1918
R.
Clark and A. J. McCaffery
Assignment of Vibrational Symmetries in the Monohalobenzenes Using Circularly Polarized Raman Spectroscopy R. Clark and A. J. McCaffery” School of Molecular Sciences, University of Sussex, Erighton BN 1 9QT. England (Received February 22, 1977)
We present a phenomenologicaldescription of the Raman scattering of circularly polarized light by molecules and its detection by polarization modulation techniques. We illustrate the method with the Raman spectra of benzene and the monohalobenzenes, which demonstrate that this technique has several advantages. First the spectra emerge with a sign and magnitude characteristic of the symmetry of the scattering tensor and secondly the spectra exhibit characteristicline shapes. The combination of these features proves very valuable in analyzing complex Raman spectra. As a result we have been able to make a number of new assignments in the spectra of the monohalobenzenes in spectral regions where there is overlap of more than one feature.
Introduction In recent years laser Raman spectroscopy has been used to tackle a very wide range of spectroscopic,chemical, and physical problems and it is now firmly established as a physical technique of great value in structural studies. Individual Raman bands have several characteristic properties such as wavelength, line shape, intensity, and polarization, from which information may be extracted and it is the last of these, the polarization of Raman scattered lines, which is of concern to us in this paper. It is well known that the polarization of scattered radiation is characteristic of the scattering mechanism and thus reveals information on the nonzero elements of the scattering tensor. This has been used for some time in a qualitative fashion to distinguish totally symmetric vibrations, which generally scatter highly polarized light, from nontotally symmetric modes which generally do not. Very recently a more quantitative approach has been in evidence particularly with regard to the resonance Raman effect and both McClainl and Spiro2have emphasized the value of full polarization measurements. Until now experimental determination of Raman polarization ratios has been accomplished using very simple and rather crude technique^.^ These suffer from several inherent difficulties, some of which are described in a paper by D a ~ s o n .In ~ other forms of spectroscopy, polarized intensities are routinely measured to a high degree of sensitivity and accuracy using modulation techniques5and there is no reason why these methods should not be applied in Raman spectroscopy. In recent we have demonstrated that substantial advantage is gained by using modulation methods, particularly if both linearly and circularly polarized intensities are recorded.8 The latter point concerning so-called “complete” polarization measurements applies particularly in the case of resonance Raman, though precise measurements of circular intensities are of considerable value in analyzing complex vibrational spectra in the nonresonant case as we demonstrate in this publication. Here we develop the preliminary communication of the circular differential techniques reported earlier6 in a study of the vibrational spectra of the monohalobenzenes. Some of the earliest experimenters in Raman spectroscopy were aware of the value of using circularly polarized light and both Han1e”l’ and B&rl2J3 recorded linear and circular intensities. Placzek,I4 in his comprehensive development of the theory of the Raman effect, derived explicit expressions for the intensity of circularly and linearly polarized scattered radiation in terms of scattering tensor invariants. Thus both theory and experiment The Journal of Physical Chemistty, Vol. 81, No. 20, 1977
presented in this paper are not truly new. The novel feature in this work is the accuracy, precision, and reliability of the polarization measurements and their presentation, with characteristic line shape, as differential quantities using modulation techniques. In the circular difference spectrum obtained from modulated Raman spectroscopy, bands emerge with a sign which is directly related to the nonzero elements of the scattering tensor. This sign persists even in fluid media (though not for the linear difference spectrum except in the resonance case8). The sign of polarization may be used to distinguish totally symmetric from nontotally symmetric modes even in complex overlapping regions. The magnitude of the circular polarization ratio, C, is of value in more subtle investigations of molecular geometries and in fully characterizing the scattering tensor. This particular aspect will be touched on later in this paper.
