- Email: [email protected]
Microwave spectrum of CH3OD
JOURNAL
OF
MOLECULAR
g&418-426
SPECTROSCOPY
Microwave
Spectrum
V. K. KAUSHIK,’ Department
of Physics,
(1980)
of CHsOD
K. TAKAGI
Toyama University, Gofuku,
Toyama 930, Japan
AND
C. MATSUMURA National Chemical Laboratory for Industry, Honmachi,
Shibuya-ku,
Tokyo 151, Japan
The microwave spectrum of CHsOD has been observed in the frequency region between 14 and 92 GHz. Ah the ground-state transitions with J I 8 and J = 2 + 1, a-type transitions in the excited torsional states (u = 1and u = 2) have been observed. The spectrum has been analyzed and rotational constants, torsional constants, torsion-vibration-rotation interaction constants, and centrifugal distortion constants have been evaluated. The Stark effect measurements have been made and the dipole moment components have been determined as ILL= 0.833 f 0.008D and h = 1.488 2 O.OlSD.
I. INTRODUCTION
The rotational spectra of the molecules capable of hindered internal rotation have been a subject of interest to microwave spectroscopists (I) because they give the accurate torsional constants. The rotational spectrum of CH30D was first observed by Venkateswarlu er al. (2) who observed the J = 1 c 0 rotational transitions in the ground and two excited torsional states. Nishikawa (3) analyzed these transitions using the internal axis system developed by Itoh (4) and obtained the molecular constants including torsion-vibration-rotation interaction constants. Later, Lees and Baker (5) extended the study of this molecule by observing the other a-type transitions and three series of Q-branch transitions. From the observed Q-branch origins of these series Lees and Baker calculated the three torsional constants Zol, ZnZ, and V,. However, because of the lack of available data these torsional constants were not determined accurately. In the present investigation we have observed all the transitions with J 5 8 in the frequency region between 14 and 92 GHz and used 28 P- and R-branch transitions to give five additional Q-branch origins. These five Q-branch origins have been combined with the three Q-branch origins determined by Lees and Baker’s transitions to calculate the torsional parameters. Finally, the Stark effect measurements have been made to determine the dipole moment components of this molecule. 1 Visiting Research Fellow of Japan Society for the Promotion of Science (JSPS). 0022-2852/80/080418-09$02.00/0 Copyright All rights
0
1980 by Academic
of reproduction
Press.
in any form
Inc. reserved.
418
MICROWAVE
419
SPECTRUM OF CH,OD
II. EXPERIMENTAL
DETAILS
The spectrum was observed using two spectrometers. In the frequency region between 14 and 18 GHz, the computer-controlled spectrometer with a 3-m-long X-band waveguide cell at the National Chemical Laboratory for Industry was used, while between 18 and 92 GHz a conventional 106kHz Stark modulated spectrometer with a 120-cm-long K-band waveguide cell was used. Appropriate Varian and OKI klystrons were used as a source. The sample of CH,OD was obtained from Tokyo Chemical Industry and was used without further purification. The observations were made at room temperature. The estimated accuracy of measured frequencies is kO.05 MHz. III. THEORY
The zeroth-order Hamiltonian for CH,OD can be expressed by considering two rigid mutually rotating groups, subjected to a threefold hindering potential. The Hamiltonian in the internal axis system may be written as
HRAsum,
(1)
H Tar = FP2, + (l/2) V,( 1 - cos 3r),
(2)
H =
H~or
+
H~syrn
+
with H R sym =
(l/2)@ + C)(P% + P”,) + AP;,
(3)
and H RAsvm
=
(WV3
-
c)(p:
-
p:)
+
Dab(PaPb
+
pbpa),
(4)
where H,,, is the torsional part of the Hamiltonian, HR Symis the rotational Hamiltonian for the rigid symmetric top, and H RASymis the part of the rotational Hamiltonian where the second term arises because the internal axes do not coincide with the i>rincipal axes. The constants in Eqs. (2) and (4) are given in Ref. (5).2 The moments of inertia are calculated in a molecular axis system with the origin at the center of mass, the a axis parallel to the methyl top axis, and c axis perpendicular to the COD plane. Za2 is the moment of inertia of the methyl top about its axis, I,, is defined as I, = I,, + Zaz, and Z&,is the product of inertia about the a and b axes. P, = -iti(day) is the torsional angular momentum where y is the angle of internal rotation between the methyl and OD groups. IV. ANALYSIS OF THE SPECTRUM
A general description of the torsion-rotation spectrum of methanol is given by Lees and Baker (5). The notation we use follows that of Lees et al. (6) for A torsional levels and of Gerry et al. (7) for E torsional levels. The A levels with K # 0 are split by molecular asymmetry into K-type doublets, which we denote by A’. The observed spectrum was analyzed using the perturbation treatment of Kivelson (8) and Kirtman (9). Initially, the u-type spectrum was analyzed and the observed constants were used to predict high-Z, u-type transitions. These high-J, u-type transitions were combined with the observed b-type P- and R-branch transitions 2 There is a misprint in the definition of p in Ref. (5). The corrected one is p = I,#[ (IJ,
- 1%).
