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Far IR spectra of acetic acids in the gas phase. A reinvestigation of the intermonomer vibrations
273
Journal of Molecular Structure, 237 (1990) 273-283 Elsevier Science Publishers B.V., Amsterdam
FAR IR SPECTRA OF ACETIC ACIDS IN THE GAS PHASE. A REINVESTIGATION OF THE INTERMONOMER VIBRATIONS*
H.R. ZELSMANN**,
Z. MIELKE’”
and Y. MARECHALt
Dkpartement de Recherche Fondamentale/Service de Physique, Groupe Physico-Chimie MolPculaire, Centre d%tudes Nuclkaires de Grenoble, 85X-38041 Grenoble Ceden (France) (Received 6 November
1989 )
ABSTRACT As part of our programme on the dimers of carboxylic acids, we report here results from the far infrared spectra in the 20-230 cm-’ region for the four isotopically substituted species of acetic acid dimers (CH,COOH )2, (CH,COOD )2, (CD,COOH )x, (CDsCOOD )z. These more confident and in parts entirely new experimental data permit us to assign the third IR active low-frequency vibration that was missing up to now. In good agreement with earlier predictions, this mode has been observed at 56 cm-’ for the totally hydrogenated dimer. Furthermore, on these new quantitative spectra the isotopic ratios of the band positions of the intermonomer vibrations are checked against those of the moments of inertia for the H-bond (or D-bond) samples separately. The comparison of the intensities of the FIR absorption bands allows us to postulate a slight but specific difference between an O-H * - *O and 0-D. * -0 bond. For the complex band centred at 171 cm-’ we propose an analysis of the band shape by Fermi resonance interactions.
INTRODUCTION
Being one of the simplest organic compounds, acetic acid is certainly one of the molecules for which we have the most complete knowledge of physical and chemical properties. On closer examination of these properties, it turns out that they are conditioned to a large extent by the ability of this molecule to form associations via hydrogen bonds. This may happen in the solid state by forming linear chains or even simpler in the gas phase by forming cyclic dimers. However, if one asks now about the interaction between two of these molecules or what does the hydrogen do when the two molecules vibrate, our understanding becomes poorer. In a recent investigation by mid-IR spectroscopy [ 11, *Presented at the IXth Workshop Bond Research at Zeist (Utrecht ), The Netherlands, lo-15 September 1989. **Universite Joseph Fourier de Grenoble. To whom correspondence should be addressed. ***On leave from Institute of Chemistry, University of Wroclaw, Wrocklaw, Poland. tC.N.R.S.
0022-2860/90/$03.50
0 1990 -
Elsevier Science Publishers
B.V.
274
quantitative formulation of the spectra has been given. The low-frequency vibrations, however, still suffered from a lack of reliable experimental data. This applies especially for the far-IR spectra as the main work [ 2-41 is rather old. A review of these results, together with those of a detailed Raman study [5] has been given in ref. 6. The objective of our present study was to obtain well-defined quantitative spectra for the four different isotopic species of gaseous acetic dimers which permit a comparison of the intensities of the FIR absorption bands and which should allow us to determine the absolute intensities with respect to the values observed in the mid-IR [ 11. Another reason for this study was the still incomplete assignment of the low-frequency spectra and the hypothetical interpretation of some bands in refs. 2-4 by Fermi resonance.
EXPERIMENTAL
Instrumental All spectra were run on an automated Polytec FIR30 interferometer equipped with a Golay and a liquid helium bolometer as detectors. The gas cell was a White multiple-path cell made of stainless steel with a total path length adjustable from 0.8 to 4.8 m and fitted with TPX windows for the far-IR. For the pressure measurements we used a Barocel 600A pressure sensor supplied by Datametrics. The control of the interferometer, the data acquisition and processing were executed by Hewlett Packard equipment. The spectra were recorded in the range of 20-230 cm-’ with an apodized spectral resolution of 2 cm-‘. A path length of 2.4 m turned out to be the optimum choice as all the measurements were repeated for different pressure settings between 1 and 6 torr. The experiment was carried out at a fixed temperature of 23 ‘C. Samples The H acetic acid was a commercial p.A. grade product from Prolabo which was dried over P,O,. The fully deuterated compound was supplied by the Commissariat h 1’Energie Atomique, Service des Molecules Marquees with a guaranteed deuterium content of 99.9%. Some residual water had to be removed by further drying. The samples of CH,COOD and CD,COOH were obtained by isotopic exchange of the acid hydrogen using the respective commercial starting material. Careful and thorough drying was necessary.
