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The methane ν1(a1) vibrational state rotational structure obtained from high-resolution CARS-spectra of the Q-branch
JOURNAL
OF
MOLECULAR
SPECTROSCOPY
77,
21-28 (1979)
The Methane v,(a,) Vibrational State Rotational Structure Obtained from High-Resolution CARS-Spectra of the Q-Branch D. N. KOZLOV, A. M. PROKHOROV, AND V.. V. SMIRNOV P. N. Lebedev
Physical Institute of the Academy of Sciences Leninsky prospect 53. Moscow, USSR
of the USSR,
The gaseous methane v,(a,) Q-branch coherent anti-Stokes Raman scattering (CARS) spectra have been investigated at a resolution of 0.002 cm-‘. A complex rotational structure of the resolved Q-branch has been experimentally observed. This structure can be ascribed to strong tetrahedral splitting of the rotational levels of the upper vibrational state, which possibly occurs due to Fermi resonance between the v,(aJ and 2v,(a,) vibrational energy levels which are close to each other. An assignment of the observed spectral lines has been made, yielding the rotational constants B, D. and D1 for the ~,(a,) vibrational state of the methane molecule. The absolute Raman frequency vi of the purely vibrational transition has been found. INTRODUCTION
Previously we presented for the first time the resolved structure of the gaseous methane vl( a J Q-branch coherent anti-Stokes Raman scattering (CARS) spectrum (I). This spectrum was recorded at room temperature and 20 Torr methane pressure using the cw high-resolution CARS-spectrometer described in detail in Ref. (2). Resolution was about 0.002 cm-l as estimated by the linewidths of the single-frequency lasers used for excitation. In Ref. (1) an attempt was also made to assign the lines of the recorded spectrum. However, the proposed assignment could not be regarded as unambiguous, and the underlying assumptions about the origin of the observed lines needed additional verification. In this paper we present and analyze spectral data provided by our new experiments, which show that the assignments of Ref. (1) should be revised. We have also now developed a new assignment which seems more likely to be valid, and is based on another approach to the origin of the Q-branch structure. TREATMENT
OF THE +(a,) Q-BRANCH CARS-SPECTRUM
The methane molecule is a spherical top of the Td symmetry point group. According to theoretical studies of the ground state rotational structure of tetrahedral molecules (3, 4) rotational levels with definite angular momentum, J, split into a number of sublevels of A, E, or F types. Respective statistical weights are gA = 5, gE = 2, g, = 3, due to sublevel symmetry type K and nuclear spin degeneracy, where K denotes the A,, AZ, E, F1, or F2 representations of the Tri 21
0022-2852/79/080021-08$02.00/O Copyright
0
I979 by Academic
All rights of reproduction
Press.
Inc.
in any form reserved.
22
KOZLOV, PROKHOROV,
AND SMIRNOV
group. The full statistical weight of a definite J, g.l,, = g,(2J
K
state thus equals: (1)
+ I),
the factor (2J + 1) arising from angular momentum component degeneracy. Symmetry considerations allow us to assume the vr(a,) vibrational state rotational structure to be similar to that of the ground state (see Fig. 1). The expression for J, K-state energies up to the terms of the 4th order in angular momentum is E rot
=
BJ(J
+
1)
-
DJ2(J
+
1)2
+
D,f(J,K)
(2)
( hc ) J,K in the notation of Kirschner and Watson (4) who give alsoP(J,K) values. The methane ground state structure constants calculated from infrared spectra of the v3cf2) band are presented by Tan-ago et al. (5): B, = 5.2410356 _+ O.OOOOO96 cm-‘, -Do = (- 1.10864 + 0.00074) 10e4 cm-‘, - [31/z/2(71/2)]D$ = (- 1.4485 t 0.0023) lo+ cm-‘.
F2 v=1,3=4 E F, Al
F2
E F, A, FIG. 1. Tetrahedral splitting of the rotational level with J = 4 in the ground and the v,(a,) vibrational states. Raman-active transitions occur between sublevels of the same symmetry type.
