusually poor The n spectrum of C 6 H 5 D was calculated by Kramers Kronig (KK) transformation of the final k spectrum with the assumption that k is zero between 6200 and 8000 cm 1. The KK transform requires a value of n, that was taken to be the refractive index at 8000 cm 1 that is due only to electronic polarization [28], n el (8000 cm 1 ). The value 1.4800 was used, and was obtained in the following way. Fits of the literature values of n of C 6 H 6 at seven different visible wavelengths and 25 C yielded [1,28] n el ˆ 1:4804 at 8000 cm 1. For C 6 H 5 D the visible-wavelength-dependence of n is not known, and the only reported values are for the Na D line [2 31], where n ˆ 1:5006 [30] at 20 C and 1.476 [31] at 25 C. 3 These values are 0.0004 smaller than the values at the Na D line for C 6 H 6, n ˆ 1:5010 [2,32] at 20 C and 1.47 [32] at 25 C. The difference between n of C 6 H 5 D and n of C 6 H 6 was assumed to be the same at 8000 cm 1 as at the Na D line, so n el (8000 cm 1 ) of C 6 H 5 Dat25 C was taken to be 1.4800. The accuracy of the n values can be estimated as follows. The value of n at wavenumber ~n i was calculated by adding the value Dn ~n i that is calculated by KK transform of the k spectrum to the value n el 8000 cm 1 ˆ1:4800: Thus, the uncertainty in n was estimated as the sum of the 0.05% uncertainty inherent in our KK transform [33], the 0.03% uncertainty in n el (8000 cm 1 ) plus the 0.08 0.15% uncertainty in Dn ~n i that results from the uncertainty in the k values. Thus, above 710 cm 1 the uncertainty in the n values is ^ 0.25%. Because the strong absorption near 610 cm 1 was poorly measured, the n values are uncertain by 1% at 640 cm 1 increasing to 10% near the 610 cm 1 peak and decreasing to 1% at 575 cm 1 and 0.5% at 500 cm 1. 3 Ref. [31] actually gives 1.5011 for C 6 H 5 Dat20 C, but it also gives 1.5015 for C 6 H 6 compared with the accepted value 1.5010, so we have reduced their value for C 6 H 5 D by 0.0005. Note also that Aldrich [2] give n ˆ 1:480 for C 6 H 5 Dat20 C, which is assumed to mean at 25 C.

J.E. Bertie et al. / Journal of Molecular Structure 550 551 (2000) 135 165 141 Table 3 Imaginary refractive indices, k, between 6200 and 500 cm 1 of liquid benzene-d 1 at 25 C a,b,c cm 1 XE YE 0 1 2 3 4 5 6 7 8 10 11 12 13 14 15 16 6200.02 2 7 0 0 0 0 1 7 14 25 36 4 5 77 10 147 178 17 213 6130.60 3 7 227 21 280 258 240 225 231 217 201 153 132 165 227 33 472 68 1031 5.46 3 7 1542 1756 172 218 2217 2341 2243 1825 1485 1218 1070 83 874 747 583 508 485 5874.11 1 7 461 430 31 361 345 312 24 266 240 227 22 230 250 264 28 315 323 5842.2 0 7 323 317 312 301 2 288 282 26 272 262 261 252 238 217 214 217 203 5825.0 0 7 181 186 16 167 154 147 136 138 125 127 123 114 127 116 11 121 118 580.51 0 7 120 118 117 120 116 111 112 113 118 108 103 103 7 2 1 2 573.11 0 7 8 2 88 85 2 85 1 86 83 84 74 72 64 57 58 46 42 5776.72 0 7 44 36 42 31 2 26 22 26 26 21 18 20 20 21 16 13 10 5760.33 0 7 10 12 16 13 18 18 24 27 27 32 43 56 61 70 65 65 60 5743.4 0 7 60 50 51 48 43 38 41 47 40 52 48 54 54 54 52 50 54 5727.55 0 7 60 56 68 63 71 72 73 80 70 78 78 85 87 2 1 1 100 5711.15 0 7 10 10 123 126 127 132 138 143 14 152 155 158 160 161 162 164 164 561.87 2 7 16 178 184 187 187 10 17 202 16 177 154 135 118 104 4 88 82 5626.30 2 7 77 70 62 56 53 50 54 70 78 80 87 111 120 103 86 76 72 5560.73 2 7 67 60 56 57 64 71 77 7 82 87 0 8 88 86 86 0 1 545.17 2 7 2 1 0 111 110 104 8 102 106 7 85 71 64 61 62 60 5425.74 3 7 61 60 70 2 112 123 127 146 11 228 255 254 314 44 408 322 250 524.60 3 7 188 164 116 3 103 8 8 7 107 11 118 113 100 103 5 83 5163.47 3 7 73 77 86 74 63 63 61 52 55 58 58 57 66 67 65 65 5 5032.33 3 7 63 56 5 62 67 71 70 6 72 75 73 75 75 72 71 75 82 401.20 3 7 87 8 87 82 86 102 127 131 127 11 11 120 113 112 125 128 143 4770.06 3 7 168 186 10 187 14 18 214 257 312 400 576 866 1504 2435 3248 410 3360 4642.78 2 7 23 2774 2544 2375 