275 RESULTS AND DISCUSSION
The intermonomer vibrations In Fig. 1 we show the two gas-phase dimer spectra of acetic acid with OH. . -0 bonds and methyl group substitution, whereas in Fig. 2 we compare the spectra of the corresponding compounds with 0-D. *-0 bonds. These spectra are normalized in pressure, taking the torr as unit of pressure. It should not be I 0.9 = O.E : \
0.7
::
0.6
: m 0.5 6 g
0.4
[r 0.3 0.2 0. I E E WRVENUMBER
(cm-l)
Fig. 1. Normalized FIR spectra of the two species of gaseous acetic acid with CH, methyl groups. Experimental conditions: temperature 23’ C; optical path length 2.4 m.
0.9 :
O.E
: \
0.7
::
0.6
h m 0.5 8 i
0.4
cc 0.3 0.2 0. I 0 0
58
10E
150 WRVENUMBER
2-a-a
250
(cm-l)
Fig. 2. Normalized FIR spectra of the two species of gaseous acetic acid with CD, methyl groups. Experimental conditions: temperature 23°C; optical path length 2.4 m
276
forgotten here that the observed pressure results from the sum of the partial pressures of monomeric and dimeric acids. The equilibrium at ambient temperature and a pressure of a few torr favours the occurrence of dimers, but there is a non-negligible percentage of molecules left which are in the monomeric state. Calculating the fraction of dimers present for a given experimental condition (which has to be done for each pressure and each isotopic substitution by the corresponding KPvalue, extracted from spectra recorded in the midIR region [l] ), it is possible to relate the absorbance readings of the spectra with the effective dimer amount. In doing so, we obtained a series of spectra that could be nicely superposedusing a scaling factor that was just the quantity of dimers. This simple and confident observation of the absorbance being proportional to the number of dimers not only justifies the presentation of normalized spectra, but allows us to consider it as an experimental proof for a simple equilibrium of monomer*dimer, thus excluding any appreciable amount of open dimers. Comparing the two spectra of Fig. 1, we see that they are of similar shape, as are the two spectra in Fig. 2. For the four spectra, we have shown in the figures the position of elementary bands as obtained by a spectral decomposition, which is helpful in a first approach for tracing back the shifts due to the isotopic effect. (It is also useful for reproducing the spectra; the full set of parameters is available upon request. ) In total there should be six low-frequency modes corresponding to the intermonomer vibrations. Due to the centre of inversion of the dimer, three of them are observable by Raman (two A, and one B,), whereas the other three (two A, and one B,) are active in the IR. We have illustrated these six intermonomer vibrations in Fig. 3. For the numbering of the modes we chose the same system as Bertie and Michaelian [ 51 since it presents the most recent experimental work in this field. The values given here are those for the fully hydrogenated acetic acid as observed by Raman [ 51, the IR results coming from our present experiment. For the drawing we used the structure of the monomer determined by van Eijck et al. [ 71. For the 48.5 cm-l band, corresponding to a twist motion of the two monomers, the isotope effect of the band position shows an excellent agreement between observed values and predicted values calculated from the respective moments of inertia [ 71. This band, as well as the more complex one centred at 171 cm-’ which is assigned to the antisymmetric intermonomer stretching vibration, confirms the findings of earlier work by IR spectroscopy [ 2-41. In addition, we found a new band at 56 cm-l which we assign to the still unobserved IR active bending motion of the dimer. Concluding from possible linear combinations and stemming on results of normal coordinate calculations [ 8101, earlier authors expected this band around 880 cm-‘. Checking the validity of our assignment by the isotope effect, it turns out that the observed and the calculated values coincide only approximately, but without being contradic-
277
~.~
o ~
00~
~
oea o
.°
X
~2
E
'
14
Z m ~r rw
O2 rW
C
m rr" r~
4-,.Q ~Orl
I
~
~,;c%___
°
~
