Infrared intensities of liquids. Part XXIII. Infrared optical constants …faculty.capebretonu.ca/dkeefe/PDF/benzene-d1 Bertie... · 2005. 7. 22. · This paper continues our report

Infrared intensities of liquids. Part XXIII.Infrared optical constants and integrated intensities of

liquid benzene-d1 at 258Cq

J.E. Bertie* , Y. Apelblat, C.D. Keefe1

Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada, T6G 2G2

Received 28 July 1999; accepted 22 September 1999

Abstract

This paper presents the first absolute infrared absorption intensities of liquid benzene-d1, C6H5D, at 258C. It also presentswhat, surprisingly, seems to be the first complete assignment of an infrared spectrum of liquid benzene-d1 recorded with post-1950 instrumentation. The spectra of the real and imaginary refractive indices are given as graphs and tables between 6200 and500 cm21, and a table is given of the peak wavenumbers, absolute integrated intensities and vibrational assignments between4800 and 500 cm21. Errors in the imaginary refractive index,k, values are estimated to be 5–7% for peaks and 5–20% for thebaseline between 6200 and 4700 cm21, 0.3–2.0% for both peaks and baseline between 4700 and 825 cm21, 3–4% for bothpeaks and baseline between 825 and 620 cm21, and 40–50% between 620 and 500 cm21 where the very strong peak near600 cm21 was too intense for us to measure accurately. Errors in the real refractive indices,n, are estimated to be 0.25% at8000 cm21 increasing to 0.5% near 800 cm21 and, due to the uncertain intensity of the peak near 600 cm21, to range up to 10%between 710 and 500 cm21. The refractive index spectra were converted to spectra of the real and imaginary dielectricconstants,e 0 ande 00, the molar absorption coefficient,Em, and the real and imaginary molar polarizabilities under the Lorentzlocal field,a 0m anda 00m. The peak heights and wavenumbers in the spectra of the different absorption quantities are compared forthe most intense bands. Integrated intensities were determined asCj, the area under bands in the~na

00m spectrum, for all bands

between 4800 and 500 cm21. The contributions from the different bands were separated by fitting the spectrum with classicaldamped 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 thecorresponding transition dipole moments are summarized and compared with literature values for the gas. Crawford’sF-sumrule shows that the measured integrated intensities of C6H5D are nicely consistent with those reported recently for C6H6 andC6D6. The total integrated intensity of the first overtone of the CH stretches is, 20 times smaller than that of the fundamentals.q 2000 Elsevier Science B.V. All rights reserved.

Keywords: Benzene-d1; Infrared intensities; Optical constants; Refractive indices; Dielectric constants

Journal of Molecular Structure 550–551 (2000) 135–165

0022-2860/00/$ - see front matterq 2000 Elsevier Science B.V. All rights reserved.PII: S0022-2860(00)00518-4

www.elsevier.nl/locate/molstruc

q Dedicated to Professor James R. Durig on the occasion of his 65th birthday.* Corresponding author. Tel.:11-780-492-3560; fax:11-780-492-8231.

E-mail address:[email protected] (J.E. Bertie).1 Current address: Department of Physical and Applied Sciences, University College of Cape Breton, Sydney, Nova Scotia, Canada B1P 6L2.

1. Introduction

This paper continues our report of absolute infraredabsorption intensities of liquids measured by trans-mission spectroscopy, by presenting quantitativeinfrared intensities of liquid benzene-d1, C6H5D, at258C. Similar measurements of the intensities ofliquid benzene [1], toluene [2], chlorobenzene [3],dichloromethane [4] and benzene-d6 [5] havebeen published recently and the first four ofthese have formed the basis of intensity standards[6]. This paper also presents the assignment ofmost of the features in the infrared spectrum of liquidC6H5D.

A number of studies of the vibrations of C6H5Dhave been reported in the literature. In 1946 Baileyet al. [7] reported and fully assigned the completeinfrared spectrum of the gas between 3400 and380 cm21, as well as the Raman spectrum, presum-ably of the liquid, over the same range. Since then, themajority of the reports have presented only complete[8–13] or partial [14,15] assignments of the 30 funda-mental vibrations, and only three reports [10,14,16]have contained assignments of some combination andovertone bands. In particular, the complete assign-ment of spectra obtained with post-1950 instrumenta-tion has not been reported previously.

There are no previous reports of the quantitativeinfrared intensities of liquid C6H5D. Three groups[17–19] have reported quantitative infrared intensitiesof gaseous benzene-d1.

In the present work experimental absorbancespectra [1] of liquid benzene-d1 at 258C weremeasured. From these spectra, spectra of the opticalconstants, i.e. of the real,n, and imaginary,k, refrac-tive indices, were calculated by methods describedpreviously [1,20]. The refractive index spectra wereconverted to spectra of the real and imaginary dielec-tric 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 directlyreflected in the spectrum of the imaginary molarpolarizability, a 00m, than in the spectra of theimaginary refractive index, the imaginary dielectricconstant, or the molar absorption coefficient [21].Thus, the imaginary molar polarizability spectrum

is the absorption quantity of greatest interest in thestudy of liquid-phase molecules. Correspondingly,the integrated intensity of bandj, Cj, is definedas the area under the band in the spectrum of~na 00m [21]

Cj Z

~na 00m ~n d ~n 1

Under the assumption that all of the hot transitionsof the fundamental contribute to the fundamentalband,Cj is related to the dipole transition moment,Rj, through Eq. (2) [21–24]

Cj NAp3hc0 gj ~n j uRj u2 2

Under the assumptions of mechanical and electricalharmonicity, Cj can also be related to the squareof the dipole moment derivative with respect tothe jth normal coordinate,m2j u2m=2Qj u2; through[21]

Cj NA24pc20gjm

2j 3

In these equations,NA is the Avogadro constant, h isPlanck’s constant,c0 is the velocity of light invacuum, andgj is the degeneracy of thejth vibra-tion. For C6H5D, gj 1 for all vibrations.

In order to calculate the integrated intensities,the a 00m spectrum must be separated into contribu-tions from the different bands. This is not trivialwhen the spectrum contains adjacent or overlappingbands. However, Eqs. (2) and (3) result from bothquantum theory and the classical damped harmonicoscillator (CDHO) model [21–24], so the separa-tion can be attempted by fitting thea 00m spectrumwith CDHO bands. When this is successful, as forbenzene-d6 [5], methanol [25] and benzene-d1, theintegrated intensityCj may be obtained directlyfrom the parameters of the CDHO band withoutnumerical integration, as is described elsewhere[5,25].

2. Experimental

Benzene-d1, labeled 98%, was purchased from

J.E. Bertie et al. / Journal of Molecular Structure 550–551 (2000) 135–165136

Cambridge Isotope Laboratory and was used as isexcept that it was kept over molecular sieve to ensuredryness. The samples were checked by gas chroma-tography and by infrared spectroscopy of the liquid.Non-benzene impurities were determined to be lessthan 0.06%. The samples were also analyzed bymass spectrometry and were found to containC6H6,

13CC5H5D and 0.45% C6D6. The intensityof the n4 band of C6H6 at 679 cm

21 in the infraredspectrum of the liquid benzene-d1

2 indicated,3.5% of C6H6. We were unable to distinguishbetween 12C6H5D and

13CC5H5D in the infraredspectrum of liquid benzene-d1, although its naturalabundance suggests the presence of about 6% of13CC5H5D.

The experimental and instrumental details of thiswork have been described [1,20] and are summarizedbriefly here. The infrared spectra were measured witha Bruker IFS 113 V spectrometer. A Globar source, a10 mm aperture, and deuterated triglycine sulfate(DTGS) detector were used. The interferogramswere recorded with 0.665 cm s21 optical retardationvelocity and 1 cm21 nominal resolution. Trapezoidalapodization, multiplicative phase correction, andone level of zero-filling were used in the Fouriertransform.

Experimental absorbance spectra of liquidbenzene-d1 were measured in fixed path length cellswith KBr windows and path lengths between 11 and1500mm. To determine the linear absorptioncoefficients at the anchor points [1,20], spectrawere also measured in KBr cells with fixed pathlengths of 500 and 1500mm, and in a NaCl cellwith variable path lengths up to 3.7 mm. The pathlengths of the cells were determined as describedpreviously [1–5].

To assist in the assignment of the bands in the spec-trum of the liquid, an infrared spectrum of gaseousbenzene-d1 was recorded on the Bruker IFS 113 Vin order to observed the band contours, and Ramanspectra were measured to observe the wavenumbershifts and polarizations. Accurate Raman wave-number shifts were obtained from an unpolarizedspectrum recorded at 2 cm21 nominal resolution ona Bruker FT-Raman spectrometer with Nd : YAG

excitation. In the software, the HeNe wavenumberwas set to its vacuum value, 15798.002 cm21, andthat of Nd:YAG was set to 9394.2 cm21. Measure-ment of both Stokes and anti-Stokes Raman shifts offour bands of chlorobenzene and one of dichloro-methane showed that the Stokes wavenumber shiftsare accurate tô 0.1 cm21. Parallel- and perpendic-ular- polarized Raman spectra were recorded with 908excitation on a dispersive SPEX spectrometer withlaser excitation at 514.5 nm, 380 mW power, slitwidth of 2 cm21 and step size 0.5 cm21. The intenseparallel-polarized bands allowed wavenumber cali-bration by comparison with the accurate though unpo-larized FT spectra.

3. Infrared intensities

3.1. Imaginary refractive index spectrum

The k spectrum was determined by the proceduresdescribed in previous papers [1–5], and the presenta-tion in this section follows the logic described in thosepapers. 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 pathlengthsused, the correspondingk values, the 95% confidencelimits of the values ofK and k and the approximatevalue of the real refractive index,n, used at eachanchor point. The baseline absorption is extremelyweak above 4500 cm-1 and could be determined toonly t10% precision with the available path lengthsup to 3.7 mm. The approximaten values were deter-mined from a preliminary calculation ofn and k byprogram RNJ46A from an uncorrected spectrumrecorded through an 11mm cell.

The experimental absorbance, EA, spectra fromcells of many thicknesses were converted toimaginary refractive index spectra by programRNJ46A, using the anchor point information. Thekspectra were only used in regions where thecorresponding EA peak maxima were between 0.2and 2.0 absorbance units. These regions, the pathlengths used, and the number of spectra averaged togive the averagek spectrum for the region, are givenin Table 2. The averagek spectra for the differentregions were merged to give thek spectrum from6200 to 620 cm21.

J.E. Bertie et al. / Journal of Molecular Structure 550–551 (2000) 135–165 137

2 Then4 band is at 673 cm21 in the absorbance spectrum of neat

C6H6(l) but shifts to 679 cm21 on dilution.


Table 1(Decadic) linear absorption coefficients for benzene-d1 at 258C

~n (cm21) Path length (mm) n ~na K ~n (cm21)b k ~nc

6350.4 0.00(,5)d 0.0000000(,15)6055.3 2.7–3.7 1.477 0.429(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) 0.00000599(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) 0.00000819(41)4547.3 1.5–3.7 1.477 2.100(25) 0.0000846(10)4299.6 2.7–3.7 1.477 0.816(10) 0.0000348(4)4117.3 1.5–3.7 1.476 3.812(30) 0.0001696(13)3947.5 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)3569.5 2.7–3.7 1.476 0.870(4) 0.0000447(2)3309.2 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)2934.1 0.5–1.5 1.480 7.625(51) 0.0004762(32)2829.5 1.5–3.7 1.478 1.777(9) 0.0001151(6)2709.5 2.7–3.7 1.477 0.755(3) 0.0000511(2)2534.9 2.7–3.7 1.477 1.440(3) 0.0001041(2)2438.0 2.7–3.7 1.476 1.893(3) 0.0001423(2)2293.9 0.5–1.5 1.474 7.516(27) 0.0006004(22)2217.3 1.5–3.7 1.477 3.601(8) 0.0002976(7)2120.4 2.7–3.7 1.475 0.753(3) 0.0000651(3)2043.7 2.7–3.7 1.474 1.294(3) 0.0001160(3)1928.5 ,0.5 1.474 9.876(28) 0.0009384(27)1858.5 1.5–3.7 1.474 4.347(9) 0.0004286(9)1792.5 ,0.5 1.474 9.542(24) 0.0009754(25)1728.9 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 5.369(16) 0.0006497(19)1415.0 0.5–1.7 1.481 7.912(34) 0.001025(4)1341.3 1.5–3.2 1.476 5.356(18) 0.0007317(25)1269.4 1.5–3.7 1.473 3.616(15) 0.0005220(21)1122.3 0.5–1.5 1.468 7.916(24) 0.001292(4)1055.3 ,0.5 1.465 13.91(8) 0.002415(1)998.5 ,0.5 1.470 20.20(11) 0.003707(20)948.8 0.5–1.5 1.464 12.87(5) 0.002485(10)901.5 0.5–1.5 1.462 9.513(83) 0.001934(17)827.8 ,0.5 1.449 14.42(9) 0.003192(20)736.6 ,0.5 1.459 13.80(7) 0.003433(17)659.0 ,0.5 1.456 28.46(16) 0.007913(44)500.9 ,1.5 1.512 1.419(37) 0.000519(13)

a This column gives the approximate value ofn used to calculate the reflection from the cell windows during the calculation ofK fromexperimental absorbance spectra.

b K values with their 95% confidence limit in the last digit (given in parentheses), are given to the precision used in further computations.c k values andDk, their 95% confidence limits in the last digit (given in parentheses) were calculated fromk 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 95% confidence limit was estimated from the maximum possible error in the absorbance (0.02) in these cells.

