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The infra-red spectrum of carbon monoxide in a β-quinol clathrate
Spectrochimica Acta, 1962,vol. 18,pp. 933to 938. PergamonPressLtd. Printedin NorthernIreland
The i&a-red spectrum of carbon monoxide in a f3-quinolclathrate D. F. BALL and D. C. MCKEAN Department of Chemistry, University of Aberdeen, Old Aberdeen (Received
17 Jawuary
1962)
Ab&&-The infrared spectrum of the CO quinol clathrate, in virtue of the appearance of a prominent Q branch, indicatesthat most of the moleoulesare unable to rotate freely in the cage, in agreement with the conclusion from specific heat data. The aide bands occurring at low temperature are attributed to combinations with the rattling and torsional frequenoies. The extra absorption found in the wings at room temperature could be due to vibration-rotation transitions, but other causes cannot be eliminated. The frequency shift of the band eentre from the gas value is 10 cm-l, where the KBM equation predicts a value of about 4 cm-l.
infra-red spectrum of a small molecule in the cage of a quinol-olethrate crystal may throw some light on its freedom of movement within the cage. Recent studies of the spectra of small molecules in solution have shown the presence of side bands which are attributed to vibration-rotation transitions in the condensed phase [l-3]. It is of especial interest to investigate the spectrum of a species in a quinol crystal in view of the comparison which can be made with the conclusions from the specificheat measurements of STAVELEY et aZ.[4]; the possibility of such a comparison being made for liquid solutions being remote at the moment. In addition much information has been obtained from studies of the magnetic susceptibility, and quadrupole spectrum [S-7]. There has been one previous investigation of infra-red spectra involving /?-q&no1 clathrates [8]_ In this work the trapped molecules were CO,, SO,, H,S and HCl. For CO,, the absorption appeared to be that of a deformed & branch. Of all the clathrates which have been prepared, the most promising for infra-red studies is that of carbon monoxide, both from the point of view of its size and also because its vibration frequency coincides with a window in the quinol infra-red spectrum. THE
PREDICTION
OF THE
SPECTRUM
If the clathrate cage had exact spherical symmetry or were large compared with the CO molecule, then the same selection rules would apply to the infra-red spectrum as in the gas phase. The P and R branches would be broadened by collisions of the trapped molecules with the walls of the cage. Despite the fact that the frequency of these collisions is equivalent to that occurring at a pressure of several hundred atmospheres in the gas, it is unlikely that the forbidden & branch will appear, in [l] W. J. JONES and N. SXEPPARD, Trans. Faces SW. 56,22 (1960). [Z] M. 0. BULANIN and N. D. ORLOVA, Optika i Spectroskopiya 4, 569 (1958). [S] J. LASCOMBE, P. V. HUONG and M. L. JOSIEN, Bull. txx. d&n. &ance 1175 (1959). [4] L. A. XC.STAVXLEY J. Phys. Chews. SoEide. l&46, (1961). and private communication. [5] J. H. VAN VIZCK, J. phy8. Chem. Solids 20, 241 (1961). [S] H. MEYER and T. A. SCOTT,J. Phys. Chem Solids. 11, 215 (1959). [7] H. MEYER, M. C. M. O’BRIEN and J. H. VAN VLECK, Proc. Roy. Sot. A 245, 414 (1957). [S] R. M. HEXTEE and T. D. GOLDFARB, J. Inorg. & Nuclear Chem. 4, 171 (1957).