tory. The same behaviour is found for the band at 171 cm-l. This fact by itself is not very surprising, but it shows that the isotopic substitution as a help for assignment of the observed bands is not so powerful in the far-IR as it is in the mid-IR. We should take it as an indication that the monomer undergoes a slight structural change upon formation of the dimer. However, the assumption that the 56 cm-l band is the intermonomer bending vibration is well supported by analogy with formic acid dimers [ 111. By transferring in a simple approach the force constants to acetic acid, Bertie and Michaelian [5] found an estimation of 59 cm-l whereas we get, with updated values for the moments of inertia, a band position of 58 cm-‘. We may consider this very satisfactory agreement to be evidence of this assignment. Intensities of the FIR absorption bands The only correct way to measure the intensity of an absorption band consists of evaluating its transition probability. This quantity is defined by eqn. (1) where the factor of proportionality contains only fundamental constants. ‘(‘)
Absorbance ( 5 ) prop’P[l-exp( -hcB/kT)]
(1)
Intensity = Sum of P ( 8) over the band For bands in the mid-IR region, especially in the case of narrow bands, this relation may be simplified by neglecting the variations of the denominator. In the far-IR region, however, we are no longer allowed to do this. The results of these integrations of the spectrum for each isotopically substituted molecule is shown in Fig. 4. It may be seen that there is a general tendency of diminishing intensity of the spectra when substituting hydrogen by deuterium. The most characteristic data are the comparisons between the intensity of an 0-H. *-0 dimer and its O-D - - -0 analog. Summing over the total FIR spectrum between 20 and 230 cm-l, we observe the ratios Intensity tot.sp. ( CH3 COOD ) 2 = o g3 + o o1 Intensity tot.sp. (CH,COOH), ’ ’ and Intensity tot.sp. (CD,COOD )z = o g8 ~ o o1 Intensity tot.sp. ( CD3 COOH ) 2 * ’ There is a significant difference for substitution on the site of the hydrogen bond for molecules with a CH3 group, which is not evident due to the error limits for the case of a molecule with a CD, group. If we compare, in the same way, the intensities of the antisymmetric inter-
279
c
(CH&OoH),
tot. probab.: 34.1 units
KH&OODl,
tot. probab.: 31.8 units
KD,COOH),
tot. probab.: 29.4 units
13.7
Ul,COOD),
units
tot. probab.: 29.7 units
Fig, 4. Intensity of the FIR absorption bands. The observed intensities (or integrated probabilities), given in dimensionless units, are indicated in the boxes on each spectrum. The width of the box represents the bounds of integration.
monomer stretch only, we get, in contrast Intensity asym.st. ( CH3 COOD j2 = o 92 + o o1 Intensity asym.st. ( CH3 COOH ) 2 ’ * and Intensity asym.st. (CD3 COOD), = o 94 ~ o o1 Intensity asym.st. (CD,COOH), ’ a As can be seen, these two ratios are the same within the estimate of the error limits of our observations. This means, in summary, that the absorption bands are slightly less intense for O-D **-0 bonds than they are for O-H- *-0 bonds, a tendency that has already been observed in the mid-IR region for the same compound [ 11.
280
Analysis by Fermi resonance It was suggested for the first time by Miyazawa and Pitzer [8] that the submaxima displayed by the antisymmetric stretching band are due to Fermi resonances. In other words the corresponding vibration is anharmonically coupled to other modes, typically by potential terms of the form Q.Qs*Qsl, where Q is the coordinate of this antisymmetric stretching vibration, while Qs and Q6r,are coordinates of other modes. Such a term usually has only small effects except when excited states of Q modes have energies comparable with energies of combined excited states in Qs and Q6,, (resonance condition). It is then at the origin of splittings in bands due to transitions between various Q levels. Let us note that direct transitions in both Q6 and Q6,, are forbidden or are at least very weak. This is a well-knoyn effect in the conventional IR region which particularly influences V, (0-H. **0) band shapes of many H-bonded molecules. In this case a procedure has been proposed [ 1,121 to eliminate these resonance effects. It is based on a short-time approximation of the fate of the vibrational excitation induced by the absorption of an IR photon at time t = 0, which implies that spectra are analyzed in a low-resolution limit. It allows calculation of the “peeled-off” spectrum that one should observe in the absence of these Fermi resonances. In practice, one has to recalculate the experimental spectrum from an assumed peeled-off spectrum to which Fermi resonances are imposed. These Fermi resonances are defined by (i) the wavenumbers 06,6Zof the combined levels of the S and 6’ modes which fall in resonance with the first excited level in Q, and (ii) the coupling strength fs,s,. In Table 1 we give the corresponding values for the four species of acetic acid. The correctness of the peeled-off spectrum and of the parameters is then tested by comparing the calculated spectrum with the