The region of the most intense band, 620–500 cm21 was not well determined, because in ourthinnest cell, 11mm, the peak EA was,2 and variedsignificantly between spectra. Initially the average ofthe four k spectra between 620 and 500 cm21 thatwere calculated from these EA spectra was mergedwith the k spectrum for the higher-wavenumberregion. The following steps were taken in an attemptto improve the reliability of thek spectrum below620 cm21. Then spectrum was calculated from thekspectrum, as described later, and was used with thekspectrum to calculate the spectrum of the imaginarymolar polarizability,a 00m [5,21,24–26]. Three CDHObands were then fitted to the wings of thea 00m band at,600 cm21, two for the strong peak near 610 cm21

and one for the weak shoulder near 625 cm21. Theneed for two bands to fit the strong peak is obviousin the original spectra. The fit was very good. The sumof the CDHO bands was then converted back to akspectrum and merged with thek spectrum for thehigher wavenumber region to give the finalk spectrumof liquid benzene-d1 from 6200 to 500 cm

21. The

improved k spectrum near 600 cm21 is comparedwith the average of the original fourk spectra in thetop box of Fig. 1.

Thek spectrum of C6H5D at 258C is shown in Fig. 2,and is tabulated in Table 3 in the Compact Tableformat [27].

3.2. Precision and accuracy of k

The accuracy of ak value is described by the abso-lute error in the value. This error cannot be knownexactly, so can only be estimated. Here the error isestimated [1–5] as the sum of the precision of thekvalue, expressed by its 95% confidence limit (95%CL), and the systematic error that arises from fixingthe baseline at the anchor points. This systematic error


Fig. 1. The 605 cm21 band of liquid C6H5D at 258C. Top: Theoriginal average imaginary refractive index,k, band and the finalk band obtained as described in the text. Bottom: The bands in thedielectric loss,e 00, and imaginary molar polarizability,a 00m, spectra.The e 00 band has been multiplied by 3 for clarity. The units ofa 00mare cm3 mol21.

Table 2Pathlengths and number of spectra recorded for the regionsprocessed

Region (cm21) Pathlength (mm) Number of spectra

6350.4–6000 1700–3700 116010.0–5700 ,500 35707.7–4700 2700–3700 84700.6–4540 ,500 34547.3–4115 1700–3700 114118.2–3950 ,500 33952.8–3725 1700–3700 233728.2–3570 500–1500 113571.0–3300 1700–3700 233308.7–3225 1500–2700 173230.1–2930 11–35 72936.0–2825 ,500 62829.5–2430 500–2700 232435.6–2215 11–50 102220.6–1980 1500–3700 281985.6–1645 11–50 101651.2–1510 50–500 91515.7–1410 11–35 71413.0–1340 35–50 61341.2–1120 ,50 31122.3–825 11–50 10827.79–620 ,11 4622–500 , 11 4

is taken to be the average of the 95% CLs of theanchor points (Table 1) at the two ends of the region.Previous studies have shown [1–4] that this method ofestimating the accuracy of intensities measured by theBruker FT spectrometer in this laboratory is supportedby measurements on other instruments in otherlaboratories.

The errors in the 6200–4700 cm21 region, wherethe absorption is very weak, come mainly from theanchor points. Thus, the errors in the peak and base-line k values are 5–7% and 5–20%, respectively.Below 4700 cm21 the absorption is much strongerand the errors from the two sources are about equal.The errors ink are 0.3–2.0% between 4700 and825 cm21, for both the peaks and the baselineabsorption. Between 825 and 620 cm21, the errorsare larger, 3–4%, mainly due to unusually poor

reproducibility. Between 620 and 500 cm21 theerror is 40%, which is the 95% CL of the peakvalue; as discussed above, this large error resultsfrom our inability to measure precisely the veryintense band near 600 cm21.

3.3. Real refractive index spectrum

The n spectrum of C6H5D was calculated byKramers–Kronig (KK) transformation of the finalkspectrum with the assumption thatk is zero between6200 and 8000 cm21. The KK transform requires avalue of n∞, that was taken to be the refractiveindex at 8000 cm21 that is due only to electronicpolarization [28],nel(8000 cm

21). The value 1.4800was used, and was obtained in the following way. Fitsof the literature values ofn of C6H6 at seven differentvisible wavelengths and 258C yielded [1,28] nel 1:4804 at 8000 cm21. For C6H5D the visible-wave-length-dependence ofn is not known, and the onlyreported values are for the NaD line [29–31], wheren1:5006 [30] at 208C and 1.4976 [31] at 258C.3 Thesevalues are, 0.0004 smaller than the values at theNaD line for C6H6, n 1:5010 [29,32] at 208C and1.4979 [32] at 258C. The difference betweenn ofC6H5D and n of C6H6 was assumed to be the sameat 8000 cm21 as at the NaD line, so nel(8000 cm

21)of C6H5D at 258C was taken to be 1.4800.

The accuracy of then values can be estimated asfollows. The value ofn at wavenumber~n i was calcu-lated by adding the valueDn ~n i that is calculated byKK transform of the k spectrum to the valuenel8000 cm21 1:4800: Thus, the uncertainty innwas estimated as the sum of the 0.05% uncertaintyinherent in our KK transform [33], the, 0.03%uncertainty innel(8000 cm

21) plus the 0.08–0.15%uncertainty inDn ~n i that results from the uncertaintyin thek values. Thus, above 710 cm21 the uncertaintyin the n values is , ^ 0.25%. Because the strongabsorption near, 610 cm21 was poorly measured,the n values are uncertain by 1% at 640 cm21

increasing to 10% near the 610 cm21 peak anddecreasing to 1% at 575 cm21 and 0.5% at 500 cm21.


Fig. 2. Imaginary refractive index spectrum,k ~n; of liquid C6H5Dat 258C. Top box, 6200–4000 cm21; middle box 4000–2100 cm21;bottom box, 2400–500 cm21. Divide the ordinate scale labels in thetop, middle and bottom boxes by 10, 20 and 60, respectively, for theupper curve in the box.

3 Ref. [31] actually gives 1.5011 for C6H5D at 208C, but it alsogives 1.5015 for C6H6 compared with the accepted value 1.5010, sowe have reduced their value for C6H5D by 0.0005. Note also thatAldrich [29] give n 1:4980 for C6H5D at 208C, which is assumedto mean “at 258C”.


Table 3Imaginary refractive indices,k, between 6200 and 500 cm21 of liquid benzene-d1 at 258C

a,b,c

cm21 XE YE 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

6200.02 2 27 0 0 0 0 1 7 14 25 36 49 59 77 109 147 178 197 2136130.60 3 27 227 291 280 258 240 225 231 217 201 153 132 165 227 339 472 689 10315999.46 3 27 1542 1756 1972 2189 2217 2341 2243 1825 1485 1218 1070 983 874 747 583 508 4855874.11 1 27 461 430 391 361 345 312 294 266 240 227 229 230 250 264 298 315 3235842.29 0 27 323 317 312 301 299 288 282 269 272 262 261 252 238 217 214 217 2035825.90 0 27 181 186 169 167 154 147 136 138 125 127 123 114 127 116 119 121 1185809.51 0 27 120 118 117 120 116 111 112 113 118 108 103 103 97 99 92 91 925793.11 0 27 89 92 88 85 92 85 91 86 83 84 74 72 64 57 58 46 425776.72 0 27 44 36 42 31 29 26 22 26 26 21 18 20 20 21 16 13 105760.33 0 27 10 12 16 13 18 18 24 27 27 32 43 56 61 70 65 65 605743.94 0 27 60 50 51 48 43 38 41 47 40 52 48 54 54 54 52 50 545727.55 0 27 60 56 68 63 71 72 73 80 70 78 78 85 87 92 91 91 1005711.15 0 27 109 109 123 126 127 132 138 143 149 152 155 158 160 161 162 164 1645691.87 2 27 169 178 184 187 187 190 197 202 196 177 154 135 118 104 94 88 825626.30 2 27 77 70 62 56 53 50 54 70 78 80 87 111 120 103 86 76 725560.73 2 27 67 60 56 57 64 71 77 79 82 87 90 89 88 86 86 90 915495.17 2 27 92 91 90 99 111 110 104 98 102 106 97 85 71 64 61 62 605425.74 3 27 61 60 70 92 112 123 127 146 191 228 255 254 314 449 408 322 2505294.60 3 27 188 164 116 93 103 98 89 97 107 119 118 113 100 103 99 95 835163.47 3 27 73 77 86 74 63 63 61 52 55 58 58 57 66 67 65 65 595032.33 3 27 63 56 59 62 67 71 70 69 72 75 73 75 75 72 71 75 824901.20 3 27 87 89 87 82 86 102 127 131 127 119 119 120 113 112 125 128 1434770.06 3 27 168 186 190 187 194 198 214 257 312 400 576 866 1504 2435 3248 4190 33604642.78 2 27 2993 2774 2544 2375 2248 2257 2302 2114 1881 1722 1700 1801 1658 1560 1825 2548 23494577.21 2 27 1825 1685 2004 2237 1777 1299 1008 874 850 918 1040 1103 997 904 895 927 9624511.65 2 27 1029 1162 1255 1292 1405 1545 1605 1519 1331 1107 943 855 805 739 698 708 7324446.08 2 27 684 616 608 657 648 608 558 526 529 573 646 703 701 678 637 568 5164380.51 2 27 506 536 571 589 602 614 619 613 600 584 558 561 583 514 466 425 3934314.94 2 27 377 371 357 349 348 352 366 378 380 386 402 430 465 525 641 803 9084249.38 2 27 878 832 835 834 819 799 800 835 908 988 1045 1025 977 1002 1084 1134 11534183.81 2 27 1086 1050 1197 1397 1324 1228 1188 1183 1233 1317 1311 1325 1432 1656 1849 1873 17754118.24 2 26 170 172 175 180 193 220 255 291 344 421 512 623 793 965 1172 1363 14074052.67 2 26 1275 1142 1145 992 809 642 540 451 380 336 291 292 327 314 253 213 2043987.10 2 27 1929 1696 1598 1508 1301 1181 1139 1105 1103 1107 1084 1105 1145 1194 1246 1361 15123921.54 2 27 1562 1697 1955 2075 1919 1813 1861 1785 1540 1410 1431 1548 1406 1225 1136 1178 13813855.97 2 27 1458 1333 1324 1430 1345 1104 909 771 680 617 584 571 553 545 547 556 5673792.33 1 27 569 569 566 560 554 555 562 576 595 618 644 671 685 680 679 692 7203759.54 1 27 743 747 738 719 694 671 658 656 659 659 657 654 653 647 636 625 6213726.76 1 27 625 634 650 672 700 730 761 793 827 866 918 984 1065 1176 1323 1535 18003693.98 1 27 2110 2540 3097 3735 4471 5213 5641 5458 4754 3922 3323 3057 3096 3345 3630 3676 33643661.19 1 27 2895 2492 2206 1981 1823 1748 1751 1805 1880 1949 1935 1812 1687 1624 1667 1816 20243628.41 1 27 2352 2778 3162 3212 2759 2373 2293 2324 2235 1998 1766 1677 1762 1982 2210 2266 20973595.62 1 27 1798 1487 1235 1049 914 811 722 646 582 532 493 465 451 447 448 453 4583562.84 1 27 457 447 436 426 414 401 392 385 377 367 353 338 323 312 305 305 3123530.06 1 27 322 329 326 319 309 303 302 304 311 318 321 323 328 333 337 341 3503497.27 1 27 365 386 397 404 428 473 538 608 627 579 527 494 478 471 475 492 5233462.56 2 27 630 743 803 859 872 986 1043 943 794 693 605 553 557 563 593 613 5753396.99 2 27 531 516 504 476 471 459 422 389 373 365 388 420 435 443 446 442 4373333.35 1 27 440 452 475 509 554 615 696 793 861 836 761 700 671 670 690 723 7603300.57 1 27 795 835 892 966 1045 1106 1162 1260 1444 1770 2287 2974 3626 3886 3533 2910 23913267.79 1 27 2048 1839 1722 1673 1686 1764 1914 2141 2419 2630 2624 2403 2105 1851 1667 1535 14383235.00 1 27 1366 1319 1294 1275 1301 1309 1296 1201 1190 1210 1302 1407 1512 1548 1631 1512 1541


