Infrared intensities of liquids XXV: Dielectric constants, molar …faculty.capebretonu.ca/dkeefe/PDF/toluene Bertie Apelblat... · 2005. 8. 14. · Infrared intensities of liquids

Infrared intensities of liquids XXV: Dielectric constants, molar

polarizabilities and integrated intensities of liquid toluene at 25 8Cbetween 4800 and 400 cmK1

John E. Bertie, Yoram Apelblat, C. Dale Keefe*

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

Received 1 February 2005; revised 10 April 2005; accepted 11 April 2005

Available online 14 June 2005

Abstract

The main purpose of this paper is to present accurate infrared integrated intensities of liquid toluene, C6H5CH3, at 25 8C. Also presented

are the decadic molar absorption coefficients, Em, the real and imaginary dielectric constants, 30 and 3 00, and the real and imaginary molar

polarizabilities, a0m and a00m. Integrated intensities were determined as Cj, the area under bands in the ~na

00m spectrum, for all bands between

4800 and 440 cmK1. The contributions from the different bands were separated by fitting the spectrum with classical damped harmonic

oscillator bands. The uncertainties in the integrated intensities of most bands are estimated to be 5–10%, with the uncertainties in very weak

bands and in shoulders possibly up to 100%. The intensity that should be assigned to the fundamentals is more difficult to estimate due to

Fermi resonance with overtone and combination bands, and a best estimate is given. The integrated intensities of the fundamental vibrations

and the corresponding transition dipole moments are summarized and are compared with literature values for the gas.

q 2005 Elsevier B.V. All rights reserved.

Keywords: Vibrational assignment; Liquid; Toluene; Dipole moment derivatives; Integrated intensities; Molar polarizability spectrum

1. Introduction

In earlier papers from this laboratory, the absolute

infrared absorption intensities of liquid benzene [1], toluene

[2], chlorobenzene [3] and dichloromethane [4], were

measured by transmission spectroscopy, and were reported

as the real, n, and imaginary, k, refractive indices and the

areas under the imaginary refractive index spectra between

specified wavenumber limits. These publications formed the

basis of secondary standards for infrared intensity measure-

ment that were adopted by IUPAC [5]. Since then, the

infrared optical properties of liquid benzene-d6 [6],

benzene-d1 [7], bromobenzene [8,9], bromobenzene-d5[10], hexafluorobenzene [11], ethylbenzene [12], fluoro-

benzene [13], and toluene-d8 [14,15] along with extensions

0022-2860/$ - see front matter q 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.molstruc.2005.04.018

* Corresponding author. Current address: Department of Physical and

Applied Sciences, Cape Breton University, 1250 Grand Lake Road,

Sydney, Nova Scotia, Canada B1P 6L2. Tel.: C1 902 563 1185; fax: C1

902 563 1880.

E-mail address: [email protected] (C.D. Keefe).

to the benzene [16] properties were published. In addition,

the integrated intensities Cj, defined by [17]

Cj Z

ð

band j

~na00m d ~n (1)

and the assignments of the infrared spectrum of benzene

[16], benzene-d6 [6], benzene-d1 [7], bromobenzene [9] and

bromobenzene-d5 [15] have been reported. In this paper, we

report the decadic molar absorption coefficients, Em, the real

and imaginary dielectric constants, 3 0 and 3 00, and the realand imaginary molar polarizabilities, a0m and a

00m spectra and

the integrated intensities Cj of neat liquid toluene between

4800 and 440 cmK1 and assign most of the features in its

infrared spectrum. As is noted in more detail below, these

quantities, the complex molar polarizability and the

integrated intensities Cj, are more closely related to theory

than are the dielectric constants or the refractive indices. In

particular, to the extent that the Lorentz local field is valid,

the imaginary molar polarizability is determined solely by

the absorption of radiation and is not influenced by the

anomalous dispersion of the refractive index through

absorption bands [17].

Journal of Molecular Structure 750 (2005) 78–93

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J.E. Bertie et al. / Journal of Molecular Structure 750 (2005) 78–93 79

A number of studies of the vibrations of C6H5CH3 have

been reported in the literature [18–38]. The majority of

these studies gave only the assignments of the fundamen-

tals, two [18,22] reported in addition partial assignments of

combination and overtone transitions. Two additional

studies [24,30] gave only the assignment of the CH out-

of-plane deformation fundamentals and a few of their

combinations and overtones between 1965 and 1565 cmK1.

There are few reports of quantitative infrared integrated

intensities of toluene [31,39–43]. Three studies were limited

to the intensities of two fundamentals [39], six fundamentals

[40] and 13 combination bands [41], respectively, and were

measured in dilute CS2 solution. Three papers [31,42,43]

presented computed infrared integrated intensities for

gaseous toluene, and one of these [43] reported in addition

12 experimental intensity values for the gas.

In this paper, the integrated intensities of all bands

between 4800 and 440 cmK1 for neat liquid toluene are

presented. These intensities were obtained from the

spectrum of the imaginary molar polarizability, a00m, oftoluene. This spectrum was calculated from our previously

reported [2] spectra of the optical constants, n and k, by

methods discussed previously [17,44] under the assumption

of the Lorentz local field.

The imaginary molar polarizability spectrum, a00mð ~nÞ, isthe theoretically most significant absorption spectrum for

the liquid phase because, to the extent that the Lorentz local

field is valid, a00mð ~nÞ is simply the sum of terms from thedifferent absorption processes in the liquid [17]. In contrast,

the refractive index spectra and the dielectric constant

spectra are influenced by overlap of the different absorption

processes, such as through the dispersion of the real

refractive index or dielectric constant [17]. Accordingly,

the integrated intensity of absorption band j, Cj, is defined

[43] as the area under the band in the spectrum of ~na00mthrough Eq. (1).

Under the assumption that the transition from the ground

state and all of the corresponding hot transitions contribute

to the observed band, Cj is related to the dipole transition

moment, Rj, through Eq. (2) [17,45–47].

