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9.4-μm CO2 laser Stark spectroscopy of the ν9 fundamental band of methylene fluoride
‘OURNAL OF MOLECULAR
SPECTROSCOPY
68, 125-13.1 (1977)
9.4~pm CO, Laser Stark Spectroscopy of the of Methylene Fluoride
Deparlmenl of Chemistry, Fwdly
vs
Fundamental
Band
of Science, h7yttshu University 33, Fukttokn 812, Ja@n
The CO* laser Stark spectroscopy was appiied to methyIene Auoride, an asymmetric-top molecule with the only nonvanishing dipole moment parallel to the b-principal axis. Stark resonances due to the vs (antisymmetric CF stretching) fundamental band were assigned with the aid of laser-microwave double resonance in the presence of a Stark field. A least-squares analysis of the Stark spectrum yielded the band origin, YO= 32 681 172.3 f 3.0 MHz (1090.1266 f 0.0001 cm-‘), and the dipole moments p” = 1.9785 f 0.0021 D and p’ = 2.0100 f 0.0014 D for the ground and vs excited vibrational states, respectively.
INTRODUCTION
The present paper describes an analysis of the 9.4~pm CO2 laser Stark spectrum of methylene fluoride, an asymmetric-top molecule with the only nonvanishing dipole moment parallel to the b-principal axis. Stark spectroscopy requires that the molecule under investigation has a prominent Stark effect, because of rather wide (l-2 cm-l) separations between the output frequencies of the COZ, N20, and CO lasers used as radiation sources. From this point of view, symmetric-top molecules are best suited to the technique, since many vibration-rotation transitions show large Stark shifts by virtue of the first-order Stark effect. SuccessfuI studies have been performed, for example, in CHsF (I), CDsF (Z), CHIC1 (3), CD&I (4), CH3Br (5), CDJ (6), and PH3 (7). Large Stark shifts produced by the presence of the ‘Ldoublet” energy levels between which nonvanishing matrix elements of the dipole moment exist have also been exploited. Examples are (i) inversion doublet: NH, (g-11) ; (ii) Z-type doublet: HCCF (12) and OCS (13) ; (iii) A-type doublet: NO (24) ; (iv) K-type doublet : H,CO (15, Ifi), D&JO (25, 17); and CH2CF, (18). K-type doublets in methytene fluoride, however, cannot give rise to large Stark effect, since the Stark interaction by means of a dipole moment parallel to the b-axis has no matrix element connecting the K-type doublet levels. Therefore, one might be prejudiced that Stark spectroscopy is not effectively applied to molecules such as methylene fluoride. However, large Stark shifts are produced in methylene fluoride due to the Stark interactions between the rotational levels JI(,K, and (J + l)~,-l,~,‘, where K’, = k’, + 1 or K, + 3, when these levels are nearly degenerate, since they are coupled by a b-dipole matrix element of appreciable magnitude. Such near-degenerate levels in the ground and the yg first excited states of CHgFs are listed in Table I, of which 1Present address:
Institute
for Molecular
Science,
Myodaiji-cho.
Okazaki,
444, Japan.
125 Copyright
@ 1977 by Academic Press, Inc. in any form reserved.
All rights of reproduction
ISSW
wJ22- 2852
126
KAWAGUCHI
AND TANAKA
TABLE Near-Degenerate Rotational Energy
Near-degenerate
I
Levels of CHZFZand Energy Differences (MHZ) Energy Difference b
Paira
Ground State
"9 state
202 - 111
1 136.6
801.4
423 - 514
8 436.4
7 988.8
14 358.6
18 123.5
717.7
5 337.9
615 - 524
15 261.2
15 867.8
'18 - 725
11 464.8
4 474.9
'23 - %6 624 - 717
_ a.
The Stark interaction due to a dipole moment parallel to the principal b-axis has nonvanishing matrix elements between these states.
b. The rotational constants in Table for the calculation.
III
were
used
The centrifugal distortion
effect wa.s neglected.
the entry is limited to those of J 5 8 with energy differences less than 20 GHz. Table I shows that the occurrence of such near degeneracy is by no means rare. In addition, to the Stark effect interactions between the levels JK,K, and J K.+I,K,_I contribute considerably, although the relevant energy differences are rather large. In the present work, we assigned more than 40 Stark resonances of the vg (antisymmetric CF stretching) fundamental band of CHgFz. A few zero-field forbidden AK, = fl (AJ = 2 and 0) transitions were also identified. Laser microwave double resonance in the presence and absence of a Stark field was effectively used for confirmation of the assignment. The vg fundamental band of CHzFz has been studied by means of medium-resolution infrared spectroscopy by Suzuki and Shimanouchi (19). Microwave spectra of CHtFz in the ground vibrational state have been reported by Lide (20) and Hirota et al. (21). Recently, Hirota (22) has made an extensive study of the microwave spectrum in the ground and excited vibrational states, yielding the rotational and centrifugal distortion constants for various vibrational states. EXPERIMENTAL
METHOD
The 9.4~pm COZ laser Stark spectrum of CHzFz was observed with the apparatus described by Yamada and Hirota (4). The spacing between the Stark electrodes was calibrated to be 0.1044 f 0.0001 cm by observing the Stark resonances due to the v3 band of methyl fluoride of which the dipole moments in the ground and vg vibrational states are accurately known (1). The experimental apparatus for observation of laser microwave double resonance in the presence and absence of Stark field has been described by Tanaka et al. (12) and by
LASER STARK SPECTRUM
Kawaguchi it (11. (6). The double-resonance absorption when the microwave frequency OBSERVED
127
OF CHSF~
effect was detected was tuned.