Theory An arbitrary polarization E, of an electromagnetic ray propagated in a direction defined to be the z axis of the coordinate frame may be described in terms of two mutually orthogonal vectors which are simultaneously orthogonal to the direction of propagation. These basis vectors are generally chosen to be the real Cartesian coordinates E,, E,, or may be the complex coordinates E+1, E-1. Linear combinations within either basis may describe any arbitrary polarization of light, circular, linear, or elliptical. If we are concerned only with linearly polarized light the real basis is most appropriate since E,, E, represent light polarized such that the electric vectors lie in the x , y directions respectively with 2 as the direction of propagation. On the other hand, circularly polarized light is best written in the complex basis since E+1,E-1 represent the two circular polarizations, left and right handed. In this latter basis Eo (=E,) is the third coordinate. The experiments described in this paper concern the scattering of circularly polarized light exclusively and thus the complex basis is most appropriate. The derivation of experimental parameters follows closely the work of McClainl except in the use of the tensor invariants which are best expressed in forms familiar to the Raman spectroscopist. This experiment therefore lies on the double circular locus of the two photon experiment plane defined by McClain, and it is clear that for the conditions of this study, a “complete”1*8 determination is not necessary. For a Raman experiment in the absence of external magnetic fields and with the excitation frequency well removed from an absorption band just two polarization measurements suffice to completely determine
Vibrational Symmetries in the Monohalobenzenes
1919
the scattering tensor pattern. These two may be circular or linear intensities. Since it is the purpose of this work to demonstrate the advantages of circular modulation methods, a phenomenological description is developed in terms of the complex coordinate frame. This coordinate system is relatively unfamiliar to the practising Raman spectroscopist, hence the relevant expressions will be developed in slightly more detail than is customary in papers of this type. The relationship between the induced dipole moment Me and the electric field Eo of the incident laser radiation is
k..] =[
[Mti M-1 Mol E - 1
[
which may be rewritten as p , u = +1,0 M, = Xa,,E-, 7 I
I
Mt1E-1 M-1.23-1 MoE-1 MtlEt1 M-lE+l M d t 1 M+lEO M-lEO MoEo a+1-1 a-1-1 ao-1 = a+1+1a-1+1 aot1 = a (1) atlo a-10 a00
3
(2)
In terms of Cartesian coordinates A 1 = (l/ds)(x f iy), 0 = z. The intensity of scattered radiation of a specified polarization is given in standard textSl4and is proportional to the square of sums of elements of the scattering tensor. Hence, as is well known, the relative intensities of the two polarizations defining the point specified in the experimental plane is diagnostic of nonzero elements in the scattering tensor. In this way we are able to determine the scattering tensor pattern and from this the symmetry of the vibrational mode inelastically scattering the detected photons for molecules of favorable symmetry groups. The halobenzenes used in this study belong to the C2”point group and, in this group, each of the normal modes may be represented by a tensor which is “pure”. The significance of this latter classification will become apparent later in the development. McClain’sl tabulation of scattering tensor patterns is particularly valuable since we may use his expression for the Raman scattering intensity, Is.
I/
- A -
a
Ih a p VIA’
(3)
where and ii are the polarization vectors of incident (I:) and scattered (I;) photons and & is the scattering tensor. The operation of this equation for the CZvpoint group reveals the key features of circular polarization measurements and modulation techniques. For a totally symmetric AI vibrational mode the tensor pattern is diagonal.’ If we stimulate Raman scattering from this mode using E+polarized light, it is straightforward to show from eq 3 that pure E+ polarized light is scattered. On the other hand, if scattering from an A2 mode is examined, eq 3 predicts that E- polarized light will be observed and in this form of inelastic scattering the molecule has acted as a half-wave retardation device. In a modulation experiment Al intensity will show up as a positive feature in the Raman spectrum while the A2 mode will be characterized by a negative band. We note at this point that it is convenient to refer to the incident polarization as (+) whatever its actual handedness, In order to discuss the Raman scattering of molecules in fluid media I,”must be averaged over all molecular orientations. This is a standard procedure which is in fact simplified by the use of complex coordinates. Following this procedure it is usual to express the elements of the scattering tensor in terms of tensor invariants. These
invariants may then be related directly to experimental observables. The expressions for the isotropic, anisotropic symmetric, and anisotropic antisymmetric tensor invariants are, respectively
Ys2 =
l/2$(aji
ya2 =
3 / 4 i -2 #j
-
ajjy
+ 3/4(ajj + aji)
(4b)
(ajj -
In eq 4a-c the aii)srepresent diagonal elements and qi)s off-diagonal elements of the tensor defined in eq 1. The tensor invariants may be directly related to experimental observables to obtain expressions for the intensity I+a and of (+) and (-) polarized scattered radiation. Our experimental measurements are in terms of circular intensity differences and sums, (I+- I-) and (I+ I-),where the superscript has now been dropped. More convenient is the circular polarization ratio which, in terms of the tensor invariants, is given by
+
I+- I - - 45E2 - 5y,2 + 5ya2 c=-It + I - 4 5 z 2 + 7ys2 + 5y,2
(5)