Cj ZNAp

3hcogj ~njjRjj2 (2)

For fundamental transitions, under the assumptions of

mechanical and electrical harmonicity, Cj can also be

related to the square of the dipole moment derivative with

respect to the jth normal coordinate, m2j Z jvm=vQjj2,through [17]

Cj ZNA

24pc2ogjm

2j (3)

In these equations, NA is Avogadro’s number, h is

Planck’s constant, co is the velocity of light in vacuum, and

gj is the degeneracy of the jth vibration. The essential

advantage that Cj has over all other integrated intensities

that have been used for liquids is that when gj and ~njjRjj2 or,for fundamentals, gj and m

2j are the same in the gas and

liquid phases the integrated intensity of a transition in the

gas, Aj,gas is simply 8p2Cj, where Cj is for the same

transition in the liquid.

In order to calculate the integrated intensities, the a00mspectrum 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 [17,45–47], so

the separation can be attempted by fitting the a00m spectrumwith CDHO bands. Gaussian bands may also be used if

necessary. When this separation is successful, as for

benzene [16], benzene-d6 [6], benzene-d1 [7], bromoben-

zene [9], bromobenzene-d5 [15], methanol [48] and, in this

paper, toluene, the integrated intensity Cj may be obtained

directly from the parameters of the CDHO band without

numerical integration, as is described elsewhere [6,16,48].

2. Experimental

The experimental and instrumental details of this work

have been described [1,3] and are summarized here briefly.

The infrared spectra were measured with a Bruker IFS 113V

spectrometer. A globar source, a 10 mm aperture, and

deuterated triglycine sulfate (DTGS) detector were used.

The interferograms were recorded with 0.665 cm sK1

optical retardation velocity and 1 cmK1 nominal resolution.

Trapezoidal apodization, multiplicative phase correction

and one level of zero-filling were used in the Fourier

transform.

To assist in the vibrational assignments of the bands in

the spectrum of the liquid, an infrared spectrum of gaseous

toluene was recorded on the Bruker IFS 113V in order to

observe the band contours, and Raman spectra were

measured to observe the polarizations.

Accurate Raman wavenumber shifts were obtained from

an unpolarized spectrum recorded at 2 cmK1 nominal

resolution on a Bruker FT-Raman spectrometer. The

HeNe wavenumber was set in the software to its vacuum

value of 15,798.002 cmK1, and that of the Nd YAG was set

to 9394.2 cmK1. Measurement of both Stokes and anti-

Stokes Raman shifts of four bands of chlorobenzene and one

band of dichloromethane showed that the Stokes wave-

number shifts reported in this paper are accurate to G0.1 cmK1. Parallel- and perpendicular-polarized Raman

spectra were recorded with 908 excitation on a dispersive

SPEX spectrometer with laser excitation at 514.5 nm,

380 mW power, slit width of 2 cmK1 and step size

0.5 cmK1. The intense parallel-polarized bands allowed

wavenumber calibration by comparison with the accurate

though unpolarized FT spectra.

Table 1

Peak wavenumbers and heights of the major bands of C6H5CH3 in spectra of different intensity quantitiesa

~n of kmax (cmK1) FWHHb (cmK1) kmax (Em)max

(l molK1 cmK1)c300max ða00mÞmax

(cm3 molK1)

ð ~na00mÞmax(cm2 molK1)

3026.8 15.1 0.0308 54.3 0.0908 0.398 (3026.95) 1205 (3026.95)

2919.8 16.2 0.0164 27.9 0.0486 0.211 616

1604.5 5.7 0.0309 28.9 0.0906 0.402 645

1495.5 4.1 0.112 97.4 0.328 1.46 (1495.7) 2182 (1495.7)

1460.1 24.1 0.0278 23.7 0.0824 (1459.9) 0.358 (1460.3) 523 (1460.4)

1081.3 9.0 0.0301 19.0 0.089 0.392 424

1030 3.5 0.040 24.1 0.119 0.519 534

728.9 7.7 0.719 305.5 2.22 (728.0) 9.97 (729.9) 7276 (729.9)

694.5 4.6 0.365 148 1.14 (692.2) 4.56 (694.8) 3170 (694.8)

464.3 4.0 0.295 79.9 0.888 (464.1) 3.79 (464.4) 1760 (464.4)

a The wavenumbers of the peaks in the different spectra are within 0.1 cmK1 of those of kmax except where they are given in parentheses beside the peak

height.b The full-width-at-half-height of the k band.c 1 l molK1 cmK1Z10 dm2 molK1Z1000 cm2 molK1.

J.E. Bertie et al. / Journal of Molecular Structure 750 (2005) 78–9380

3. Results

3.1. Spectra of other intensity quantities

The spectra of the optical constants, n and k, of toluene

were obtained by methods discussed before [17,44] and

have been reported [2]. These spectra were used in program

DEQUANT1 to compute spectra of the decadic molar

absorption coefficient, Em, the complex dielectric constant,

3 0 and 3 00, and under the assumption of the Lorentz localfield, the real and imaginary molar polarizability, a0m anda00m, through Eqs. (4)–(8)

Em Z 4p ~nk=ð2:303CÞ (4)

30 Z n2 Kk2 (5)

300 Z 2nk (6)

a0m Z3Vm4p

ð30 K1Þð30 C2ÞC3002ð30 C2Þ2 C3002 (7)

a00m Z9Vm4p

300

ð30 C2Þ2 C3002 (8)

In these equations, C is the mole concentration, VmZCK1

is the molar volume and for toluene is 106.85 cm3 molK1, as

calculated from the density [49] 0.86230 g cmK3 at 25 8C andthe molecular weight 92.14 g molK1.

For the 10 most intense peaks in the k spectrum, Table 1

lists the peak wavenumber and the full-width-at-half-height

(FWHH) 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 or very broad

absorptions. For several bands of toluene the peak

1 Available on JEB’s web site http://www.ualberta.ca/~jbertie/jebhome.

htm.

wavenumbers in the 3 00, a00m and ~na00m spectra differ from

that in the k spectrum by 0.1 cmK1 or more, and are given in

Table 1 in parentheses beneath the value for the peak height.