2248 2257 2302 2114 1881 1722 1700 1801 1658 1560 1825 2548 234 4577.21 2 7 1825 1685 2004 2237 1777 12 1008 874 850 18 1040 1103 7 04 85 27 62 4511.65 2 7 102 1162 1255 122 1405 1545 1605 151 1331 1107 43 855 805 73 68 708 732 4446.08 2 7 684 616 608 657 648 608 558 526 52 573 646 703 701 678 637 568 516 4380.51 2 7 506 536 571 58 602 614 61 613 600 584 558 561 583 514 466 425 33 4314.4 2 7 377 371 357 34 348 352 366 378 380 386 402 430 465 525 641 803 08 424.38 2 7 878 832 835 834 81 7 800 835 08 88 1045 1025 77 1002 1084 1134 1153 4183.81 2 7 1086 1050 117 137 1324 1228 1188 1183 1233 1317 1311 1325 1432 1656 184 1873 1775 4118.24 2 6 170 172 175 180 13 220 255 21 344 421 512 623 73 65 1172 1363 1407 4052.67 2 6 1275 1142 1145 2 80 642 540 451 380 336 21 22 327 314 253 213 204 387.10 2 7 12 166 158 1508 1301 1181 113 1105 1103 1107 1084 1105 1145 114 1246 1361 1512 321.54 2 7 1562 167 155 2075 11 1813 1861 1785 1540 1410 1431 1548 1406 1225 1136 1178 1381 3855.7 2 7 1458 1333 1324 1430 1345 1104 0 771 680 617 584 571 553 545 547 556 567 372.33 1 7 56 56 566 560 554 555 562 576 55 618 644 671 685 680 67 62 720 375.54 1 7 743 747 738 71 64 671 658 656 65 65 657 654 653 647 636 625 621 3726.76 1 7 625 634 650 672 700 730 761 73 827 866 18 84 1065 1176 1323 1535 1800 363.8 1 7 2110 2540 307 3735 4471 5213 5641 5458 4754 322 3323 3057 306 3345 3630 3676 3364 3661.1 1 7 285 242 2206 181 1823 1748 1751 1805 1880 14 135 1812 1687 1624 1667 1816 2024 3628.41 1 7 2352 2778 3162 3212 275 2373 223 2324 2235 18 1766 1677 1762 182 2210 2266 207 355.62 1 7 178 1487 1235 104 14 811 722 646 582 532 43 465 451 447 448 453 458 3562.84 1 7 457 447 436 426 414 401 32 385 377 367 353 338 323 312 305 305 312 3530.06 1 7 322 32 326 31 30 303 302 304 311 318 321 323 328 333 337 341 350 347.27 1 7 365 386 37 404 428 473 538 608 627 57 527 44 478 471 475 42 523 3462.56 2 7 630 743 803 85 872 86 1043 43 74 63 605 553 557 563 53 613 575 336. 2 7 531 516 504 476 471 45 422 38 373 365 388 420 435 443 446 442 437 3333.35 1 7 440 452 475 50 554 615 66 73 861 836 761 700 671 670 60 723 760 3300.57 1 7 75 835 82 66 1045 1106 1162 1260 1444 1770 2287 274 3626 3886 3533 210 231 3267.7 1 7 2048 183 1722 1673 1686 1764 114 2141 241 2630 2624 2403 2105 1851 1667 1535 1438 3235.00 1 7 1366 131 124 1275 1301 130 126 1201 110 1210 1302 1407 1512 1548 1631 1512 1541

142 J.E. Bertie et al. / Journal of Molecular Structure 550 551 (2000) 135 165 Table 3 (continued) cm 1 XE YE 0 1 2 3 4 5 6 7 8 10 11 12 13 14 15 16 3202.22 1 7 1558 1614 1740 1804 14 2122 233 2607 284 3124 3158 3144 3112 3157 3272 3563 382 316.43 1 7 438 4727 4775 4524 427 4065 408 4158 4310 4414 4462 4640 4830 5072 5113 5167 5278 3136.65 1 6 542 562 53 631 678 708 732 764 78 845 05 71 1051 1155 1274 141 1583 3103.87 1 5 177 200 22 270 327 417 555 748 1008 1274 1543 2001 247 2500 2084 160 146 3071.08 1 5 1403 1450 157 1686 160 1572 1384 1230 110 1014 67 1 848 811 832 88 77 3038.30 1 5 1055 1176 1344 1410 1351 1357 1377 1421 1421 1287 1211 1332 1467 1270 0 77 637 3003.5 2 6 4847 4045 301 2305 183 1533 1308 1127 82 861 777 68 604 525 477 465 46 23.5 1 7 46 4748 4787 4761 4844 5131 5712 648 634 6563 5883 5412 517 5125 5248 5431 5461 207.16 1 6 534 510 48 483 508 578 618 568 515 485 41 543 60 57 105 38 777 2874.38 1 7 7004 6878 616 6858 684 6773 5820 4618 3721 3088 2636 2322 2107 158 1827 164 1573 2841.5 1 7 1468 1375 127 1233 1186 1158 1151 115 1175 113 1212 123 1268 127 1286 130 1368 2808.81 1 7 1451 1485 1448 1407 130 1372 1337 131 1355 1473 1635 1660 1584 1500 1401 1308 1244 2776.03 1 7 1208 118 1188 1217 1276 1334 1304 1206 1116 1055 1017 2 88 66 28 8 2743.24 1 7 86 05 857 71 742 706 677 64 623 600 57 561 546 533 523 515 511 2710.46 1 7 510 511 515 521 531 546 564 582 58 612 61 620 620 624 630 63 650 2677.67 1 7 661 677 68 723 755 70 816 838 872 28 1023 117 1434 1748 201 2135 185 2644.8 1 7 1745 