In this study of scattering by vibrational modes of molecules stimulated by laser radiation far from an absorption band, and in the absence of magnetic fields, it can be shown that 7,”vanishes. Thus we look for experimental conditions under which C is nonzero by virtue of contributions from the isotropic or from the symmetric anisotropic invariants. For molecules belonging to symmetry groups in which the scattering tensors are “pure” with only a single nonzero invariant in each tensor’ two simple situations emerge. First for symmetric, or trace, scattering a’ # 0 ys,2= 0, and C = 1.0. Secondly for antisymmetric scattering a’ = 0 y: # 0,72 ,= 0, and C = -5/7. Thus the function (I+ - I-)changes sbgn for the two forms of scattering described above. Furthermore the quantitative values for C are indicative of scattering mechanism. These two properties are of considerable value in assigning a Raman spectrum. The sign of polarization indicates the symmetry of the normal mode directly since for molecules of most symmetry groups it is the totally symmetric modes which have symmetric tensor patterns and thus positive values of (I+ - I-). Nontotally symmetric modes on the other hand have antisymmetric tensor patterns and thus have negative circular polarizations. This is particularly useful for analyzing complex Raman spectra since a count of totally symmetric modes may be made directly. Shoulders on strong bands may be easily discerned in this differential technique. The quantitative values of C for individual bands may be measured to a high degree of precision and this may be of considerable value. Deviations from the theoretical values quoted above are indicative of overlapping bands, antisymmetry or mixing in the scattering tensor for example and thus may provide a subtle probe of hidden complexities. This phenomenon is indeed observed for more than one band in the spectra reported here. If complete1polarization measurements are available as in the modification of the above techniques described by Horvath and McCafferys a full determination of the nonzero elements of the scattering tensor is feasible in circumstances where the simple formulae for C break down. These instances include the antisymmetric scattering found in the resonance and electronic Raman effects, scattering from certain molecules in the presence of magnetic fields,16and in molecules for which the inertial The Journal of Physical Chemistty, Vol. 8 1, No. 20, 1977
R. Clark and A. J. McCaffery
1920
and polarizability tensor axes are not coincident.16
Experimental Section The experimental details of our polarization-modulated Raman spectrometer have been given in earlier publications.' Here we give only a brief outline of the method and its main features. The use of polarization modulators is well established in other forms of spectroscopy6 and our application is a straightforward extension of the techniques established by Kemp5 to Raman spectroscopy. The measurement of circular polarization ratios requires either 180 or 360° geometry, i.e., the collected light must be back or forward scattered. Recently we have demonstrateds that backscattering has advantages particularly in the resonance case. For both forms however the Principle is the same. Circularly polarized laser radiation is produced using a X/4 retardation device and the scattered radiation is phari(zation-analyzed by means of a photoelastic modulator followed by a calcite linear polarizer. This produces an intensity modulation proportional to the degree of polarization of the scattered radiation and which is amplified synchronously with a reference signal from the modulator. A simultaneous d.c. signal is proportional to the total emitted intensity and is amplified by a Keithley picoammeter. The two signals, circular intensity difference (proportional to I+ - I-)and total intensity (proportional to I+ + I-) are presented on a two-pen chart recorder. Wavelength analysis is by means of a Spex 1406 monochromator. The two scales may be calibrated relative to one another by standard techniques7 and thus a sensitive and precise polarization measuring device is available. The advantages of this form of presentation are that the line shapes of both functions emerge routinely. In regions of heavy band overlap this may be very valuable as demonstrated in this publication. Light of only a single polarization enters the monochromator hence depolarization devices are not needed and the problem of variable response of gratings to light of different polarizations and frequencies is avoided. Full polarization information is obtained in just a single run, the two functions emerging simultaneously; changes in the sample or the instrument do not affect comparability therefore. Overlapping bands of opposite polarization may be resolved very easily and in general it should not be necessary to curve-fit in order to extract meaningful data. We feel that this form of Raman spectroscopy has a great many advantages over conventional techniques and it is particularly suited to routine determination. There is of course a change of geometry compared to some commercial spectrometers and this may make the modification more difficult, With regard to sampling procedures, there is no limitation on the sample type which does not apply to all forms of polarization spectroscopy, including Raman, and for Raman spectroscopy of complex systems the modulation techniques we have described have a great deal of practical advantage. The liquids used in this study, benzene and the monohalobenzenes, were carefully purified by distillation and GLC analysis showed them to be at least 99.5% pure. Path lengths were usually 1cm, though cells of up to 15 cm in length may be used to enhance the signal intensity. Excitation was by means of the 5145-A line of a Spectra-Physics argon ion laser. Results and Discussion We begin with a discussion of the main features of the Raman spectrum of benzene, the parent hydrocarbon of The Journal of Physical Chemistry, Vol. 81, No. 20, 1977
1000
c m-'
2000
3000
Flgure 1. The Raman spectrum (lower curve) and circular polarization (upper curve) of liquid benzene. The lower curve is the function ( I + I_)while the upper curve is ( I + - I-). In ail cases the input light is assumed to have (+) polarization with positive signed peaks lying above the baseline and neaative below.