The a00m spectrum of liquid toluene between 4800 and440 cmK1 is shown in Fig. 1. The n, k, 3 0, 3 00 and a00m spectra,and program DEQUANT, are available in digital form from

JEB’s web site http://www.ualberta.ca/~jbertie/jebhome.

htm as well as CDK’s website http://faculty.capebretonu.

ca/dkeefe/spectra.

3.2. Vibrational integrated intensities

With methods discussed previously [6,7,16], in order to

separate the contributions to the intensity from the different

bands, the a00m spectrum was fitted between 4800 and440 cmK1 with CDHO bands. For C6H5CH3, 189 bands

were fitted to the a00m spectrum. An entire spectrum, calledthe fitted spectrum, was created by adding the 189 bands,

each of which extended from 4800 to 440 cmK1. The

integrated intensity Cj of each of these bands was

determined as described previously [6,7,16,17]. The peak

wavenumbers, FWHH and Cj of these fitted bands are listed

in Table 2, together with the wavenumbers of features in the

experimental a00m spectrum, the infrared spectrum of the gas,and the Raman spectrum of the liquid.

The quality of the fit is shown graphically in Fig. 1,

which includes the fitted spectrum as well as the

experimental a00m spectrum, and in Fig. 2 which showsmore detailed views of the fit in two regions. Each curve in

Fig. 1 and the upper curve in each box of Fig. 2 consist of

both the experimental a00m spectrum and the fitted spectrum,which essentially overlap even in the expanded views in

Fig. 2. The lower curves in Fig. 2 show the individual bands

required for the fit, truncated to extend only three FWHH

from the band peak.

The quality of the fit can be described in several ways. Of

first importance is that the presence of nearly all of the 189

bands is obvious in the experimental a00m spectrum, either as

http://www.ualberta.ca/~jbertie/jebhome.htmhttp://www.ualberta.ca/~jbertie/jebhome.htmhttp://www.ualberta.ca/~jbertie/jebhome.htmhttp://www.ualberta.ca/~jbertie/jebhome.htmhttp://www.ualberta.ca/~jbertie/jebhome.htmhttp://www.ualberta.ca/~jbertie/jebhome.htm

Fig. 1. Imaginary molar polarizability spectrum, a00mð ~nÞ, of liquid toluene at25 8C and the fitted spectrum, i.e. the sum of the CDHO bands fitted to it.

The experimental and fitted spectra essentially overlap, even when

expanded, except near 3250 and near 650–750 cmK1 in the expanded

spectra where the lower curve is the experimental spectrum. Divide the

ordinate scale labels in the middle and bottom boxes by 20 and 50,

respectively, for the expanded upper curves in the box. The unit of a00m iscm3 molK1.


peaks, shoulders, changes in slope, or asymmetric tails, as is

illustrated in Fig. 2. Further, the overall average percent

difference between the fitted and experimental a00m peakvalues is 0.9%. The average percent difference is also 0.9%

for a00m values smaller than 0.1 cm3 molK1, and is near 0.5%

for stronger absorption. Further, the largest absolute

difference is 6.0!10K2 cm3 molK1 at the 730 cmK1 peak,which corresponds to 0.6% of the height of the peak. No other

difference in peak values exceeded 1!10K2 cm3 molK1. Animportant check on the quality of the fit is the comparison of

the area under the experimental and fitted spectra over a wide

wavenumber range. The total area under the fitted spectrum is

0.5% larger than the area under the experimental spectrum,

being only 0.05% larger between 4800 and 800 cmK1 but

0.9% larger below 800 cmK1.

The accuracy of the integrated intensities Cj in Table 2

cannot be stated with great reliability. The above evidence

argues that the fit contributes an error of less than 1% to

the integrated intensities for most of the bands. A first

estimate is, then, that the uncertainty in the Cj is 1% plus

the percent uncertainty in the a00m values which is about

the same as that in the k values. This gives w4% as theestimated uncertainty in the Cj. The problem with this

estimate is that, while the overall area is well described by

the fitted bands, the fit is unlikely to be unique. The Cj of

a fitted band is its intensity integrated from zero to

infinity, and is very sensitive to the width of the band.

The uncertainty due to this source is difficult to estimate

usefully. The effect of the bandwidth is partly offset in the

cases where it may cause the greatest problem, namely

when an observed band is fitted by several bands, by

adding together individual Cj values into a total Cj of the

observed band; these total Cj values are reported in

Table 2 in the column headed ‘sum of Cj’. Based on our

earlier work [6,7,16] and on studies in which the same

spectrum has been fitted with different number of bands

by different people, we conservatively estimate that in

most cases the total Cj of an observed band above

800 cmK1 is reliable to 5G5%, while the Cj of very weakbands and shoulders may be in error by a factor of two.

The accuracy of Cj for very, very weak bands is indicated

by the number of significant figures used.

4. Discussion

4.1. Vibrational assignments

The instantaneous symmetry of the toluene molecule is at

most Cs. Frequently, however, the CH3 group is considered

to be freely rotating, which means that the methyl group can

be approximated by a point of mass 15 in a GF calculation

of the ring system and the molecular symmetry can be

approximated by C2v. Of the 39 vibrations of toluene, 30 are

of the ring system and are similar to the vibrations of other

monosubstituted benzenes. Under C2v symmetry, these form

the representation 11A1C3A2C6B1C10B2, where the x-axis is taken perpendicular to the molecular plane so that A1and B2 reflect in-plane motion. All vibrations are Raman

active and all except the A2 vibrations are infrared active.

Traditionally, the methyl vibrations are considered under

C2v symmetry. However, as pointed out by Keefe et al. [14],

it is better to consider the methyl vibrations as C3v. Under

C3v, the three stretching, three HCH deformation, two

rocking and one torsion vibrations of the CH3 group form

the representation 2A1CA2C3E. Thus in this paper we use2A1CA2C3E as the representation formed by the CH3group vibrations under C3v and 11A1C3A2C6B1C10B2 asthe representation formed by the vibrations of the phenyl

group under C2v.