METHANE
HIGH-RESOLUTION
23
CARS-SPECTRA
In Raman spectra the vibration-rotation transitions between the ground and the +( a J vibrational states are allowed only between the rotational states of the same J value and symmetry (Fig. 1). The expression for the frequencies of transitions is, therefore, VJ,K = VI - a,J(J
+ 1) - &J”(J + l)2 +
(3)
y&J,K),
with the constants -cyl = B, - Bo, p1 = D, - D,,, y, = Dj - De, showing the difference between the vl(al) vibrational state structure constants and those of the ground state. This difference is mainly determined by the anharmonicity, which gives rise to vibration-rotation interaction and Fermi resonance between the vl(at) and the 2v,(a,) vibrations. The Fermi resonance in methane reveals itself in the intense spontaneous Raman scattering (6) and CARS (7) on the 2v,(a,) overtone. The influence of Coriolis resonance between the ~,(a,) and the vg(f2) vibrations is weak, because of the large frequency shift v3-v1 5 100 cm-‘, and has not been taken into consideration. In the last few years CARS has been developed to be a powerful and potentially important spectroscopic technique. The physical principles of CARS and its advantages are treated in detail in the review by Tolles ef al. (8) and by Akhmanov and Koroteev (9). The CARS-signal generation can be described in terms of the third order nonlinear susceptibility tensor x$(-v,,, vl, vI, -vs), where vz and v, are the pumping light frequencies, and vas = v1 + (vI - v,) is the scattered light frequency. CARSspectra recorded with parallel or orthogonal linear polarizations of the exciting beams by scanning vs, yield the dispersion of 1x& 12. The susceptibility x$\ is a sum of resonant x$;iF and nonresonant x~$$‘”parts, but since in gases x\;iTR is four to five orders of magnitude smaller than xgkl, their interference can be neglected when analyzing the structure in the spectrum. The dispersion of the resonant part of the third order nonlinear susceptibility of a molecule at rest can be approximately expressed as follows:
1
l3)R _
Xijkl
1 gJ,Kbexp
J.K
!
-
c 1
g,,,
BoJ(J
+ 1) T
J,K
1 r ’ 1
+ 1)
B,J(J T
(4)
lvJa - (vL - v,)] - i + [
where are homogeneous linewidths of the vibration-rotation spectrum, and T is the rotational temperature. The Q-branch exhibits its structure at rather low methane densities (pressure less than 100 Torr at room temperature). If now 0: and DQ values differ only slightly from each other, the Q-branch lines result from all possible transitions between the rotational states with the same J value, and their relative intensities are governed by the expression: rJ&
IJ-
(5)
24
KOZLOV,
PROKHOROV,
AND
SMIRNOV
If 0: and Dp are greatly different, the Q-branch structure becomes more complicated since the lines result from transitions between different J, K states. The relative intensities of the resolved lines are given by: + 1)
B,J(J
Z
T ANALYSIS
II
2 *
OF THE SPECTRA
The resolved structure of the methane molecule Y~(a,) Q-branch CARS-spectrum presented previously in Ref. (I) was recorded with parallel linear polarizations of the exciting beams and yielded the dispersion of 1x% 1’. The assignment of six regularly situated sharp lines, proposed in Ref. (I), was based on the assumption that terms YJ(J,K) in Eq. (3) for transition frequencies are small compared to linewidths. The same assumption pas made by Clements and Stoicheff (10) to analyze the unresolved vl(al) Q-branch structure of the conventional Raman spectrum. In this case, as was mentioned above, the individual lines Q(J) must have frequency positions according to uJ = v1 - ~YJ(J + 1) - &.P(J + 1)2 and the intensities given by Eq. (.5), the Q(6) line being the strongest one. Deviations in intensities of lines 3 and 6, large widths of lines 6 and 8, and presence of the unidentified lines 2, 4 and 9, 10, 11 in high-pressure unresolved CARS-spectrum (Fig. 2) was accounted for by the possible appearance of u3cf2) P-branch lines in the Q-branch frequency domain (6, 1l), and their overlapping with some of the Q-branch lines. However, there were the following doubts in the validity of these presumptions. 5
CH4 IOO Torr
300°K
SCALE 4
FIG. 2. The broad-scale
~,(a,) Q-branch CARS-spectrum
at 100 Torrpressure
I---
0,l cm-
and room temperature.