+ Z:B)1’2/
420
KAUSHIK,
TAKAGI, AND MATSUMURA TABLE I
K = 1, A Doublet Transitions J-value
3
vobs (MHz)
v (MHZ) cal
6160.87(=)
4
13600.16
of CH,OD (MHZ) "obs - "cal
6160.94
-0.07
13600.08
0.08
5
20396.67
20396.59
0.08
6
28547.81
28547.72
0.09
7
38049.06
38049.11
-0.05
8
48894.00
48994.13
-0.13
(a) Calculated from the combination relation of observed transitions.
to give Q-branch origins. Finally, the Q-branch origins were used to calculate the torsional parameters and barrier height.
4.1. a-Type Transitions Since CH,OD is a slightly asymmetric top, these transitions follow a nearly symmetric rotator pattern with the groups at multiples of (B + C). Most of these transitions have been reported by Lees and Baker (5). In the present work all the TABLE II a-Type Molecular Parameters of CHsOD (MHz) B+C 2
22711.90 f 0.25 -65.14 i 0.24
KV
-2.605 f 0.019
GV
-0.200 + 0.025
Lv
0.196 + 0.025
DJK
0.0478 + 0.0080
DJ b
(a) ab
676.2 * 5.4
(B-c) 2 v=o
724.59 * 0.35
(B-C)
713.32 ?:0.40
(B-C)
721.47 ?:0.40
T-
2
v=l
v=2
(a) Constant fixed to Lees and Baker's
(5) value.
MICROWAVE
SPECTRUM TABLE
OF CH,OD
421
III
Observed a-Type Transitions of CH,OD (MHz)
v=o
v=2
V=l
Transition
lo-O0
A+
Zo-lo A
+
Zl-l1 A
'ohs
Vobs-vcal
45359.40(a)
-0.02
45266.3Zta)
-0.19
45193.74(a)
-1.78
90705.81(a)
-0.12
90534.53(a)
-0.46
90386.35(a)
-2.75
0.39
9ll2o.50(a)
4.18
91064.2ZCa)
-0.08
89707.61(=)
-0.08
92075.51(a)
Zl-l1 A+
89355.10(@
0.39
30-20 A+
136026.40
-0.21
31-21 A
138101.53
0.67
32-22 A
+
'ohs
"ohs-"al
89961.64(=) 135806.92
4.18 -0.50
"obs
Vobs-vcal
135576.86
-1.96
136102.82
0.73
135663.76(b)
-27.63
135528.06
-1.31
32-22 A
136055.46
0.51
135652.7ZCb1
-26.51
135526.43
0.19
40-30 A+
181308.30
-0.28
-0.59
180764.21
1.46
41-31 A
184113.18
0.91
41-31 A+
178673.89
1.69
42-32 A+
181507.14
1.14
180875.33(b)
-35.76
180701.68
-2.56
42-32 A
181388.97
0.79
180847.82(b)
-32.90
180697.36
0.96
43-33 A
181428.24
0.43
181046.09
43-33 A+
181428.24
1.03
181046.09
lo-O0 E
45344.16(')
181085.21
0.12
45260.02(")
4.22 4.70 -0.20
45190.13(a)
0.07 0.21
zo-lo E
9O669.98(a)
1.22
90514.92(a)
-1.08
90379.72(a)
Zl-ll E
90743.56(')
-0.09
90487.27(a)
-7.57
90368.92(")
1.15
2_l-l_l E
90703.65(")
-0.59
90500.49(a)
2.52
90381.11(')
-6.20
30-20 E
135958.38
3.53
31-21 E
136171.61
-0.96
3_1-2_l E
135972.50
-1.56
32-22 E
136098.96
-3.63
135764.85
3_2-2_2 E
136107.60
0.03
135894.26
40-30 E
181191.27
8.27
180990.87
135760.11
-2.79
135568.97
1.21
135552.04
1.98
6.80
135587.02
6.66
-5.62
180756.34
2.15
180733.23
2.79
-2.50
41-31 E
181666.31
-2.60
4_l-3_1 E
181142.85
-3.48
42-32 E
181486.11
-6.50
181024.22
-3.28
180806.46
-7.25
181126.40
-2.07
180776.29
10.27
180712.52
-7.53
4-2-3-z E
181504.50
0.13
43-33 E
181451.29
-2.48
4_3-3_3 E
181428.24
1.02
(a)
Present measureIrent.