In this paper, to facilitate comparison with other

monosubstituted benzenes, the 30 phenyl vibrations are

numbered from 1 to 30 and the methyl vibrations

are numbered 31–36. Within these two blocks the vibrations

are numbered in this paper according to the Herzberg [50]

notation, as recommended by Miller [51]. The relationship

Table 2

Integrated intensities and dipole moment transitions of liquid toluene


Table 2 (continued)


Table 2 (continued)

aWavenumbers of peaks in the imaginary molar polarizability spectrum of liquid toluene.bThe following abbreviations are used to describe the peak prominence qualitatively: v, very; w, weak; m, medium; s, strong; br, broad and sh, shoulder.cBand contours in the infrared spectrum of the gas. For toluene, type A, B and C type bands arise from A1, B2 and B1 transitions, respectively. ? and ?? indicate

increasing uncertainty in determining the band contour type. Q indicates that a Q branch is visible in the spectrum but whether the band is A or C could not be

determined.dp means polarized, dp means depolarized. ? indicates some uncertainty in determining the band polarization ratio. Many weak depolarized peaks were omitted

from the table.eThe sum of the Cj that contribute to the observed feature, or the sum of the Cj of a group of interdependent bands.fThe unit is cmK1. ~nj and Gj are the peak wavenumber and the full width at half-height of the band, respectively. I indicates that the very weak feature was

ignored in the fit.gThe unit is km molK1.hCalculated wavenumbers are given in brackets. ? indicates the assignment is uncertain; ?? indicates the assigned transition is not infrared active in the gas

phase.


Fig. 2. Details of the fit of the a00m spectrum between 3200 and 2800 cmK1

and 1125 and 925 cmK1. The upper curve in each box consists of both the

experimental and the fitted a00m spectra of liquid toluene at 25 8C, whichessentially overlap. The lower curves in each box are the individual CDHO

bands used for the fit, abbreviated to G3 FWHH from the peak for clarity.

2 The term depolarized denotes that the depolarization ratio equals 0.75

for linear polarized incident light and polarized denotes that the

depolarization ratio is less than 0.75.


to Wilson’s notation [52,53] and to the wavenumbers of

C6H5D and C6H6 are in Table 8 of reference [7].

The nine CH3 modes can only be considered to have C3vsymmetry if it is assumed that the CH3 group rotates freely.

The symmetric stretching mode, n31, symmetric defor-

mation mode, n32, and CH3 torsion, n33, can then be

meaningfully assigned to the A1, A1, and A2 represen-

tations, respectively. The asymmetric stretching and

deformation, modes and the CH3 rocking modes then

form three degenerate pairs, n34, n35 and n36, and can be

assigned formally to E representations.

In this work, features in the a00m spectrum of the liquidwere assigned with the aid of (1) GF calculation of the

fundamental wavenumbers of C6H5CH3 with the CH3 group

as a point of mass 15, from Goodman’s [54] benchmark

potential for benzene, (2) the parallel- and perpendicular-

polarized Raman spectra of C6H5CH3(l) and (3) infrared

spectra of C6H5CH3(g). The moments of inertia of toluene

[55] are IaZ88.2G0.1, IbZ200.8G0.1 and IcZ289.1G0.1 amu Å2, which means that A, B and C-type bands of

Ueda and Shimanouchi’s [56] class 5 result from transitions

allowed by the A1, B2 and B1 components of the dipole

moment, respectively, or, in the case of fundamental

transitions, by A1, B2 and B1 vibrations, respectively.

The assignment of the a00m spectrum is given in Table 2.The assignments of the fundamentals agree essentially with

those of Balfour [34] and Schrotter and co-workers [36].

The assignments for which the evidence is unclear are

discussed briefly below.

The A2 vibrations are inactive in the infrared, but may

appear as very weak bands in the liquid. They are active in

the Raman spectra and should be depolarized2, but are

possibly weak. The only weak, depolarized Raman band

without a corresponding band in the infrared spectrum of the

gas is found at 842 cmK1, coincident with the weak band in

the infrared spectrum of the liquid at 843 cmK1 and is

assigned to n13. Previously, most studies [21,22,25–34]

assigned n12 between 970 and 962 cmK1 and only

two studies [18,36] assigned it to the Raman band at

w990 cmK1. The weak Raman band at 991 cmK1 is clearlypolarized in our spectrum, and therefore cannot be assigned

to n12. Thus, without conclusive experimental evidence, we

follow the majority of the authors and assign the observed

weak band in the infrared spectrum of the liquid at

966.4 cmK1 to n12. Previous studies [20,22,24,25,28–32,

34,36] assigned n14 between 408 and 401 cmK1. We found

no experimental evidence for n14, so we follow these studies

and assign it at 405G5 cmK1. The A2 methyl torsion, n33,has not been observed, but has been assigned in three works

[24,30,38] in which it was computed at 44, 15 and 30 cmK1,

respectively. We do not assign this vibration.

The aromatic B1 vibrations are well assigned, with all

supported by either the gas or the Raman data except for the

assignment of n15 at 981 cmK1. The assignment of n15 to the

980.7 cmK1 band in the liquid, where a corresponding

complex weak feature is also observed in the spectrum of

the gas, follows previous assignments [21,22,28–30,34] of

978G4 cmK1. Of the three degenerate methyl E vibrationswhich have been traditionally considered as B1 and B2, we

only differ with Balfour’s [34] assignment of n34. Balfour

assigned it at 2979 cmK1. Our Raman spectrum indicates

that the 2979 cmK1 band is polarized and therefore cannot

arise from an E transition (or B1 under C2v). Thus, we assign

the broad band in the infrared spectrum of the liquid at

2950 cmK1 to n34. It is worth noting that although Balfour

considered the methyl vibrations under C2v symmetry, he

assigned the other two B1 and B2 methyl vibrations as

degenerate pairs, which is equivalent to treating the methyl

group under C3v symmetry. Thus, n35 is assigned at

1460 cmK1 and n36 at 1040 cmK1.

Balfour [34] and Schrotter [36] assigned n24 at 1468 and

1441 cmK1, respectively. We assign the broad band at

1460 cmK1 in the infrared spectrum of the liquid to the

asymmetric CH3 deformation, n35(E). In the Raman spectra a

weak depolarized band is observed at w1442 cmK1, which


agrees with Schrotter’s observed band at 1441 cmK1, so we

follow Schrotter and assign n24(B2) at 1442 cmK1.