as a change in infrared
STARK SPECTRUM
The vg fundamental band corresponding to the CF antisymmetric stretching vibration of CHzFn is in the R-branch region of the 9.4~pm CO* laser. The Stark spectrum was recorded for the R(30)-R(40) laser lines with the laser polarization parallel to the Stark field, resulting in the AM = 0 selection rule. Measurements with the perpendicular polarization corresponding to the AM = fl selection rule were also made for the R(30) and R(36) laser lines. Most of the prominent Stark resonances observed were identified as due to low-J vibration-rotation transitions of the vg fundamental band. Table II summarizes the assigned Stark resonances. For most of the observed transitions, the Stark component corresponding to the smaller M value was observed at the louer resonant field, in remarkable contrast with the case of symmetric top molecules in which the Stark component with the larger M value normally appears at the lower field. TABLE II The Y.4-pm CO2 Laser Stark Spectrum of the ~0Fundamental
Laser Line
R(40)
Transitiona Resonant Field 04) (kV/cm)
Transltlona ReSonant Field (M) (kV/cm)
Dif'i (MHz)
1%1 1'1
4.516 21.932
9.4 -3.3
R(36)
202'303
;:;
22.203 28.789
6:;:
22.688 -2.7 24.125f -0.3 26.558 2.1 30.538 -2.4 24.767f -12.7
R(34)
423'524
624t625
2_2 3.3 4-4 5-5 3. 3
:I", 33.672 34.103 2. 2 35.475 3. 3 38.307 4. ‘I 44.254
-5.3 -2.1 -3.8 -0.2 3.1
4+4 5-5 6+6
26.558 29.307 33.086
-11.7 -8.0 -14.6
413'514
43 4 3. 3
48.232 56.805
14.6 19.')
2+2 3.3 4+4 202' 212c o*o
31.898 35.576 45.751 15.343
-0.5 1.5 0.9 9.2
513.61'
;:; 2. ? 3-3 4.4
25,395 26.001 28.094 32.768 44.262
1.4 1.9 2.3 16.4 2.6
1* 1 5*5
21.184 32.399
11.2 2.0
;: 2
12.866 13.731
3.4 -0.8
4.4
55.110
6.9
81R. 8*if o-o
4-4 8-8
49.893 12.083
-11.4 -10.5
'L-l 2- 2 3. 3
606f 16.2 15 . 16.264 -14.1 -3.8 17.399 -7.4
16 9 5:1 o'l
4-4 5. 5 6. 6
19.432 -19.2 23.696 -21.5 35.534f -24.1
515'514
R(36)
LaSer Line
lll^l10 523f524
423.422
R(38)
Dif! (MHZ)
Band of C&F2
414+413 818'817
111‘ 303d O+O 1.0 1 O
15.407f 14.588 16.563 19.339
H(32)
R(30)
505.524
6.9 6.5
a. Rotational levels in the jg state and those in t!leground state arc on the left- and right-hand side of the arrows, respectively. b. Transition frequency calculated at the indicated Stark field minus the laser frequency. c,d,e. These transitions are forbidden at zero-Stark field, but allowed in the presence of Stark field by borrowing intensity from the transitions 111-Z12, 202-303, and 725-826, respectively. f. Not included in the least squares calculation.
128
KAWAGUCHI
423
l
AND
TANAKA
52.+h+O
FIG. 1. Stark spectrum of CHZFZ observed with the R(34) line of the 9.4.pm CO2 laser. The laser polarization was parallel to the Stark field, corresponding to the AM = 0 selection rule. The spectral pattern of the 428 + 52* transition in which the Stark component with the smaller M value is observed at the lower Stark field is typical for this molecule.
This is accounted for by the fact that Stark shifts in CH,F, are mostly due to interactions between near-degenerate rotational levels which differ in J by unity, with the result that the M = 0 Stark component is shifted farthest and the M = 1, 2, 3, . . . components to decreasing extents. Figure 1 shows a typical recorder trace in which the Stark components of the 423+ 524 transition are illustrated. It also includes an exceptional example, the 4i3 +- 514 transition of which the component with the larger M value is observed at the lower field. It may also be noted that we observed a number of zero-field forbidden transitions. Since the vg band is of “a-type,” the AK, = f 1 vibration-rotation transitions are forbidden in the absence of Stark field. No AJ = 2 transition is allowed at the zeroStark field. However, the admixture of the rotational levels induced by Stark field make these transitions possible. Figure 2 illustrates the emergence of the zero-field forbidden Iii+ 303 transition as an example. The nearly degenerate levels lri and 202of the vg vibrational state between which a b-dipole matrix element exists are strongly mixed when the electric field is applied, and the 111+- 303 transition is made observable by borrowing intensity from the 202+- 303 transition. The assignment was definitely confirmed by double-resonance experiments in the presence of a Stark field. The experiment performed with the R(36) laser line is described as an example. The Stark field of 15.421 kV/cm was applied to tune the supposed M= 1 component of the Ill+- 303 infrared transition into resonance with the laser line. Then, microwave frequency was swept and double-resonance signals were observed near 46 072 and 43 085 MHz. The former frequency was assigned to the 211+ 111,A4 = 1 +-- 1 transition in the YYstate, and the latter to the 312 +- 303, iM = 1 +- 1 transition in the
LASEK
STARK
SPECTRUM
129
OF C&l”.z
state, resulting in a confirmation of the assignment of the Stark resonance. that the former microwave transition is forbidden in the absence of the Stark field. Similarly, the 2W?+- c&, M = 2 +- 2 infrared transition was definitely assigned by the double resonance with the 312 +- 303, A4 = 2 +-- 2 microwave transition in the ground state. The assignment of the M = 1 +- 1 and 2 +- 2 components of the 5~ +- 616infrared transition was confirmed by the double resonance with the corresponding M components of the ground state, 61~+- 6@~, and the ~9, 51~+- 505 microwave transitions. In the course of the analysis, it appeared likely that the 3c1 +- 328 infrared transition coincides with the R(40) laser line within the Doppler width. The coincidence was confirmed by a zero-field laser-microwave double-resonance experiment in which we observed the 3rl +- 41J microwave transition of the yg state at 46 841.4 f 1.0 MHz.