(b) Frequencies not included in the least square fit.
= 2 t 1 transitions in the three torsional states (V = 0, 1, 2) have been measured. The J = 1 + 0 transitions have also been measured with a better accuracy. In addition, five transitions between K-type doublets with K = 1 have also been
J
422
KAUSHIK,
TAKAGI, AND MATSUMURA TABLE IV
CH,OD Q-Branch Series Transition Frequencies’“) (MHz) 1+0 A
J-value
(b'
I+0 E
2cl E
110188.86
(0.03)(d)
110262.64
(0.04)
18957.95
CO.071
18991.67
(0.03)
110475.76(-0.12)
196586.65
(0.02)
19005.64(-0.04)
140175.20(-0.011
110950.75
(0.031
196406.57
(0.011
143741.65
110846.30
(0.18)
196053.82(-0.03)
(0.01)
(0.01)
113350.80(-0.43) 115674.45 159437.60
the
ib) Observed (c) present Cd) The
E
196659.35(-0.02)
137370.45
(al All
-I+0
(0.00)
frequencies by Lees
except
and Baker
195459.89
(0.01)
(0.38)
119025.80(-0.12)
(cl have
been
and assigned
18957.17(-0.11) 18792.97(-0.08) 18454.76
(0.04)
17888.64
(0.19) (=)
17O56.86(-O.1O)(c)
measured
by Lees
in the present
and
Baker
I?).
study.
measurement.
figures
in parentheses
are
the difference
between
observed
and
calculated
frequencies.
measured. The observed frequencies of these transitions are given in Table I. Unlike the other isotopes of CH30H the frequencies of these transitions cannot be expressed by (l/2)@ - C)J(J
+ 1)(X = +1, u = 0, u = O/K = -1, z) = 0, u = O),
(5)
where (KwIK’v’~‘) are the overlap integrals between the indicated states. This arises because of the fact that the contribution of the asymmetry parameter Dab to these frequencies is sufficiently large for this molecule. The D,,, was fixed to the value reported by Lees and Baker (5), while (B - C)/2 was determined from the observed frequencies of the 2,-l, A+ and 21-1, A- transitions. Once (B - C)/2 and Dab values are known, the frequencies of the K-type doublet transitions with K = 1 can be calculated. However, there is small difference between observed and calculated values at high J. This difference which arises because of the centrifugal distortion effect can be fitted to v&X + YJ(J + l)] where X and Y are constants analogous to the centrifugal distorsion constants (10) dWx and dwJ. The agreement between observed and calculated frequencies is shown in Table I and the values of X and Y obtained are x = (0.738 + 0.052) x 10-4 TABLE V Q-Branch Expansion Coefficients of CH,OD (MHz) Coefficient
"0
I+0 A
133236.24
a
0.396
b
-0.00134
2*1 E
I*0 E
t 0.04 f 0.002 f 0.00003
110158.23 0.148 -0.04709
t 0.22 t 0.016 * 0.00022
196647.66 -1.689 -0.00023
-l*O
? 0.05 f 0.005 f 0.00011
18923.05 -0.946 -0.04266
E
+ 0.10 t 0.007 ? 0.00009
MICROWAVE
423
SPECTRUM OF CH,OD TABLE VI
CH,OD b-Type Transitions (MHz) Transition
" obs
Transition
11-20 A+
41861.43
l_l-Oo E
64302.16
40-31 A+
52098.82
11-Z. E
19518.79
42-51 A
83903.30
2o-l_l E
71711.91
63498.66
22-31 E
60487.65
52-61 A
+
u
obs
S2-61 A
34537.32
30-21 E
25695.84
62-71 A+
23407.52
32-41 E
14920.43
63-72 A+
82040.93
3_2-4_l E
88340.24
63-72 A
83534.60
40-31 E
70715.45
71-62 A
15467.91
4_2-5_l E
43658.76
73-02 A+
36018.48
51-42 E
30839.20
73-82 A
38510.10
61-52 E
76868.83
8l-72 A+
15720.99
63-72 E
85003.12
81-72 A
66100.09
7-l-6-2 E
43945.92
73-82 E
39246.81
8-l-7-2 E
86510.22
and Y = -(0.766 The frequencies the relation
of the u-type,
+ 0.012) x 10-5.