The main differences between previous assignments [18,

21,22,24–28,30,31,33,34,36], and also between them and this

work, concern the CH stretching modes. The strong A-type

band at 3073 cmK1 in the infrared spectrum of the gas, has a

counterpart in the medium–strong infrared band in the liquid at

3062.1 cmK1 and in the polarized Raman shoulder at

w3065 cmK1. The magnitude of the wavenumber shift forCH stretches between the gas and the liquid is in agreement

with observations of benzene [50], and thus n1(A1) is assigned

at 3062.1 cmK1. Similarly, a B-type contour at 3096 cmK1 in

the gas spectrum corresponds to the medium–strong band at

3086.4 cmK1 in the liquid and is assigned to n21(B2).

The assignment of the other three CH stretches is less

evident. There is an intense polarized Raman band at

3055 cmK1, implying an A1 fundamental. The 3062 band in

the infrared spectrum of the liquid was already assigned to

n1. However, it is rather broad and clearly asymmetric to

lower wavenumbers and could mask n2. Thus we tentatively

assign n2(A1) at 3055 cmK1. The remaining unassigned

features in the various spectra are a weak depolarized

Raman band at 3038 cmK1, a weaker polarized band at

3002 cmK1, a broad and complex feature in the infrared

spectrum of the gas between 3044 and 3032 cmK1 with

perhaps an A-type band at the high wavenumber end and a

B-type band at the low wavenumber end of the range, the

locally strongest peak in the infrared spectrum of the liquid

at 3027.0 cmK1, and a medium shoulder-like peak at

w3003 cmK1. We follow the assignment by most exper-imental studies [18,21,25,28,34,36] and assign the strong

band at 3027.0 to n22(B2). n3(A1) could then be either

assigned at 3038 or at w3003 cmK1. The latter assignmentcan be supported by the weak polarized Raman band which

implies an A1 transition. However, the 3003 band in the

infrared spectrum of the liquid is (a) weaker than the other

CH stretches, (b) located at a much lower wavenumber than

in other monosubstituted benzenes such as the lighter

C6H5D [7] and the heavier C6H5Cl [57] and (c) could be

explained as the second overtone of n9. Thus, we tentatively

assign the depolarized Raman band at 3038 cmK1 to n3, in

agreement with some of the earlier studies [21,25,28,34],

since an A1 transition can yield a depolarized Raman band.

With this assignment of the fundamentals, most of the

remaining bands in the spectrum can be assigned to binary

combination and overtone transitions. As with the funda-

mentals, the combinations and overtones of the phenyl

vibrations are considered under C2v and the combinations

and overtones of the methyl vibrations are considered under

C3v. However, to consider combinations of the methyl and

phenyl vibrations, the molecule needs to be considered

under Cs symmetry. Thus all the combinations of the methyl

vibrations with the phenyl vibrations are active. These

assignments are shown in Table 2 with the sum or difference

of the fundamental wavenumbers given in parentheses. Gas-

phase band shapes and Raman polarization data were used

to guide these assignments. In some cases two possible

assignments are given and in others it is noted that several

possible binary combinations exist. In general, bands are not

assigned to ternary overtone or combination transitions

because too many possibilities exist.

4.2. Intensities of the fundamental vibrations

In Table 2 the intensity of a fundamental is shown as the

sum of the bands that were required to fit the observed peak.

For example, bands at 1604.9 and 1602.9 cmK1 were

needed to fit the n4 peak at 1604.6 cmK1, and the intensity of

n4 is shown as the sum of the intensities of these two bands.

From these intensities of individual fundamentals, and from

the intensities of the degenerate pairs for the asymmetric

CH3 group vibrations, the transition moment, Rj, wascalculated from Eq. (2) and the square of the dipole moment

derivative with respect to the normal coordinates, m2j Zjvm=vQjj2 was calculated under the approximations ofelectrical and mechanical harmonicity from Eq. (3), both

as described previously [6,7,16,48]. Numerically, Eq. (2) is

ðjRjj=DÞ Zffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi31:50 ðCj=km moleK1Þ=ðgj ð ~nj=cmK1ÞÞ

q

where D is Debye and 1 DZ3.336!10K30 C mZ0.0208 enmZ0.208 e Å, where e is the elementary charge, and Eq.(3) is (mj/D Å

K1 uK1/2)2Z1.8686 (Cj/km molK1)/gj, where

1 D ÅK1 uK1/2Z10 D nmK1 uK1/2Z8.186!10K7 C kgK1/2Z0.208 e uK1/2. In these calculations, the degeneracy, gj,equalled 2 for the degenerate pairs of asymmetric methyl

group vibrations, and 1 for all others. The intensities,

transition moments, and squares of the dipole moment

derivatives, of the fundamental vibrations of toluene are

presented in Table 3.

However, as discussed previously for C6D6 [6], C6H5D

[7] and C6H6 [16], this procedure must frequently under-

estimate the intensity of the fundamental, because overtone

and combination bands in the vicinity of the fundamental

borrow intensity from the fundamental. This is evident from

the observation that overtone and combination bands in the

vicinity of strong fundamentals are frequently far more

intense than those in regions where there is no strong

fundamental absorption. Thus, in many cases, the Rj and m2j

values listed in Table 3 are probably too small, since they

were calculated from the Cj of only the band assigned to the

individual fundamental.