experimental spectrum. Such a comparison is shown in Fig. 5. In order to obtain a satisfactory fit as displayed in this figure, we were obliged to assume three resonance levels instead of only one. The resonance with the strongest coupling fa,s, seems obvious because it is responsible for the marked minimum shown by all four experimental bands. The second resonance introduces the shoulder appearing on all four spectra some 20 cm-’ below the band centre and the third resonance helps to get a better fit on the low frequency side of this complex band. As its contribution is minor, it is not easily recognized on the spectra. The interesting point of the peeled-off spectra for the four species is that all four, within the limit of the low resolution required by the peel-off procedure, have the same simple band shape. As the introduction of Fermi resonances changes neither the intensity nor the centre of intensity (or average frequency) of a band [ 1,121, the peeled-off spectra have intensities equal to the corresponding experimental spectrum and the bands conserve their average positions. This is shown in Fig. 6. It may be asked now, how can the quite similar parameters (Table 1) reconstitute different shapes of experimental
281 TABLE 1 Fermi resonance parameters for the four isotopic species of acetic acid Fermi resonances
Centre of intensity D, (cm-‘)
Molecule
Position 8,,. (cm-‘)
Strength f6.6. (cm-‘)
(CH,COOH),
170.5
138 155 175.3
6 8 13
(CH,COOD),
166.5
136 154 174.0
6 8 12.5
(CD,COOH),
158.0
125 146 169.5
6 8 14
(CD,COOD)2
156.0
124 146 168.5
6 8 13.5
spectra, especially the difference between the CH3 and the CD3 species. The substitution from CH3 to CD, manifests itself in a change of the moment of inertia for each monomer. As the antisymmetrical stretching vibration, which in fact is a pseudo-rotation around the c axis, is conditioned by this moment of inertia, the position of this band will shift to lower frequencies. This means that the relative position of the corresponding levels which are necessary for the Fermi resonances is no longer the same, thus leading to different shapes of the spectra. An interpretation of these Fermi resonance parameters for the two stronger interactions shows that they obey very well the principle of linear combination va+ V#= Ps,s,. In detail we have for CH,COOH v,,(4)+
~2sh4u)
99 cm-‘+56
=b.d&)
cm-‘=155
cm-’
and dAg)
+
~28
GL)
=fia,cv
(4)
not observed+ 56 cm-’ = 175.3 cm-’ Good agreement is also obtained for the other three species, so that we are allowed to draw conclusions about the non-identified Raman mode z+. We
282 (CH,COOH), m d
d 0 100
150
zoo
250
GjAVENUMBER
Fig. 5. Comparison of the experimental (CH,COOH), spectrum (thin line) with the calculated spectrum (thick line) taking account of Fermi resonances. The positions of the individual resonances are indicated by arrows. The “peeled-off” spectrum, drawn at half scale, has to be understood as an absorption band of equal intensity and width that is no longer disturbed by Fermi resonance interactions.
N
d
I>
0
1 WAVENUMBER
Fig. 6. Peeled-off spectra for the four isotopic species of acetic acid. The order of the labels corresponds to the decreasing order of intensity of the bands.
283
propose a value of slightly less than 120 cm-‘. Looking at the Raman spectrum [ 51, this assumption seems reasonable because the 99 cm-’ Raman band shows a long tail towards higher wavenumbers, probably containing the missing 120 cm- ’ band which could not be clearly resolved. Concerning the third resonance value, we feel that it is too weak to give any valid explanation at this time. In spite of this fact, and as we have shown by this example, the analysis by Fermi resonances is able to give a new insight and a more detailed interpretation of spectra. CONCLUSION
The results of this experiment can be summarized in three essential points. (a) The intensities of the intermonomer bands decrease when CH, is replaced by CDS, which may certainly be attributed to the variation of the moments of inertia. They also decrease when O-H***0 bonds are replaced by 0-D. --0bonds. This effect is less marked than in the mid-IR region [ 11, but indicates that bands due to H-bonds are anomalously more intense than bands due to D-bonds for all vibrations. (b) The third IR band corresponding to the out-of-plane bending vibration, which up to now has been missing, has been clearly identified at 56 cm-‘. (c) The differences in shape of the antisymmetric stretching vibration band shown by the four species are only due to Fermi resonances. After elimination of these resonances, the four bands have the same shape.