Table 3 (continued)

cm21 XE YE 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

3202.22 1 27 1558 1614 1740 1804 1949 2122 2339 2607 2894 3124 3158 3144 3112 3157 3272 3563 39823169.43 1 27 4398 4727 4775 4524 4279 4065 4098 4158 4310 4414 4462 4640 4830 5072 5113 5167 52783136.65 1 26 542 562 593 631 678 708 732 764 798 845 905 971 1051 1155 1274 1419 15833103.87 1 25 177 200 229 270 327 417 555 748 1008 1274 1543 2001 2497 2500 2084 1690 14693071.08 1 25 1403 1450 1579 1686 1690 1572 1384 1230 1109 1014 967 919 848 811 832 898 9773038.30 1 25 1055 1176 1344 1410 1351 1357 1377 1421 1421 1287 1211 1332 1467 1270 990 779 6373003.59 2 26 4847 4045 3019 2305 1839 1533 1308 1127 982 861 777 698 604 525 477 465 4692939.95 1 27 4699 4748 4787 4761 4844 5131 5712 6498 6934 6563 5883 5412 5179 5125 5248 5431 54612907.16 1 26 534 510 489 483 508 578 618 568 515 485 491 543 690 957 1095 938 7772874.38 1 27 7004 6878 6916 6858 6894 6773 5820 4618 3721 3088 2636 2322 2107 1958 1827 1694 15732841.59 1 27 1468 1375 1297 1233 1186 1158 1151 1159 1175 1193 1212 1239 1268 1279 1286 1309 13682808.81 1 27 1451 1485 1448 1407 1390 1372 1337 1319 1355 1473 1635 1660 1584 1500 1401 1308 12442776.03 1 27 1208 1189 1188 1217 1276 1334 1304 1206 1116 1055 1017 999 992 988 966 928 8992743.24 1 27 896 905 857 791 742 706 677 649 623 600 579 561 546 533 523 515 5112710.46 1 27 510 511 515 521 531 546 564 582 598 612 619 620 620 624 630 639 6502677.67 1 27 661 677 698 723 755 790 816 838 872 928 1023 1179 1434 1748 2019 2135 19852644.89 1 27 1745 1577 1510 1520 1608 1717 1778 1850 1996 2359 2925 3079 2635 2285 2140 2024 18842612.11 1 27 1791 1801 1927 2168 2475 2838 3610 4604 4446 3712 3234 3028 2954 3145 3713 4535 47742579.32 1 27 4069 3241 2650 2257 1948 1763 1691 1712 1800 1860 1791 1679 1608 1590 1622 1619 15302546.54 1 27 1432 1344 1247 1151 1084 1053 1041 1046 1096 1222 1458 1698 1660 1504 14272515.68 2 27 1264 1086 1034 986 1026 1083 1184 1253 1368 1435 1325 1217 1211 1238 1294 1589 20352452.04 1 27 2256 2529 2455 2095 1801 1615 1500 1434 1404 1429 1538 1538 1537 1523 1507 1496 15082419.26 1 27 1455 1504 1503 1610 1708 1853 1882 1767 1682 1670 1671 1664 1647 1610 1632 1604 15532386.48 1 27 1567 1675 1796 1904 2016 2068 2134 2270 2489 2636 2814 2815 2721 2651 2601 2609 27532353.69 1 27 3035 3542 4043 4140 4044 3988 4176 4787 6103 7895 8705 7870 6705 6172 6069 6286 70532320.91 1 26 867 1113 1342 1475 1617 1717 1548 1235 985 820 710 642 604 590 600 626 6712288.12 1 25 75 86 101 120 142 179 254 397 631 897 1007 891 690 516 391 307 2522255.34 1 26 2158 1888 1615 1334 1122 965 847 763 701 662 645 629 581 511 449 400 3572222.56 1 27 3262 3027 2961 2984 3067 3269 3640 4077 4353 4079 3577 3221 3042 2832 2643 2634 27552189.77 1 27 2727 2465 2190 1983 1827 1724 1704 1765 1810 1723 1583 1460 1367 1298 1242 1201 11922156.99 1 27 1245 1400 1701 2000 1946 1686 1447 1268 1139 1049 988 928 862 805 761 726 6952124.20 1 27 671 656 651 657 676 704 735 777 831 852 828 800 782 768 760 759 7652091.42 1 27 779 799 818 833 843 850 847 838 831 832 841 857 882 920 968 1009 10292058.64 1 27 1044 1083 1160 1251 1220 1159 1152 1155 1155 1139 1134 1140 1148 1148 1139 1138 11592025.85 1 27 1208 1294 1425 1599 1786 1927 1957 1922 1918 1988 2130 2345 2663 3210 4153 5531 65531993.07 1 26 677 660 644 644 769 873 1057 1313 1604 1907 2145 2236 2259 2277 2333 2473 27691958.36 2 26 3892 4830 4315 3032 2027 1472 1188 1017 932 1033 1376 2037 2807 2939 2695 2863 35431892.79 2 26 4087 3356 2334 1630 1092 743 552 468 441 430 430 477 574 780 1106 1413 15581827.22 2 26 1774 2356 3482 4537 4251 3056 2049 1420 1091 976 1044 1343 1924 2746 3249 2924 24791761.65 2 26 2162 1810 1564 1682 1630 1241 886 684 587 575 663 866 1313 22791709.58 1 26 3007 3764 4271 4149 3591 2948 2363 1933 1583 1308 1080 905 787 726 666 652 6441676.80 1 27 6422 6608 6965 7636 8298 8232 7479 6518 5710 5015 4461 4216 4351 4466 4688 5038 56161644.02 1 26 638 748 907 1126 1404 1715 2035 2296 2410 2358 2196 1984 1777 1609 1495 1457 15271611.23 1 26 1622 1749 1700 1476 1361 1355 1442 1650 2059 2642 2728 2425 2048 1763 1592 1509 15061578.45 1 26 1643 1994 2047 1729 1437 1233 1112 1027 962 927 927 964 1041 1163 1315 1445 14761545.66 1 26 1396 1269 1152 1068 1015 982 952 920 891 862 829 787 742 701 670 654 6551513.84 0 26 648 649 653 656 666 677 702 742 679 830 877 950 1025 1111 1206 1321 14391497.45 0 25 154 166 174 183 195 209 227 249 278 316 365 416 467 541 653 822 10701481.06 0 25 1419 1876 2439 3205 4323 5732 6725 6293 4828 3509 2650 2145 1836 1591 1383 1241 11741464.67 0 25 1174 1232 1341 1475 1585 1608 1552 1485 1463 1517 1698 2068 2736 3847 5394 6617 64581448.28 0 25 5202 3880 2907 2265 1854 1537 1247 1001 813 673 565 482 418 364 321 284 2531428.99 2 26 1707 1298 1125 1031 1031 1122 1195 1462 2141 3544 5347 6003 4603 2992 2146 2042 22831363.42 2 26 1928 1349 1034 937 819 745 734 777 782 763 776 907 1119 1063 1088 1149 1089

One other source of error must be addressed. TheDn ~n i values from the KK transform should be addedto the valuesnel ~n i; instead of being added tonel(8000 cm

21) [28]. For C6H6 nel is 1.4804 at8000 cm21, 1.4770 at 4000 cm21 and 1.4760 at0 cm21, so an error that increases with decreasingwavenumber from 0% at 8000 cm21 to , 0.3% at0 cm21 exists for C6H6 when nel(8000 cm

21) is used[28]. The correct numbers are not known for C6H5D,but then values probably also contain errors of thismagnitude. Thus, the total uncertainty in then valuesis 0.25% near 8000 cm21 increasing to, 0.5% near

800 cm21, below which the uncertainty in the610 cm21 peak causes the larger errors discussedabove.

The final n spectrum of C6H5D at 258C is shownin Fig. 3 and is tabulated in the Compact Tableformat [27] in Table 4. The finalk and n spectraare available in digital form through J.E.B.’s website http://www.ualberta.ca/~jbertie/jebhome.htm.The programs Comptab and Trecover forcreating Compact Tables and recovering spectrafrom them [27], are also available through thissite.


Table 3 (continued)

cm21 XE YE 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1297.86 2 26 1071 981 839 723 639 574 539 523 533 585 653 735 828 839 810 841 9511232.29 2 26 1119 1432 1941 2381 2158 1874 1676 1528 1517 1636 1900 2149 2486 3037 3669 3860 36141166.72 2 26 3524 3734 3988 3782 2999 2415 2012 1724 1522 1387 1334 1301 1299 13451115.62 0 26 1374 1412 1463 1536 1643 1776 1924 2094 2253 2347 2345 2283 2186 2093 2021 1960 19271099.22 0 26 1899 1892 1886 1904 1929 1983 2047 2105 2166 2258 2373 2516 2698 2923 3230 3625 41721082.83 0 25 490 592 733 939 1234 1616 1973 2098 1938 1670 1418 1216 1042 889 755 643 5511066.44 0 26 4771 4179 3714 3348 3067 2854 2693 2569 2489 2446 2435 2418 2423 2431 2459 2502 25621050.05 0 25 265 276 290 306 327 354 386 429 484 557 662 806 1008 1292 1703 2313 31911033.66 0 25 4217 4902 4824 4223 3504 2835 2266 1814 1471 1210 1016 867 756 672 607 556 5181017.26 0 26 4852 4601 4413 4297 4218 4192 4221 4305 4485 4730 4939 4931 4731 4454 4202 4004 3872999.91 1 26 3751 3708 3764 3912 4151 4431 4750 5049 5494 6143 6154 5263 4485 4096 3811 3625 3439967.12 1 26 3260 3100 2934 2806 2696 2624 2557 2505 2470 2466 2501 2555 2635 2753 2960 3336 3950934.34 1 25 495 616 803 1214 1876 1929 1320 859 622 514 441 356 292 249 222 204 195901.56 1 26 1934 1988 2135 2478 2867 2627 2304 2133 2072 2103 2163 2272 2467 2789 3155 3465 3771869.74 0 25 393 419 451 498 564 657 789 983 1268 1692 2291 2994 3508 3495 3038 2468 1983853.34 0 25 1625 1375 1196 1062 953 860 777 707 648 599 555 519 485 457 431 410 391835.99 1 26 3616 3398 3266 3217 3190 3119 3204 3378 3494 3637 3806 3909 4131 4422 4737 5192 5821803.20 1 24 66 75 89 113 147 168 183 222 309 492 879 1630 2399 2309 1654 1069 667770.42 1 25 4216 2790 1944 1427 1098 879 736 645 579 513 474 445 422 406 379 360 347737.64 1 25 348 344 352 363 378 401 427 460 500 548 619 713 859 1062 1433 2104 3312705.82 0 24 423 534 658 819 1063 1454 2058 2722 2824 2226 1574 1116 811 601 462 370 309689.42 0 25 2658 2371 2188 2119 2131 2278 2573 3094 3818 4644 5183 5137 4604 3942 3382 2953 2600672.07 1 25 1928 1470 1189 1020 909 839 803 792 808 869 989 1101 1089 1043 1020 1026 1081639.28 1 24 116 127 142 163 193 240 323 397 423 495 644 913 1424 2390613.25 0 24 3083 3889 4634 5105 5319 5565 6042 6559 6601 5869 4688 3554 2674 2041 1592 1270 1033596.86 0 25 8553 7193 6130 5285 4603 4045 3582 3194 2867 2587 2346 2137 1955 1796 1655 1530 1419577.57 2 25 1077 845 681 560 469 398 342 298 261 231 205 184 166 150 137 125 115512.01 2 26 1054 974 902 837

a The column headed cm21 contains the wavenumber of the firstn or k value in the row. The column headedXE andYE contain theX- and theY-exponent for the row, respectively. The columns headed 0,1,2,…6, contain the ordinate values, and the headings give the indices of theordinate values in the row. In a row which starts with~n0; the wavenumber corresponding to the ordinate indexedJ is ~nJ ~n02 15798:002=16384J2XE: The k values in the row are the ordinate value times 10YE. Thus the entries indexed 16 in the first rowshows that:k 213× 1027 andn 1:4795 at ~n 6200:0215798:002=16384 × 16× 22 6138:31 cm21:

b Thek values in the table can be interpolated via the 4-point spline interpolation programTrecover [27] to the original wavenumber spacing,0.482117 cm21, to give the originalk values with errors,1% below 4500 cm21, 2% between 4500 and 5000 cm21, and 5% above 5000 cm21,except for isolated spikes. Then values can be recovered viaTrecover with errors,0.1% in nearly all cases.

c Then values are based onnel8000 cm21 1:4800.