+
this series. This molecule has 30 normal modes and in the D6h point group, seven of these are Raman active in their fundamentals. Two of these Raman-active modes have Al, symmetry, four have Etg,and one has El, symmetry. Two totally symmetric modes are prominent in the spectrum (Figure 11, the C-H stretch (vl) at 3062 cm-l and the ring breathing mode (v2)at 992 cm-l. Both show strong positive polarizations with C = 1.0. All other bands in the spectrum have negative C values and are thus nontotally symmetric modes. The assignment of these main features is well known.17 The El, C-H out-of-plane bending mode (ull) is at 849 cm-l and is the weakest of the bands shown. The EZggroup of bands includes v18, the lowest energy band shown, at 606 cm-l. This is the C-C-C in-plane bending mode. The other E2, modes exhibit features at 1178,1585, and 3047 cm-l and are u17, the C-H in-plane bending vibration, v16 the C-C stretch, and ~ 1 the 5 C-H antisymmetric stretching vibration, respectively. v16 is in fact one component of a resonance doublet with the combination v 2 + vlS which also has EZgsymmetry. All of the E modes have C = -0.7. The introduction of just a single halogen substituent into the benzene molecule reduces the overall symmetry from D6h to CZuand results in a much more complex vibrational spectrum. All 30 vibrational modes become allowed in the Raman spectrum and consequently the halobenzenes represent a considerable assignment problem. Some years ago Whiffeds undertook a thorough study of these molecules and the terminology and classification of bands used here are very similar to those of Whiffen. Group theory indicates that of the 30 fundamental modes in the monohalobenzenes there are eleven of Al symmetry, three of A2, six B1, and ten B2 modes. There is a significant deviation from the notation adopted by Whiffen here since spectroscopic conventionlgnow requires the plane of the benzene ring to define the yz plane of the molecular coordinate frame. As a result the modes labeled B1 by Whiffen are now considered to be Bz and conversely the Bz modes of Whiffen appear in this work as B1. It is most convenient to consider the vibrations in terms of approximate normal modes and group frequencies and for this reason the bands are divided into five categories to aid the identifications. These correspond approximately to the group vibrations of parent hydrocarbon, namely, C-H stretch, C-H bend, C-C stretch, ring bend, though now we have new modes involving the substituent X and these form a separate category. (i) The C-H Stretching Frequencies V C - ~There are five C-H stretching modes which are expected to scatter radiation in the region near 3000 cm-l and the circularly
1921
Vibrational Symmetries in the Monohalobenzenes
Si00
C k ’
3100
3000
cm”
1100
,
500
1000
c m-l
1500
Flgure 4. Raman spectrum (lower curve) and circular polarization of fluorobenzene to 1650 cm-’. Signs are as in Figure 1.