REFERENCES
7 8 9 10 11 12
Y. Marechal, J. Chem. Phys., 87 (1987) 6344. G.L. Carlson, R.E. Witkowski and W.G. Fateley, Spectrochim. Acta, 22 (1966) 1117. R.J. Jakobsen, Y. Mikawa and J.W. Brasch, Spectrochim. Acta Part A, 23 (1967) 2199. D. Clague and A. Novak, J. Mol. Struct., 5 (1970) 149. J.E. Bertie and K.H. Michaelian, J. Chem. Phys., 77 (1982) 5267. E. Knozinger and 0. Schrems, in J.R. Durig (Ed.), Vibrational Spectra and Structure, Vol. 16, Elsevier, Amsterdam, 1987, Chap. 3. B.P. van Eijck, J. van Opheusden, M.M.M. van Schaik and E. van Zoeren, J. Mol. Spectrosc., 86 (1981) 465. T. Miyazawa and K.S. Pitzer, J. Am. Chem. Sot., 81 (1958) 74. S. Kishida and K. Nakamoto, J. Chem. Phys., 41 (1964) 1558. K. Fukushima and B.J. Zwolinski, J. Chem. Phys., 50 (1969) 737. J.E. Bertie and K.H. Michaelian, J. Chem. Phys., 76 (1982) 866. Y. Marechal, Chem. Phys., 79 (1983) 69.
Journal of Molecular Structure, 237 (1990) 273-283 Elsevier Science Publishers B.V., Amsterdam
FAR IR SPECTRA OF ACETIC ACIDS IN THE GAS PHASE. A REINVESTIGATION OF THE INTERMONOMER VIBRATIONS*
H.R. ZELSMANN**,
Z. MIELKE’”
and Y. MARECHALt
Dkpartement de Recherche Fondamentale/Service de Physique, Groupe Physico-Chimie MolPculaire, Centre d%tudes Nuclkaires de Grenoble, 85X-38041 Grenoble Ceden (France) (Received 6 November
1989 )
ABSTRACT As part of our programme on the dimers of carboxylic acids, we report here results from the far infrared spectra in the 20-230 cm-’ region for the four isotopically substituted species of acetic acid dimers (CH,COOH )2, (CH,COOD )2, (CD,COOH )x, (CDsCOOD )z. These more confident and in parts entirely new experimental data permit us to assign the third IR active low-frequency vibration that was missing up to now. In good agreement with earlier predictions, this mode has been observed at 56 cm-’ for the totally hydrogenated dimer. Furthermore, on these new quantitative spectra the isotopic ratios of the band positions of the intermonomer vibrations are checked against those of the moments of inertia for the H-bond (or D-bond) samples separately. The comparison of the intensities of the FIR absorption bands allows us to postulate a slight but specific difference between an O-H * - *O and 0-D. * -0 bond. For the complex band centred at 171 cm-’ we propose an analysis of the band shape by Fermi resonance interactions.
INTRODUCTION
Being one of the simplest organic compounds, acetic acid is certainly one of the molecules for which we have the most complete knowledge of physical and chemical properties. On closer examination of these properties, it turns out that they are conditioned to a large extent by the ability of this molecule to form associations via hydrogen bonds. This may happen in the solid state by forming linear chains or even simpler in the gas phase by forming cyclic dimers. However, if one asks now about the interaction between two of these molecules or what does the hydrogen do when the two molecules vibrate, our understanding becomes poorer. In a recent investigation by mid-IR spectroscopy [ 11, *Presented at the IXth Workshop Bond Research at Zeist (Utrecht ), The Netherlands, lo-15 September 1989. **Universite Joseph Fourier de Grenoble. To whom correspondence should be addressed. ***On leave from Institute of Chemistry, University of Wroclaw, Wrocklaw, Poland. tC.N.R.S.
0022-2860/90/$03.50
0 1990 -
Elsevier Science Publishers
B.V.
274
quantitative formulation of the spectra has been given. The low-frequency vibrations, however, still suffered from a lack of reliable experimental data. This applies especially for the far-IR spectra as the main work [ 2-41 is rather old. A review of these results, together with those of a detailed Raman study [5] has been given in ref. 6. The objective of our present study was to obtain well-defined quantitative spectra for the four different isotopic species of gaseous acetic dimers which permit a comparison of the intensities of the FIR absorption bands and which should allow us to determine the absolute intensities with respect to the values observed in the mid-IR [ 11. Another reason for this study was the still incomplete assignment of the low-frequency spectra and the hypothetical interpretation of some bands in refs. 2-4 by Fermi resonance.