3.4. Spectra of other intensity quantities

The spectra of the molar absorption coefficient,4

Em, and the real and imaginary dielectric constants,e 0 ande 00, were calculated from the spectra ofn andkby programDequant, which is available throughJ.E.B.’s web site. The molar absorption coefficientspectrum is shown in Fig. 4.

These intensity quantities are all macroscopicproperties of the liquid. The spectrum of amicroscopic molecular property, the imaginarymolar polarizability [21,24,26],a 00m, was calculatedunder the approximation of the Lorentz local field,

again by programDequant. The a 00m spectrum isshown in Fig. 5. The molar concentration and molarvolume equaled 11.21 mol l21 and 89.21 cm3 mol21

in these calculations, calculated from the density[35] 0.8869 g cm23 at 258 and molecular weight79.121 g mol21.

For the 27 most intense bands in thek spectrum,Table 5 lists the peak wavenumber and full-width-at-half-height in thek spectrum and the peak heights inthe spectra of these different intensity quantities.

The peakwavenumbers and shapesare different in thespectra of these different intensity quantities for verystrong absorption bands. For C6H5D, the differencebetween the peak wavenumbers exceeds 0.1 cm21 foronly the three strongest bands, those at 779, 699 and606 cm21. For these three bands Table 5 shows thepeak wavenumbers in thee 00, a 00m and ~na 00m spectra inparentheses underneath the peak heights. The differ-ence in peak shape is detectable only for the strongestband, that at 606 cm21. Fig. 1 includes this band in thee 00 anda 00m spectra, with thee 00 values multiplied by 3in order to give roughly the same peak height for both.The Em band essentially coincides with thek bandwhen scaled to the same peak height, and the~na 00mband essentially coincides with thea 00m band. The(negligible) difference between thea 00m and ~na 00mpeak wavenumbers is due to the mechanical anharmo-nicity of the vibration and the differences between thek, e 00 anda 00m bands are due to the long-range dielectriceffects in the interaction of the infrared light with theliquid [21].

4. Vibrational integrated intensities

As was discussed previously [5] for C6D6, in orderto separate the contributions to the intensity from thedifferent bands, thea 00m spectrum was fitted between4800 and 500 cm21 with CDHO bands. For C6H5D,298 bands were fitted to thea 00m spectrum. Each ofthese fitted bands extended from 4800 to 500 cm21,and we call their sum the fitted spectrum. The inte-grated intensityCj of each of these bands was deter-mined analytically throughCj Sjp=2; whereSj is afitting parameter that equals the peak height of thecorresponding~na 00m band multiplied by the full-width-at-half-height [5,21,25]. In the terminology of Ref.[21], Sj is NAm

2j =12p2c2: The peak wavenumbers,


Fig. 3. Real refractive index spectrum,n ~n; of liquid C6H5D at258C. Top box, 6200–4000 cm21 andn 1:478 to 1.480; middlebox, 4000–2100 cm21 andn 1:458 to 1.495; bottom box, 2400–500 cm21 andn 1:10 to 2.00. The top spectrum in the bottom boxwas offset by multiplying the original spectrum (bottom) by 5 andsubtracting 5.6.

4 The symbolEm is used instead of the recommended [34]e forthe molar absorption coefficient, in order to avoid confusion withthe dielectric constants.


Table 4Real refractive indices,n, between 6200 and 500 cm21 of liquid benzene-d1 at 258C

a,b,c

cm21 XE 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

6200.02 2 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 147956130.60 3 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14794 14794 14794 14794 14794 147945999.46 3 14794 14794 14794 14795 14795 14795 14796 14796 14796 14796 14796 14796 14796 14796 14796 14796 147965874.11 1 14796 14796 14796 14796 14796 14796 14796 14796 14796 14796 14796 14796 14796 14796 14796 14796 147965842.29 0 14796 14796 14796 14796 14796 14796 14796 14796 14796 14796 14796 14796 14796 14796 14796 14796 147965825.90 0 14796 14796 14796 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 147955809.51 0 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 147955793.11 0 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 147955776.72 0 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 147955760.33 0 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 147955743.94 0 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 147955727.55 0 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 147955711.15 0 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 147955691.87 2 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 147955626.30 2 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 14795 147955560.73 2 14795 14794 14794 14794 14794 14794 14794 14794 14794 14794 14794 14794 14794 14794 14794 14794 147945495.17 2 14794 14794 14794 14794 14794 14794 14794 14794 14794 14794 14794 14794 14794 14794 14794 14794 147945425.74 3 14794 14794 14794 14794 14794 14794 14794 14794 14794 14794 14794 14794 14794 14794 14794 14794 147945294.60 3 14794 14794 14794 14794 14794 14794 14794 14794 14794 14794 14794 14794 14794 14794 14793 14793 147935163.47 3 14793 14793 14793 14793 14793 14793 14793 14793 14793 14793 14793 14793 14793 14793 14793 14793 147935032.33 3 14793 14793 14793 14793 14793 14793 14793 14793 14793 14792 14792 14792 14792 14792 14792 14792 147924901.20 3 14792 14792 14792 14792 14792 14792 14792 14792 14792 14792 14792 14792 14792 14792 14791 14791 147914770.06 3 14791 14791 14791 14791 14791 14791 14791 14790 14790 14790 14790 14789 14789 14789 14789 14790 147924642.78 2 14792 14792 14792 14792 14792 14792 14792 14792 14792 14792 14792 14792 14792 14792 14791 14791 147924577.21 2 14792 14792 14792 14792 14793 14793 14792 14792 14792 14792 14792 14792 14792 14792 14791 14791 147914511.65 2 14791 14791 14791 14791 14791 14791 14791 14792 14792 14792 14792 14792 14792 14791 14791 14791 147914446.08 2 14791 14791 14791 14791 14791 14791 14791 14791 14791 14791 14791 14791 14791 14791 14791 14791 147914380.51 2 14790 14790 14790 14790 14790 14790 14790 14790 14790 14790 14790 14790 14790 14790 14790 14790 147904314.94 2 14790 14790 14790 14790 14790 14789 14789 14789 14789 14789 14789 14789 14789 14789 14789 14789 147894249.38 2 14789 14789 14789 14789 14789 14789 14788 14788 14788 14788 14788 14788 14788 14788 14788 14788 147884183.81 2 14788 14788 14788 14788 14788 14788 14788 14787 14787 14787 14787 14787 14787 14786 14786 14787 147864118.24 2 14786 14786 14786 14785 14785 14785 14784 14784 14783 14783 14782 14782 14782 14782 14783 14785 147884052.67 2 14791 14792 14793 14795 14795 14795 14795 14795 14794 14794 14793 14792 14792 14793 14793 14792 147923987.10 2 14792 14792 14791 14791 14791 14791 14791 14790 14790 14790 14790 14790 14789 14789 14789 14789 147893921.54 2 14789 14789 14789 14789 14789 14789 14789 14789 14789 14789 14789 14789 14789 14789 14789 14789 147883855.97 2 14789 14789 14789 14789 14789 14789 14789 14789 14788 14788 14788 14788 14788 14788 14788 14787 147873792.33 1 14787 14787 14787 14787 14787 14787 14787 14787 14787 14787 14787 14787 14787 14787 14787 14787 147863759.54 1 14786 14786 14786 14786 14786 14786 14786 14786 14786 14786 14786 14786 14786 14786 14786 14786 147863726.76 1 14785 14785 14785 14785 14785 14785 14785 14785 14785 14784 14784 14784 14784 14784 14784 14783 147833693.98 1 14783 14783 14783 14783 14783 14784 14785 14786 14787 14787 14787 14786 14786 14786 14786 14786 147873661.19 1 14787 14787 14787 14787 14786 14786 14786 14786 14786 14786 14786 14786 14786 14785 14785 14785 147853628.41 1 14785 14785 14785 14786 14786 14786 14786 14786 14786 14786 14786 14786 14785 14785 14786 14786 147863595.62 1 14786 14786 14786 14786 14786 14786 14786 14786 14785 14785 14785 14785 14785 14785 14785 14785 147853562.84 1 14784 14784 14784 14784 14784 14784 14784 14784 14784 14784 14784 14784 14784 14783 14783 14783 147833530.06 1 14783 14783 14783 14783 14783 14783 14783 14783 14783 14783 14782 14782 14782 14782 14782 14782 147823497.27 1 14782 14782 14782 14782 14782 14781 14781 14781 14781 14781 14781 14781 14781 14781 14781 14781 147813462.56 2 14781 14780 14780 14780 14780 14780 14780 14780 14780 14780 14780 14779 14779 14779 14779 14779 147793396.99 2 14778 14778 14778 14778 14778 14777 14777 14777 14777 14776 14776 14776 14776 14775 14775 14775 147753333.35 1 14774 14774 14774 14774 14774 14774 14773 14773 14773 14773 14773 14773 14773 14772 14772 14772 147723300.57 1 14772 14771 14771 14771 14771 14770 14770 14770 14769 14769 14769 14769 14769 14770 14771 14771 147713267.79 1 14770 14770 14770 14769 14769 14768 14768 14768 14768 14768 14768 14768 14768 14768 14767 14767 147673235.00 1 14766 14766 14766 14765 14765 14764 14764 14764 14763 14763 14762 14762 14762 14761 14761 14761 14760


Table 4 (continued)