933
D. F. BALL and D. C. MCKEAN
934
view of the work of Vodar [9]. In fact the cage is known not to be spherically symmetrical [lo] and the Van der Waals length of the CO molecule (3.8 8) is only slightly less than the free-space diameter of the cage (4.0 d) [lo, 111. In the opposite case where the molecule is completely hindered, a single line corresponding to the transition Au = 1 will appear. This frequency could combine with the torsional or “rattling” frequency of the molecule to give rise to combination and difference bands, in the anharmonic approximation. In the intermediate case of a partially restricted rotator, the energy levels will be those discussed by STERN [12] (and in the one-dimensional case by PAULING [L3]). R e1ow the barrier these are essentially torsional levels, while above they will progressively approximate to free rotor levels. The spectrum expected will comprise a central Q branch arising from vibrational transitions in states below the barrier, and sidebands due to vibrational transitions from states above the barrier. No detailed account of the selection rule has been given for transitions in the neighbourhood of the barrier. It is of interest that barriers to rotation within the cage of about 200 and 900 Cal/mole respectively have been obtained recently for oxygen and nitrogen [4, 6, 71. EXPERIMENTAL
The clathrate samples were dispersed in KBr and NaBr disks and spectra were initially run using a Perkin-Elmer Infracord spectrometer. Selected disks were then examined both at and below room temperature using a Hilger H800 instrument equipped with a 7500 1.p.i. grating and an F-centre filter with cut-off at 2.3 ,u. The high-temperature spectrum was run using a Grubb-Parsons spectrometer fitted with a NaCl prism. The background was obtained by using nitrogen and krypton clathrate samples. RESULTS Fig. 1 shows the spectrum obtained at room temperature in a KBr disk on the Infracord spectrometer. Although the band is relatively weak, wings on each side of a prominent Q branch can be seen. By use of the difference technique the band shape can be exaggerated. Fig. 2 shows the resulting spectrum in a KBr disk over a range of temperature from 150°C to - 130°C. At low temperatures there is a pronounced Christiansen effect. At high temperatures the band is so broadened that no peaks can be recognized. Cooling the specimen restored the original spectrum. Fig. 3 shows an improved spectrum in a NaBr disk. The refractive index of the NaBr more nearly matches that of the quinol crystal: however it is now slightly higher than that of the quinol, whereas the KBr one was lower, and therefore the direction of the Christiansen effect is reversed. At room temperature the wings and central Q branch are found at 2175, 2090 and 2133 cm-l respectively. At low temperature the Q branch is greatly sharpened and a weak peak is found at 2186 cm-l which is without doubt due to CY3016. In
[9]B. VODAR,J. phys. radium 15, 58 (1954). [lo] [ll] [12] [13]
D. J. T. L.
E. PALIN and H. M. POWELL, J. Chem. Sot.208 (1947); 815 (1948). H. VAN DER WAALS, Trans. Faruday Sot. 52, 184 (1956). E. STERN, Proc. Roy. Sot. A 130,551 (1931). PAULING, Phys. Rev. 36, 430 (1930).
The infrared
ol
’
700
spectrum
of carbon monoxide
in a &quinol
935
clathrate
I 800
900
IO00
1500
2000
3000
cm-f Fig.
1. Spectrum
of CO-/&quinol
I
2080
clathrate
in KBr
disk. (Infra-red
I
I
I
2100
2140
2180
spectrometer)
cm-’
Fig. 2. CO-_B-quinol clathrate in KBr disk, at various temperatures. (Spectrometer: HSOO and ~rub~Pa~ons)
D. F. BALL and D. C. MCKEA~
936
-55-x
\ - I3OOC
I
2060
,
I
2100
2140
I
2180
cm-’
Fig. 3. CO-_8-quinol
clathrate in NaBr disk, at various temperatures. (Spectrometer: HEOO)
to the above Q branches there are three regions of weak absorption which do not have counterparts in the spectrum of the N, clathrate: two definite bands at 2180 and 2195 cm-l and an indefinite one near 2070 cm-l. The bands at 2195 and 2070 cm-1 can also be discerned in the room temperature spectrum. addition
INTERPRETATION
OF THE SPECTRUM
The presence of the central Q branch indicates clearly that many of the molecules This confirms the conare unable to rotate freely in the cage at room temperature. clusion of STAVELEY et al. [4] that a barrier of appreciable size exists. An approximate value obtained from the specific heat data is 1.2 kcal. The torsional frequency is then estimated to be about 54 cm-l, using the formula [14] o = 2/( V0/27r21). The “rattling” frequency of the molecule in the cage can also be estimated from the treatment of Van der Waals [ 1 l] which is utilized in the analysis of the specific heat data [5]. The value found is 40 cm-l. It follows that both types of motion could give rise to combination and difference frequencies roughly coinciding with the observed sidebands. It seems plausible then to ascribe the lowtemperature bands at 2180 and 2195 cm-l to such combinations.* Both bands * A similar interpretation of a broad bend in the spectrum of crystalline CO is given by EWING and PIMENTEL[15]. [14] C. H. TOWNES and A. L. SCHA~LOW, Microwuve Spectroscopy p. 323. McGraw-Hill, New York (1955). [15] G. E. EWING and G. C. PIMENTEL,J. Chem. Phys. 85, 925 (1961).