METHANE HIGH-RESOLUTION
CARS-SPECTRA
25
CH4 20 forr SCALE 4
300. K cc
0,03 cn-’
I !
FIG. 3. Central portion of the vl(ul) Q-branch CARS-spectrum at 20 Torr pressure and room temperature.
First, the intensities of the v3cf2) P-branch lines should be at least an order of magnitude weaker than that of the Q(6) line, since they result from transitions from the rotational states with J = 10. This consideration is confirmed by the analysis of the Raman spectrum obtained by Berger (12), in which the resolved lines 77 and 79 assigned to the vI(aI) Q-branch (lines 9 and 11 of our spectrum in Fig. 2, unidentified in Ref. (I)) are much stronger than the I+(&) P(10) lines. To see whether the unidentified lines are from the z+(&) P-branch, a CARSspectrum with orthogonal polarizations of the exciting beams, giving the diswas recorded persion of 1x\%L,I2 in the frequency region under consideration, at 100 Tot-r pressure and room temperature. The x\$! tensor component is proportional to the depolarization ratio, p, of the scattered light, which is determined by the symmetry of the scattering vibration, and equal to 0 or 3/4for ~,(a,) or z+cf2), respectively. Thus, in this kind of spectrum, none of the Q-branch lines can be observed, while the P-branch lines become only l/p2 = 2 times weaker. Changing the polarizations from parallel to orthogonal during the experiment results in a decrease of the signal by two orders of magnitude, its frequency dependence being of the same form. This fact allows us to conclude that all the lines of the spectrum in Fig. 2 should be assigned to the vI(aJ Q-branch. Second, the appearance of wide unresolved lines 2, 6, and 8 (Fig. 3) can be ascribed to a more complex Q-branch structure, connected, for example, with strong tetrahedral splitting in the upper vibrational state, introduced by the term %~(J,K) in Eq. (3). Our further experiments were aimed at resolving the Q-branch lines of the spectrum in Fig. 3. Since linewidths at 20 Torr pressure and room temperature are approximately 0.015 cm-’ and are close to the Doppler limited linewidth (l$*RS - 0.006 cm-‘), the gas was cooled by liquid nitrogen.‘This results in a Doppler-
26
KOZLOV, PROKHOROV,
AND SMIRNOV
width decrease and a scattered light signal increase for the transition between the levels with small J values, allowing us to use lower gas densities. The methane CARS-spectrum recorded at 0.5 Torr pressure and 80 K temperature is shown in Fig. 4. Resolution was as high as 0.002 cm-‘, and frequency scale nonlinearity did not exceed 2%. It is clearly seen that each broad line of the spectrum in Fig. 3 arises from an overlapping of a number of single lines whose intensities and frequency positions cannot be explained on the basis of our former assumptions. We now suppose that all the spectral lines in Fig. 4 belong to the vl(al) Q branch, and result from transitions between separate J, K states with selection rules AJ = 0, AK = 0 (see Fig. 1). Equations (3) and (6) for transition frequencies and line intensities enable us to assign these lines and to calculate the constants ol, pl, and y1 from the line spacing data, using a least-squares procedure: tY1 = (-8.98
-t 0.15) low3 cm-‘,
p, = (2.62 + 0.43) lop5 cm-‘, y1 = (3.30 * 0.07) lo+ cm-‘. The measured frequency shifts of the lines in Fig. 4, relative to the line assigned to the purely vibrational transition between J = 0, K = Al states, are presented in Table I. The experimental error for the line spacings less than 0.1 cm-’ does not exceed 0.002 cm-‘. The assignment of the observed lines and their frequency shifts, computed according to Eq. (3), are also given in Table I. Asterisks indi-
E Fa 2 2
AZ 3 CH4
0,sTorr 8PK SCALE +
A, F, E
444 I
FIG. 4. The ~,(a,) Q-branch and 80 K temperature.