cm21 XE 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

3202.22 1 14759 14759 14758 14758 14757 14757 14756 14756 14755 14755 14755 14754 14754 14753 14752 14751 147513169.43 1 14750 14750 14750 14750 14749 14748 14747 14746 14745 14744 14743 14742 14741 14740 14739 14738 147363136.65 1 14735 14733 14732 14730 14728 14727 14725 14723 14720 14718 14715 14712 14709 14705 14701 14697 146923103.87 1 14687 14680 14673 14665 14654 14642 14630 14619 14612 14614 14615 14622 14670 14646 14789 14796 147863071.08 1 14775 14766 14767 14782 14803 14823 14833 14833 14831 14826 14821 14819 14814 14804 14794 14786 147833038.30 1 14780 14779 14786 14805 14815 14818 14825 14833 14850 14860 14856 14853 14880 14911 14919 14915 149083003.59 2 14895 14888 14882 14874 14867 14861 14856 14851 14847 14844 14841 14838 14835 14833 14830 14828 148262939.95 1 14825 14824 14823 14822 14821 14820 14820 14819 14820 14820 14820 14819 14818 14817 14817 14816 148162907.16 1 14816 14815 14815 14814 14813 14813 14813 14813 14813 14812 14811 14810 14809 14809 14812 14814 148142874.38 1 14813 14813 14813 14813 14813 14813 14814 14814 14813 14813 14812 14812 14811 14810 14810 14810 148092841.59 1 14809 14808 14808 14808 14807 14807 14807 14806 14806 14806 14805 14805 14805 14805 14804 14804 148042808.81 1 14804 14804 14803 14803 14803 14803 14803 14802 14802 14802 14802 14802 14802 14802 14802 14801 148012776.03 1 14801 14801 14801 14800 14800 14800 14800 14800 14800 14800 14800 14799 14799 14799 14799 14799 147992743.24 1 14799 14798 14798 14798 14798 14798 14798 14798 14797 14797 14797 14797 14797 14797 14797 14796 147962710.46 1 14796 14796 14796 14796 14795 14795 14795 14795 14795 14795 14795 14794 14794 14794 14794 14794 147942677.67 1 14794 14793 14793 14793 14793 14793 14793 14793 14792 14792 14792 14792 14792 14791 14792 14792 147922644.89 1 14792 14792 14792 14791 14791 14791 14791 14791 14791 14790 14790 14791 14791 14791 14791 14791 147912612.11 1 14790 14790 14790 14789 14789 14789 14789 14789 14791 14791 14791 14791 14790 14790 14790 14790 147912579.32 1 14792 14792 14792 14792 14791 14791 14791 14790 14790 14790 14790 14790 14790 14790 14790 14790 147902546.54 1 14789 14789 14789 14789 14789 14789 14788 14788 14788 14788 14788 14788 14788 14788 14882515.68 2 14788 14787 14787 14787 14786 14786 14786 14786 14785 14785 14785 14785 14785 14784 14784 14783 147832452.04 1 14783 14784 14784 14784 14784 14784 14784 14783 14783 14783 14783 14783 14783 14782 14782 14782 147822419.26 1 14782 14782 14781 14781 14781 14781 14781 14781 14781 14781 14780 14780 14780 14780 14780 14779 147792386.48 1 14779 14779 14778 14778 14778 14778 14777 14777 14777 14777 14777 14777 14776 14776 14776 14775 147752353.48 1 14774 14774 14774 14774 14774 14773 14772 14771 14771 14771 14772 14774 14773 14773 14771 14770 147692320.91 1 14768 14767 14768 14769 14771 14774 14777 14778 14778 14776 14775 14773 14772 14770 14768 14766 147642288.12 1 14761 14759 14756 14753 14749 14743 14735 14728 14727 14744 14777 14807 14822 14825 14823 14820 148172255.34 1 14814 14812 14811 14809 14807 14805 14803 14802 14800 14799 14798 14797 14797 14796 14795 14795 147942222.56 1 14793 14792 14791 14790 14790 14789 14789 14788 14789 14789 14789 14788 14788 14788 14787 14787 147872189.77 1 14787 14786 14786 14786 14786 14785 14785 14784 14784 14784 14784 14784 14783 14783 14783 14782 147822156.99 1 14782 14781 14781 14781 14781 14781 14781 14781 14781 14780 14780 14780 14780 14779 14779 14779 147792124.20 1 14778 14778 14778 14778 14777 14777 14777 14777 14777 14776 14776 14776 14776 14776 14775 14775 147752091.42 1 14775 14774 14774 14774 14774 14774 14773 14773 14773 14773 14772 14772 14772 14771 14771 14771 147712058.64 1 14770 14770 14770 14770 14770 14769 14769 14769 14768 14768 14768 14767 14767 14767 14766 14766 147652025.85 1 14765 14764 14764 14763 14763 14763 14762 14762 14761 14760 14760 14759 14758 14757 14756 14755 147551993.07 1 14755 14755 14754 14752 14751 14749 14748 14747 14746 14747 14748 14750 14751 14751 14751 14749 147481958.36 2 14749 14762 14779 14786 14784 14780 14775 14772 14767 14762 14757 14755 14758 14764 14766 14764 147651892.79 2 14776 14788 14790 14789 14786 14782 14778 14775 14772 14769 14766 14763 14760 14757 14755 14754 147541827.22 2 14751 14748 14748 14760 14776 14784 14783 14779 14774 14769 14764 14759 14756 14757 14765 14773 147751761.65 2 14776 14775 14773 14771 14774 14774 14772 14769 14765 14761 14757 14753 14747 147441709.58 1 14745 14749 14758 14769 14776 14779 14780 14779 14778 14776 14775 14773 14771 14769 14767 14766 147641676.80 1 14763 14762 14761 14760 14760 14760 14760 14760 14759 14757 14756 14754 14753 14752 14750 14748 147471644.02 1 14745 14743 14742 14740 14739 14739 14740 14742 14746 14749 14751 14752 14752 14751 14750 14748 147461611.23 1 14746 14746 14748 14747 14745 14743 14740 14738 14736 14739 14745 14749 14750 14749 14747 14745 147431578.45 1 14740 14741 14745 14746 14746 14744 14742 14740 14738 14736 14734 14732 14730 14729 14728 14728 147281545.66 1 14729 14728 14727 14725 14723 14721 14719 14717 14715 14713 14711 14709 14706 14703 14699 14696 146921513.84 0 14690 14688 14686 14683 14681 14678 14675 14672 14670 14666 14663 14660 14656 14653 14649 14645 146411497.45 0 14637 14632 14628 14622 14616 14609 14602 14593 14584 14573 14562 14551 14537 14519 14498 14474 144471481.06 0 14422 14399 14380 14365 14370 14444 14624 14841 14957 14972 14947 14915 14889 14868 14845 14820 147961464.67 0 14773 14753 14738 14730 14729 14733 14731 14719 14697 14668 14631 14590 14548 14527 14575 14742 149611448.28 0 15099 15141 15134 15110 15088 15072 15056 15038 15020 15003 14987 14973 14960 14949 14939 14930 149211428.99 2 14893 14872 14856 14842 14831 14821 14811 14801 14791 14784 14789 14810 14826 14825 14817 14809 148081363.42 2 14810 14808 14803 14798 14795 14792 14788 14785 14783 14781 14778 14775 14775 14774 14773 14772 14772

~n j ; full-widths-at-half-height,G j, andCj of these fittedbands are listed in Table 6, together with the wave-numbers of features in the experimentala 00m spectrumand 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 theexperimentala 00m spectrum, and in Fig. 6 whichshows more detail in two regions, one of whichincludes the region of greatest misfit above800 cm21, near 1056 cm21. Each curve in Fig. 5 andthe upper curve in each box of Fig. 6 consist of both

the experimentala 00m spectrum and the fitted spectrum,which essentially overlap even in the expanded viewsin Fig. 5. The lower curves in Fig. 6 show the indi-vidual bands required for the fit, truncated for clarityto extend only three full-widths-at-half-height fromthe band center.

The quality of the fit can be described in severalways. Of first importance is that the presence of nearlyall of the 298 bands is obvious in the experimentala 00mspectrum, either as peaks, shoulders, changes in slope,or asymmetric tails, as is illustrated in Fig. 6. Second,


Table 4 (continued)

cm21 XE 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1297.86 2 14771 14771 14769 14768 14765 14763 14761 14759 14756 14754 14752 14750 14748 14747 14745 14742 147391232.29 2 14736 14733 14732 14736 14740 14939 14738 14735 14731 14728 14724 14722 14719 14718 14720 14726 147291166.72 2 14729 14728 14732 14739 14741 14739 14735 14731 14727 14722 14718 14713 14708 147031115.62 0 14701 14700 14698 14696 14695 14693 14692 14692 14692 14692 14693 14693 14693 14692 14690 14689 146871099.22 0 14685 14683 14681 14678 14676 14673 14670 14667 14664 14661 14657 14653 14648 14643 14637 14630 146231082.83 0 14615 14606 14596 14588 14584 14594 14628 14679 14724 14749 14760 14765 14767 14766 14763 14758 147521066.44 0 14746 14740 14734 14728 14722 14716 14710 14705 14700 14695 14690 14685 14680 14676 14670 14665 146591050.05 0 14654 14647 14641 14634 14626 14617 14608 14597 14584 14570 14554 14535 14514 14492 14469 14451 144531033.66 0 14507 14624 14756 14850 14902 14923 14927 14919 14906 14891 14877 14863 14850 14838 14827 14818 148091017.26 0 14801 14794 14787 14781 14776 14770 14765 14761 14757 14755 14755 14756 14756 14755 14753 14750 14747999.91 1 14741 14736 14730 14725 14722 14718 14716 14715 14714 14718 14728 14733 14731 14727 14724 14721 14718967.12 1 14715 14712 14708 14705 14701 14697 14693 14689 14684 14680 14675 14670 14664 14657 14650 14641 14631934.34 1 14621 14612 14598 14587 14621 14715 14758 14753 14738 14725 14718 14711 14702 14693 14684 14676 14669901.56 1 14662 14654 14647 14641 14640 14639 14634 14627 14620 14612 14604 14596 14587 14578 14569 14559 14548869.74 0 14541 14532 14523 14512 14499 14485 14469 14451 14433 14419 14419 14452 14529 14623 14692 14724 14730853.34 0 14724 14715 14704 14695 14687 14679 14672 14664 14657 14650 14643 14636 14629 14623 14616 14610 14603835.99 1 14591 14578 14566 14553 14541 14528 14515 14501 14488 14474 14459 14442 14423 14404 14382 14357 14329803.20 1 14300 14265 14221 14173 14130 14089 14015 13898 13739 13530 13299 13293 14035 15140 15713 15813 15718770.42 1 15565 15420 15298 15200 15119 15052 14996 14948 14908 14872 14839 14809 14782 14757 14732 14707 14682737.64 1 14658 14633 14608 14583 14557 14528 14499 14468 14433 14394 14349 14297 14234 14157 14058 13936 13788705.82 0 13712 13642 13568 13471 13359 13278 13376 13969 15022 15777 15966 15917 15802 15669 15537 15418 15315689.42 0 15225 15144 15070 15001 14936 14873 14814 14766 14744 14766 14841 14932 14997 15052 15020 15008 14996672.07 1 14958 14905 14905 14852 14801 14755 14712 14669 14627 14543 14503 14476 14646 14407 14360 14307 14249639.28 1 14185 14115 14037 13946 13841 13720 13596 13509 13357 13118 12805 12408 11915 11494613.25 0 11427 11601 12096 12786 13390 13821 14345 15319 16750 18108 18876 19058 18918 18655 18368 18095 17850596.86 0 17632 17441 17273 17125 16994 16877 16772 16678 16593 16516 16446 16382 16323 16268 16218 16171 16128577.57 2 15982 15867 15775 15700 15637 15583 15537 15497 15462 15430 15402 15377 15355 15334 15315 15298 15282512.01 2 15267 15253 15240 15228

a The column headed cm21 contains the wavenumber of the firstn or k value in the row. The column headedXE andYE contain theX- and theY-exponent for the row, respectively. The columns headed 0,1,2,…16, contain the ordinate values, and the headings give the indices of theordinate values in the row. In a row which starts with~n0; the wavenumber corresponding to the ordinate indexedJ is ~nJ ~n02 15798:002=16384J2XE: Then values are given directly with the decimal point implicitly after the first digit. Thus the entries indexed16 in the first row of the tables show that:k 213× 1027 andn 1:4795 at ~n 6200:0215798:002=16384 × 16× 22 6138:31 cm21:

b Thek values in the table can be interpolated via the 4-point spline interpolation programTrecover [27] to the original wavenumber spacing,0.482117 cm21, to give the originalk values with errors,1% below 4500 cm21, 2% between 4500 and 5000 cm21, and 5% above 5000 cm21,except for isolated spikes. Then values can be recovered via TRECOVER with errors,0.1% in nearly all cases.

c Then values are based onnel8000 cm21 1:4800.

the overall average percent difference between thefitted and experimentala 00m values is 1.6%. Theaverage percent difference is also 1.6% fora 00m valuessmaller than 0.1 cm3 mol21, and is near 1.25% forstronger absorption. Third, the largest absolute differ-ences between fitted and experimentala 00m values are0.04 cm3 mol21 near 607 cm21, the peak of thestrongest band wherea 00mmax < 6:7 cm3 mol21;and , 0.01 cm3 mol21 near 680, 715 and 785 cm21

in the wings of the second and third strongest bands.Above 800 cm21, the largest absolute difference is2:5 × 1023 cm3 mol21 at 1056 cm21, and the differenceexceeds 3× 1024 cm3 mol21 only in three otherplaces, near 1415, 1510 and 2010 cm21. At these latterfour places, the difference is 0.4%, 0.06%, 2% and1.3%, where % means percentage of the heights of

the neighboring peaks. Fourth, and for our purposean important overall check on the quality of the fit,is the comparison of the areas under the experimentaland fitted spectra over a wide wavenumber range. Thetotal area under the fitted spectrum is 0.16% greaterbetween 4800 and 500 cm21, being only 0.02%greater between 4800 and 825 cm21 but 0.22% greaterbelow 825 cm21.

The accuracy of the integrated intensitiesCj inTable 6 cannot be stated with great reliability. Theabove evidence argues that the fit contributes anerror of less than 0.25% to the integrated intensities.A first estimate is, then, that the error in theCj is0.25%, plus the percent error in thea 00m values whichis about the same as that in thek values. This gives# 2% as the estimated error in theCj above 825 cm

21,


Fig. 4. Molar (decadic) absorption coefficient spectrum,Em ~n; i.e.Beer–Lambert absorption coefficient spectrum, of liquid C6H5D at258C. Top box 6200–4000 cm21; middle box 4000–2100 cm21;bottom box, 2400–500 cm21. In the top, middle and bottom boxesthe ordinate scale labels must be divided by 10, 20 and 15, respec-tively, for the upper spectrum. The unit is l mol21 cm21, i.e.10 dm2 mol21.