The infra-red spectrum of carbon monoxide in a /?-quinol clathrate
937
however could arise from combination with translation only, since there are in fact two different rattling frequencies in the cage. The enhancement of intensity at 2175 and 2090 cm-l which occurs on warming to room temperature may derive from four sources: (1) The broadening of the Q branch.? (2) Displaced combination frequencies arising from the higher levels of the torsional or rattling motions. (3) Vibration-rotational transitions amongst states well above the barrier. (4) Combination frequencies involving cage vibrations of low frequency and large amplitude. It does not seem possible to eliminate with certainty any of these possibilities at the present time. Theoretical considerations suggest that the rattling frequency will tend to increase with rise in temperature, due to the shape of the potential well, and if the value of the torsional frequency is in fact about 62 cm-l, intensity at 45 cm-l distance from the band centre may well be due to vibration-rotation transitions. In considering the latter interpretation it is of interest to note that the predicted P-R separation in the gas at room temperature is only 55 cm-l in contrast to the observed separation of 85 cm-l. This divergence is observed for the side bands found in solutions: and in no way invalidates an assignment to rotation structure. Its origin is perhaps due to the fact that for the partially restricted rotator the rotational levels of low J are missing : or rather they have become torsional states. On this view, the peak of the side band appears approximately at the point where the vibrational-rotational transition probability falls off more steeply with decrease in quantum number than the J population in the vibrational ground state increases. If this is supposed to occur just above the barrier, then the value of BJ(J + 1) corresponding to the peak of the side band might give a crude estimate of the height of the barrier. In the CO clathrate the peak occurs at a frequency which in the gas phase corresponds to the transition J = 11 --t J = 12. The corresponding value of BJ(J + 1) is about 250 cm-l, or 720 Cal/mole. This value is considerably less than the figure of 1200 Cal/mole estimated from the specific heat data, and the argument is almost certainly naive. However a detailed theoretical treatment of the system might well enable a reliable deduction of the barrier height to be made from the “PR” sideband separation in the condensed phase. FREQUENCY
SHIPT
A different problem is the displacement of 10 cm-l of the Q branch frequency from the band centre found in the gas. This may be compared with the shift of 3.7 cm-l found in a nitrogen matrix [16]. A calculation of the Kirkwood-Bauer and Magat type [17], using a bulk refractive index of 1.6, a cavity radius of 2 A and an effective charge for the CO molecule of 3.14 D/A predicts a frequency shift of 4 cm-i. It seems possible that this treatment does not predict the full dipole-induced t The lack of any structure at 150°C is presumably due to the same effect which is broadening the & branch at lower temperatures. [16] A. G. MAKI, J. Chem. Phys. 35, 931 (1961). [17] cf. A. D. E. PULLIN, Spectrochim. Acta. 13, 125 (1958).
938
D. F. BALL and D. C. MCI&AN
dipole contribution to the shift. On the one hand the centre of gravity of the dipole change may well lie away from the centre of the cavity: this effect can produce an appreciable increase in the shift. On the other hand, it may well be unrealistic to attribute to the walls of the cage a refractive index which characterizes the bulk of the medium. The local polarizability may well be higher than the bulk one. It would be premature to attribute the whole of the difference between the observed shift and that calculated from the KBM equation to dispersion forces. AcknowledgementWe are greatly indebted to Mr. L. A. K. STAVELEY for the samples of clathrates and for his interest in the work. We thank also Dr. V. C. FARMER of the Macaulay Institute for Soil Research for running the spectrum in his hot cell, in the Grubb-Parsons spectrometer of his Institute.