ground Note
ANALYSIS
Stark shifts of the rotational levels relevant to the observed Stark spectrum are mostly due to the interaction between nearly degenerate levels, and estimation of Stark shifts by the second-order perturbation method is of little use. Therefore, the Stark shifted rotational energy levels were calculated by numerical diagonalization of the
0
IO
20
30
KV/Cm
FIG. 2. Energy level diagram showing the Stark components pertinent to the emergence of the zerofield forbidden ill+- 303 transition. The M = 0 and 1 components of the 11~ and 202 levels are mixed in the presence of a Stark field. The vertical arrows are observed transitions.
130
KAWAGUCHI
AND TANAKA
TABLE
III
Molecular Constants of Methylene Fluoride *
"0
32 681 172.3 i 3.0 1 090.1266
MHz
i 0.0001 cm-1
il’
2.0100
+ 0.0014 D
P I'
1.9785
+ 0.0021 D
h (MHZ)
Ground State
"9 state
A
49 142.817 735
48 698.788 056
B
10 604.704 976
10 531.095 018
C
9 249.843 682
8 980.533 313
T
-2.300 614
-3.315 786
-0.061 506
-0.106 305
Assumed
aaaa
'bbbb T cccc
-0.027 226
0.237 152
0.157 490
-2.803 406
-0.037 565
0.054 560
Tl T
2
a. The uncertainties are 2.5 standard deviations. b. Ref (2,.
As for the definition of the
centrifugal distortion constants, see Ref (1).
effective Hamiltonian, H = Hrot + Hs, where Hrot represents the rotational energy including the centrifugal distortion effect and Hs is the Stark energy. The centrifugal distortion effect was taken into account to the fourth power of angular momentum operators as in Ref. (21). The matrix elements of the effective Hamiltonian were evaluated in terms of the Wang-type base functions, 1J, K, M, &t>, which are linear combinations of symmetric matrix rotor eigenfunctions. Hrot is diagonal in J, M, and f, and has nonvanishing elements with AK = 0, f2, and f4. Nonvanishing matrix elements of Hs are
(J,K,M,=t
I&lJ,K-
(J,K,M,f
IHslJ-
LM,f) = /.dW(J - K + l)(J + K)1*/‘2J(J + 11, l,K-
l,M,r) = pE(J2 - iW)i[(J
+ K -
l)(J
+ K)]t/2J(4J2
-
l):,
and (J, K -
1, M, f
[Hsl J -
1, K, M, =F> = -/.iE(J2
-
P)f[(J
- K)(J
- K + 1)]i/2J(4J2
-
l)“,
except that the matrix elements must be multiplied by 21 in case K = 1. p and E are the dipole moment and the strength of the applied electric field, respectively. The matrix may be factored into two, corresponding to symmetric and antisymmetric eigenstates with respect to the feasible permutation of equivalent nuclei. The matrix
LASER
STARK
SPECTRUM
131
OF CHZ,
was truncated so that all base functions with the J values exceeding that of the interested level by more than 3 were ignored. Special care should be taken in order to avoid errors introduced by the truncation, since the matrix sometimes contains rotational levels which are quite different in J but close in energy. The calculation in the present work was confirmed to be free from the truncation error by comparing with the calculation in which a larger number of base functions were retained. For each of the assigned Stark resonances listed in Table II, the rovibrational transition frequency was calculated at the Stark field corresponding to the center of the observed resonance. Those transition frequencies were fitted by a least-squares method to the CO2 laser frequencies for which we used the \*alues reported by Petersen rt (11. (23). The rotational and centrifugal distortion constants both in the ground and vg vibrational states were fixed to the recent microwave values by Hirota (22). Adjusted ljarameters were thus the band origin Q, and the dipole moments U” and /I’ in the ground and vg states, respectively. The resulting constants given in Table III together with the assumed constants reproduce the observed spectrum satisfactorily as indicated b! “Dif.” in Table II. Table IV lists the zero-field frequencies of the vibration-rotation transitions of (‘HsF:! observed in the present experiment. These frequencies calculated from the TABLE
IV
The vo Band of CHtF2 (MHz)
Lasera
.c
Transition
cal?
Line
K(30)
505
.
524
32
517
702.6
1159.0
818
1
82b"
32
515
092.5
-1451.1
kC3L)
5
.
615
32
554
232.6
3803.4
Ii!J4)
423
.
'14
32
x7
408.C
-6128.6
413
.
514
3'
575
905.7
-7630.9
818
-
'17
32
bib
2LJx.u
111
.
3036
3?
bl9
YOO.4
4030.7
2
i
303
32
620
ill.2
4841.5 -4516.8
Pi36)
1<(36)
K(4Uj
14
02
202
.