1577 1510 1520 1608 1717 1778 1850 16 235 225 307 2635 2285 2140 2024 1884 2612.11 1 7 171 1801 127 2168 2475 2838 3610 4604 4446 3712 3234 3028 254 3145 3713 4535 4774 257.32 1 7 406 3241 2650 2257 148 1763 161 1712 1800 1860 171 167 1608 150 1622 161 1530 2546.54 1 7 1432 1344 1247 1151 1084 1053 1041 1046 106 1222 1458 168 1660 1504 1427 2515.68 2 7 1264 1086 1034 86 1026 1083 1184 1253 1368 1435 1325 1217 1211 1238 124 158 2035 2452.04 1 7 2256 252 2455 205 1801 1615 1500 1434 1404 142 1538 1538 1537 1523 1507 146 1508 241.26 1 7 1455 1504 1503 1610 1708 1853 1882 1767 1682 1670 1671 1664 1647 1610 1632 1604 1553 2386.48 1 7 1567 1675 176 104 2016 2068 2134 2270 248 2636 2814 2815 2721 2651 2601 260 2753 2353.6 1 7 3035 3542 4043 4140 4044 388 4176 4787 6103 785 8705 7870 6705 6172 606 6286 7053 2320.1 1 6 867 1113 1342 1475 1617 1717 1548 1235 85 820 710 642 604 50 600 626 671 2288.12 1 5 75 86 101 120 142 17 254 37 631 87 1007 81 60 516 31 307 252 2255.34 1 6 2158 1888 1615 1334 1122 65 847 763 701 662 645 62 581 511 44 400 357 2222.56 1 7 3262 3027 261 284 3067 326 3640 4077 4353 407 3577 3221 3042 2832 2643 2634 2755 218.77 1 7 2727 2465 210 183 1827 1724 1704 1765 1810 1723 1583 1460 1367 128 1242 1201 112 2156. 1 7 1245 1400 1701 2000 146 1686 1447 1268 113 104 88 28 862 805 761 726 65 2124.20 1 7 671 656 651 657 676 704 735 777 831 852 828 800 782 768 760 75 765 201.42 1 7 77 7 818 833 843 850 847 838 831 832 841 857 882 20 68 100 102 2058.64 1 7 1044 1083 1160 1251 1220 115 1152 1155 1155 113 1134 1140 1148 1148 113 1138 115 2025.85 1 7 1208 124 1425 15 1786 127 157 122 118 188 2130 2345 2663 3210 4153 5531 6553 13.07 1 6 677 660 644 644 76 873 1057 1313 1604 107 2145 2236 225 2277 2333 2473 276 158.36 2 6 382 4830 4315 3032 2027 1472 1188 1017 32 1033 1376 2037 2807 23 265 2863 3543 182.7 2 6 4087 3356 2334 1630 102 743 552 468 441 430 430 477 574 780 1106 1413 1558 1827.22 2 6 1774 2356 3482 4537 4251 3056 204 1420 101 76 1044 1343 124 2746 324 224 247 1761.65 2 6 2162 1810 1564 1682 1630 1241 886 684 587 575 663 866 1313 227 170.58 1 6 3007 3764 4271 414 351 248 2363 133 1583 1308 1080 05 787 726 666 652 644 1676.80 1 7 6422 6608 665 7636 828 8232 747 6518 5710 5015 4461 4216 4351 4466 4688 5038 5616 1644.02 1 6 638 748 07 1126 1404 1715 2035 226 2410 2358 216 184 1777 160 145 1457 1527 1611.23 1 6 1622 174 1700 1476 1361 1355 1442 1650 205 2642 2728 2425 2048 1763 152 150 1506 1578.45 1 6 1643 14 2047 172 1437 1233 1112 1027 62 27 27 64 1041 1163 1315 1445 1476 1545.66 1 6 136 126 1152 1068 1015 82 52 20 81 862 82 787 742 701 670 654 655 1513.84 0 6 648 64 653 656 666 677 702 742 67 830 877 50 1025 1111 1206 1321 143 147.45 0 5 154 166 174 183 15 20 227 24 278 316 365 416 467 541 653 822 1070 1481.06 0 5 141 1876 243 3205 4323 5732 6725 623 4828 350 2650 2145 1836 151 1383 1241 1174 1464.67 0 5 1174 1232 1341 1475 1585 1608 1552 1485 1463 1517 168 2068 2736 3847 534 6617 6458 1448.28 0 5 5202 3880 207 2265 1854 1537 1247 1001 813 673 565 482 418 364 321 284 253 1428. 2 6 1707 128 1125 1031 1031 1122 115 1462 2141 3544 5347 6003 4603 22 2146 2042 2283 1363.42 2 6 128 134 1034 37 81 745 734 777 782 763 776 07 111 1063 1088 114 108

J.E. Bertie et al. / Journal of Molecular Structure 550 551 (2000) 135 165 143 Table 3 (continued) cm 1 XE YE 0 1 2 3 4 5 6 7 8 10 11 12 13 14 15 16 127.86 2 6 1071 81 83 723 63 574 53 523 533 585 653 735 828 83 810 841 51 1232.2 2 6 111 1432 141 2381 2158 1874 1676 1528 1517 1636 100 214 2486 3037 366 3860 3614 1166.72 2 6 3524 3734 388 3782 2 2415 2012 1724 1522 1387 1334 1301 12 1345 1115.62 0 6 1374 1412 1463 1536 1643 1776 124 204 2253 2347 2345 2283 2186 203 2021 160 127 10.22 0 6 18 182 1886 104 12 183 2047 2105 2166 2258 2373 2516 268 223 3230 3625 4172 1082.83 0 5 40 52 733 3 1234 1616 173 208 138 1670 1418 1216 1042 88 755 643 551 1066.44 0 6 4771 417 3714 3348 3067 2854 263 