EXPERIMENTAL
Instrumental All spectra were run on an automated Polytec FIR30 interferometer equipped with a Golay and a liquid helium bolometer as detectors. The gas cell was a White multiple-path cell made of stainless steel with a total path length adjustable from 0.8 to 4.8 m and fitted with TPX windows for the far-IR. For the pressure measurements we used a Barocel 600A pressure sensor supplied by Datametrics. The control of the interferometer, the data acquisition and processing were executed by Hewlett Packard equipment. The spectra were recorded in the range of 20-230 cm-’ with an apodized spectral resolution of 2 cm-‘. A path length of 2.4 m turned out to be the optimum choice as all the measurements were repeated for different pressure settings between 1 and 6 torr. The experiment was carried out at a fixed temperature of 23 ‘C. Samples The H acetic acid was a commercial p.A. grade product from Prolabo which was dried over P,O,. The fully deuterated compound was supplied by the Commissariat h 1’Energie Atomique, Service des Molecules Marquees with a guaranteed deuterium content of 99.9%. Some residual water had to be removed by further drying. The samples of CH,COOD and CD,COOH were obtained by isotopic exchange of the acid hydrogen using the respective commercial starting material. Careful and thorough drying was necessary.
275 RESULTS AND DISCUSSION
The intermonomer vibrations In Fig. 1 we show the two gas-phase dimer spectra of acetic acid with OH. . -0 bonds and methyl group substitution, whereas in Fig. 2 we compare the spectra of the corresponding compounds with 0-D. *-0 bonds. These spectra are normalized in pressure, taking the torr as unit of pressure. It should not be I 0.9 = O.E : \
0.7
::
0.6
: m 0.5 6 g
0.4
[r 0.3 0.2 0. I E E WRVENUMBER
(cm-l)
Fig. 1. Normalized FIR spectra of the two species of gaseous acetic acid with CH, methyl groups. Experimental conditions: temperature 23’ C; optical path length 2.4 m.
0.9 :
O.E
: \
0.7
::
0.6
h m 0.5 8 i
0.4
cc 0.3 0.2 0. I 0 0
58
10E
150 WRVENUMBER
2-a-a
250
(cm-l)
Fig. 2. Normalized FIR spectra of the two species of gaseous acetic acid with CD, methyl groups. Experimental conditions: temperature 23°C; optical path length 2.4 m
276
forgotten here that the observed pressure results from the sum of the partial pressures of monomeric and dimeric acids. The equilibrium at ambient temperature and a pressure of a few torr favours the occurrence of dimers, but there is a non-negligible percentage of molecules left which are in the monomeric state. Calculating the fraction of dimers present for a given experimental condition (which has to be done for each pressure and each isotopic substitution by the corresponding KPvalue, extracted from spectra recorded in the midIR region [l] ), it is possible to relate the absorbance readings of the spectra with the effective dimer amount. In doing so, we obtained a series of spectra that could be nicely superposedusing a scaling factor that was just the quantity of dimers. This simple and confident observation of the absorbance being proportional to the number of dimers not only justifies the presentation of normalized spectra, but allows us to consider it as an experimental proof for a simple equilibrium of monomer*dimer, thus excluding any appreciable amount of open dimers. Comparing the two spectra of Fig. 1, we see that they are of similar shape, as are the two spectra in Fig. 2. For the four spectra, we have shown in the figures the position of elementary bands as obtained by a spectral decomposition, which is helpful in a first approach for tracing back the shifts due to the isotopic effect. (It is also useful for reproducing the spectra; the full set of parameters is available upon request. ) In total there should be six low-frequency modes corresponding to the intermonomer vibrations. Due to the centre of inversion of the dimer, three of them are observable by Raman (two A, and one B,), whereas the other three (two A, and one B,) are active in the IR. We have illustrated these six intermonomer vibrations in Fig. 3. For the numbering of the modes we chose the same system as Bertie and Michaelian [ 51 since it presents the most recent experimental work in this field. The values given here are those for the fully hydrogenated acetic acid as observed by Raman [ 51, the IR results coming from our present experiment. For the drawing we used the structure of the monomer determined by van Eijck et al. [ 71. For the 48.5 cm-l band, corresponding to a twist motion of the two monomers, the isotope effect of the band position shows an excellent agreement between observed values and predicted values calculated from the respective moments of inertia [ 71. This band, as well as the more complex one centred at 171 cm-’ which is assigned to the antisymmetric intermonomer stretching vibration, confirms the findings of earlier work by IR spectroscopy [ 2-41. In addition, we found a new band at 56 cm-l which we assign to the still unobserved IR active bending motion of the dimer. Concluding from possible linear combinations and stemming on results of normal coordinate calculations [ 8101, earlier authors expected this band around 880 cm-‘. Checking the validity of our assignment by the isotope effect, it turns out that the observed and the calculated values coincide only approximately, but without being contradic-