AJ = 1, AK = 0 transitions
were then fitted to
TABLE VII CH,OD Q-Branch Origins (MHz) K'+K
PO
'ohs
estimated Uncertainty
'cal
'ohs - veal
A
133236
1
133211.6
24.4
2+1 A
320788
3.5
320851.3
-63.3
3+2 A
400520
47
400492.0
28.0
l+O E
110158
1
110160.3
-2.3
2+1 E
196647
1
196617.2
29.8
3~2 E
403003
77
402944.4
58.6
-1+0 E
18923
1
18935.2
-12.2
269285
27
269278.8
6.2
-2+-l E
424
KAUSHIK,
TAKAGI, AND MATSUMURA TABLE VIII
Rotational Constants of CH,OD
I?I+l,K+J,K
-
A
110125.46 MHz
B
23436.49 MHz
F
C
21987.31 MHz
p
~~~
876.2
MHz
522825.16 MHz 0.69979
2(J + 1)[(1/2)(B + C) + F”(1 - cos 3y)
vasYm =
+Gr(P$)
+ &K(PY)
- D.,,#]
- 405(5 + 1)3, (6)
where vaSymis the asymmetry contribution to the frequency (see below for its definition). Thus obtained a-type parameters along with the (B - C)/2 values of ground and excited torsional states are given in Table II. The agreement between observed and calculated frequencies of these transitions is shown in Table III. 4.2. b-Type Transitions (a) Q-Branch series. Three series of E species, i.e., K = 1 + 0 E, 2 * 1 E, and - 1 t 0 E have been reported by Lees and Baker (5). We have added two more transitions to the - 1 t 0 E series. By using the observed frequencies of the li-2,, A+ and 4,-31 A+ transitions, four transitions of K = 1 + 0 A series were definitely assigned. These transition frequencies were reported by Lees and Baker (5) but left unassigned. The frequencies of Q-branch series transitions can be fitted to the relation vobs -
vasym = v. +
aJ(J + 1) + bJ2(J + 1)2,
(7)
where v. is the Q-branch origin and v,,~,,,comes from the expectation value ( HR A,m) which has been obtained by diagonalyzing the matrix for Hamiltonian (1). The TABLE IX Barrier Height and Inertial ConstantP’
of CH,OD
Parameter "3
man
365.88
I
1.41237
* 0.09
m-1
370.28
t 0.00026
amuA2
1.39507
m-1
and Dennison
366.25
aI&2
? 0.05
c*-1
1.41344
f 0.00018
mb2
3.21387
f 0.00042
&x2
=1 I
3.21461
f 0.00046
mu;;2
'b
21.53354
f 0.00055
a~&~
21.5370
t 0.0018
amb2
Ic
22.98489
t 0.00063
a&,*
22.9951
f 0.0020
am~2
I ab
0.8051
f 0.0049
amIz2
0.8050
f 0.0051
amG2
0.0390
2 0.0014
emu;;2
0.0630
f 0.0027
a&'
3.22593
a&2
=2
A(lc-lb-lal)
(a) Conversion (b) Taken
factor
from Table
= 505376
MHz
I of reference
mJ2. 11; using
1 am
= 1.66043
x10
-24
gm.
MICROWAVE
SPECTRUM TABLE
OF CH,OD
425
X
Stark Shift of CH,OD Transitions’“’
Transition
20-10 A
+
21-11 A+ 2-1-l-l E
Observed Shifttb)
Calculated Shift (b)
(-0.129 + 0.184 M2,E2
(-0.1308 + 0.1860 M2)E2
(-1.042 + 3.305
(-1.0415 + 3.3052 M2,E2
M2)&2
0.1374 M&
0.138 M&
(a) The Stark field was calibrated on the basis of u(OCS) = 0.71521 D given by Muenter
(13).