256 248 2446 2435 2418 2423 2431 245 2502 2562 1050.05 0 5 265 276 20 306 327 354 386 42 484 557 662 806 1008 122 1703 2313 311 1033.66 0 5 4217 402 4824 4223 3504 2835 2266 1814 1471 1210 1016 867 756 672 607 556 518 1017.26 0 6 4852 4601 4413 427 4218 412 4221 4305 4485 4730 43 431 4731 4454 4202 4004 3872.1 1 6 3751 3708 3764 312 4151 4431 4750 504 544 6143 6154 5263 4485 406 3811 3625 343 67.12 1 6 3260 3100 234 2806 266 2624 2557 2505 2470 2466 2501 2555 2635 2753 260 3336 350 34.34 1 5 45 616 803 1214 1876 12 1320 85 622 514 441 356 22 24 222 204 15 01.56 1 6 134 188 2135 2478 2867 2627 2304 2133 2072 2103 2163 2272 2467 278 3155 3465 3771 86.74 0 5 33 41 451 48 564 657 78 83 1268 162 221 24 3508 345 3038 2468 183 853.34 0 5 1625 1375 116 1062 53 860 777 707 648 5 555 51 485 457 431 410 31 835. 1 6 3616 338 3266 3217 310 311 3204 3378 344 3637 3806 30 4131 4422 4737 512 5821 803.20 1 4 66 75 8 113 147 168 183 222 30 42 87 1630 23 230 1654 106 667 770.42 1 5 4216 270 144 1427 108 87 736 645 57 513 474 445 422 406 37 360 347 737.64 1 5 348 344 352 363 378 401 427 460 500 548 61 713 85 1062 1433 2104 3312 705.82 0 4 423 534 658 81 1063 1454 2058 2722 2824 2226 1574 1116 811 601 462 370 30 68.42 0 5 2658 2371 2188 211 2131 2278 2573 304 3818 4644 5183 5137 4604 342 3382 253 2600 672.07 1 5 128 1470 118 1020 0 83 803 72 808 86 8 1101 108 1043 1020 1026 1081 63.28 1 4 116 127 142 163 13 240 323 37 423 45 644 13 1424 230 613.25 0 4 3083 388 4634 5105 531 5565 6042 655 6601 586 4688 3554 2674 2041 152 1270 1033 56.86 0 5 8553 713 6130 5285 4603 4045 3582 314 2867 2587 2346 2137 155 176 1655 1530 141 577.57 2 5 1077 845 681 560 46 38 342 28 261 231 205 184 166 150 137 125 115 512.01 2 6 1054 74 02 837 a The column headed cm 1 contains the wavenumber of the first n or k value in the row. The column headed XE and YE contain the X- and the Y-exponent for the row, respectively. The columns headed 0,1,2, 6, contain the ordinate values, and the headings give the indices of the ordinate values in the row. In a row which starts with ~n 0 ; the wavenumber corresponding to the ordinate indexed J is ~n J ˆ ~n 0 1578:002=16384 J2 XE : The k values in the row are the ordinate value times 10 YE. Thus the entries indexed 16 in the first row shows that: k ˆ 213 10 7 and n ˆ 1:475 at ~n ˆ 6200:02 1578:002=16384 16 2 2 ˆ 6138:31 cm 1 : b The k values in the table can be interpolated via the 4-point spline interpolation program Trecover [27] to the original wavenumber spacing, 0.482117 cm 1, to give the original k values with errors 1% below 4500 cm 1, 2% between 4500 and 5000 cm 1, and 5% above 5000 cm 1, except for isolated spikes. The n values can be recovered via Trecover with errors 0.1% in nearly all cases. c The n values are based on n el 8000 cm 1 ˆ1:4800. One other source of error must be addressed. The Dn ~n i values from the KK transform should be added to the values n el ~n i ; instead of being added to n el (8000 cm 1 ) [28]. For C 6 H 6 n el is 1.4804 at 8000 cm 1, 1.4770 at 4000 cm 1 and 1.4760 at 0cm 1, so an error that increases with decreasing wavenumber from 0% at 8000 cm 1 to 0.3% at 0cm 1 exists for C 6 H 6 when n el (8000 cm 1 ) is used [28]. The correct numbers are not known for C 6 H 5 D, but the n values probably also contain errors of this magnitude. Thus, the total uncertainty in the n values is 0.25% near 8000 cm 1 increasing to 0.5% near 800 cm 1, below which the uncertainty in the 610 cm 1 peak causes the larger errors discussed above. The final n spectrum of C 6 H 5 Dat25 C is shown in Fig. 3 and is tabulated in the Compact Table format [27] in Table 4. The final k and n spectra are available in digital form through J.E.B. s web site http://www.ualberta.ca/~jbertie/jebhome.htm. The programs Comptab and Trecover for creating Compact Tables and recovering spectra from them [27], are also available through this site.