277
~.~
o ~
00~
~
oea o
.°
X
~2
E
'
14
Z m ~r rw
O2 rW
C
m rr" r~
4-,.Q ~Orl
I
~
~,;c%___
°
~
tory. The same behaviour is found for the band at 171 cm-l. This fact by itself is not very surprising, but it shows that the isotopic substitution as a help for assignment of the observed bands is not so powerful in the far-IR as it is in the mid-IR. We should take it as an indication that the monomer undergoes a slight structural change upon formation of the dimer. However, the assumption that the 56 cm-l band is the intermonomer bending vibration is well supported by analogy with formic acid dimers [ 111. By transferring in a simple approach the force constants to acetic acid, Bertie and Michaelian [5] found an estimation of 59 cm-l whereas we get, with updated values for the moments of inertia, a band position of 58 cm-‘. We may consider this very satisfactory agreement to be evidence of this assignment. Intensities of the FIR absorption bands The only correct way to measure the intensity of an absorption band consists of evaluating its transition probability. This quantity is defined by eqn. (1) where the factor of proportionality contains only fundamental constants. ‘(‘)
Absorbance ( 5 ) prop’P[l-exp( -hcB/kT)]
(1)
Intensity = Sum of P ( 8) over the band For bands in the mid-IR region, especially in the case of narrow bands, this relation may be simplified by neglecting the variations of the denominator. In the far-IR region, however, we are no longer allowed to do this. The results of these integrations of the spectrum for each isotopically substituted molecule is shown in Fig. 4. It may be seen that there is a general tendency of diminishing intensity of the spectra when substituting hydrogen by deuterium. The most characteristic data are the comparisons between the intensity of an 0-H. *-0 dimer and its O-D - - -0 analog. Summing over the total FIR spectrum between 20 and 230 cm-l, we observe the ratios Intensity tot.sp. ( CH3 COOD ) 2 = o g3 + o o1 Intensity tot.sp. (CH,COOH), ’ ’ and Intensity tot.sp. (CD,COOD )z = o g8 ~ o o1 Intensity tot.sp. ( CD3 COOH ) 2 * ’ There is a significant difference for substitution on the site of the hydrogen bond for molecules with a CH3 group, which is not evident due to the error limits for the case of a molecule with a CD, group. If we compare, in the same way, the intensities of the antisymmetric inter-
279
c
(CH&OoH),
tot. probab.: 34.1 units
KH&OODl,
tot. probab.: 31.8 units
KD,COOH),
tot. probab.: 29.4 units
13.7
Ul,COOD),
units
tot. probab.: 29.7 units
Fig, 4. Intensity of the FIR absorption bands. The observed intensities (or integrated probabilities), given in dimensionless units, are indicated in the boxes on each spectrum. The width of the box represents the bounds of integration.
monomer stretch only, we get, in contrast Intensity asym.st. ( CH3 COOD j2 = o 92 + o o1 Intensity asym.st. ( CH3 COOH ) 2 ’ * and Intensity asym.st. (CD3 COOD), = o 94 ~ o o1 Intensity asym.st. (CD,COOH), ’ a As can be seen, these two ratios are the same within the estimate of the error limits of our observations. This means, in summary, that the absorption bands are slightly less intense for O-D **-0 bonds than they are for O-H- *-0 bonds, a tendency that has already been observed in the mid-IR region for the same compound [ 11.
280
Analysis by Fermi resonance It was suggested for the first time by Miyazawa and Pitzer [8] that the submaxima displayed by the antisymmetric stretching band are due to Fermi resonances. In other words the corresponding vibration is anharmonically coupled to other modes, typically by potential terms of the form Q.Qs*Qsl, where Q is the coordinate of this antisymmetric stretching vibration, while Qs and Q6r,are coordinates of other modes. Such a term usually has only small effects except when excited states of Q modes have energies comparable with energies of combined excited states in Qs and Q6,, (resonance condition). It is then at the origin of splittings in bands due to transitions between various Q levels. Let us note that direct transitions in both Q6 and Q6,, are forbidden or are at least very weak. This is a well-knoyn effect in the conventional IR region which particularly influences V, (0-H. **0) band shapes of many H-bonded molecules. In this case a procedure has been proposed [ 1,121 to eliminate these resonance effects. It is based on a short-time approximation of the fate of the vibrational excitation induced by the absorption of an IR photon at time t = 0, which implies that spectra are analyzed in a low-resolution limit. It allows calculation of the “peeled-off” spectrum that one should observe in the absence of these Fermi resonances. In practice, one has to recalculate the experimental spectrum from an assumed peeled-off spectrum to which Fermi resonances are imposed. These