In an attempt to provide a realistic estimate of the

uncertainty of the intensities of the fundamentals in spite of

this phenomenon, we show in Table 4 the sum of the intensities

of all bands in the region of many fundamentals, along with our

best estimate of what we can say reliably about the absolute

intensities of the fundamental vibrations of liquid toluene. In

many cases this has required the intensities of several

fundamentals to be added together. In all cases except for

the sum of the methyl C–H stretches this provides an intensity

with an estimated uncertainty less than 16%. For the sum of

Table 3

Comparison of intensities of fundamentals of liquid and gaseous toluenea

njb cmK1 Cj,liq

c jRjjd jvm/vQj2 d Aj,gasbThis worke Ref. [43] exp Ref. [43] calc Ref. [31] calc

n21 3086.4 0.0618 0.0251 0.340 4.88 19.16 43.01

n1 3062.1 0.0984 0.0318 0.429 7.77 0.49 14.52

n2 w3055 0.0511 0.0230 0.309 4.03 4.03 14.62n3 w3038 n.a. n.a. n.a. n.a. 3.40 5.57n22 3027.0 0.336 0.0591 0.792 26.5 31.85 3.61

n1Cn2Cn3C

n21Cn22

0.547 43.2 64.63 58.93 81.33

n34 w2950 0.167 0.0299 0.395 13.1 18.52 18.44 46.71n31 2919.9 0.165 0.0422 0.555 13.0 11.05 10.42 27.05

n31Cn34 0.332 26.2 29.57 28.86 73.76

n4 1604.6 0.0571 0.0335 0.327 4.51 0.61 6.31

n23 1586.7 0.0209 0.0204 0.198 1.65 0.95 0.83

n4Cn23 0.0780 6.16 7.26 1.56 7.14n5 1495.7 0.160 0.0580 0.547 12.6 14.87 11.50 15.95

n35 1460.3 0.251 0.052 0.484 19.8 6.54 3.61 5.30

n24 w 1442 n.a. n.a. n.a n.a 3.78 14.56n5Cn24Cn35 0.411 32.4 21.41 18.89 35.81n32 1378.9 0.0560 0.0358 0.323 4.42 3.08 3.26 0.39

n25 1332.0 0.0049 0.0108 0.096 0.39 0.02 0.00

n26 1312.7 0.0020 0.0069 0.061 0.16 0.03

n25Cn26 0.0069 0.54 0.03

n6 1210.2 0.0047 0.0111 0.094 0.37 0.03

n7 1178.6 0.0096 0.016 0.134 0.76 0.22

n27 1155.9 0.030 0.028 0.237 2.37 0.20

n28 1081.4 0.0542 0.0397 0.318 4.28 4.30 3.52 3.70

n36 1041.4 0.0215 0.0180 0.142 1.70 2.67 1.43 9.46

n8 1030.1 0.0191 0.0242 0.189 1.51 2.30 1.41

n9 1002.3 0.0023 0.0085 0.065 0.18 0.13

n15 980.7 0.0070 0.015 0.114 0.55 0.22

n12 966.4 0.0075 0.0156 0.118 0.59 0.00

n16 895.4 0.0127 0.0211 0.154 1.00 0.39

n13 842.7 0.0088 0.018 0.128 0.69 0.00

n10 785.6 0.0047 0.0137 0.094 0.37 0.72 0.35

n17 729.9 0.748 0.180 1.18 59.1 34.48 47.18

n18 694.8 0.221 0.100 0.643 17.5 18.88 27.99

n29 622.0 0.0016 0.0090 0.055 0.13 0.01 0.09

n11 521.0 0.0032 0.0139 0.077 0.25 0.08 0.77

n19 464.4 0.111 0.0868 0.455 8.76 6.00 8.47

n11Cn19 0.114 9.00 6.24 6.08 9.24n14 w400 n.a. n.a. n.a. n.a 0.00n30 346 n.a. n.a. n.a. n.a. 0.42

n20 217 n.a. n.a. n.a. n.a. 2.48

n33 ? n.a. n.a. n.a. n.a.

a n.a. means that infrared intensities are not available for these modes. n14, n30, n20 and n33 lie below the wavenumber range of this work and n3 and n24 were

only observed in Raman spectra.b Plus signs in this column mean the sum of the intensities of the fundamentals.c Intensity units are km molK1.d The unit of the transition moment Rj is the debye, D, where 1 DZ3.336!10

K30 C mZ0.0208 e nmZ0.208 e Å, where e is the elementary charge. The unitof jvm/vQjj is (D ÅK1 uK1/2)Z10 D nmK1 uK1/2Z8.186 !10K7 C kgK1/2Z0.208 e uK1/2.

e For the column headed ‘This work’ the values were calculated from Aj,gasZ8p2 Cj,liq (see text).


the methyl C–H stretches the estimated uncertainty is either 10

or 25%, depending on whether one believes that the overtone

and combination bands between 2900 and 2800 cmK1 can

gain intensity from the methyl C–H stretches. We think it

likely that they can, so we prefer to estimate the uncertainty at

25%. For the sum of the aromatic C–H stretches the

uncertainty is only 3%, while for the sum of the aliphatic

and aromatic CH stretches combined the uncertainty is 13%.

All previously reported intensities of liquid toluene were

measured in dilute CS2 solutions [39–41], so are not suitable

for comparison with the pure liquid. Accordingly, the only

meaningful comparison of the present results that can be

made is with integrated intensities reported for the gas [31,

43]. Galabov et al. [43] measured intensities of the gas, and

computed intensities via a double-mode refinement process

using their experimental intensities and via ab initio

Table 4

Evaluated intensities of fundamentals of liquid toluene compared with experimental intensities of gaseous toluene

Fundamentals or regiona Sum of Cj Evaluated Cj AjZ8p2Cj Exptl Aj of gas [43]

Aromatic CH: n1Cn2Cn3Cn21Cn22 0.547 0.56G3 44G1.5 64.6

All bands 3120–3000 cmK1 0.583

Methyl CH: n31Cn34 0.332 0.37G10 29G3 29.6All bands 3000–2900 cmK1 0.403

Methyl CH: n31Cn34 0.332 0.43G25 34G9 29.6

All bands 3000–2800 cmK1 0.539

All CH 0.879 1.0G13 79G10 94.2All bands 3120–2800 cmK1 1.122

n4Cn23 0.78 0.090G15 7.1G1 7.26

All bands 1660–1550 cmK1 0.103

n5Cn24Cn35 0.411 0.44G6 34.G2 21.4

All bands 1550–1400 cmK1 0.459

n32 0.056G5 4.4G0.2 3.08

n25Cn26 0.0069 0.0075G8 0.59G0.05All bands 1336–1300 cmK1 0.0080

n6Cn7Cn27 0.0443 0.047G6 3.7G0.2

All bands 1210–1155 cmK1 0.0494

n28 0.0542G5 4.3G0.2 4.30n36Cn8Cn9Cn15 0.0498 0.077G15 6.1G1

All bands 1060–980 cmK1 0.105

n12 0.0075G10 5.9G0.6n16 0.0127 0.014G12 1.1G0.1

All bands 915–890 cmK1 0.0162

n16Cn13 0.0215 0.025G13 2.0G0.3

All bands 915–840 cmK1 0.0280

n10 0.0047G5 0.37G0.02 41.0

n17 0.748G5 59G3

n18 0.221G5 17.5G0.9

n29 0.0016G10 0.13G0.01n11 0.0032G5 0.25G0.01 6.24

n19 0.111G5 8.8G0.5

a Plus signs in this column mean the sum of the intensities of the fundamentals.