212d
32
642
915.4
515
*
514
32
653
941.3
6509.1
414
+
413
32
662
931.U
15498.8
1 _ 11 '24
110
32
67Y
103.8
6,5
32
675
864.1
-2344.3
523
524
32
676
4j9.L
-1788.8
42d
32
1x76 fJ;5.1
322'
32
h78
-
423 321
.
ri. 'ihe '1.4 ,m
band
__
frequency
'l'ruiaition
428.3
of
:~~~l~:~ular constji~~ts
tile co2 at
-2153.3
2L8.1,
0.2
laser.
zel-0 field,
list.ed
875.4
calculCitad
111 'I'C~iilk2 I LI
.
usin?
the
132
KAWAGUCHI
AND
TANAKA
molecular constants in Table III might be useful for future applications. The A’s give some idea as to how far the transitions were shifted by the Stark effect. The vaIue of A for the 321~ 322 transition shows that the transition is in exact coincidence with the R(40) laser line at zero field. DISCUSSION
Since the CHZF, molecule has its permanent dipole moment parallel to the principal b-axis, large Stark shifts are mostly due to accidentally near-degenerate levels between which b-dipole matrix elements are appreciable. In fact, most of the Stark resonances observed in the present work involve such near-degenerate levels in the upper or lower state of the transition. This fact gives some noticeable features to the Stark spectrum of this molecule. The Stark spectrum is less crowded than that of a symmetric-top molecule with rotational constants of comparable magnitude, since only selected transitions give rise to Stark resonances. The spectral pattern formed by successive M components of a vibration rotation transition is quite different from that of a symmetric top molecule, and we have no simple way to assign the M and J quantum numbers. The assignment must depend on the comparison of the observed patterns with exact calculations. The laser-microwave double-resonance technique was a very useful method for assignment in the present experiment. It was used from the earliest stage to test probable assignments. Observation of double resonance for a few Stark resonances greatly facilitated the assignment of the whole spectrum. The dipole moment of methylene fluoride was precisely determined for the ground and the vg first excited states. The ground-state dipole moment is consistent with the value, j.~” = 1.96 f 0.02 D, obtained by Lide (20). The observed change of the dipole moment due to the vibrational excitation, p’ - p” = 0.0315 f 0.0029 D, is of reasonable magnitude for a CF stretching vibration. The vg band origin, 1090.1266 f 0.0001 cm-‘, determined in the present work is consistent with but of greatly improved accuracy over the result by Suzuki and Shimanouchi (19). ACKNOWLEDGMENT We would like to thank Professor Eizi Hirota for making the result of his recent microwave work available to us prior to publication. The calculations in the present work were carried out at the Computer Center of Kyushu University.
RECENED: May 12, 1977 REFERENCES 1. S. M. FREUND, G. DUXBURY, M. R~LIHELD,J. T. TIEDJE, AND T. OKA, J. Mol. Speclrosc. 38 (1974). 2. G. DUXBURY, S. M. FREUND,AND J. W. C. JOHXS, J. Mol. Spectrosc. 62, 99 (1976). 3. F. SHIMIZU,J. Phys. 5’06. Japan 38, 1106 (1975). 4. C. YAMADAAND E. HIROTA,.I. Mol. Spectrosc. 64, 31 (1977). 5. M. IEHI, E. KUYAMOTO,K. KAWAGUCHI,C. YAMADA,T. TANAKA, AND E. HIROTA, to appear. 6. K. KAWAGUCHI,C. YAMADA,T. TANAKA, AND E. HIROTA,J. Mol. Spectrosc. 64, 125 (1977). 7. Y. SHIMIZU,J. Phys. Sot. Japatt 38, 293 (1975). 8. F. SHIMIZU, J. Chem. Phys. 51,27.54 (1969); 52,3572 (1970); 53, 1149 (1970).
52,
LASER STARK SPECTRUM 9. 'I'.UEDA
Hgnsch,
AND
K.
SHIMODA,in “Laser Spectroscopy”
and S. E. Harris, Eds.),
OF C&F2
(S. Haroche, J. C. Pebay-Peyroula,
133 T. W.
p. 186, Lecture Notes in Physics, Vol. 43, Springer-Verlag.
Heidelberg, 1975. 10. J. W. C. JOHNS, A. R. W. MCKELLAR, AND A. TROMBETTI,J.
Il. 12. 13. 14. 15. 16. 17. IR. 19. 20.
21. Z’. 23.
Mol. Speclrosc. 55, 131 (1975). D. LAUGHTON, S. M. FREUND, AND T. OKA, J. Mol. Spectrosc. 62, 263 (1976). T. TANAKA, C. YAMADA, AND E. HIROTA, J. Mol. Spectrosc. 63, 142 (1976). A. G. MAKI AND S. 111. FREUND, J. Mol. Spectrosc. 62, 90 (1976). A. R. HOY, J. W. C. JOHNS, AND A. R. W. MCKELLAR, Cwznd. J. Phys. 53, 2029 (1975). J. W. C. JOHKS AND A. R. W. MCKELLAR, J. Mol. Spectrosc. 48, 354 (1973). J. W. C. JOHKS AND A. R. W. MCKELLAR, J. Chrm. Phys. 63, 1682 (1975). D. COPFEY, JK., C. YA~DA, AND E. HIROTA, J. Mol. Spectrosc. 64, 98 (1977). G. DUXBURY, T. J. GAMBLE, AND H. HERMAN, IEEE Trans. MTT22, 1108 (1974). I. SUZUKI AND T. SHIYAKOUCHI,J. Mol. Speclrosc. 46, 130 (1973,. D. R. LIDE, Jr., J. .4mer. Chem. Sot. 74, 3548 (1952). E. HIROTA, T. TANAKA, A. SAKAKIUA\KA,Y. OH.\SHI, AND Y. JIORIX~, .I. Mol. Speclrosc. 34, 222 (1970). E. HIROTA, private communication. 1:. R. PETERSEN, D. G. MCDONALD, J. D. CUPU, AND B. I,. DANIELSEN, in “Laser Spectroscopy” CR. G. Brewer and A. Mooradian, Eds.), Plenum, New York, 1974.