144 3.4. Spectra of other intensity quantities J.E. Bertie et al. / Journal of Molecular Structure 550 551 (2000) 135 165 Fig. 3. Real refractive index spectrum, n ~n ; of liquid C 6 H 5 Dat 25 C. Top box, 6200 4000 cm 1 and n ˆ 1:478 to 1.480; middle box, 4000 2100 cm 1 and n ˆ 1:458 to 1.45; bottom box, 2400 500 cm 1 and n ˆ 1:10 to 2.00. The top spectrum in the bottom box was offset by multiplying the original spectrum (bottom) by 5 and subtracting 5.6. again by program Dequant. The am 00 spectrum is shown in Fig. 5. The molar concentration and molar volume equaled 11.21 mol l 1 and 8.21 cm 3 mol 1 in these calculations, calculated from the density [35] 0.886 g cm 3 at 25 and molecular weight 7.121 g mol 1. For the 27 most intense bands in the k spectrum, Table 5 lists the peak wavenumber and full-width-athalf-height in the k spectrum and the peak heights in the spectra of these different intensity quantities. The peak wavenumbers and shapes are different in the spectra of these different intensity quantities for very strong absorption bands. For C 6 H 5 D, the difference between the peak wavenumbers exceeds 0.1 cm 1 for only the three strongest bands, those at 77, 6 and 606 cm 1. For these three bands Table 5 shows the peak wavenumbers in the e 00, am 00 and ~na 00 m spectra in parentheses underneath the peak heights. The difference in peak shape is detectable only for the strongest band, that at 606 cm 1. Fig. 1 includes this band in the e 00 and am 00 spectra, with the e 00 values multiplied by 3 in order to give roughly the same peak height for both. The E m band essentially coincides with the k band when scaled to the same peak height, and the ~na 00 m band essentially coincides with the am 00 band. The (negligible) difference between the am 00 and ~na 00 m peak wavenumbers is due to the mechanical anharmonicity of the vibration and the differences between the k, e 00 and am 00 bands are due to the long-range dielectric effects in the interaction of the infrared light with the liquid [21]. The spectra of the molar absorption coefficient, 4 E m, and the real and imaginary dielectric constants, e 0 and e 00, were calculated from the spectra of n and k by program Dequant, which is available through J.E.B. s web site. The molar absorption coefficient spectrum is shown in Fig. 4. These intensity quantities are all macroscopic properties of the liquid. The spectrum of a microscopic molecular property, the imaginary molar polarizability [21,24,26], am, 00 was calculated under the approximation of the Lorentz local field, 4 The symbol E m is used instead of the recommended [34] e for the molar absorption coefficient, in order to avoid confusion with the dielectric constants. 4. Vibrational integrated intensities As was discussed previously [5] for C 6 D 6, in order to separate the contributions to the intensity from the different bands, the am 00 spectrum was fitted between 4800 and 500 cm 1 with CDHO bands. For C 6 H 5 D, 28 bands were fitted to the am 00 spectrum. Each of these fitted bands extended from 4800 to 500 cm 1, and we call their sum the fitted spectrum. The integrated intensity C j of each of these bands was determined analytically through C j ˆ S j p=2; where S j is a fitting parameter that equals the peak height of the corresponding ~na 00 m band multiplied by the full-widthat-half-height [5,21,25]. In the terminology of Ref. [21], S j is N A m 2 j = 12p 2 c 2 : The peak wavenumbers,

J.E. Bertie et al. / Journal of Molecular Structure 550 551 (2000) 135 165 145 Table 4 Real refractive indices, n, between 6200 and 500 cm 1 of liquid benzene-d 1 at 25 C a,b,c cm 1 XE 0 1 2 3 4 5 6 7 8 10 11 12 13 14 15 16 6200.02 2 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 6130.60 3 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1474 1474 1474 1474 1474 1474 5.46 3 1474 1474 1474 1475 1475 1475 1476 1476 1476 1476 1476 1476 1476 1476 1476 1476 1476 5874.11 1 1476 1476 1476 1476 1476 1476 1476 1476 1476 1476 1476 1476 1476 1476 1476 1476 1476 5842.2 0 1476 1476 1476 1476 1476 1476 1476 1476 1476 1476 1476 1476 1476 1476 1476 1476 1476 5825.0 0 1476 1476 1476 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 580.51 0 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 573.11 0 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 5776.72 0 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 5760.33 0 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 5743.4 0 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 5727.55 0 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 5711.15 0 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 561.87 2 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 5626.30 2 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 1475 5560.73 2 1475 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 545.17 2 