(b) In units of 10m5 MHz (volt/cm)-2 for 20-10 A+ and 21-11 A+ and MHz (volt/cm)
-1
for 2-l-l-l E.
usual empirical relation i+,bs= v,, + a.Z(.Z + 1) + b.Z2(J + 1)2 (5) is not used here because vaSymis so large for CH30D that this relation does not give a good fit for higher J. The differences (v&s - vasy,,,)are fit by Eq. (7). Unlike the constants yo, a, and b used by Lees and Baker (S), our constants do not contain contribution from HR Asym- The observed frequencies are given in Table IV and the coefficients v,, a, and b are given in Table V. (b) P and R branches. Twenty-eight randomly spaced P- and R-branch transitions have been observed in the frequency region studied and have been assigned using the Stark effect measurements. The frequencies of these transitions are given in Table VI.
4.3. Extrapolation
of Q-Branch Origins
In order to obtain torsional parameters it is necessary to have as many Q-branch origins as possible, which are the v. values in Eq. (7). Besides the four Q-branch origins obtained directly from Q-branch series, the method of Gerry et al. (7) was followed to extrapolate the Q-branch origins from b-type P- and R-branch transitions. The eight Q-branch origins with their estimated uncertainties are given in Table VII. The Q-branch origins thus obtained were fitted to V, and the inertial constants I,, andI,, with each Q-branch origin weighted by the inverse square of its estimated uncertainty. The standard deviation of the fit was 19.8 MHz. The comparison between observed and calculated Q-branch origins is shown in Table VII. Although several higher-order torsional terms contribute to the Q-branch origin (5) this method gives fairly accurate values of Vt, Zal, and I,,. The rotational constants and the inertial constants obtained as a result of analysis are given in Tables VIII and IX, respectively. For comparison the inertial constants obtained by Lees and Baker (5) and the torsional constants obtained by Kwan and Dennison (11) have also been included in Table IX. Because of the fact that the data used by Lees and Baker were not sufficient to determine the torsional constants well, our torsional constants differ considerably from their constants.
426
KAUSHIK,
TAKAGI,
AND MATSUMURA
However, our constants agree closely with those of Kwan and Dennison, who took every higher-order term in their analysis. V. DIPOLE MOMENT
The components of dipole moment pa and & of CHBOD were determined from the Stark effect measurements of the 2,- 1, A+ and 20-l,, A+ transitions, which have relatively large Stark effects. The observed Stark shifts of the 2,,-lo A+ and 2,- 1, A+ transitions, which have second-order Stark effects of the form (A + BW) it?, were fitted to pz and &. The dipole moment components obtained are pa = 0.833 ? 0.008 D and &, = 1.488 ‘_ 0.015 D. These pa and ,..&b values were used to calculate the Stark shifts of M = + 1 components of the 2-r- 1-r E transition taking the effect of the D&.&b term (12) into consideration. The calculated Stark shift shows a good agreement with the observed shift. The observed and calculated shifts are given in Table X. It should be noted that the a axis in the internal axis system is tilted from the methyl axis by an angle of tan-l (Dab/B) (4, 14, 15). The value of dipole moment cr. = 1.705 + 0.017 D for CHBOD can be compared with that of CH30H (p = 1.69 D) reported by earlier workers (12). The difference in pa and ,..&bvalues from those of CH,OH (CL,,= 0.885 D, pI = 1.44 D) can be explained by the rotation of inertial axes with respect to the molecular frame when the hydrogen atom is replaced by the deuterium atom. ACKNOWLEDGMENTS The authors thank Professors T. Kojima and E. Hirota for their helpful criticism of the manuscript. This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education. RECEIVED:
June 4, 1979 REFERENCES