SPECTROSCOPY
68, 125-13.1 (1977)
9.4~pm CO, Laser Stark Spectroscopy of the of Methylene Fluoride
Deparlmenl of Chemistry, Fwdly
vs
Fundamental
Band
of Science, h7yttshu University 33, Fukttokn 812, Ja@n
The CO* laser Stark spectroscopy was appiied to methyIene Auoride, an asymmetric-top molecule with the only nonvanishing dipole moment parallel to the b-principal axis. Stark resonances due to the vs (antisymmetric CF stretching) fundamental band were assigned with the aid of laser-microwave double resonance in the presence of a Stark field. A least-squares analysis of the Stark spectrum yielded the band origin, YO= 32 681 172.3 f 3.0 MHz (1090.1266 f 0.0001 cm-‘), and the dipole moments p” = 1.9785 f 0.0021 D and p’ = 2.0100 f 0.0014 D for the ground and vs excited vibrational states, respectively.
INTRODUCTION
The present paper describes an analysis of the 9.4~pm CO2 laser Stark spectrum of methylene fluoride, an asymmetric-top molecule with the only nonvanishing dipole moment parallel to the b-principal axis. Stark spectroscopy requires that the molecule under investigation has a prominent Stark effect, because of rather wide (l-2 cm-l) separations between the output frequencies of the COZ, N20, and CO lasers used as radiation sources. From this point of view, symmetric-top molecules are best suited to the technique, since many vibration-rotation transitions show large Stark shifts by virtue of the first-order Stark effect. SuccessfuI studies have been performed, for example, in CHsF (I), CDsF (Z), CHIC1 (3), CD&I (4), CH3Br (5), CDJ (6), and PH3 (7). Large Stark shifts produced by the presence of the ‘Ldoublet” energy levels between which nonvanishing matrix elements of the dipole moment exist have also been exploited. Examples are (i) inversion doublet: NH, (g-11) ; (ii) Z-type doublet: HCCF (12) and OCS (13) ; (iii) A-type doublet: NO (24) ; (iv) K-type doublet : H,CO (15, Ifi), D&JO (25, 17); and CH2CF, (18). K-type doublets in methytene fluoride, however, cannot give rise to large Stark effect, since the Stark interaction by means of a dipole moment parallel to the b-axis has no matrix element connecting the K-type doublet levels. Therefore, one might be prejudiced that Stark spectroscopy is not effectively applied to molecules such as methylene fluoride. However, large Stark shifts are produced in methylene fluoride due to the Stark interactions between the rotational levels JI(,K, and (J + l)~,-l,~,‘, where K’, = k’, + 1 or K, + 3, when these levels are nearly degenerate, since they are coupled by a b-dipole matrix element of appreciable magnitude. Such near-degenerate levels in the ground and the yg first excited states of CHgFs are listed in Table I, of which 1Present address:
Institute
for Molecular
Science,
Myodaiji-cho.
Okazaki,
444, Japan.
125 Copyright
@ 1977 by Academic Press, Inc. in any form reserved.
All rights of reproduction
ISSW
wJ22- 2852
126
KAWAGUCHI
AND TANAKA
TABLE Near-Degenerate Rotational Energy
Near-degenerate
I
Levels of CHZFZand Energy Differences (MHZ) Energy Difference b
Paira
Ground State
"9 state
202 - 111
1 136.6
801.4
423 - 514
8 436.4
7 988.8
14 358.6
18 123.5
717.7
5 337.9
615 - 524
15 261.2
15 867.8
'18 - 725
11 464.8
4 474.9
'23 - %6 624 - 717
_ a.
The Stark interaction due to a dipole moment parallel to the principal b-axis has nonvanishing matrix elements between these states.
b. The rotational constants in Table for the calculation.
III
were
used
The centrifugal distortion
effect wa.s neglected.
the entry is limited to those of J 5 8 with energy differences less than 20 GHz. Table I shows that the occurrence of such near degeneracy is by no means rare. In addition, to the Stark effect interactions between the levels JK,K, and J K.+I,K,_I contribute considerably, although the relevant energy differences are rather large. In the present work, we assigned more than 40 Stark resonances of the vg (antisymmetric CF stretching) fundamental band of CHgFz. A few zero-field forbidden AK, = fl (AJ = 2 and 0) transitions were also identified. Laser microwave double resonance in the presence and absence of a Stark field was effectively used for confirmation of the assignment. The vg fundamental band of CHzFz has been studied by means of medium-resolution infrared spectroscopy by Suzuki and Shimanouchi (19). Microwave spectra of CHtFz in the ground vibrational state have been reported by Lide (20) and Hirota et al. (21). Recently, Hirota (22) has made an extensive study of the microwave spectrum in the ground and excited vibrational states, yielding the rotational and centrifugal distortion constants for various vibrational states. EXPERIMENTAL
METHOD
The 9.4~pm COZ laser Stark spectrum of CHzFz was observed with the apparatus described by Yamada and Hirota (4). The spacing between the Stark electrodes was calibrated to be 0.1044 f 0.0001 cm by observing the Stark resonances due to the v3 band of methyl fluoride of which the dipole moments in the ground and vg vibrational states are accurately known (1). The experimental apparatus for observation of laser microwave double resonance in the presence and absence of Stark field has been described by Tanaka et al. (12) and by
LASER STARK SPECTRUM
Kawaguchi it (11. (6). The double-resonance absorption when the microwave frequency OBSERVED
127
OF CHSF~
effect was detected was tuned.