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 5425.74 3 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 524.60 3 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 1474 1473 1473 1473 5163.47 3 1473 1473 1473 1473 1473 1473 1473 1473 1473 1473 1473 1473 1473 1473 1473 1473 1473 5032.33 3 1473 1473 1473 1473 1473 1473 1473 1473 1473 1472 1472 1472 1472 1472 1472 1472 1472 401.20 3 1472 1472 1472 1472 1472 1472 1472 1472 1472 1472 1472 1472 1472 1472 1471 1471 1471 4770.06 3 1471 1471 1471 1471 1471 1471 1471 1470 1470 1470 1470 1478 1478 1478 1478 1470 1472 4642.78 2 1472 1472 1472 1472 1472 1472 1472 1472 1472 1472 1472 1472 1472 1472 1471 1471 1472 4577.21 2 1472 1472 1472 1472 1473 1473 1472 1472 1472 1472 1472 1472 1472 1472 1471 1471 1471 4511.65 2 1471 1471 1471 1471 1471 1471 1471 1472 1472 1472 1472 1472 1472 1471 1471 1471 1471 4446.08 2 1471 1471 1471 1471 1471 1471 1471 1471 1471 1471 1471 1471 1471 1471 1471 1471 1471 4380.51 2 1470 1470 1470 1470 1470 1470 1470 1470 1470 1470 1470 1470 1470 1470 1470 1470 1470 4314.4 2 1470 1470 1470 1470 1470 1478 1478 1478 1478 1478 1478 1478 1478 1478 1478 1478 1478 424.38 2 1478 1478 1478 1478 1478 1478 14788 14788 14788 14788 14788 14788 14788 14788 14788 14788 14788 4183.81 2 14788 14788 14788 14788 14788 14788 14788 14787 14787 14787 14787 14787 14787 14786 14786 14787 14786 4118.24 2 14786 14786 14786 14785 14785 14785 14784 14784 14783 14783 14782 14782 14782 14782 14783 14785 14788 4052.67 2 1471 1472 1473 1475 1475 1475 1475 1475 1474 1474 1473 1472 1472 1473 1473 1472 1472 387.10 2 1472 1472 1471 1471 1471 1471 1471 1470 1470 1470 1470 1470 1478 1478 1478 1478 1478 321.54 2 1478 1478 1478 1478 1478 1478 1478 1478 1478 1478 1478 1478 1478 1478 1478 1478 14788 3855.7 2 1478 1478 1478 1478 1478 1478 1478 1478 14788 14788 14788 14788 14788 14788 14788 14787 14787 372.33 1 14787 14787 14787 14787 14787 14787 14787 14787 14787 14787 14787 14787 14787 14787 14787 14787 14786 375.54 1 14786 14786 14786 14786 14786 14786 14786 14786 14786 14786 14786 14786 14786 14786 14786 14786 14786 3726.76 1 14785 14785 14785 14785 14785 14785 14785 14785 14785 14784 14784 14784 14784 14784 14784 14783 14783 363.8 1 14783 14783 14783 14783 14783 14784 14785 14786 14787 14787 14787 14786 14786 14786 14786 14786 14787 3661.1 1 14787 14787 14787 14787 14786 14786 14786 14786 14786 14786 14786 14786 14786 14785 14785 14785 14785 3628.41 1 14785 14785 14785 14786 14786 14786 14786 14786 14786 14786 14786 14786 14785 14785 14786 14786 14786 355.62 1 14786 14786 14786 14786 14786 14786 14786 14786 14785 14785 14785 14785 14785 14785 14785 14785 14785 3562.84 1 14784 14784 14784 14784 14784 14784 14784 14784 14784 14784 14784 14784 14784 14783 14783 14783 14783 3530.06 1 14783 14783 14783 14783 14783 14783 14783 14783 14783 14783 14782 14782 14782 14782 14782 14782 14782 347.27 1 14782 14782 14782 14782 14782 14781 14781 14781 14781 14781 14781 14781 14781 14781 14781 14781 14781 3462.56 2 14781 14780 14780 14780 14780 14780 14780 14780 14780 14780 14780 1477 1477 1477 1477 1477 1477 336. 2 14778 14778 14778 14778 14778 14777 14777 14777 14777 14776 14776 14776 14776 14775 14775 14775 14775 3333.35 1 14774 14774 14774 14774 14774 14774 14773 14773 14773 14773 14773 14773 14773 14772 14772 14772 14772 3300.57 1 14772 14771 14771 14771 14771 14770 14770 14770 1476 1476 1476 1476 1476 14770 14771 14771 14771 3267.7 1 14770 14770 14770 1476 1476 14768 14768 14768 14768 14768 14768 14768 14768 14768 14767 14767 14767 3235.00 1 14766 14766 14766 14765 14765 14764 14764 14764 14763 14763 14762 14762 14762 14761 14761 14761 14760

146 J.E. Bertie et al. / Journal of Molecular Structure 550 551 (2000) 135 165 Table 4 (continued) cm 1 XE 0 1 2 3 4 5 6 7 8 10 11 12 13 14 15 16 3202.22 1 1475 1475 14758 14758 14757 14757 14756 14756 14755 14755 14755 14754 14754 14753 14752 14751 14751 316.43 1 14750 14750 14750 14750 1474 14748 14747 14746 14745 14744 14743 14742 14741 14740 1473 14738 14736 3136.65 1 14735 14733 14732 14730 14728 14727 14725 14723 14720 14718 14715 14712 1470 14705 14701 1467 1462 3103.87 1 14687 14680 14673 14665 14654 14642 14630 1461 14612 14614 14615 14622 14670 14646 1478 1476 14786 3071.08 1 14775 14766 14767 14782 14803 14823 14833 14833 14831 14826 14821 1481 14814 14804 1474 14786 14783 3038.30 1 14780 1477 14786 14805 14815 14818 14825 14833 14850 14860 14856 14853 14880 1411 141 1415 1408 3003.5 2 1485 14888 14882 14874 14867 14861 14856 14851 14847 14844 14841 14838 14835 14833 14830 14828 14826 23.5 1 14825 14824 14823 14822 14821 14820 14820 1481 14820 14820 14820 1481 14818 14817 14817 14816 14816 207.16 1 14816 14815 14815 14814 14813 14813 14813 14813 14813 14812 14811 14810 1480 1480 14812 14814 14814 2874.38 1 14813 14813 14813 14813 14813 14813 14814 14814 14813 14813 14812 14812 14811 14810 14810 14810 1480 2841.5 1 1480 14808 14808 