Fig. 5. Imaginary molar polarizability spectrum,a 00m ~n; of liquidC6H5D at 258C and the fitted spectrum, i.e. the sum of the CDHObands fitted to it. The experimental and fitted spectra essentiallyoverlap throughout. Top box, 6200–4000 cm21; middle box,4000–2100 cm21; bottom box, 2400–500 cm21. Divide the ordi-nate scale labels in the top, middle and bottom boxes by 10, 20and 60, respectively, for the upper curve in the box. The unit ofa 00m is cm3 mol21.

,4% between 825 and 620 cm21, and,50% for thestrong bands below 620 cm21.

The problem with this estimate is that, while theoverall area is well described by the fitted bands, thefit is unlikely to be unique. TheCj of a fitted band is itsintensity integrated from zero to infinity, and is verysensitive to the width of the fitted band. The error dueto this source is difficult to estimate usefully. We haveattempted to do so in our earlier work [5] and havecontinued since then by having several people fit thesame spectrum independently. These studies showedwhat is perhaps intuitively correct, namely that thesensitivity to the fitted bandwidth causes the greatestproblem when a fairly broad region of weak absorp-tion, or the tail of a stronger band, has severalapparent band maxima or shoulders and is fitted by

several bands. The potential errors can be largelyoffset by adding together individualCj values into a“sum ofCj” for the observed region or band (Table 6).

It is particularly important to be aware of thisproblem for C6H5D, because many of the fittedbands have full-widths-at-half-heights of 25 cm21 ormore, much larger than the norm. These are particu-larly frequent where the absorption is very weakabove 3500 cm21, but they occur as low as1100 cm21. They are believed to indicate regionswhere the bands required to fit the spectrum do notreflect the transitions that contribute to the absorption,either because numerous transitions overlap orbecause the transitions do not yield CDHO bands.Two regions may be described as examples. Between4275 and 4100 cm21, three broad bands at 4248, 4214


Table 5Peak wavenumber and heights of major bands of C6H5D in spectra of different intensity quantities

a,b

~n of kmax (cm21) FWHH (cm21) kmax (Em)max (l mol

21 cm21)b e 00max (a 00m)max (cm3 mol21) ~na 00mmax (cm2 mol21)

3079.8 28.0 0.02579 38.67 0.0759 0.2797 8613064.3 41.5 0.01702 25.40 0.0504 0.1834 5623032.8 82.3 0.01412 20.85 0.0418 0.1521 4613023.8 82.0 0.01440 21.20 0.0428 0.1546 4683015.3 81.6 0.01468 21.55 0.0437 0.1572 4742269.0 10.8 0.01007 11.13 0.0298 0.1087 2471953.9 19.9 0.00485 4.62 0.0143 0.0524 1021892.9 32.3 0.00409 3.77 0.0121 0.0441 83.51814.5 18.4 0.00462 4.08 0.0136 0.0499 90.51772.9 27.0 0.00326 2.81 0.0096 0.0352 62.31705.1 14.8 0.00430 3.57 0.0127 0.0464 79.21475.1 5.7 0.06766 48.58 0.1988 0.7358 10851460.1 42.6 0.01613 11.46 0.0475 0.1746 2551449.8 5.7 0.06744 47.60 0.2002 0.7249 10511387.4 16.5 0.00606 4.10 0.0180 0.0653 90.61175.3 50.5 0.00388 2.22 0.0114 0.0420 49.31158.3 48.9 0.00400 2.26 0.0118 0.0433 50.11076.2 8.2 0.02100 11.00 0.0616 0.2283 2461032.3 7.1 0.04960 24.93 0.1457 0.5391 5571007.2 99.9 0.00496 2.43 0.0146 0.0536 54.0981.6 81.3 0.00625 2.99 0.0184 0.0677 66.5925.6 7.6 0.02046 9.22 0.0601 0.2225 206857.7 7.1 0.03572 14.91 0.1041 0.3911 336779.3 8.0 0.2480 94.08 0.7245 (779.0) 2.7510 (779.7) 2145 (779.7)698.5 5.1 0.2883 98.03 0.8507 (698.2) 3.1750 (698.7) 2219 (698.7)679.4 9.5 0.05236 17.32 0.1559 0.5607 381606.0 10.5 0.6673 196.80 2.2210 (605.3) 6.7140 (607.0) 4076 (607.0)

a The wavenumbers of the peaks in the different spectra are within 0.1 cm21 of those ofkmax, except where they are shown in parenthesis afterthe peak height.

b 1 l mol21 cm21 10 dm2 mol21.


Table 6Observed and fitted bands, assignment, and integrated intensities of liquid C6H5D

Assignmenta Observed~n j (cm21) Fitted band Sum ofCj

b

a 00mc,d Ramane ~n jf G j

f Cjg

4792 sh I4760 sh 4764.9 42.2 0.000254736 sh I

n5 1 n21 (B2) 4668 sh 4666.7 23.7 0.00302n1 1 n5; n21 1 n23 (A1) 4653.4 vw 4653.4 17.5 0.00374 0.0092n1 1 n23 (B2) 4640 sh 4638.5 25.2 0.00244

9=;n5 1 n22 (B2) 4620.4 vw

4619.5 5.4 0.00004�

4618.6 28.3 0.00297 0.00370n22 1 n23 (A1) 4600.4 vw 4599.7 13.0 0.00069

9=;4583.7 vw 4583.5 11.2 0.00156

4567.1 5.7 0.000104566.3 vw 4566.0 17.9 0.00183 0.00204

8>=>>;4465 br sh 4463.4 24.2 0.00036

2n4 (A1) 4450.2 vvw4451.0 9.8 0.00010

�4446.5 11.1 0.00011

�0.00021

4433.2 vvw 4434.2 10.0 0.00006,4428 tail

�4429.4 24.3 0.00048

�0.00054

4410.3 13.0 0.000064402.1 vvw 4404.5 10.7 0.00009 0.00091

n21 1 n25 (A1) 4395 sh

8>>>=>>>>;4312 sh 4310.6 23.0 0.000084286 sh 4287.6 31.5 0.00018

n7 1 n21 (B2) 4252.4 vvw4254.0 13.6 0.00030

�4248.3 33.4 0.00065

�0.00095

n1 1 n7; n21 1 n27 (A1) 4238 vvw 4237.0 18.0 0.00020n3 1 n27 (B2) 4209.7 vvw

4214.8 43.8 0.00119n7 1 n22 (B2)

�4210.7 14.9 0.00023

�0.00142

n22 1 n27 (A1)4194 sh 4191.4 20.9 0.000674188.6 vw

�4185.9 8.8 0.00007

�0.00074

4171.6 vw 4172.4 11.0 0.00039,4166 tail

�4167.4 13.0 0.00013

�0.00052

n21 1 n28 (A1) 4160.2 21.7 0.00043n1 1 n28 (B2) 4147.9 vw 4148.8 12.1 0.00022

n3 1 n28 (B2) 4127.5 vw4129.1 12.8 0.00030

�4127.0 36.0 0.00173

�0.00203

n22 1 n28 (A1) 4112 sh In8 1 n22; n10 1 n21 (B2) 4061 sh 4061.8 33.9 0.0205n3 1 n9 (A1) 4061.4 6.4 0.0005 0.0239n1 1 n15 (B1) 4056.9 w

8


Table 6 (continued)


b


f Cjg

n1 1 n10 (A1), n3 1 n15 (B1) 4046.2 w 4044.9 9.5 0.00208n9 1 n22 (B2) 4039.4 8.3 0.00059 0.0102n3 1 n10 (A1)

8


Table 6 (continued)


b


f Cjg

n4 1 n28 (B2) 3344 vvw br I3319.8 4.2 0.00004

3317.5 vvw

�3316.5 5.8 0.00008

�0.00012

3293 sh I

n4 1 n9 (A1) 3275.7 vw3275.8 10.3 0.00159

0.00221

�3272.9 26.6 0.00062

�n4 1 n10 (A1) 3249.5 vw

3250.0 11.9 0.000660.00124

�3248.1 15.8 0.00058

�3224.3 vw I3208.8 vw 3209.7 3.6 0.00003

2n5 (A1) 3182 vw 3184 p3186.0 9.4 0.00036

0.00065�

3181.5 10.3 0.00029

�n5 1 n23 (B2) 3166.2 vw 3167 p

3167.6 11.0 0.000870.00164

�3164.4 18.3 0.00077

�2n23 (A1) ,3150 vw sh I

,3142 vw sh 3144 p 3145.7 18.6 0.00101n4 1 n29 (B2) ,3126 vw sh 3127.9 9.7 0.00038

3088 sh 3087.0 8.3 0.0193n21 (B2) 3079.8 m 3080.5 7.5 0.0447 0.124

8>=>>;3015.3 m 3014.9 8.3 0.03983005 sh 3004.5 25.2 0.0305

3000 pn4 1 n18 (B1) ,2970 tail 2971.4 31.5 0.002642n6 (A1) 2947 p

2936 sh 2935 p 2937.8 10.5 0.00037

n6 1 n24 (B2) 2924.5 vw ,2923 p2924.9 6.3 0.00027

0.00217�

2924.1 13.2 0.00190

�n5 1 n25 (B2) 2909.7 vw br 2907 p

2911.1 13.7 0.001090.00170

�2906.5 11.2 0.00061

�2n24; n23 1 n25 (A1) 2895.8 vw 2896 p 2895.6 9.5 0.00143n23 1 n26 (A1), n4 1 n19 (B1) 2880.3 vw 2882 p 2880.5 6.6 0.00215

2875.1 18.6 0.00259 0.0070n4 1 n11 (A1), n4 1 n30 (B2) 2871 vw 2870.9 4.4 0.00012

2866 vw 2865.2 11.4 0.00216

9>>>>=>>>>;2818 sh I

2810.6 26.3 0.00055

2807.1 vw2808.9 2.3 0.000012807.1 3.0 0.00002

0.00068

8>>>:2804.8 4.3 0.00002

2800 sh2801.1 6.5 0.00004

�2797.9 7.0 0.00004

9>>>>>>=>>>>>>;n6 1 n25 (B2) 2788.2 vw

2793.8 12.4 0.00004�

2788.7 8.2 0.000212783 sh 2783.7 11.4 0.00022

0.00058

n6 1 n26 (B2) ,2776 tail 2775.8 12.9 0.00011

9>>=>>;


Table 6 (continued)


b


f Cjg

n5 1 n7; n24 1 n25 (A1) 2766.0 vw 2766 p 2765.6 12.7 0.00033n5 1 n27; n7 1 n23 (B2) 2751 sh 2752.3 15.6 0.00017n24 1 n26 (A1) 2748 pn23 1 n27 (A1) 2741.9 vvw 2741 p 2740.9 18.8 0.00022

2690 sh 2689.7 16.9 0.00008n5 1 n28 (B2) 2667 sh 2669.6 17.9 0.00011n6 1 n7; n23 1 n28 (A1), n4 1 n20 (B1) 2648.9 vw 2649.2 11.6 0.000732n25 (A1), n6 1 n27 (B2) 2635 sh 2635.0 10.9 0.00020n5 1 n8 (A1), n7 1 n24 (B2) 2624.3 vw 2628 p 2624.4 6.8 0.00043n25 1 n26 (A1) 2616 sh 2620.2 27.8 0.00131

2n26; n5 1 n9 (A1) 2597.9 vw 2591 p2598.1 5.6 0.00013

0.00135�

2597.8 10.1 0.00122

�n5 1 n15 (B1), n9 1 n23 (B2) 2581.8 vw

2581.6 7.6 0.000780.00244

�2581.6 23.0 0.00166

�2562.0 vw 2562.9 7.0 0.00012

n10 1 n23 (B2) 2558 tail 2559.4 9.4 0.00016 0.00081n6 1 n28 (B2) 2551.4 vw 2551.4 10.6 0.00022v12 1 n23 (B1) 2545 sh 2545.4 17.1 0.00031

9>>=>>;n24 1 n28 (A1) 2524.6 vw 2525 p 2525.1 6.3 0.00015 0.00076n5 1 n16 (B1) 2518 sh 2519.8 20.4 0.00061

�n6 1 n8 (A1) 2509 sh I

2498 sh In7 1 n25 (B2) 2492 sh 2493.4 27.0 0.00046 0.00089n6 1 n9 (A1), n8 1 n24 (B2) 2481.9 vw 2481.2 16.6 0.00043