3000
Cm-1
3;OO
Flguro 2. Raman spectra (lower curves) and circular polarizations(upper curves) of the monohalobenzenesin the region 3000 to 3150 cm-’. Signs are as in Figure 1.
r
500
cm-‘
I000
1500
Figure 5. Raman spectrum (lower curve) and circular polarization of chlorobenzene to 1650 cm-’. Signs are as in Figure 1.
d X
I
x
I
b
x
x
x
500
cm-l
1000
1500
Flgure 8. Raman spectrum (lower curve) and circular polarlzatlon of bromobenzene to 1650 cm-‘. Signs are as for Flgure 1. Figure 3. The normal modes of the 25 fundamentals of the monohalobenzenes which occur below 1650 cm-’ (from ref 18). Refer to Table I for symmetry designations.
polarized Raman spectra of the four monohalobenzenes in this region are shown in Figure 2. All the other fundamentals lie below 1650 cm-l but various combination bands and overtones contribute weak features around the C-H stretch bands which maybe Fermi resonance enhanced. Inspection of Figure 2 however reveals that in the spectra of all four halobenzenes there is a strong peak at 3070 cm-I having C = 1.0 while to lower energy there is a shoulder having opposite polarization. This may be seen clearly in the circular polarization signal though is illdefined in the conventional Raman spectrum. This can be interpreted as being due to a t least one of the B2 V C - ~ modes lying about 10 cm-l below the main Al uGH mode. In fluorobenzene there is a pronounced shoulder to high energy of the main peak and this has positive polarization. There is also some sign of this shoulder in the other spectra
in Figure 2. This presumably is another of the VC-H Al modes though a combination Fermi resonance enhanced cannot be ruled out. The circular polarization results clearly establish however that this composite band has a nontotally symmetric component to long wavelength and an AI component to short. (ii) The Substituent-SensitiveVibrations.,.,v The remaining vibrations are those lying below 1650 cm-l and do not involve the C-H stretch. Figure 3 shows the 25 normal modes considered by Whiffeds and the letters on this figure are used in the discussion belbw to refer to individual vibrations. The symmetry designations are shown in Table I. The first group we shall consider are the six modes which involve the motion of the substituent and hence may be expected to decrease in frequency as the mass of the halogen substituent increases. Of these six modes, three have Al symmetry, two have B1,and one has B2symmetry. The circularly polarized Raman spectra of the four monohalobenzenes up to 1650 cm-l are shown The Journal of Physical Chemistry, Vol. 81, No. 20, 1977
1922
R. Clark and A. J. McCaffery
TABLE I: Assignment of the Fundamental Frequencies (cm-' ) of the Monohalobenzenes from the Circularly Polarized Raman Spectra 6'
Assignment
C, H5C1
H5
C,
H5Br
C6H51
U
C
U
C
U
C
U
C
3070
t 1.0
3071
t 1.0
3066
t 1.0
3065
+ 1.0
3050
1 (+ 1 - 0.7
3050
(-
1 (i- 1
3055
(-
1
3050
(-
-0.7
1477 1579
(t)
- 0.7
1473 1574
(+ 1 - 0.7
(+) (- 1 (- 1 - 0.3 (+ 1 - 0.3 (-
1372 1445 1325
(t)
1370 1442 1323
(+) (- ) (- 1
1367 1442 1324
(t1 (- ) (- 1
- 0.4
-0.7
1180 1176 1158
(- ) t 0.4 - 0.7
1178 1178 1162
(- 1 t 1.0
- 0.7
t 1.0
1173 1165 1158 1067 1023
1018
t 1.0
1020
t 1.0
t 1.0
1003
t 1.0
998
t1.0
1002
+1.0
1 1 1 1
900 829 736
(((-
1 1 1
909 839 7 38
(- 1 (-) (- 1
610 402
- 0.7 (- 1
687 616 406
-0.7
(-
1474 1597 1605 1376 1456 1302 1165 1160 1154 1068 1024 1008
1478 1583
(-1 (- 1
(i-)
901 833 760
(((-
1 1 1
905 831 744
(((-
691 617 408
(- 0.7 (- 1 t 1.0 t 1.0 (t) (- 1 (- 1 - 0.7
700 616 393
(- 0.7 (- 1
t 0.5
(-
1
(-
1
1221 1084 1075 t1.0 t1.0 1062 +l.O 808 707 + 1.0 670 t 1.0 +1.0 658 523 410 + 1.0 313 t 1.0 270 + 1.0 523 299 - 0.7 248 -0.7 221 -0.7 503 470 459 455 (- 1 (- 1 (244 199 - 0.7 177 - 0.7 - 0.7 169 a For weak or overlapping lines, only the sign of C is given. The notation is from Whiffen18 with b, and b2 interchanged (see text).