CARS-spectrum
I--
0.03 cn-’
F!)Fa E Fz F’;’ 656 54
Y
with fully resolved
Y/
structure
Az
5 ‘5’
6
at 0.5 Torr pressure
METHANE
HIGH-RESOLUTION TABLE
27
CARS-SPECTRA
I
The Relative Frequency Shifts of the Lines of CH, v1 Q-Branch CARS-Spectrum Measured frequency shifts (cm-‘)
Assignment
(J 4
0.0000*
0 A, 1 Fl
0.0177
2E
0.0528*
2 F2 3 F, 3 & 3 A, 4 A, 4 F, 4E 5 F;”
0.098 1 0.1076 0.1167 0.1408 0.1551 0.1632 0.1945*
4 F2 6E
0.2 180*
5 Fz 6 F:”
0.2290* 0.2647 0.2863 0.2975
6 A, 5E 5 FiZ’
Calculated frequency shifts (cm-‘) 0.0000 0.0178 0.0517 0.0537 0.0980 0.1059 0.1158 0.1413 0.1552 0.1651 0.1913 0.1948 0.2180 0.2180 0.2298 0.2655 0.2872 0.3001
cate the lines which were not used in the computation procedure. The comparison of our spectral data with those of Berger (12) allows us to calculate with the precision of about 0.01 cm-’ the absolute Raman frequency of the above-mentioned purely vibrational line, which has the following value: v1 = Q,,~, = 2916.50 cm-l. Finally, the values of the methane molecule rotational constants for the v,( a J vibrational state are computed to be
B, = 5.25002 2 0.00015 cm-‘, D1 = (1.371 t 0.043) 10m4cm-‘, 0:
= (3.73 i 0.07) 10e5 cm-‘.
It is noteworthy that the ~,(a,)-state tetrahedral splitting constant Dt is an order of magnitude larger than that of the ground state. The value of p1 is also too large in relation to the value of (Ye,and has the opposite sign. This fact accounts for the appearance of numerous lines resulting from transitions with J F 10 in the left wing of the ~(a,) Q-branch, where u.,,~< v,. These lines were observed by Berger (12) in his Raman spectra. A possible explanation of large p1 and y1 values is the influence of Fermi resonance between the ~,(a,) and the 24~7,) vibrational states. The investigation and comparison of the ~,(a,) Q-branch structures of spherical top molecules with various Fermi resonance conditions, e.g., CD4, GeH,, or SiH4, may help to verify this supposition.
28
KOZLOV, PROKHOROV,
AND SMIRNOV
SUMMARY
Gaseous methane vI(aI) Q-branch spectra have been experimentally investigated by means of high-resolution CARS-spectroscopy. The fine structure of the Q branch has been observed. This result has been ascribed to strong tetrahedral splitting of the rotational levels of the q(u,) vibrational state. The Q-branch lines have been assigned to transitions between individual rotational sublevels of the ground and upper vibrational states having the same symmetry type and angular momentum value. The rotational structure constants for the vI(aI) vibrational state have been calculated. ACKNOWLEDGMENTS The authors would like to thank V. I. Fabelinsky for his assistance in computer the spectral data and V. N. Zhiganov for his help with the experimental setup. RECEIVED:
processing
of
June 20, 1978 REFERENCES
1. M. R. ALIEV, D. N. KOZLOV, AND V. V. SMIRNOV, Pis’ma ZhETF, 26, 31-34 (1977). 2. B. B. KRYNETSKY, L. A. KULEVSKY, V. I. MISHIN, A. M. PROKHOROV, A. D. SAVEL’EV, AND V. V. SMIRNOV, Opr. Commun. 21, 225-228 (1977). 3. K. T. HECHT, J. Mol. Spectrosc. 5, 355-389 (l%O). 4. S. M. KIRSCHNER AND J. K. G. WATSON, J. Mol. Spectrosc. 47, 347-350 (1973). 5. G. TARRAGO, M. DANG-NHU, G. POUSSIGLJE,G. GUELACHVILI, AND C. AMIOT, J. Mol. Spectrosc. 57, 246-263 (1975). 6. J. HERRANZ AND B. P. STOICHEFF, .I. Mol. Spectrosc. 10, 448-483 (1963). 7. J. W. NIBLER, J. R. MCDONALD, AND A. B. HARVEY, in “Proceedings of the Vth International Conference on Raman Spectroscopy, Freiburg, 1976, ” pp. 717-725. 8. W. M. TOLLES, J. W. NIBLER, J. R. MCDONALD, AND A. B. HARVEY, Appl. Spectrosc. 31, 253-272 (1977). 9. S. A. AKHMANOV AND N. I. KOROTEEV, Uspekhi Fiz. Nauk 123, 405-471 (1977). 10. W. R. L. CLEMENTS AND B. P. STOICHEFF, J. Mol. Spectrosc. 33, 183-186 (1970). II. A. S. PINE, J. Opt. Sot. Amer. 66, 97- 108 (1976). 12. H. BERGER, J. Mol. Spectrosc. 66, 55-61 (1977).