14808 14807 14807 14807 14806 14806 14806 14805 14805 14805 14805 14804 14804 14804 2808.81 1 14804 14804 14803 14803 14803 14803 14803 14802 14802 14802 14802 14802 14802 14802 14802 14801 14801 2776.03 1 14801 14801 14801 14800 14800 14800 14800 14800 14800 14800 14800 147 147 147 147 147 147 2743.24 1 147 1478 1478 1478 1478 1478 1478 1478 1477 1477 1477 1477 1477 1477 1477 1476 1476 2710.46 1 1476 1476 1476 1476 1475 1475 1475 1475 1475 1475 1475 1474 1474 1474 1474 1474 1474 2677.67 1 1474 1473 1473 1473 1473 1473 1473 1473 1472 1472 1472 1472 1472 1471 1472 1472 1472 2644.8 1 1472 1472 1472 1471 1471 1471 1471 1471 1471 1470 1470 1471 1471 1471 1471 1471 1471 2612.11 1 1470 1470 1470 1478 1478 1478 1478 1478 1471 1471 1471 1471 1470 1470 1470 1470 1471 257.32 1 1472 1472 1472 1472 1471 1471 1471 1470 1470 1470 1470 1470 1470 1470 1470 1470 1470 2546.54 1 1478 1478 1478 1478 1478 1478 14788 14788 14788 14788 14788 14788 14788 14788 1488 2515.68 2 14788 14787 14787 14787 14786 14786 14786 14786 14785 14785 14785 14785 14785 14784 14784 14783 14783 2452.04 1 14783 14784 14784 14784 14784 14784 14784 14783 14783 14783 14783 14783 14783 14782 14782 14782 14782 241.26 1 14782 14782 14781 14781 14781 14781 14781 14781 14781 14781 14780 14780 14780 14780 14780 1477 1477 2386.48 1 1477 1477 14778 14778 14778 14778 14777 14777 14777 14777 14777 14777 14776 14776 14776 14775 14775 2353.48 1 14774 14774 14774 14774 14774 14773 14772 14771 14771 14771 14772 14774 14773 14773 14771 14770 1476 2320.1 1 14768 14767 14768 1476 14771 14774 14777 14778 14778 14776 14775 14773 14772 14770 14768 14766 14764 2288.12 1 14761 1475 14756 14753 1474 14743 14735 14728 14727 14744 14777 14807 14822 14825 14823 14820 14817 2255.34 1 14814 14812 14811 1480 14807 14805 14803 14802 14800 147 1478 1477 1477 1476 1475 1475 1474 2222.56 1 1473 1472 1471 1470 1470 1478 1478 14788 1478 1478 1478 14788 14788 14788 14787 14787 14787 218.77 1 14787 14786 14786 14786 14786 14785 14785 14784 14784 14784 14784 14784 14783 14783 14783 14782 14782 2156. 1 14782 14781 14781 14781 14781 14781 14781 14781 14781 14780 14780 14780 14780 1477 1477 1477 1477 2124.20 1 14778 14778 14778 14778 14777 14777 14777 14777 14777 14776 14776 14776 14776 14776 14775 14775 14775 201.42 1 14775 14774 14774 14774 14774 14774 14773 14773 14773 14773 14772 14772 14772 14771 14771 14771 14771 2058.64 1 14770 14770 14770 14770 14770 1476 1476 1476 14768 14768 14768 14767 14767 14767 14766 14766 14765 2025.85 1 14765 14764 14764 14763 14763 14763 14762 14762 14761 14760 14760 1475 14758 14757 14756 14755 14755 13.07 1 14755 14755 14754 14752 14751 1474 14748 14747 14746 14747 14748 14750 14751 14751 14751 1474 14748 158.36 2 1474 14762 1477 14786 14784 14780 14775 14772 14767 14762 14757 14755 14758 14764 14766 14764 14765 182.7 2 14776 14788 1470 1478 14786 14782 14778 14775 14772 1476 14766 14763 14760 14757 14755 14754 14754 1827.22 2 14751 14748 14748 14760 14776 14784 14783 1477 14774 1476 14764 1475 14756 14757 14765 14773 14775 1761.65 2 14776 14775 14773 14771 14774 14774 14772 1476 14765 14761 14757 14753 14747 14744 170.58 1 14745 1474 14758 1476 14776 1477 14780 1477 14778 14776 14775 14773 14771 1476 14767 14766 14764 1676.80 1 14763 14762 14761 14760 14760 14760 14760 14760 1475 14757 14756 14754 14753 14752 14750 14748 14747 1644.02 1 14745 14743 14742 14740 1473 1473 14740 14742 14746 1474 14751 14752 14752 14751 14750 14748 14746 1611.23 1 14746 14746 14748 14747 14745 14743 14740 14738 14736 1473 14745 1474 14750 1474 14747 14745 14743 1578.45 1 14740 14741 14745 14746 14746 14744 14742 14740 14738 14736 14734 14732 14730 1472 14728 14728 14728 1545.66 1 1472 14728 14727 14725 14723 14721 1471 14717 14715 14713 14711 1470 14706 14703 146 1466 1462 1513.84 0 1460 14688 14686 14683 14681 14678 14675 14672 14670 14666 14663 14660 14656 14653 1464 14645 14641 147.45 0 14637 14632 14628 14622 14616 1460 14602 1453 14584 14573 14562 14551 14537 1451 1448 14474 14447 1481.06 0 14422 143 14380 14365 14370 14444 14624 14841 1457 1472 1447 1415 1488 14868 14845 14820 1476 1464.67 0 14773 14753 14738 14730 1472 14733 14731 1471 1467 14668 14631 1450 14548 14527 14575 14742 1461 1448.28 0 150 15141 15134 15110 15088 15072 15056 15038 15020 15003 1487 1473 1460 144 143 1430 1421 1428. 2 1483 14872 14856 14842 14831 14821 14811 14801 1471 14784 1478 14810 14826 14825 14817 1480 14808 1363.42 2 14810 14808 14803 1478 1475 1472 14788 14785 14783 14781 14778 14775 14775 14774 14773 14772 14772