gg


molecular orbital calculations of benzene, toluene and

toluene-d8. Xie and Boggs [31] used scaled ab initio

calculations to obtain wavenumbers and infrared intensities

of gaseous toluene.

In order to compare our results with their data, a

comparison of the integrated intensities Cj of the liquid,

Cjliq, with the integrated intensities Aj of the gas, Ajgas, is

made through Eq. (9)

8p2Cj liqAj gas

Zf ~njjRjj2gliqf ~njjRjj2ggas

Zm2j liq

m2j gas(9)

where the first equality is generally true and the second is for

fundamentals under the double harmonic approximation [6,

7,16,17,58]. Thus, if the molecular intensity properties are

the same in the gas and liquid phases, the ratio in Eq. (9)

equals 1.0, and a corresponding value of Aj gas can be

calculated from the liquid intensity through Aj gasZ8p2

Cj liq. This second method is used in Tables 3 and 4 to give

values of Aj from this work. In Table 3 these values are in

the column headed ‘This work’, with the results of Galabov

et al. [43] and Xie and Boggs [31] in the columns headed

‘Ref. [43] exp’ ‘Ref. [43] calc’ and ‘Ref. [31] calc’. In

Table 4 the column headed ‘AjZ8p2Cj’ gives the Aj values

calculated from the Cj in the previous column and the last

column gives Galabov’s experimental values for the gas.

Our experimental intensities of the liquid agree well with

those of Galabov et al. [43] for the gas in some cases, but

there are clearly several differences. Our values are clearly

w50% or more larger at low wavenumber, with the sum ofn11 and n19 and the sum of n10, n17, n18 and n29. Our value is

also about 50% higher for the sum of n5, n24, and n35 and for

the symmetric CH3 deformation, n32. The total intensity of

the C–H stretching bands agrees rather well, as does the

total intensity of the CH3 stretches whether the combination

bands between 2800 and 2900 cmK1 are included in the

uncertainty or not, although this is largely due to the large

uncertainty. However, the gas-phase intensity of the sum of

the aromatic C–H stretches is about 50% greater than our

liquid phase sum. The C–H or C–D stretches of C6H6,

C6H5D and C6D6 absorb about 50% less strongly in the

liquid than in the gas [6,7,16], and the present data suggests

that the same may be true for toluene. However, it must be

remembered that our present understanding of the CH

stretching region is not well supported by unambiguous

evidence.

Table 3 includes the calculated gas-phase intensities of

Galabov et al. [43] and of Xie and Boggs [31] as well as


Galabov’s experimental values for the gas. Galabov’s

calculations agree quite well with his experimental values,

while the calculations of Xie and Boggs seem to agree less

well. This is difficult to evaluate, or to determine its

significance for the liquid, because the different calculations

give different assignments in many cases.

5. Summary

Infrared absorption intensities of liquid toluene, at 25 8Cand the first detailed assignment of the infrared spectrum of

liquid C6H5CH3 are reported.

The molar polarizability spectra were calculated from the

refractive index spectra under the assumption of the Lorentz

local field. The integrated intensities CjZÐ~na00m d ~n, were

determined analytically after the contributions from the

different vibrations were separated by fitting the spectrum of

the imaginary molar polarizability, a00m, with classicaldamped harmonic oscillator bands. The intensities of the

different fundamentals are reported and compared with the

literature intensity values for the gas. For the fundamental

bands, the intensities were used to calculate the transition

moments and the dipole moment derivatives under the

double harmonic approximation.

Acknowledgements

The authors thank Dr G.R. Loppnow and M.S. Ngari of

the Chemistry Department, University of Alberta and Dr

Kirk Michaelian of CANMET Western Research Centre,

Devon, Alberta for the Raman spectra. JEB and CDK thank

the Natural Sciences and Engineering Research Council of

Canada (NSERC) for research grants in support of this

work. Much of this work was carried out when CDK held

NSERC and Izaak Walton Killam graduate scholarships at

the University of Alberta.

References

[1] J.E. Bertie, R.N. Jones, C.D. Keefe, Appl. Spectrosc. 47 (1993) 891.

[2] J.E. Bertie, R.N. Jones, Y. Apelblat, C.D. Keefe, Appl. Spectrosc. 48

(1994) 127.

[3] J.E. Bertie, R.N. Jones, Y. Apelblat, Appl. Spectrosc. 48 (1994) 144.

[4] J.E. Bertie, Z. Lan, R.N. Jones, Y. Apelblat, Appl. Spectrosc. 49

(1995) 840.

[5] J.E. Bertie, C.D. Keefe, R.N. Jones, Tables of Intensities for the

Calibration of Infrared Spectroscopic Measurements in the Liquid

Phase, Blackwell Scientific Publications, Oxford, 1995.

[6] J.E. Bertie, C.D. Keefe, Fresenius J. Anal. Chem. 362 (1998) 91.

[7] J.E. Bertie, Y. Apelblat, C.D. Keefe, J. Mol. Struct. 550/551 (2000)

135.

[8] C.D. Keefe, J. Pittman Appl. Spectrosc. 52 (1998) 1062.

[9] C.D. Keefe, L.A. Donovan, S.D. Fleet, J. Phys. Chem. A. 103 (1999)

6420.

[10] C.D. Keefe, L.A. Donovan, J. Mol. Struct. 597 (2001) 259.