OF
MOLECULAR
SPECTROSCOPY
77,
21-28 (1979)
The Methane v,(a,) Vibrational State Rotational Structure Obtained from High-Resolution CARS-Spectra of the Q-Branch D. N. KOZLOV, A. M. PROKHOROV, AND V.. V. SMIRNOV P. N. Lebedev
Physical Institute of the Academy of Sciences Leninsky prospect 53. Moscow, USSR
of the USSR,
The gaseous methane v,(a,) Q-branch coherent anti-Stokes Raman scattering (CARS) spectra have been investigated at a resolution of 0.002 cm-‘. A complex rotational structure of the resolved Q-branch has been experimentally observed. This structure can be ascribed to strong tetrahedral splitting of the rotational levels of the upper vibrational state, which possibly occurs due to Fermi resonance between the v,(aJ and 2v,(a,) vibrational energy levels which are close to each other. An assignment of the observed spectral lines has been made, yielding the rotational constants B, D. and D1 for the ~,(a,) vibrational state of the methane molecule. The absolute Raman frequency vi of the purely vibrational transition has been found. INTRODUCTION
Previously we presented for the first time the resolved structure of the gaseous methane vl( a J Q-branch coherent anti-Stokes Raman scattering (CARS) spectrum (I). This spectrum was recorded at room temperature and 20 Torr methane pressure using the cw high-resolution CARS-spectrometer described in detail in Ref. (2). Resolution was about 0.002 cm-l as estimated by the linewidths of the single-frequency lasers used for excitation. In Ref. (1) an attempt was also made to assign the lines of the recorded spectrum. However, the proposed assignment could not be regarded as unambiguous, and the underlying assumptions about the origin of the observed lines needed additional verification. In this paper we present and analyze spectral data provided by our new experiments, which show that the assignments of Ref. (1) should be revised. We have also now developed a new assignment which seems more likely to be valid, and is based on another approach to the origin of the Q-branch structure. TREATMENT
OF THE +(a,) Q-BRANCH CARS-SPECTRUM
The methane molecule is a spherical top of the Td symmetry point group. According to theoretical studies of the ground state rotational structure of tetrahedral molecules (3, 4) rotational levels with definite angular momentum, J, split into a number of sublevels of A, E, or F types. Respective statistical weights are gA = 5, gE = 2, g, = 3, due to sublevel symmetry type K and nuclear spin degeneracy, where K denotes the A,, AZ, E, F1, or F2 representations of the Tri 21
0022-2852/79/080021-08$02.00/O Copyright
0
I979 by Academic
All rights of reproduction
Press.
Inc.
in any form reserved.