(000
500
1500
cm-'
Flgure 7. Raman spectrum (lower curve) and circular polarization of iodobenzene to 1650 cm-'. Signs are as for Figure 1.
in Figures 4-7 and it is clear that although these spectra are complex, strong similarities exist in the vibrational spectra of these compounds. Identification of the substituent-sensitive bands is best accomplished using the correlation chart drawn in Figure 8 where the strongly shifted bands.are immediately apparent. The three intense peaks at lowest energy in iodobenzene (Figure 7) clearly move to higher energy as we progress up the series and correspond'' to a B1, a Bz, and an A2 vibration. The B1 lies lowest in energy1' followed by the Bz,generally weaker than the Al which has the highest energy of this group. Both the B1 and B2have negative polarization as required by theory while the Al bands all have C = 1.0. The other AI bands are found near 700 and 1100 cm-I (Figure 8) in The Journal of Physical Chemistry, Vol. 81, No. 20, 1977
Figure 8. Correlation chart depicting the assignments of the features below 1650 cm-l in the four monohalobenzenes. The substituent sensitive bands may be clearly seen from the chart by their wavelength shifts with substituent.
chloro, bromo, and iodobenzenes and have polarization data consistent with these assignments. The remaining B1 is at 470 cm-l and does not shift greatly with substituent except for fluorine. The assignments in fluorobenzene require more careful study. The highest frequency A1 band of the low energy group is shifted 150 cm-I compared to chlorobenzene and the close-by Bz band seems to disappear. However the circular polarization trace shows that the polarization ratio of the Al band is much reduced from theoretical and that there are "wings" of opposite polarization on either side of the main peak. This indicates two transitions of different symmetry that are nearly coincident. The nontotally symmetric component is most
1923
Vibrational Symmetries in the Monohalobenzenes
likely the missing B2 x-sens mode and this example provides an illustration of the power of the differential technique in decomposing two overlapping bands. The remaining substituent sensitive bands in fluorobenzene may be identified by reference to Figure 8. (iii) The Ring Modes + c c and ac-c-c. The assignment of the substituent-sensitive modes enables us to identify the low frequency ring modes. The lowest energy of these is an A2 mode assigned as the peak at 400 cm-l in fluorobenzene. This band is nearly obscured by the strong 410-cm-l band in chlorobenzene though a shoulder having the required negative polarization may be discerned. It is clearly visible in the other halobenzenes. The other 4c-c band which has B1 symmetry lies just below 700 cm-’ but is obscured in both chloro- and bromobenzene. The inplane ring deformation ac-c-c (B,) is clearly visible near 610 cm-’ in all of the spectra and the Al ring-breathing mode is prominent near 1000 cm-l. (iv) The C-H Deformations 7 c - H and &-Ha There are five out-of-plane C-H deformations (7C-H) to be assigned in the region 700-900 cm-’ lS all of which are nontotally symmetric (Table I). Three of these may be identified directly from the spectra in this region, though one is obscured in fluorobenzene. The remaining two, which should have negative polarizations, are not apparent in our spectra. Of the five in-plane C-H deformations (&H) two have Al symmetry and should have positive C values. The circular polarization is quite valuable in assigning these frequencies since there are overtone and combination bands which may interfere in the region around 1100 cm-l. The lowest frequency &-H deformation mode is the Al band at about 1020 cm-’. There is a B2mode in this group at 1068cm-’ which is obscured in bromo- and iodobenzenes while the other Al and two B2 bands lie just below 1200 cm-l. That this group of three modes lie together in this region is apparent from the circular polarization though not from the Raman spectrum. Bromobenzene is perhaps the most marked of the four species in this respect though close inspection of all the spectra show evidence for the two negative and one positive overlapping bands. The apparent doublet in the circular polarization spectrum of fluorobenzene at 1140 cm-l has a C value of -0.3. The structure and polarization ratio may be explained if we assume that the three /3C-Hmodes lie together with the Al band in the center of two B2 bands. In bromobenzene (Figure 6) two separate peaks are visible just below 1200 cm-l but the circular polarization indicates that the higher energy peak is in fact a doublet of bands having opposite polarizations. In chlorobenzene the magnitude of C for the higher energy B2band again indicates an underlying Al while in iodobenzene the shoulder on the Al feature has positive C and hence cannot be one of the B2 modes. A resonance enhanced combination (f y, for example) is the most likely cause of this shoulder. On the other hand the magnitude of the Al C value is only 0.5 which suggests that the B2 & - H is buried underneath this feature. (v) The C-C Stretching Region VC-C. The C-C stretch region lies between 1300 and 1600 cm-l and consists of two Ai's and three B2’S. The most prominent feature is at approximately 1600 cm-’ and contrary to previous
+
assignmentsl8Pz0there is no Al mode in this region. The C values in all four spectra are -0.7 and the main feature must be a B2mode. There is also a possibility of resonance between this and the s + p combination tone, a combination which involves two strong ring modes, and this is clearly shown in the splitting of the fluorobenzene line. Between 1300 and 1500 cm-l there are four bands which occur in essentially the same place in all four spectra, two with positive and two with negative polarization. These are most clearly seen in chloro- and bromobenzenes. They are assigned as the remaining two B2’S and the Al’s the latter two having positive polarization.