Fermi resonances are defined by (i) the wavenumbers 06,6Zof the combined levels of the S and 6’ modes which fall in resonance with the first excited level in Q, and (ii) the coupling strength fs,s,. In Table 1 we give the corresponding values for the four species of acetic acid. The correctness of the peeled-off spectrum and of the parameters is then tested by comparing the calculated spectrum with the experimental spectrum. Such a comparison is shown in Fig. 5. In order to obtain a satisfactory fit as displayed in this figure, we were obliged to assume three resonance levels instead of only one. The resonance with the strongest coupling fa,s, seems obvious because it is responsible for the marked minimum shown by all four experimental bands. The second resonance introduces the shoulder appearing on all four spectra some 20 cm-’ below the band centre and the third resonance helps to get a better fit on the low frequency side of this complex band. As its contribution is minor, it is not easily recognized on the spectra. The interesting point of the peeled-off spectra for the four species is that all four, within the limit of the low resolution required by the peel-off procedure, have the same simple band shape. As the introduction of Fermi resonances changes neither the intensity nor the centre of intensity (or average frequency) of a band [ 1,121, the peeled-off spectra have intensities equal to the corresponding experimental spectrum and the bands conserve their average positions. This is shown in Fig. 6. It may be asked now, how can the quite similar parameters (Table 1) reconstitute different shapes of experimental
281 TABLE 1 Fermi resonance parameters for the four isotopic species of acetic acid Fermi resonances
Centre of intensity D, (cm-‘)
Molecule
Position 8,,. (cm-‘)
Strength f6.6. (cm-‘)
(CH,COOH),
170.5
138 155 175.3
6 8 13
(CH,COOD),
166.5
136 154 174.0
6 8 12.5
(CD,COOH),
158.0
125 146 169.5
6 8 14
(CD,COOD)2
156.0
124 146 168.5
6 8 13.5
spectra, especially the difference between the CH3 and the CD3 species. The substitution from CH3 to CD, manifests itself in a change of the moment of inertia for each monomer. As the antisymmetrical stretching vibration, which in fact is a pseudo-rotation around the c axis, is conditioned by this moment of inertia, the position of this band will shift to lower frequencies. This means that the relative position of the corresponding levels which are necessary for the Fermi resonances is no longer the same, thus leading to different shapes of the spectra. An interpretation of these Fermi resonance parameters for the two stronger interactions shows that they obey very well the principle of linear combination va+ V#= Ps,s,. In detail we have for CH,COOH v,,(4)+
~2sh4u)
99 cm-‘+56
=b.d&)
cm-‘=155
cm-’
and dAg)
+
~28
GL)
=fia,cv
(4)
not observed+ 56 cm-’ = 175.3 cm-’ Good agreement is also obtained for the other three species, so that we are allowed to draw conclusions about the non-identified Raman mode z+. We
282 (CH,COOH), m d
d 0 100
150
zoo
250
GjAVENUMBER
Fig. 5. Comparison of the experimental (CH,COOH), spectrum (thin line) with the calculated spectrum (thick line) taking account of Fermi resonances. The positions of the individual resonances are indicated by arrows. The “peeled-off” spectrum, drawn at half scale, has to be understood as an absorption band of equal intensity and width that is no longer disturbed by Fermi resonance interactions.
N
d
I>
0
1 WAVENUMBER
Fig. 6. Peeled-off spectra for the four isotopic species of acetic acid. The order of the labels corresponds to the decreasing order of intensity of the bands.
283
propose a value of slightly less than 120 cm-‘. Looking at the Raman spectrum [ 51, this assumption seems reasonable because the 99 cm-’ Raman band shows a long tail towards higher wavenumbers, probably containing the missing 120 cm- ’ band which could not be clearly resolved. Concerning the third resonance value, we feel that it is too weak to give any valid explanation at this time. In spite of this fact, and as we have shown by this example, the analysis by Fermi resonances is able to give a new insight and a more detailed interpretation of spectra. CONCLUSION
The results of this experiment can be summarized in three essential points. (a) The intensities of the intermonomer bands decrease when CH, is replaced by CDS, which may certainly be attributed to the variation of the moments of inertia. They also decrease when O-H***0 bonds are replaced by 0-D. --0bonds. This effect is less marked than in the mid-IR region [ 11, but indicates that bands due to H-bonds are anomalously more intense than bands due to D-bonds for all vibrations. (b) The third IR band corresponding to the out-of-plane bending vibration, which up to now has been missing, has been clearly identified at 56 cm-‘. (c) The differences in shape of the antisymmetric stretching vibration band shown by the four species are only due to Fermi resonances. After elimination of these resonances, the four bands have the same shape.
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