22
KOZLOV, PROKHOROV,
AND SMIRNOV
group. The full statistical weight of a definite J, g.l,, = g,(2J
K
state thus equals: (1)
+ I),
the factor (2J + 1) arising from angular momentum component degeneracy. Symmetry considerations allow us to assume the vr(a,) vibrational state rotational structure to be similar to that of the ground state (see Fig. 1). The expression for J, K-state energies up to the terms of the 4th order in angular momentum is E rot
=
BJ(J
+
1)
-
DJ2(J
+
1)2
+
D,f(J,K)
(2)
( hc ) J,K in the notation of Kirschner and Watson (4) who give alsoP(J,K) values. The methane ground state structure constants calculated from infrared spectra of the v3cf2) band are presented by Tan-ago et al. (5): B, = 5.2410356 _+ O.OOOOO96 cm-‘, -Do = (- 1.10864 + 0.00074) 10e4 cm-‘, - [31/z/2(71/2)]D$ = (- 1.4485 t 0.0023) lo+ cm-‘.
F2 v=1,3=4 E F, Al
F2
E F, A, FIG. 1. Tetrahedral splitting of the rotational level with J = 4 in the ground and the v,(a,) vibrational states. Raman-active transitions occur between sublevels of the same symmetry type.
METHANE
HIGH-RESOLUTION
23
CARS-SPECTRA
In Raman spectra the vibration-rotation transitions between the ground and the +( a J vibrational states are allowed only between the rotational states of the same J value and symmetry (Fig. 1). The expression for the frequencies of transitions is, therefore, VJ,K = VI - a,J(J
+ 1) - &J”(J + l)2 +
(3)
y&J,K),
with the constants -cyl = B, - Bo, p1 = D, - D,,, y, = Dj - De, showing the difference between the vl(al) vibrational state structure constants and those of the ground state. This difference is mainly determined by the anharmonicity, which gives rise to vibration-rotation interaction and Fermi resonance between the vl(at) and the 2v,(a,) vibrations. The Fermi resonance in methane reveals itself in the intense spontaneous Raman scattering (6) and CARS (7) on the 2v,(a,) overtone. The influence of Coriolis resonance between the ~,(a,) and the vg(f2) vibrations is weak, because of the large frequency shift v3-v1 5 100 cm-‘, and has not been taken into consideration. In the last few years CARS has been developed to be a powerful and potentially important spectroscopic technique. The physical principles of CARS and its advantages are treated in detail in the review by Tolles ef al. (8) and by Akhmanov and Koroteev (9). The CARS-signal generation can be described in terms of the third order nonlinear susceptibility tensor x$(-v,,, vl, vI, -vs), where vz and v, are the pumping light frequencies, and vas = v1 + (vI - v,) is the scattered light frequency. CARSspectra recorded with parallel or orthogonal linear polarizations of the exciting beams by scanning vs, yield the dispersion of 1x& 12. The susceptibility x$\ is a sum of resonant x$;iF and nonresonant x~$$‘”parts, but since in gases x\;iTR is four to five orders of magnitude smaller than xgkl, their interference can be neglected when analyzing the structure in the spectrum. The dispersion of the resonant part of the third order nonlinear susceptibility of a molecule at rest can be approximately expressed as follows:
1
l3)R _
Xijkl
1 gJ,Kbexp
J.K
!
-
c 1
g,,,
BoJ(J
+ 1) T
J,K
1 r ’ 1
+ 1)
B,J(J T
(4)
lvJa - (vL - v,)] - i + [
where are homogeneous linewidths of the vibration-rotation spectrum, and T is the rotational temperature. The Q-branch exhibits its structure at rather low methane densities (pressure less than 100 Torr at room temperature). If now 0: and DQ values differ only slightly from each other, the Q-branch lines result from all possible transitions between the rotational states with the same J value, and their relative intensities are governed by the expression: rJ&
IJ-
(5)
24
KOZLOV,
PROKHOROV,
AND
SMIRNOV
If 0: and Dp are greatly different, the Q-branch structure becomes more complicated since the lines result from transitions between different J, K states. The relative intensities of the resolved lines are given by: + 1)
B,J(J
Z
T ANALYSIS
II
2 *
OF THE SPECTRA
The resolved structure of the methane molecule Y~(a,) Q-branch CARS-spectrum presented previously in Ref. (I) was recorded with parallel linear polarizations of the exciting beams and yielded the dispersion of 1x% 1’. The assignment of six regularly situated sharp lines, proposed in Ref. (I), was based on the assumption that terms YJ(J,K) in Eq. (3) for transition frequencies are small compared to linewidths. The same assumption pas made by Clements and Stoicheff (10) to analyze the unresolved vl(al) Q-branch structure of the conventional Raman spectrum. In this case, as was mentioned above, the individual lines Q(J) must have frequency positions according to uJ = v1 - ~YJ(J + 1) - &.P(J + 1)2 and the intensities given by Eq. (.5), the Q(6) line being the strongest one. Deviations in intensities of lines 3 and 6, large widths of lines 6 and 8, and presence of the unidentified lines 2, 4 and 9, 10, 11 in high-pressure unresolved CARS-spectrum (Fig. 2) was accounted for by the possible appearance of u3cf2) P-branch lines in the Q-branch frequency domain (6, 1l), and their overlapping with some of the Q-branch lines. However, there were the following doubts in the validity of these presumptions. 5
CH4 IOO Torr
300°K
SCALE 4
FIG. 2. The broad-scale
~,(a,) Q-branch CARS-spectrum
at 100 Torrpressure
I---
0,l cm-
and room temperature.