J.E. Bertie et al. / Journal of Molecular Structure 550 551 (2000) 135 165 147 Table 4 (continued) cm 1 XE 0 1 2 3 4 5 6 7 8 10 11 12 13 14 15 16 127.86 2 14771 14771 1476 14768 14765 14763 14761 1475 14756 14754 14752 14750 14748 14747 14745 14742 1473 1232.2 2 14736 14733 14732 14736 14740 143 14738 14735 14731 14728 14724 14722 1471 14718 14720 14726 1472 1166.72 2 1472 14728 14732 1473 14741 1473 14735 14731 14727 14722 14718 14713 14708 14703 1115.62 0 14701 14700 1468 1466 1465 1463 1462 1462 1462 1462 1463 1463 1463 1462 1460 1468 14687 10.22 0 14685 14683 14681 14678 14676 14673 14670 14667 14664 14661 14657 14653 14648 14643 14637 14630 14623 1082.83 0 14615 14606 1456 14588 14584 1454 14628 1467 14724 1474 14760 14765 14767 14766 14763 14758 14752 1066.44 0 14746 14740 14734 14728 14722 14716 14710 14705 14700 1465 1460 14685 14680 14676 14670 14665 1465 1050.05 0 14654 14647 14641 14634 14626 14617 14608 1457 14584 14570 14554 14535 14514 1442 1446 14451 14453 1033.66 0 14507 14624 14756 14850 1402 1423 1427 141 1406 1481 14877 14863 14850 14838 14827 14818 1480 1017.26 0 14801 1474 14787 14781 14776 14770 14765 14761 14757 14755 14755 14756 14756 14755 14753 14750 14747.1 1 14741 14736 14730 14725 14722 14718 14716 14715 14714 14718 14728 14733 14731 14727 14724 14721 14718 67.12 1 14715 14712 14708 14705 14701 1467 1463 1468 14684 14680 14675 14670 14664 14657 14650 14641 14631 34.34 1 14621 14612 1458 14587 14621 14715 14758 14753 14738 14725 14718 14711 14702 1463 14684 14676 1466 01.56 1 14662 14654 14647 14641 14640 1463 14634 14627 14620 14612 14604 1456 14587 14578 1456 1455 14548 86.74 0 14541 14532 14523 14512 144 14485 1446 14451 14433 1441 1441 14452 1452 14623 1462 14724 14730 853.34 0 14724 14715 14704 1465 14687 1467 14672 14664 14657 14650 14643 14636 1462 14623 14616 14610 14603 835. 1 1451 14578 14566 14553 14541 14528 14515 14501 14488 14474 1445 14442 14423 14404 14382 14357 1432 803.20 1 14300 14265 14221 14173 14130 1408 14015 1388 1373 13530 132 1323 14035 15140 15713 15813 15718 770.42 1 15565 15420 1528 15200 1511 15052 146 1448 1408 14872 1483 1480 14782 14757 14732 14707 14682 737.64 1 14658 14633 14608 14583 14557 14528 144 14468 14433 1434 1434 1427 14234 14157 14058 1336 13788 705.82 0 13712 13642 13568 13471 1335 13278 13376 136 15022 15777 1566 1517 15802 1566 15537 15418 15315 68.42 0 15225 15144 15070 15001 1436 14873 14814 14766 14744 14766 14841 1432 147 15052 15020 15008 146 672.07 1 1458 1405 1405 14852 14801 14755 14712 1466 14627 14543 14503 14476 14646 14407 14360 14307 1424 63.28 1 14185 14115 14037 1346 13841 13720 1356 1350 13357 13118 12805 12408 1115 1144 613.25 0 11427 11601 1206 12786 1330 13821 14345 1531 16750 18108 18876 1058 1818 18655 18368 1805 17850 56.86 0 17632 17441 17273 17125 164 16877 16772 16678 1653 16516 16446 16382 16323 16268 16218 16171 16128 577.57 2 1582 15867 15775 15700 15637 15583 15537 1547 15462 15430 15402 15377 15355 15334 15315 1528 15282 512.01 2 15267 15253 15240 15228 a The column headed cm 1 contains the wavenumber of the first n or k value in the row. The column headed XE and YE contain the X- and the Y-exponent for the row, respectively. The columns headed 0,1,2, 16, contain the ordinate values, and the headings give the indices of the ordinate values in the row. In a row which starts with ~n 0 ; the wavenumber corresponding to the ordinate indexed J is ~n J ˆ ~n 0 1578:002=16384 J2 XE : The n values are given directly with the decimal point implicitly after the first digit. Thus the entries indexed 16 in the first row of the tables show that: k ˆ 213 10 7 and n ˆ 1:475 at ~n ˆ 6200:02 1578:002=16384 16 2 2 ˆ 6138:31 cm 1 : b The k values in the table can be interpolated via the 4-point spline interpolation program Trecover [27] to the original wavenumber spacing, 0.482117 cm 1, to give the original k values with errors 1% below 4500 cm 1, 2% between 4500 and 5000 cm 1, and 5% above 5000 cm 1, except for isolated spikes. The n values can be recovered via TRECOVER with errors 0.1% in nearly all cases. c The n values are based on n el 8000 cm 1 ˆ1:4800. ~n j ; full-widths-at-half-height, G j, and C j of these fitted bands are listed in Table 6, together with the wavenumbers of features in the experimental am 00 spectrum and the Raman spectrum of the liquid. The quality of the fit is shown graphically in Fig. 5, which includes the fitted spectrum as well as the experimental am 00 spectrum, and in Fig. 6 which shows more detail in two regions, one of which includes the region of greatest misfit above 800 cm 1, near 1056 cm 1. Each curve in Fig. 5 and the upper curve in each box of Fig. 6 consist of both the experimental am 00 spectrum and the fitted spectrum, which essentially overlap even in the expanded views in Fig. 5. The lower curves in Fig. 6 show the individual bands required for the fit, truncated for clarity to extend only three full-widths-at-half-height from the band center. The quality of the fit can be described in several ways. Of first importance is that the presence of nearly all of the 28 bands is obvious in the experimental am 00 spectrum, either as peaks, shoulders, changes in slope, or asymmetric tails, as is illustrated in Fig. 6. Second,