�n6 1 n15 (B1) 2466 sh 2466.8 16.7 0.00024n6 1 n10; n26 1 n27 (A1), n9 1 n24 (B2) 2455 sh 2452 p 2455.4 9.5 0.00022 0.00120n5 1 n29 (B2) 2449.4 vw 2449.3 9.3 0.00058

,2440 tail 2441.8 12.6 0.00016

9>>=>>;n23 1 n29 A1; n10 1 n24 B2 2430.9 vw br 2431.0 13.6 0.00032n12 1 n24; n13 1 n23 (B1) ,2422 tail 2421.5 15.8 0.00030

2408.3 vw2410.9 12.7 0.00024

0.00144

�2407.7 9.2 0.00018

n6 1 n16 (B1) 2400 sh 2399.9 11.7 0.00022n25 1 n28 (A1) 2392 sh 2392.6 11.8 0.00018

9>>>>>>=>>>>>>;2380 sh 2379.6 15.0 0.00039

n26 1 n28 (A1) 2370 p 2367.1 15.0 0.00085n5 1 n17 (B1) 2366 vw br

�2359.1 13.3 0.00018

�0.00103

2n7 A1; n8 1 n25 B1 2348.3 vw 2349.4 9.2 0.00066 0.00076�

2345.4 6.5 0.00010

�n6 1 n29; n7 1 n27; n8 1 n26 B2 2334.5 vw 2334.7 9.1 0.00218 0.0023

2328.1 6.0 0.00009

�2n27 (A1) 2317 sh 2317.5 6.4 0.00066

n24 1 n29 (A1) 2311.4 w 2311.5 p2312.4 15.8 0.00682

0.00787

�2310.6 6.7 0.00105

�n4 (A1) 2269.0 m 2270 p

2270.2 7.1 0.0150�

2267.0 9.2 0.0186 0.0432n6 1 n17 B1; n7 1 n28 B2 2253 sh 2257.7 21.3 0.00956

9=;n27 1 n28 (A1) 2233 sh 2233.5 13.8 0.00113

n7 1 n8 (A1) 2207.1 vw2207.3 12.9 0.00106

0.00117

�2206.4 6.7 0.00011

�n5 1 n11 (A1) 2200 sh 2198 p 2199.0 6.6 0.00011


Table 6 (continued)


b


f Cjg

n5 1 n30; n8 1 n27(B2) 2190.9 vw 2190.1 12.4 0.00059n25 1 n29; n23 1 n30 (A1) 2174.6 vw 2173.5 p 2173.8 12.1 0.00030n7 1 n15; n13 1 n25 B1; n9 1 n27 B2 2165 sh 2164.9 8.4 0.000042n28 A1; n13 1 n26 B1 2150.5 vw 2150.3 8.7 0.00038n10 1 n27 (B2) ,2138 tail 2141.9 11.2 0.00009n8 1 n28 (B2) 2107 vvw br

2107.6 4.9 0.000030.00005

n7 1 n16 (B1)

�2102.1 7.7 0.00002

�n6 1 n11 A1; n6 1 n19 B1 2081 vvw br 2086.9 9.1 0.00003 0.00005n6 1 n30; n9 1 n28 (B2)

�2079.9 6.8 0.00002

�2n8 A1; n10 1 n28 (B2) 2061 sh 2062.2 7.6 0.00004n24 1 n30 A1; n11 1 V24 B2 2052.3 vw 2052.6 6.3 0.00007n12 1 n28 (B1) 2043.5 vw 2044.9 2.7 0.00001n7 1 n29 (B2) 2034.2 vw I2n9; n8 1 n10; n27 1 n29 (A1) 2014.7 vw 2016.4 1.2 0.00001

n9 1 n15 (B1) 1993.3 vw br1995.8 3.9 0.00026

0.00066�

1992.4 5.8 0.00040

�2n15 A1; n5 1 n20; n14 1 n23; (B1) 1972 sh 1974.3 12.8 0.00499 0.00623n10 1 n15 (B1)

�1968.8 9.3 0.00124

�n12 1 n15 B2; n7 1 n17; n8 1 n16 (B1) 1953.9 mw 1953.7 17.0 0.0258n28 1 n29 A1; n9 1 n16 (B1) 1935 sh In15 1 n16 (A1) 1909.6 mw

1912.3 11.2 0.004830.00938

n10 1 n16 (B1)

�1907.4 13.3 0.00455

�n8 1 n29 (B2) 1892.9 mw 1892.6 16.4 0.0191n10 1 n29; n13 1 n15 (B2) 1834 sh

1835.7 10.3 0.002060.00373

n12 1 n29 (B1)

�1828.0 11.8 0.00167

�1817.4 12.2 0.0091

n12 1 n13 A1; n8 1 n17 B1 1814.5 mw 1812.8 9.9 0.0064 0.01918


Table 6 (continued)


b


f Cjg

n29 1 n30 A1; n11 1 n29; n13 1 n19 B2 1460.0 ms 1461.5 6.5 0.0105 0.0161�

1459.1 5.1 0.0056

�n24 (B2) 1449.9 ms 1451 dp 1449.9 5.1 0.0798

,1445 tail 1449.9 7.9 0.0116

�0.0913

2n18 (A1) 1397 p

n14 1 n15 B2 1387.4 mw 1390.2 11.5 0.0072 0.0185�

1385.4 12.8 0.0113

�n12 1 n14; n15 1 n20 (A

1), n10 1 n20 (B1) 1367.2 w

1367.0 11.9 0.003330.00413

�1363.4 10.6 0.00080

�n12 1 n20 (B2) 1352 sh 1350.8 13.1 0.00069

1334.4 vw 1334 dp 1333.8 18.5 0.00143n25 (B2) 1316.7 w 1317 dp 1317.1 12.1 0.00158n16 1 n20; n18 1 n19 (A1) 1305.8 w 1309.3 9.2 0.00044n11 1 n18 (B1)

�1304.8 10.3 0.00087 0.0056

n26B2 1297.6 w br 1296 dp 1296.4 14.4 0.00165�

1285.0 21.3 0.00101

9>>>>=>>>>;n14 1 n29 (B1) ,1260 tail 1261.2 20.0 0.00048 0.00166n13 1 n14 (A1) 1249.2 vw br

�1250.2 16.3 0.00118

�n13 1 n20 (B2) ,1235 tail 1233.7 18.7 0.000732n19 (A1) 1220.1 w 1220 sh p 1220.8 14.4 0.00485n11 1 n19 (B1) ,1213 w sh 1210.4 17.0 0.00185

,1192 w sh 1192.0 19.8 0.00246n7 (A1), n14 1 n17 (B2) 1175.3 mw 1176 dp 1176.5 18.9 0.0094 0.0258n27 (B2) 1158.4 mw 1158.5 dp

1158.2 25.2 0.0131�

1156.9 10.1 0.0008

9>>=>>;3n20 (B1) ,1132 tail 1132.7 37.4 0.00245n14 1 n18 (B2) 1106.4 w 1106.5 dp 1106.8 7.8 0.00127 0.00490

1101.4 28.2 0.00363

�n28 (B2) 1076.1 m 1076 dp 1076.4 5.6 0.0156 0.0297

1070 tail

�1073.2 11.2 0.0141

�1032.7 5.4 0.0353

n8 (A1) 1032.3 ms 1032 p 1030.2 7.3 0.0202 0.06091026 tail

8

and 4127 cm21 provide the general level of absorptionand the remaining ten normally sharp bands providethe spectral structure. The total integrated intensityCjof the three broad bands is 0.00357 km mol21, andthat of the ten sharp bands is 0.00294 km mol21.Between 3950 and 3820 cm21, three broad bands at3936, 3910 and 3856 cm21 provide the general levelof absorption and the remaining seven normally sharpbands provide the structure of the absorption. Thetotal Cj of the broad bands is 0.0046 km mol

21, andthat of the seven sharper bands is 0.0030 km mol21.The totalCj over the whole of each region is believedto be accurate to a few percent. But the assignment ofintensity to particular transitions within these regionsclearly hinges on the distribution of the intensity in thebroad bands, and we know of no evidence to guidethis distribution. In order to keep Table 6 relatively

simple, theCj values have not been added together forall such regions above 3500 cm21, but where thesevery broad fitted bands occur the reader should beaware that the intensity assigned to a particular transi-tion in the table may be in error by a factor of 2 ormore.

Based on all of our studies and earlier work [5], weestimate that the error in the totalCj of an observedband above 620 cm21 is usually between 2 and 10%,but it may reach 100% for very weak bands andshoulders or where a much broader fitted band ispresent in the immediate vicinity. The estimated accu-racy of Cj for extremely weak bands is indicated bythe number of significant figures used in Table 6. Theerror in the total Cj of the strong bands below620 cm21 may be,50% because of the uncertaintyin the original intensity measurement.


Table 6 (continued)


b


f Cjg

2n14 (A1) 804 sh 803 p 802.6 9.8 0.00143n7 2 n20 (B1) 794 sh 794.8 4.6 0.00328

780.7 5.6 0.118n17 (B1) 779.6 s 780 dp 778.6 5.1 0.070 0.239

,775 tail

8

5. Discussion

5.1. Vibrational assignments

Table 6 shows the assignments of the features in thea 00m and Raman spectra of liquid C6H5D. Thesymmetry of the transition dipole or transition polar-izability is shown in parentheses. For transitions fromthe ground state, this symmetry is also that of theupper state.

The 30 normal vibrations of C6H5D form the repre-sentation 11A1 1 3A2 1 6B1 1 10B2 under the pointgroup C2v; where thex-axis is taken perpendicular tothe molecular plane so the A1 and B2 representationsdescribe in-plane motion. All vibrations are Ramanactive and all except the A2 vibrations are infraredactive.

The assignments were made with the aid of: (1)GFcalculation of the fundamental wavenumbers ofC6H5D from Goodman’s [36] benchmark potentialfor gaseous benzene; (2) parallel- and perpendicular-polarized Raman spectra of liquid C6H5D; and (3)infrared spectra of gaseous C6H5D. The Ramanbands are included in Table 6 with their polarizationand assignment. The infrared bands of the gas are nottabulated because they were of very limited use. Mostbands had complex shapes that contained several Q-branches and the band shapes were inconclusive indi-cators of the symmetry of the transition moment underour resolution. From the work of Pliva et al. [37],the moments of inertia of C6H5D are Ia 88:32;Ib 94:43 and Ic 182:75; all in u Å21,5 whichmeans that A, B and C-type bands of Ueda andShimanouchi’s [38] class 1 result from A1, B2 andB1 transition moments, respectively, i.e. from tran-sitions allowed by the A1, B2 and B1 components ofthe dipole moment, or, in the case of fundamentaltransitions, from A1, B2 and B1 vibrations, respec-tively. The A and C bands are clearly distinct underhigh resolution [39] but not under our,1 cm21 reso-lution. The only reliable information our spectra of thegas added to that presented by Snels et al. from theirhigh resolution study [39] is that the band near1382 cm21 is of B-type and that at 1214 cm21 ispredominantly B-type with the possible addition ofmuch weaker A- or C-type bands. Thus, in bothcases, the predominant intensity is due to a B2transition.

The features in thea 00m spectrum below 4800 cm21

are given in Table 6 with their assignment, the CDHObands required to fit them, and their integrated inten-sities. The features in the remaining part of thea 00mspectrum of Fig. 5, between 6200 and 4800 cm21,were not fitted and are summarized in Table 7.These bands were not assigned except as shown inthe footnote to Table 7. This is partly because theyare largely due to ternary and higher combinationtransitions, which are too numerous to allow mean-ingful assignment, and partly because current opinion[40] is that descriptions in terms of normal vibrationsprobably have little validity near the first overtone of


Fig. 6. Details of the fit to thea 00m spectrum between 3100 and3000 cm21 and between 1120 and 900 cm21. The upper curve ineach box consists of both the experimental and the fitteda 00m spectraof C6H5D at 258C, which essentially overlap. The lower curves in eachbox are the individual CDHObandsused for the fit, abbreviated to^ 3full-width-at-half-height from the peak for clarity.

5 u is the unified atomic mass unit [34], with magnitude the(atomic mass of12C)/12.

the CH stretching mode in C6H6, and presumably thesame holds for C6H5D.

The assignment of the fundamentals in Table 6 isessentially that summarized recently by Snels et al.[39], and it is noteworthy that, apart from the three A2vibrations, 22 of the 27 assignments are unchangedfrom the early work of Bailey et al. [7].