The i&a-red spectrum of carbon monoxide in a f3-quinolclathrate D. F. BALL and D. C. MCKEAN Department of Chemistry, University of Aberdeen, Old Aberdeen (Received
17 Jawuary
1962)
Ab&&-The infrared spectrum of the CO quinol clathrate, in virtue of the appearance of a prominent Q branch, indicatesthat most of the moleoulesare unable to rotate freely in the cage, in agreement with the conclusion from specific heat data. The aide bands occurring at low temperature are attributed to combinations with the rattling and torsional frequenoies. The extra absorption found in the wings at room temperature could be due to vibration-rotation transitions, but other causes cannot be eliminated. The frequency shift of the band eentre from the gas value is 10 cm-l, where the KBM equation predicts a value of about 4 cm-l.
infra-red spectrum of a small molecule in the cage of a quinol-olethrate crystal may throw some light on its freedom of movement within the cage. Recent studies of the spectra of small molecules in solution have shown the presence of side bands which are attributed to vibration-rotation transitions in the condensed phase [l-3]. It is of especial interest to investigate the spectrum of a species in a quinol crystal in view of the comparison which can be made with the conclusions from the specificheat measurements of STAVELEY et aZ.[4]; the possibility of such a comparison being made for liquid solutions being remote at the moment. In addition much information has been obtained from studies of the magnetic susceptibility, and quadrupole spectrum [S-7]. There has been one previous investigation of infra-red spectra involving /?-q&no1 clathrates [8]_ In this work the trapped molecules were CO,, SO,, H,S and HCl. For CO,, the absorption appeared to be that of a deformed & branch. Of all the clathrates which have been prepared, the most promising for infra-red studies is that of carbon monoxide, both from the point of view of its size and also because its vibration frequency coincides with a window in the quinol infra-red spectrum. THE
PREDICTION
OF THE
SPECTRUM
If the clathrate cage had exact spherical symmetry or were large compared with the CO molecule, then the same selection rules would apply to the infra-red spectrum as in the gas phase. The P and R branches would be broadened by collisions of the trapped molecules with the walls of the cage. Despite the fact that the frequency of these collisions is equivalent to that occurring at a pressure of several hundred atmospheres in the gas, it is unlikely that the forbidden & branch will appear, in [l] W. J. JONES and N. SXEPPARD, Trans. Faces SW. 56,22 (1960). [Z] M. 0. BULANIN and N. D. ORLOVA, Optika i Spectroskopiya 4, 569 (1958). [S] J. LASCOMBE, P. V. HUONG and M. L. JOSIEN, Bull. txx. d&n. &ance 1175 (1959). [4] L. A. XC.STAVXLEY J. Phys. Chews. SoEide. l&46, (1961). and private communication. [5] J. H. VAN VIZCK, J. phy8. Chem. Solids 20, 241 (1961). [S] H. MEYER and T. A. SCOTT,J. Phys. Chem Solids. 11, 215 (1959). [7] H. MEYER, M. C. M. O’BRIEN and J. H. VAN VLECK, Proc. Roy. Sot. A 245, 414 (1957). [S] R. M. HEXTEE and T. D. GOLDFARB, J. Inorg. & Nuclear Chem. 4, 171 (1957).