[11] C.D. Keefe, S. MacInnis, T. Burchell, J. Mol. Struct. 610 (2002) 253.

[12] C.D. Keefe, E. Brand, J. Mol. Struct. 691 (2004) 181.

[13] C.D. Keefe, J. Barrett, L.L. Jessome, J. Mol. Struct. 734 (2005) 67.

[14] C.D. Keefe, J.K. Pearson, A. MacDonald, J. Mol. Struct. 655 (2003)

69.

[15] C.D. Keefe, J.K. Pearson, J. Mol. Struct., in press.

[16] J.E. Bertie, C.D. Keefe, J. Mol. Struct. 695–696C (2004) 39.

[17] J.E. Bertie, S.L. Zhang, C.D. Keefe, J. Mol. Struct. 324 (1994) 157.

[18] J.K. Wilmshurst, H.J. Bernstein, Can. J. Chem. 35 (1957) 911.

[19] M.A. Kovner, B.N. Snegirev, Opt. i Spekt. 5 (1958) 134.

[20] M.A. Kovner, B.N. Snegirev, Opt. Spectrosc. 9 (1960) 90.

[21] N. Fuson, C. Garrigou-Lagrange, M. Josien, Spectrochim. Acta 16

(1960) 106.

[22] E.W. Schmid, J. Brandmuller, G. Nonnenmacher, Z. Elektrochem. 64

(1960) 726.

[23] Y. Kakiuti, H. Saito, T. Yokoyama, J. Mol. Spectrosc. 32 (1969) 247.

[24] C.L. Lau, R.G. Snyder, Spectrochim. Acta 27 (1971) 2073.

[25] D. Haaland, G.C. Nieman, J. Chem. Phys. 59 (1973) 4435.

[26] L.M. Sverdlov, M.A. Kovner, E.P. Krainov, Vibrational spectra of

polyatomic molecules, Halsted Press, New York, 1974.

[27] G. Varsanyi, Assignments for Vibrational Spectra of Seven Hundred

Benzene Derivatives, vol. 1, Wiley, New York, 1974.

[28] V.J. Morrison, J.D. Laposa, Spectrochim. Acta 32A (1976) 443.

[29] A. Kuwae, K. Machida, Spectrochim. Acta 34A (1978) 785.

[30] J.A. Draeger, Spectrochim. Acta 41A (1985) 607.

[31] Y. Xie, J.E. Boggs, J. Comput. Chem. 7 (1986) 158.

[32] M. Tasumi, T. Urano, M. Nakata, J. Mol. Struct. 146 (1986) 383.

[33] J.J.P. Stewart, S.R. Bosco, W.R. Carper, Spectrochim. Acta 42A

(1986) 13.

[34] W.J. Balfour, Y. Fried, Can. J. Phys. 72 (1994) 1218.

[35] W.J. Balfour, R.S. Ram, Can. J. Phys. 72 (1994) 1225.

[36] V.M. Grosev, H.W. Schrotter, J. Jomuscheit, J. Raman Spectrosc. 26

(1995) 137.

[37] T.S. Bican, H.W. Schrotter, V.M. Grosev, J. Raman Spectrosc. 26

(1995) 787.

[38] H.F. Hameka, J.O. Jensen, J. Mol. Struct. (Theochem) 331 (1995) 203.

[39] R.R. Randle, D.H. Whiffen, Trans. Faraday Soc. 52 (1956) 9.

[40] M. Akiyama, Spectrochim. Acta 40A (1984) 781.

[41] Y. Kakiuti, Y. Suzuki, M. Onda, J. Mol. Spectrosc. 27 (1968)

402.

[42] M.A. Kovner, B.N. Snegirev, Opt. Spectrosc. 11 (1961) 313.

[43] B. Galabov, S. Ilieva, T. Gounev, D. Steele, J. Mol. Struct. 273 (1992) 85.

[44] J.E. Bertie, C.D. Keefe, R.N. Jones, Can. J. Chem. 69 (1991) 1609.

[45] J. Fahrenfort, Infra-Red Spectroscopy and Molecular Structure: An

Outline of the Principles in: M. Davies (Ed.),, Elsevier, Amsterdam,

1963.

[46] J.W. Warner, M. Wolfsberg, J. Chem. Phys. 78 (1983) 1722.

[47] M.J. Dignam, Appl. Spectrosc. Rev. 21 (1988) 99.

[48] J.E. Bertie, S.L. Zhang, J. Mol. Struct. 413/414 (1997) 333.

[49] J. Timmermans, in: Physico-Chemical Constants of Pure Organic

Compounds, vol. 2, Elsevier, Amsterdam, 1965. p. 100.

[50] G. Herzberg, Molecular Spectra and Molecular Structure. II. Infrared

and Raman Spectra of Polyatomic Molecules, D. Van Nostrand

Company, Inc., Princeton, 1945.

[51] F.A. Miller, J. Raman Spectrosc. 19 (1988) 219.

[52] E.B. Wilson Jr., Phys. Rev. 45 (1934) 706.

[53] E.B. Wilson Jr., J.C. Decius, P.C. Cross, Molecular Vibrations: The

Theory of Infrared and Raman Vibrational Spectra, McGraw-Hill,

New York, 1955.

[54] L. Goodman, A. Ozkabak, S. Thakur, J. Phys. Chem. 95 (1991) 9044.

[55] H.D. Rudolph, H. Dreizler, A. Jaeschke, P.Z. Wendling,

Z. Naturforsch, 22A (1967) 940.

[56] T. Udea, T. Shimanouchi, J. Mol. Spectrosc. 28 (1968) 350.

[57] J.E. Bertie, Y. Apelblat, unpublished.

[58] J.E. Bertie, C.D. Keefe, J. Chem. Phys. 101 (1994) 4610.

Infrared intensities of liquids XXV: Dielectric constants, molar polarizabilities and integrated intensities of liquid toluene at 25C between 4800 and 400cm-1IntroductionExperimentalResultsSpectra of other intensity quantitiesVibrational integrated intensities

DiscussionVibrational assignmentsIntensities of the fundamental vibrations

SummaryAcknowledgementsReferences

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