Conclusion In this paper we have developed further this novel form of Raman spectroscopy, namely, the measurement of circularly polarized intensities using modulation techniques, The main features of this method are that bands emerge with a characteristic sign which is directly related to the symmetry of the vibrational mode responsible for the band. In addition, quantitative values of polarization parameters are available routinely and this factor, together with the display of the characteristic line shape of the polarization enables the identification of overlapping peaks of opposite sign. We have presented the phenomenological theory of scattering of circularly polarized light and have demonstrated the technique with the Raman spectra of benzene and the four monohalobenzenes. With the aid of the circular polarization methods we have been able to make a number of new assignments and it is clear from this presentation and other papers in this seriess that modulation methods can make significant improvements to the technique of Raman spectroscopy and that this is of particular value in analyzing the spectra of complex molecules. Acknowledgment. We thank the Science Research Council for support of this investigation and for a postgraduate studentship to R.C. References and Notes (1) W. M. McClain, J . Chem. Phys., 55, 2789 (1971). (2) J. Nestor and T. G. Spiro, J . Raman Spectrosc., 1, 539 (1973). (3) C. E. Hathaway in “The Raman Effect”, Vol. 1, A. Anderson, Ed., Marcel Dekker, New York, N.Y., 1973, p 183. (4) P. Dawson, Spectrochim. Acta, Part A , 28, 715 (1972). (5) J. C. Kemp, J. Opt. SOC.Am., 59, 950 (1969). (6) R. Clark, S. R. Jeyes, A. J. McCaffery, and R. A. Shatwell, J . Am. Chem. SOC.,97, 7015 (1974). (7) A. J. McCaffery and R. A. Shatwell, Rev. Sci. Instrum., 47, 2 (1976). (8) L. I. Horvath and A. J. McCaffery, J. Chem. SOC.,Faraday Trans. 2, 73, 562 (1977). (9) W.Hanle, Z . Phys., 32, 556 (1931). (10) W. Hanle, Ann. Phys., 11, 885 (1931). (11) W. Hanle, Ann. Phys., 15, 345 (1932). (12) R. Bar, Helv. Phys. Acta, 4, 130 (1931). (13) R. Bar, Z. Phys., 79, 455 (1932). (14) G. Placzek, “Handbuch der Radiologie”, Vol. 6, E. Marx, Ed., 2nd ed, Akademische Verlagsgesellschaft. Leipzig, 1934, p 205. (15) L. D. Barron, Mol. Phys., 31, 129 (1976). (16) A. J. McCaffery,!. A. Madden, R. Clark, and S. Witty,to be published. (17) G. Herzberg, Infra-Red and Raman Spectra of Polyatornic Molecules”, Van Nostrand, Princeton, N.J., 1945. (18) D. H. Whiffen, J . Chem. SOC., 1350 (1956). (19) D. H. Whiffen, J . Chem. Phys., 23, 19 (1955). (20) C. T. Meneely, C. Y. She, and D. F. Edwards, J. Mol. Spectrosc., 39, 73 (1971).
The Journal of Physical Chemistry, Vol. 8 1, No. 20, 1977