as a change in infrared
STARK SPECTRUM
The vg fundamental band corresponding to the CF antisymmetric stretching vibration of CHzFn is in the R-branch region of the 9.4~pm CO* laser. The Stark spectrum was recorded for the R(30)-R(40) laser lines with the laser polarization parallel to the Stark field, resulting in the AM = 0 selection rule. Measurements with the perpendicular polarization corresponding to the AM = fl selection rule were also made for the R(30) and R(36) laser lines. Most of the prominent Stark resonances observed were identified as due to low-J vibration-rotation transitions of the vg fundamental band. Table II summarizes the assigned Stark resonances. For most of the observed transitions, the Stark component corresponding to the smaller M value was observed at the louer resonant field, in remarkable contrast with the case of symmetric top molecules in which the Stark component with the larger M value normally appears at the lower field. TABLE II The Y.4-pm CO2 Laser Stark Spectrum of the ~0Fundamental
Laser Line
R(40)
Transitiona Resonant Field 04) (kV/cm)
Transltlona ReSonant Field (M) (kV/cm)
Dif'i (MHz)
1%1 1'1
4.516 21.932
9.4 -3.3
R(36)
202'303
;:;
22.203 28.789
6:;:
22.688 -2.7 24.125f -0.3 26.558 2.1 30.538 -2.4 24.767f -12.7
R(34)
423'524
624t625
2_2 3.3 4-4 5-5 3. 3
:I", 33.672 34.103 2. 2 35.475 3. 3 38.307 4. ‘I 44.254
-5.3 -2.1 -3.8 -0.2 3.1
4+4 5-5 6+6
26.558 29.307 33.086
-11.7 -8.0 -14.6
413'514
43 4 3. 3
48.232 56.805
14.6 19.')
2+2 3.3 4+4 202' 212c o*o
31.898 35.576 45.751 15.343
-0.5 1.5 0.9 9.2
513.61'
;:; 2. ? 3-3 4.4
25,395 26.001 28.094 32.768 44.262
1.4 1.9 2.3 16.4 2.6
1* 1 5*5
21.184 32.399
11.2 2.0
;: 2
12.866 13.731
3.4 -0.8
4.4
55.110
6.9
81R. 8*if o-o
4-4 8-8
49.893 12.083
-11.4 -10.5
'L-l 2- 2 3. 3
606f 16.2 15 . 16.264 -14.1 -3.8 17.399 -7.4
16 9 5:1 o'l
4-4 5. 5 6. 6
19.432 -19.2 23.696 -21.5 35.534f -24.1
515'514
R(36)
LaSer Line
lll^l10 523f524
423.422
R(38)
Dif! (MHZ)
Band of C&F2
414+413 818'817
111‘ 303d O+O 1.0 1 O
15.407f 14.588 16.563 19.339
H(32)
R(30)
505.524
6.9 6.5
a. Rotational levels in the jg state and those in t!leground state arc on the left- and right-hand side of the arrows, respectively. b. Transition frequency calculated at the indicated Stark field minus the laser frequency. c,d,e. These transitions are forbidden at zero-Stark field, but allowed in the presence of Stark field by borrowing intensity from the transitions 111-Z12, 202-303, and 725-826, respectively. f. Not included in the least squares calculation.
128
KAWAGUCHI
423
l
AND
TANAKA
52.+h+O
FIG. 1. Stark spectrum of CHZFZ observed with the R(34) line of the 9.4.pm CO2 laser. The laser polarization was parallel to the Stark field, corresponding to the AM = 0 selection rule. The spectral pattern of the 428 + 52* transition in which the Stark component with the smaller M value is observed at the lower Stark field is typical for this molecule.
This is accounted for by the fact that Stark shifts in CH,F, are mostly due to interactions between near-degenerate rotational levels which differ in J by unity, with the result that the M = 0 Stark component is shifted farthest and the M = 1, 2, 3, . . . components to decreasing extents. Figure 1 shows a typical recorder trace in which the Stark components of the 423+ 524 transition are illustrated. It also includes an exceptional example, the 4i3 +- 514 transition of which the component with the larger M value is observed at the lower field. It may also be noted that we observed a number of zero-field forbidden transitions. Since the vg band is of “a-type,” the AK, = f 1 vibration-rotation transitions are forbidden in the absence of Stark field. No AJ = 2 transition is allowed at the zeroStark field. However, the admixture of the rotational levels induced by Stark field make these transitions possible. Figure 2 illustrates the emergence of the zero-field forbidden Iii+ 303 transition as an example. The nearly degenerate levels lri and 202of the vg vibrational state between which a b-dipole matrix element exists are strongly mixed when the electric field is applied, and the 111+- 303 transition is made observable by borrowing intensity from the 202+- 303 transition. The assignment was definitely confirmed by double-resonance experiments in the presence of a Stark field. The experiment performed with the R(36) laser line is described as an example. The Stark field of 15.421 kV/cm was applied to tune the supposed M= 1 component of the Ill+- 303 infrared transition into resonance with the laser line. Then, microwave frequency was swept and double-resonance signals were observed near 46 072 and 43 085 MHz. The former frequency was assigned to the 211+ 111,A4 = 1 +-- 1 transition in the YYstate, and the latter to the 312 +- 303, iM = 1 +- 1 transition in the
LASEK
STARK
SPECTRUM
129
OF C&l”.z
state, resulting in a confirmation of the assignment of the Stark resonance. that the former microwave transition is forbidden in the absence of the Stark field. Similarly, the 2W?+- c&, M = 2 +- 2 infrared transition was definitely assigned by the double resonance with the 312 +- 303, A4 = 2 +-- 2 microwave transition in the ground state. The assignment of the M = 1 +- 1 and 2 +- 2 components of the 5~ +- 616infrared transition was confirmed by the double resonance with the corresponding M components of the ground state, 61~+- 6@~, and the ~9, 51~+- 505 microwave transitions. In the course of the analysis, it appeared likely that the 3c1 +- 328 infrared transition coincides with the R(40) laser line within the Doppler width. The coincidence was confirmed by a zero-field laser-microwave double-resonance experiment in which we observed the 3rl +- 41J microwave transition of the yg state at 46 841.4 f 1.0 MHz.