The vibrations are numbered in this paperaccording to Herzberg’s notation [41], as recom-mended by Miller [42]. Snels et al. [39] used Wilson’snotation [43,44]. For convenience, the two notationsare given in Table 8, together with the wavenumbersof the fundamentals of liquid C6H5D and liquid C6H6.

Only a few comments on the assignment are neces-sary. We have found no evidence of the A2 vibrations,and follow their traditional [39] assignment near 970,

850 and 398 cm21, which seems to originate in thecalculations of Whiffen [8]. The B2 vibration n25 iscalculated to lie near 1330 cm21, and is assigned at1333 cm21 in the gas. It has resisted unambiguousidentification in the liquid and is assigned at1317 cm21, to the onlya 00m feature in this region thatcannot be assigned to an overtone or binarycombination.

The B1 vibrations are well assigned, with theintensen19(B1) clearly identified at 607 cm

21 in thegas [39] and liquid (Figs. 1 and 5, Table 6). It istempting to assign the secondary peak at 610 cm21


Table 7Features between 6250 and 4800 cm21 in the a 00m spectrum ofC6H5D at 258C

a

~n (cm21)

6145 sh 5390 sh6120 vvw 5345 sh6085 sh br 5324b vvw5994 sh 5287 sh5978 sh 5262 vvvw5961c vw 5222 vvvw5910 sh 5211 sh5875 sh 5194 vvvw5842 vvw 5180 sh5790 sh 5150 vvvw5748 vvvw 5120 vvvw5700 sh 5093 vvvw5680 sh 5068 vvvw5665 vvw 5051 vvvw5630 sh 5032 vvvw5595 sh 4990 sh, br5580 vvvw 4965 vvvw5536 sh 4942 vvvw5521 vvvw 4892 vvvw5497 vvvw 4848 vvvw5478 vvvw 4819 vvvw5460 vvvw

a The wavenumbers of these weak features are expected to be thesame in transmission spectra or in the spectra of other infraredabsorption intensity quantities.

b nCH 1 nCD:c 2nCH. The intensity of 2nCH is C2CH 0:018 km mol21; deter-

mined as the area under the~na 00m spectrum between 6190 and5500 cm21.

Table 8Vibrational notation for C6H5D and fundamental wavenumbers ofliquid C6H5D and C6H6

Symmetry Notation ~n (cm21)

Herzberg Wilsona C6H5D (l) C6H6 (l)b

A1 n1 n20a 3064 3036A1 n2 n7a 3060 3046A1 n3 n2 3056 3059A1 n4 n13 2269 3062A1 n5 n8a 1593 1586A1 n6 n19a 1475 1479A1 n7 n9a 1175 1177A1 n8 n18a 1032 1037A1 n9 n12 1007 1010A1 n10 n1 981 993A1 n11 n6a 610 606A2 n12 n17a ,967 971A2 n13 n10a ,850 850A2 n14 n16a ,400 403B1 n15 n5 988 994B1 n16 n17b 926 971B1 n17 n10b 780 850B1 n18 n4 699 703B1 n19 n11 607 676B1 n20 n16b ,380 403B2 n21 n20b 3080 3036B2 n22 n7b 3033 3046B2 n23 n8b 1575 1586B2 n24 n19b 1450 1479B2 n25 n3 1317 1346B2 n26 n14 1298 1310B2 n27 n15 1158 1148B2 n28 n18b 1076 1037B2 n29 n9b 858 1177B2 n30 n6b 602 606

a From Refs. [43,44].b From Refs. [45,46].

in the infrared spectrum of the liquid (Fig. 1) ton11(A1)This band has never been observed [7–16,39], even inthe high-resolution spectrum of Snels et al. [39], butcalculations [17,39] clearly show that it is very closeto n30(B2) which is identified at 602 cm

21 by the depo-larized Raman peak. Thus the literature suggests thatn11 is very weak in the infrared, and that the entireintense band near 607 cm21 should be assigned ton19(B1). This is confirmed by the comparison of theintegrated intensities of C6H6(l), C6D6(l) andC6H5D(l) given later in this article. We thus concludethat the secondary peak at 610 cm21 is probably anartifact due to our difficulty in measuring this intenseband (see above), and assignn11(A1) coincident withn30(B2) at 602 cm

21.The only other comments on the assignment of the

fundamentals concern the CH stretching modes. In thegas one A1 mode is assigned at 3068 cm

21 and two areassigned together at 3087 cm21, and the two B2 modesare both assigned at 3096 cm21. These coincidentassignments are unlikely to be correct, and are aclear indication that little evidence is available for areliable assignment. In the liquid we assign two of thethree A1 vibrations to the two features on the intenseand broad polarized Raman band which extends from3115 to 3015 cm21, namely the shoulder at 3064 cm21

and the peak at 3056 cm21. The 3064 cm21 featurecoincides with the second strongest infrareda 00mpeak, and the nearesta 00m feature to 3056 cm21 is ashoulder at 3052 cm21. There is no clear evidenceof the third A1 vibration. It either has extremelyweak Raman intensity or contributes to the aboveRaman band. We assign it, reasonably but arbitrarily,at 3060 cm-1, in the middle of the polarized Ramanband. One of the two B2 vibrations is assigned to thestrongesta 00m peak at 3079.8 cm21, following Bailey etal. [7]. The second,n22, has been assigned near3042 cm21 to a Raman peak that was reported byBrodersen and Langseth [9]. Our Raman spectra alsosuggest the presence of a depolarized Raman bandnear 3040 cm21, coincident with a slight shoulder inthea 00m spectrum, so we could assignn22 at 3040 cm21.However, the 3040 cm21 shoulder can be assigned to acombination transitionn5 1 n25 (Table 6), but no suchassignment can be found for the moderately intenseinfrared peak at 3032.8 cm21. Thus, we assignn22 at3032.8 cm21, recognizing that clear evidence for itsassignment is lacking. This assignment of the CH

stretching modes is consistent with our recent assign-ments for chlorobenzene and toluene [47].

With this assignment of the fundamentals, most ofthe remaining bands in the spectrum can be assignedto binary combination and overtone transitions asshown in Table 6. The initial assignments weremade by correlation with the active combinationbands of C6H6 [45] and C6D6 [5] and were completedby considering the remaining binary combinationsand first overtones active underC2n: No assignmentswere made to ternary combinations because there aretoo many possibilities to allow a plausible assign-ment with the available evidence. Further, in theabsence of evidence about temperature dependence,assignments to difference bands were made onlybelow 1000 cm21 in those cases where no feasibleassignment to binary sum or overtone transitionexisted and only one difference band assignmentwas feasible.

It can be noted in Table 6 that in nearly all casesthe sum of the fundamentals is very close to theobserved wavenumber. This is not expected to bethe case for the overtones of the CH and CD stretchingvibrations. The overtone of the CH stretchingvibrations is clearly the strongest band in the region,at 5961 cm21 (Fig. 5, Table 7), but the overtone ofthe CD stretch is not obvious. The CH stretchingfundamental of C6D5H is [9] at 3050 cm

21 and theCD stretch of C6H5D is at 2269 cm

21 (Table 6). Ifthese are treated as the vibrations of a CH or CDdiatomic, withvHe =v

De

GH=GDp

and the approxima-tion that vex

He =vex

De GH=GD; where theG matrix

elements are simply the inverse of the reducedmasses of the diatomic, the first overtone is predictedto be at 5950 cm21 for CH and 4457 cm21 for CD.The predicted CH overtone wavenumber agrees wellwith that observed, and the CD stretching overtonecan be expected near 4457 cm21. The overtone ofthe CD stretch could be assigned at 4489 cm21 or tothe much weaker band at 4450 cm21. It is tentativelyassigned to the weaker band at 4450.2 cm21 becausethe only binary combination band expected between4400 and 4500 isn22 1 n24 at 4483 cm

21.

5.2. Intensities of the gas-allowed fundamentals

The intensities of the 27 gas-allowed infrared-active fundamentals require additional evaluation.


In Table 6, the intensities of fitted bands have beengrouped to describe the observed peaks or regionsof overlap. However, the total intensity of somefundamentals is probably underestimated by thisprocedure. Thus, the CH stretches, the CD stretch,the n6=n24 pair, and then7=n27 pair cause regions in

which the intensities of all bands are greater thanin the surrounding region. As discussed for C6D6[5], the greater intensity is taken from the funda-mental by overtone or combination levels of thesame symmetry.

It is not always clear where such fundamental


Table 9Integrated intensities, transition moments and dipole moment derivatives of fundamentals of liquid C6H5D

~n j (cm21) Cj (km mol

21)a uRju (D)b u2m=2Qu2 /D Å21 u21/2b

Rangec Accepted

n21 (B2) 3079.8 3100–3070 cm21: 0.124 0.124 0.0356 0.232

n1 (A1) 3064.3 3070–3060 cm21: 0.115 0.115 0.0344 0.215

n2 (A1) 3060d 0.0d

n3 (A1) 3056e 3060–3050 cm21: 0.0214 0.021 0.0149 0.0400

n22 (B2) 3032.9 3035–3030 cm21: 0.0141 0.014 0.0121 0.0263

n1 1 n2 1 n3 1 n21 1 n22 As above: 0.274 0.36f

3200–2950 cm21: 0.45

�(25%)

n4 (A1) 2269.0 2275–2250 cm21: 0.0432 0.051 0.0266 0.0953

2375–2150 cm21: 0.0584

�(14%)

n5 (A1) 1592.6 1600–1580 cm21: 0.00676 0.0068 0.0116 0.0126

n23 (B2) 1575.2 1580–1560 cm21: 0.00534 0.0053 0.0103 0.0100

n6 (A1) 1475.2 1480–1470 cm21: 0.0901 0.090 0.0439 0.168

n24 (B2) 1449.9 1455–1440 cm21: 0.0913 0.091 0.0445 0.171

n6 1 n24 As above: 0.181 0.191510–1410 cm21: 0.204

�(5%)

n25 (B2) 1316.7 1327–1311 cm21: 0.00158 0.0016 0.0061 0.0030

n26 (B2) 1297.6 1300–1270 cm21: 0.00266 0.0027 0.0080 0.0050

n7 (A1) 1175.3 1185–1167 cm21: 0.0094 0.0094 0.0158 0.0175

n27 (B2) 1158.4 1167–1150 cm21: 0.0139 0.014 0.0194 0.0260

n7 1 n27 As above: 0.0233 0.0261200–1120 cm21: 0.0283

�(10%)

n28 (B2) 1076.1 1097–1055 cm21: 0.0297 0.030 0.0295 0.055

n8 (A1) 1032.3 1055–1013 cm21: 0.0609 0.061 0.0431 0.114

n9 (A1) 1007.1 1010–998 cm21: 0.0055 0.0055 0.0131 0.0103

n15 (B1) ,988 998–985 cm21: 0.00613 0.0061 0.0140 0.0115n10 (A1) 981.6 985–975 cm

21: 0.00549 0.0055 0.0133 0.0103n16 (B1) 925.6 945–918 cm

21: 0.0271 0.027 0.0304 0.0506n29 (B2) 857.7 870–830 cm

21: 0.0408 0.041 0.0387 0.0762n17 (B1) 779.6 790–740 cm

21: 0.239 0.24 0.0983 0.447n18 (B1) 698.7 730–685 cm

21: 0.178 0.18 0.0896 0.333n19 (B1) 607.3 620–590 cm

21: 0.599 0.60 0.176 1.12n11 (A1) ,602 Not observed ,0 ,0 ,0n30 (B2) 601.8

d 0.0d

n20 (B1) ,380d ,0d

a The estimated error inCj is 2–10% or as given in parentheses.b The unit of the transition momentRj is the Debye, D, where 1 D 3:336× 10230 C m 0:0208e nm 0:208e �A; wheree is the elemen-

tary charge. The unit ofu2m=2Qu j is D �A21u21=2 10 D nm21 u21=2 8:186× 1027 C kg21=2 0:208e u21=2:c Cj includes the complete area of each fitted peak whose peak maximum lies in this range.d Observed only in the Raman spectrum.e 3056 cm21 is the wavenumber shift of the Raman peak.n3 is assigned to the 3052 cm

21 shoulder in the infrared spectrum.f The integrated intensity of the first overtone

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Infrared intensities of liquids. Part XXIII. Infrared optical constants …faculty.capebretonu.ca/dkeefe/PDF/benzene-d1 Bertie... · 2005. 7. 22. · This paper continues our report