METHANE HIGH-RESOLUTION
CARS-SPECTRA
25
CH4 20 forr SCALE 4
300. K cc
0,03 cn-’
I !
FIG. 3. Central portion of the vl(ul) Q-branch CARS-spectrum at 20 Torr pressure and room temperature.
First, the intensities of the v3cf2) P-branch lines should be at least an order of magnitude weaker than that of the Q(6) line, since they result from transitions from the rotational states with J = 10. This consideration is confirmed by the analysis of the Raman spectrum obtained by Berger (12), in which the resolved lines 77 and 79 assigned to the vI(aI) Q-branch (lines 9 and 11 of our spectrum in Fig. 2, unidentified in Ref. (I)) are much stronger than the I+(&) P(10) lines. To see whether the unidentified lines are from the z+(&) P-branch, a CARSspectrum with orthogonal polarizations of the exciting beams, giving the diswas recorded persion of 1x\%L,I2 in the frequency region under consideration, at 100 Tot-r pressure and room temperature. The x\$! tensor component is proportional to the depolarization ratio, p, of the scattered light, which is determined by the symmetry of the scattering vibration, and equal to 0 or 3/4for ~,(a,) or z+cf2), respectively. Thus, in this kind of spectrum, none of the Q-branch lines can be observed, while the P-branch lines become only l/p2 = 2 times weaker. Changing the polarizations from parallel to orthogonal during the experiment results in a decrease of the signal by two orders of magnitude, its frequency dependence being of the same form. This fact allows us to conclude that all the lines of the spectrum in Fig. 2 should be assigned to the vI(aJ Q-branch. Second, the appearance of wide unresolved lines 2, 6, and 8 (Fig. 3) can be ascribed to a more complex Q-branch structure, connected, for example, with strong tetrahedral splitting in the upper vibrational state, introduced by the term %~(J,K) in Eq. (3). Our further experiments were aimed at resolving the Q-branch lines of the spectrum in Fig. 3. Since linewidths at 20 Torr pressure and room temperature are approximately 0.015 cm-’ and are close to the Doppler limited linewidth (l$*RS - 0.006 cm-‘), the gas was cooled by liquid nitrogen.‘This results in a Doppler-
26
KOZLOV, PROKHOROV,
AND SMIRNOV
width decrease and a scattered light signal increase for the transition between the levels with small J values, allowing us to use lower gas densities. The methane CARS-spectrum recorded at 0.5 Torr pressure and 80 K temperature is shown in Fig. 4. Resolution was as high as 0.002 cm-‘, and frequency scale nonlinearity did not exceed 2%. It is clearly seen that each broad line of the spectrum in Fig. 3 arises from an overlapping of a number of single lines whose intensities and frequency positions cannot be explained on the basis of our former assumptions. We now suppose that all the spectral lines in Fig. 4 belong to the vl(al) Q branch, and result from transitions between separate J, K states with selection rules AJ = 0, AK = 0 (see Fig. 1). Equations (3) and (6) for transition frequencies and line intensities enable us to assign these lines and to calculate the constants ol, pl, and y1 from the line spacing data, using a least-squares procedure: tY1 = (-8.98
-t 0.15) low3 cm-‘,
p, = (2.62 + 0.43) lop5 cm-‘, y1 = (3.30 * 0.07) lo+ cm-‘. The measured frequency shifts of the lines in Fig. 4, relative to the line assigned to the purely vibrational transition between J = 0, K = Al states, are presented in Table I. The experimental error for the line spacings less than 0.1 cm-’ does not exceed 0.002 cm-‘. The assignment of the observed lines and their frequency shifts, computed according to Eq. (3), are also given in Table I. Asterisks indi-
E Fa 2 2
AZ 3 CH4
0,sTorr 8PK SCALE +
A, F, E
444 I
FIG. 4. The ~,(a,) Q-branch and 80 K temperature.