933
D. F. BALL and D. C. MCKEAN
934
view of the work of Vodar [9]. In fact the cage is known not to be spherically symmetrical [lo] and the Van der Waals length of the CO molecule (3.8 8) is only slightly less than the free-space diameter of the cage (4.0 d) [lo, 111. In the opposite case where the molecule is completely hindered, a single line corresponding to the transition Au = 1 will appear. This frequency could combine with the torsional or “rattling” frequency of the molecule to give rise to combination and difference bands, in the anharmonic approximation. In the intermediate case of a partially restricted rotator, the energy levels will be those discussed by STERN [12] (and in the one-dimensional case by PAULING [L3]). R e1ow the barrier these are essentially torsional levels, while above they will progressively approximate to free rotor levels. The spectrum expected will comprise a central Q branch arising from vibrational transitions in states below the barrier, and sidebands due to vibrational transitions from states above the barrier. No detailed account of the selection rule has been given for transitions in the neighbourhood of the barrier. It is of interest that barriers to rotation within the cage of about 200 and 900 Cal/mole respectively have been obtained recently for oxygen and nitrogen [4, 6, 71. EXPERIMENTAL
The clathrate samples were dispersed in KBr and NaBr disks and spectra were initially run using a Perkin-Elmer Infracord spectrometer. Selected disks were then examined both at and below room temperature using a Hilger H800 instrument equipped with a 7500 1.p.i. grating and an F-centre filter with cut-off at 2.3 ,u. The high-temperature spectrum was run using a Grubb-Parsons spectrometer fitted with a NaCl prism. The background was obtained by using nitrogen and krypton clathrate samples. RESULTS Fig. 1 shows the spectrum obtained at room temperature in a KBr disk on the Infracord spectrometer. Although the band is relatively weak, wings on each side of a prominent Q branch can be seen. By use of the difference technique the band shape can be exaggerated. Fig. 2 shows the resulting spectrum in a KBr disk over a range of temperature from 150°C to - 130°C. At low temperatures there is a pronounced Christiansen effect. At high temperatures the band is so broadened that no peaks can be recognized. Cooling the specimen restored the original spectrum. Fig. 3 shows an improved spectrum in a NaBr disk. The refractive index of the NaBr more nearly matches that of the quinol crystal: however it is now slightly higher than that of the quinol, whereas the KBr one was lower, and therefore the direction of the Christiansen effect is reversed. At room temperature the wings and central Q branch are found at 2175, 2090 and 2133 cm-l respectively. At low temperature the Q branch is greatly sharpened and a weak peak is found at 2186 cm-l which is without doubt due to CY3016. In
[9]B. VODAR,J. phys. radium 15, 58 (1954). [lo] [ll] [12] [13]
D. J. T. L.
E. PALIN and H. M. POWELL, J. Chem. Sot.208 (1947); 815 (1948). H. VAN DER WAALS, Trans. Faruday Sot. 52, 184 (1956). E. STERN, Proc. Roy. Sot. A 130,551 (1931). PAULING, Phys. Rev. 36, 430 (1930).
The infrared
ol
’
700
spectrum
of carbon monoxide
in a &quinol
935
clathrate
I 800
900
IO00
1500
2000
3000
cm-f Fig.
1. Spectrum
of CO-/&quinol
I
2080
clathrate
in KBr
disk. (Infra-red
I
I
I
2100
2140
2180
spectrometer)
cm-’
Fig. 2. CO-_B-quinol clathrate in KBr disk, at various temperatures. (Spectrometer: HSOO and ~rub~Pa~ons)
D. F. BALL and D. C. MCKEA~
936
-55-x
\ - I3OOC
I
2060
,
I
2100
2140
I
2180
cm-’
Fig. 3. CO-_8-quinol
clathrate in NaBr disk, at various temperatures. (Spectrometer: HEOO)
to the above Q branches there are three regions of weak absorption which do not have counterparts in the spectrum of the N, clathrate: two definite bands at 2180 and 2195 cm-l and an indefinite one near 2070 cm-l. The bands at 2195 and 2070 cm-1 can also be discerned in the room temperature spectrum. addition
INTERPRETATION
OF THE SPECTRUM
The presence of the central Q branch indicates clearly that many of the molecules This confirms the conare unable to rotate freely in the cage at room temperature. clusion of STAVELEY et al. [4] that a barrier of appreciable size exists. An approximate value obtained from the specific heat data is 1.2 kcal. The torsional frequency is then estimated to be about 54 cm-l, using the formula [14] o = 2/( V0/27r21). The “rattling” frequency of the molecule in the cage can also be estimated from the treatment of Van der Waals [ 1 l] which is utilized in the analysis of the specific heat data [5]. The value found is 40 cm-l. It follows that both types of motion could give rise to combination and difference frequencies roughly coinciding with the observed sidebands. It seems plausible then to ascribe the lowtemperature bands at 2180 and 2195 cm-l to such combinations.* Both bands * A similar interpretation of a broad bend in the spectrum of crystalline CO is given by EWING and PIMENTEL[15]. [14] C. H. TOWNES and A. L. SCHA~LOW, Microwuve Spectroscopy p. 323. McGraw-Hill, New York (1955). [15] G. E. EWING and G. C. PIMENTEL,J. Chem. Phys. 85, 925 (1961).