ground Note
ANALYSIS
Stark shifts of the rotational levels relevant to the observed Stark spectrum are mostly due to the interaction between nearly degenerate levels, and estimation of Stark shifts by the second-order perturbation method is of little use. Therefore, the Stark shifted rotational energy levels were calculated by numerical diagonalization of the
0
IO
20
30
KV/Cm
FIG. 2. Energy level diagram showing the Stark components pertinent to the emergence of the zerofield forbidden ill+- 303 transition. The M = 0 and 1 components of the 11~ and 202 levels are mixed in the presence of a Stark field. The vertical arrows are observed transitions.
130
KAWAGUCHI
AND TANAKA
TABLE
III
Molecular Constants of Methylene Fluoride *
"0
32 681 172.3 i 3.0 1 090.1266
MHz
i 0.0001 cm-1
il’
2.0100
+ 0.0014 D
P I'
1.9785
+ 0.0021 D
h (MHZ)
Ground State
"9 state
A
49 142.817 735
48 698.788 056
B
10 604.704 976
10 531.095 018
C
9 249.843 682
8 980.533 313
T
-2.300 614
-3.315 786
-0.061 506
-0.106 305
Assumed
aaaa
'bbbb T cccc
-0.027 226
0.237 152
0.157 490
-2.803 406
-0.037 565
0.054 560
Tl T
2
a. The uncertainties are 2.5 standard deviations. b. Ref (2,.
As for the definition of the
centrifugal distortion constants, see Ref (1).
effective Hamiltonian, H = Hrot + Hs, where Hrot represents the rotational energy including the centrifugal distortion effect and Hs is the Stark energy. The centrifugal distortion effect was taken into account to the fourth power of angular momentum operators as in Ref. (21). The matrix elements of the effective Hamiltonian were evaluated in terms of the Wang-type base functions, 1J, K, M, &t>, which are linear combinations of symmetric matrix rotor eigenfunctions. Hrot is diagonal in J, M, and f, and has nonvanishing elements with AK = 0, f2, and f4. Nonvanishing matrix elements of Hs are
(J,K,M,=t
I&lJ,K-
(J,K,M,f
IHslJ-
LM,f) = /.dW(J - K + l)(J + K)1*/‘2J(J + 11, l,K-
l,M,r) = pE(J2 - iW)i[(J
+ K -
l)(J
+ K)]t/2J(4J2
-
l):,
and (J, K -
1, M, f
[Hsl J -
1, K, M, =F> = -/.iE(J2
-
P)f[(J
- K)(J
- K + 1)]i/2J(4J2
-
l)“,
except that the matrix elements must be multiplied by 21 in case K = 1. p and E are the dipole moment and the strength of the applied electric field, respectively. The matrix may be factored into two, corresponding to symmetric and antisymmetric eigenstates with respect to the feasible permutation of equivalent nuclei. The matrix
LASER
STARK
SPECTRUM
131
OF CHZ,
was truncated so that all base functions with the J values exceeding that of the interested level by more than 3 were ignored. Special care should be taken in order to avoid errors introduced by the truncation, since the matrix sometimes contains rotational levels which are quite different in J but close in energy. The calculation in the present work was confirmed to be free from the truncation error by comparing with the calculation in which a larger number of base functions were retained. For each of the assigned Stark resonances listed in Table II, the rovibrational transition frequency was calculated at the Stark field corresponding to the center of the observed resonance. Those transition frequencies were fitted by a least-squares method to the CO2 laser frequencies for which we used the \*alues reported by Petersen rt (11. (23). The rotational and centrifugal distortion constants both in the ground and vg vibrational states were fixed to the recent microwave values by Hirota (22). Adjusted ljarameters were thus the band origin Q, and the dipole moments U” and /I’ in the ground and vg states, respectively. The resulting constants given in Table III together with the assumed constants reproduce the observed spectrum satisfactorily as indicated b! “Dif.” in Table II. Table IV lists the zero-field frequencies of the vibration-rotation transitions of (‘HsF:! observed in the present experiment. These frequencies calculated from the TABLE
IV
The vo Band of CHtF2 (MHz)
Lasera
.c
Transition
cal?
Line
K(30)
505
.
524
32
517
702.6
1159.0
818
1
82b"
32
515
092.5
-1451.1
kC3L)
5
.
615
32
554
232.6
3803.4
Ii!J4)
423
.
'14
32
x7
408.C
-6128.6
413
.
514
3'
575
905.7
-7630.9
818
-
'17
32
bib
2LJx.u
111
.
3036
3?
bl9
YOO.4
4030.7
2
i
303
32
620
ill.2
4841.5 -4516.8
Pi36)
1<(36)
K(4Uj
14
02
202
.