CARS-spectrum
I--
0.03 cn-’
F!)Fa E Fz F’;’ 656 54
Y
with fully resolved
Y/
structure
Az
5 ‘5’
6
at 0.5 Torr pressure
METHANE
HIGH-RESOLUTION TABLE
27
CARS-SPECTRA
I
The Relative Frequency Shifts of the Lines of CH, v1 Q-Branch CARS-Spectrum Measured frequency shifts (cm-‘)
Assignment
(J 4
0.0000*
0 A, 1 Fl
0.0177
2E
0.0528*
2 F2 3 F, 3 & 3 A, 4 A, 4 F, 4E 5 F;”
0.098 1 0.1076 0.1167 0.1408 0.1551 0.1632 0.1945*
4 F2 6E
0.2 180*
5 Fz 6 F:”
0.2290* 0.2647 0.2863 0.2975
6 A, 5E 5 FiZ’
Calculated frequency shifts (cm-‘) 0.0000 0.0178 0.0517 0.0537 0.0980 0.1059 0.1158 0.1413 0.1552 0.1651 0.1913 0.1948 0.2180 0.2180 0.2298 0.2655 0.2872 0.3001
cate the lines which were not used in the computation procedure. The comparison of our spectral data with those of Berger (12) allows us to calculate with the precision of about 0.01 cm-’ the absolute Raman frequency of the above-mentioned purely vibrational line, which has the following value: v1 = Q,,~, = 2916.50 cm-l. Finally, the values of the methane molecule rotational constants for the v,( a J vibrational state are computed to be
B, = 5.25002 2 0.00015 cm-‘, D1 = (1.371 t 0.043) 10m4cm-‘, 0:
= (3.73 i 0.07) 10e5 cm-‘.
It is noteworthy that the ~,(a,)-state tetrahedral splitting constant Dt is an order of magnitude larger than that of the ground state. The value of p1 is also too large in relation to the value of (Ye,and has the opposite sign. This fact accounts for the appearance of numerous lines resulting from transitions with J F 10 in the left wing of the ~(a,) Q-branch, where u.,,~< v,. These lines were observed by Berger (12) in his Raman spectra. A possible explanation of large p1 and y1 values is the influence of Fermi resonance between the ~,(a,) and the 24~7,) vibrational states. The investigation and comparison of the ~,(a,) Q-branch structures of spherical top molecules with various Fermi resonance conditions, e.g., CD4, GeH,, or SiH4, may help to verify this supposition.
28
KOZLOV, PROKHOROV,
AND SMIRNOV
SUMMARY
Gaseous methane vI(aI) Q-branch spectra have been experimentally investigated by means of high-resolution CARS-spectroscopy. The fine structure of the Q branch has been observed. This result has been ascribed to strong tetrahedral splitting of the rotational levels of the q(u,) vibrational state. The Q-branch lines have been assigned to transitions between individual rotational sublevels of the ground and upper vibrational states having the same symmetry type and angular momentum value. The rotational structure constants for the vI(aI) vibrational state have been calculated. ACKNOWLEDGMENTS The authors would like to thank V. I. Fabelinsky for his assistance in computer the spectral data and V. N. Zhiganov for his help with the experimental setup. RECEIVED:
processing
of
June 20, 1978 REFERENCES
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