The infra-red spectrum of carbon monoxide in a /?-quinol clathrate
937
however could arise from combination with translation only, since there are in fact two different rattling frequencies in the cage. The enhancement of intensity at 2175 and 2090 cm-l which occurs on warming to room temperature may derive from four sources: (1) The broadening of the Q branch.? (2) Displaced combination frequencies arising from the higher levels of the torsional or rattling motions. (3) Vibration-rotational transitions amongst states well above the barrier. (4) Combination frequencies involving cage vibrations of low frequency and large amplitude. It does not seem possible to eliminate with certainty any of these possibilities at the present time. Theoretical considerations suggest that the rattling frequency will tend to increase with rise in temperature, due to the shape of the potential well, and if the value of the torsional frequency is in fact about 62 cm-l, intensity at 45 cm-l distance from the band centre may well be due to vibration-rotation transitions. In considering the latter interpretation it is of interest to note that the predicted P-R separation in the gas at room temperature is only 55 cm-l in contrast to the observed separation of 85 cm-l. This divergence is observed for the side bands found in solutions: and in no way invalidates an assignment to rotation structure. Its origin is perhaps due to the fact that for the partially restricted rotator the rotational levels of low J are missing : or rather they have become torsional states. On this view, the peak of the side band appears approximately at the point where the vibrational-rotational transition probability falls off more steeply with decrease in quantum number than the J population in the vibrational ground state increases. If this is supposed to occur just above the barrier, then the value of BJ(J + 1) corresponding to the peak of the side band might give a crude estimate of the height of the barrier. In the CO clathrate the peak occurs at a frequency which in the gas phase corresponds to the transition J = 11 --t J = 12. The corresponding value of BJ(J + 1) is about 250 cm-l, or 720 Cal/mole. This value is considerably less than the figure of 1200 Cal/mole estimated from the specific heat data, and the argument is almost certainly naive. However a detailed theoretical treatment of the system might well enable a reliable deduction of the barrier height to be made from the “PR” sideband separation in the condensed phase. FREQUENCY
SHIPT
A different problem is the displacement of 10 cm-l of the Q branch frequency from the band centre found in the gas. This may be compared with the shift of 3.7 cm-l found in a nitrogen matrix [16]. A calculation of the Kirkwood-Bauer and Magat type [17], using a bulk refractive index of 1.6, a cavity radius of 2 A and an effective charge for the CO molecule of 3.14 D/A predicts a frequency shift of 4 cm-i. It seems possible that this treatment does not predict the full dipole-induced t The lack of any structure at 150°C is presumably due to the same effect which is broadening the & branch at lower temperatures. [16] A. G. MAKI, J. Chem. Phys. 35, 931 (1961). [17] cf. A. D. E. PULLIN, Spectrochim. Acta. 13, 125 (1958).
938
D. F. BALL and D. C. MCI&AN
dipole contribution to the shift. On the one hand the centre of gravity of the dipole change may well lie away from the centre of the cavity: this effect can produce an appreciable increase in the shift. On the other hand, it may well be unrealistic to attribute to the walls of the cage a refractive index which characterizes the bulk of the medium. The local polarizability may well be higher than the bulk one. It would be premature to attribute the whole of the difference between the observed shift and that calculated from the KBM equation to dispersion forces. AcknowledgementWe are greatly indebted to Mr. L. A. K. STAVELEY for the samples of clathrates and for his interest in the work. We thank also Dr. V. C. FARMER of the Macaulay Institute for Soil Research for running the spectrum in his hot cell, in the Grubb-Parsons spectrometer of his Institute.