212d
32
642
915.4
515
*
514
32
653
941.3
6509.1
414
+
413
32
662
931.U
15498.8
1 _ 11 '24
110
32
67Y
103.8
6,5
32
675
864.1
-2344.3
523
524
32
676
4j9.L
-1788.8
42d
32
1x76 fJ;5.1
322'
32
h78
-
423 321
.
ri. 'ihe '1.4 ,m
band
__
frequency
'l'ruiaition
428.3
of
:~~~l~:~ular constji~~ts
tile co2 at
-2153.3
2L8.1,
0.2
laser.
zel-0 field,
list.ed
875.4
calculCitad
111 'I'C~iilk2 I LI
.
usin?
the
132
KAWAGUCHI
AND
TANAKA
molecular constants in Table III might be useful for future applications. The A’s give some idea as to how far the transitions were shifted by the Stark effect. The vaIue of A for the 321~ 322 transition shows that the transition is in exact coincidence with the R(40) laser line at zero field. DISCUSSION
Since the CHZF, molecule has its permanent dipole moment parallel to the principal b-axis, large Stark shifts are mostly due to accidentally near-degenerate levels between which b-dipole matrix elements are appreciable. In fact, most of the Stark resonances observed in the present work involve such near-degenerate levels in the upper or lower state of the transition. This fact gives some noticeable features to the Stark spectrum of this molecule. The Stark spectrum is less crowded than that of a symmetric-top molecule with rotational constants of comparable magnitude, since only selected transitions give rise to Stark resonances. The spectral pattern formed by successive M components of a vibration rotation transition is quite different from that of a symmetric top molecule, and we have no simple way to assign the M and J quantum numbers. The assignment must depend on the comparison of the observed patterns with exact calculations. The laser-microwave double-resonance technique was a very useful method for assignment in the present experiment. It was used from the earliest stage to test probable assignments. Observation of double resonance for a few Stark resonances greatly facilitated the assignment of the whole spectrum. The dipole moment of methylene fluoride was precisely determined for the ground and the vg first excited states. The ground-state dipole moment is consistent with the value, j.~” = 1.96 f 0.02 D, obtained by Lide (20). The observed change of the dipole moment due to the vibrational excitation, p’ - p” = 0.0315 f 0.0029 D, is of reasonable magnitude for a CF stretching vibration. The vg band origin, 1090.1266 f 0.0001 cm-‘, determined in the present work is consistent with but of greatly improved accuracy over the result by Suzuki and Shimanouchi (19). ACKNOWLEDGMENT We would like to thank Professor Eizi Hirota for making the result of his recent microwave work available to us prior to publication. The calculations in the present work were carried out at the Computer Center of Kyushu University.
RECENED: May 12, 1977 REFERENCES 1. S. M. FREUND, G. DUXBURY, M. R~LIHELD,J. T. TIEDJE, AND T. OKA, J. Mol. Speclrosc. 38 (1974). 2. G. DUXBURY, S. M. FREUND,AND J. W. C. JOHXS, J. Mol. Spectrosc. 62, 99 (1976). 3. F. SHIMIZU,J. Phys. 5’06. Japan 38, 1106 (1975). 4. C. YAMADAAND E. HIROTA,.I. Mol. Spectrosc. 64, 31 (1977). 5. M. IEHI, E. KUYAMOTO,K. KAWAGUCHI,C. YAMADA,T. TANAKA, AND E. HIROTA, to appear. 6. K. KAWAGUCHI,C. YAMADA,T. TANAKA, AND E. HIROTA,J. Mol. Spectrosc. 64, 125 (1977). 7. Y. SHIMIZU,J. Phys. Sot. Japatt 38, 293 (1975). 8. F. SHIMIZU, J. Chem. Phys. 51,27.54 (1969); 52,3572 (1970); 53, 1149 (1970).
52,
LASER STARK SPECTRUM 9. 'I'.UEDA
Hgnsch,
AND
K.
SHIMODA,in “Laser Spectroscopy”
and S. E. Harris, Eds.),
OF C&F2
(S. Haroche, J. C. Pebay-Peyroula,
133 T. W.
p. 186, Lecture Notes in Physics, Vol. 43, Springer-Verlag.
Heidelberg, 1975. 10. J. W. C. JOHNS, A. R. W. MCKELLAR, AND A. TROMBETTI,J.
Il. 12. 13. 14. 15. 16. 17. IR. 19. 20.
21. Z’. 23.
Mol. Speclrosc. 55, 131 (1975). D. LAUGHTON, S. M. FREUND, AND T. OKA, J. Mol. Spectrosc. 62, 263 (1976). T. TANAKA, C. YAMADA, AND E. HIROTA, J. Mol. Spectrosc. 63, 142 (1976). A. G. MAKI AND S. 111. FREUND, J. Mol. Spectrosc. 62, 90 (1976). A. R. HOY, J. W. C. JOHNS, AND A. R. W. MCKELLAR, Cwznd. J. Phys. 53, 2029 (1975). J. W. C. JOHKS AND A. R. W. MCKELLAR, J. Mol. Spectrosc. 48, 354 (1973). J. W. C. JOHKS AND A. R. W. MCKELLAR, J. Chrm. Phys. 63, 1682 (1975). D. COPFEY, JK., C. YA~DA, AND E. HIROTA, J. Mol. Spectrosc. 64, 98 (1977). G. DUXBURY, T. J. GAMBLE, AND H. HERMAN, IEEE Trans. MTT22, 1108 (1974). I. SUZUKI AND T. SHIYAKOUCHI,J. Mol. Speclrosc. 46, 130 (1973,. D. R. LIDE, Jr., J. .4mer. Chem. Sot. 74, 3548 (1952). E. HIROTA, T. TANAKA, A. SAKAKIUA\KA,Y. OH.\SHI, AND Y. JIORIX~, .I. Mol. Speclrosc. 34, 222 (1970). E. HIROTA, private communication. 1:. R. PETERSEN, D. G. MCDONALD, J. D. CUPU, AND B. I,. DANIELSEN, in “Laser Spectroscopy” CR. G. Brewer and A. Mooradian, Eds.), Plenum, New York, 1974.