I. J. SHERIDANAND W. GORDY,J. Chem. Phys. 19, %5-970(1951); B. P. DAILEY, H. MINDEN, AND R. G. SHULMAN, Phys. Rev. 75, 13 19 (1949); H. T. MINDEN AND B. P. DAILEY, Phys. Rev. 82, 338 (1951); B. BAK, L. HANSEN, AND J. RASTRUP ANDERSEN,J. Chem. Phys. 21, 1612-1613 (1953); K. TAKAGI AND T. KOJIMA, J. Phys. Sot. Japan 30, 1145-1157 (1971); T. KOJIMA, J. Phys. Sot. Japan 15, 1284-1291 (1960); R. M. LEES, J. Chem. Phys. 56,5887-5890 (1972); R. M. LEES, J. Chem. Phys. 57, 824-826 (1972); R. M. LEES, J. Chem. Phys. 57,2249-2252
(1972). 2. P. VENKATESWARLU,H. D. EDWARDS, AND W. GORDY, J. Chem. Phys. 23, 1195-1199 (1955). 3. T. NISHIKAWA, J. Phys. Sot. Japan 11,781-786 (1956). 4. T. ITOH, J. Phys. Sot. Japan 11,264-271 (1956). 5. R. M. LEES AND J. G. BAKER, J. Chem. Phys. 48, 5299-5318 (1968). 6. R. M. LEES, F. J. LOVAS, W. H. KIRCHHOFF,AND D. R. JOHNSON,J. Phys. Chem. Ref. Data 2, 205-210 (1973). 7. M. C. L. GERRY,R. M. LEES, AND G. WINNEWISSER,J. Mol. Spectrosc. 61,231-242 (1976). 8. D. KIVELSON,J. Chem. Phys. 22, 1733-1739(1954); D. KIVELSON,J. Chem. Phys. 23,2230-2235 (1955); D. KIVELSON,J. Chem. Phys. 23,2236-2243 (1955). 9. B. KIRTMAN,J. Chem. Phys. 37, 2516-2539 (1962). 10. J. K. G. WATSON,J. Chem. Phys. 45, 1360-1361 (1966). Il. Y. Y. KWAN AND D. M. DENNISON,J. Mol. Specfrosc. 43, 291-319 (1972). 12. E. V. IVASH AND D. M. DENNISON,J. Chem. Phys. 21, 1804-1816 (1953). 13. J. S. MUENTER,J. Chem. Phys. 48, 4544-4547 (1968). 14. K. T. HECHTAND D. M. DENNISON,J. Chem. Phys. 26, 31-47 (1957). 15. C. C. LIN AND J. D. SWALEN, Rev. Mod. Phys. 31, 841-892 (1959).
OF
MOLECULAR
g&418-426
SPECTROSCOPY
Microwave
Spectrum
V. K. KAUSHIK,’ Department
of Physics,
(1980)
of CHsOD
K. TAKAGI
Toyama University, Gofuku,
Toyama 930, Japan
AND
C. MATSUMURA National Chemical Laboratory for Industry, Honmachi,
Shibuya-ku,
Tokyo 151, Japan
The microwave spectrum of CHsOD has been observed in the frequency region between 14 and 92 GHz. Ah the ground-state transitions with J I 8 and J = 2 + 1, a-type transitions in the excited torsional states (u = 1and u = 2) have been observed. The spectrum has been analyzed and rotational constants, torsional constants, torsion-vibration-rotation interaction constants, and centrifugal distortion constants have been evaluated. The Stark effect measurements have been made and the dipole moment components have been determined as ILL= 0.833 f 0.008D and h = 1.488 2 O.OlSD.
I. INTRODUCTION
The rotational spectra of the molecules capable of hindered internal rotation have been a subject of interest to microwave spectroscopists (I) because they give the accurate torsional constants. The rotational spectrum of CH30D was first observed by Venkateswarlu er al. (2) who observed the J = 1 c 0 rotational transitions in the ground and two excited torsional states. Nishikawa (3) analyzed these transitions using the internal axis system developed by Itoh (4) and obtained the molecular constants including torsion-vibration-rotation interaction constants. Later, Lees and Baker (5) extended the study of this molecule by observing the other a-type transitions and three series of Q-branch transitions. From the observed Q-branch origins of these series Lees and Baker calculated the three torsional constants Zol, ZnZ, and V,. However, because of the lack of available data these torsional constants were not determined accurately. In the present investigation we have observed all the transitions with J 5 8 in the frequency region between 14 and 92 GHz and used 28 P- and R-branch transitions to give five additional Q-branch origins. These five Q-branch origins have been combined with the three Q-branch origins determined by Lees and Baker’s transitions to calculate the torsional parameters. Finally, the Stark effect measurements have been made to determine the dipole moment components of this molecule. 1 Visiting Research Fellow of Japan Society for the Promotion of Science (JSPS). 0022-2852/80/080418-09$02.00/0 Copyright All rights
0
1980 by Academic
of reproduction
Press.
in any form
Inc. reserved.
418
MICROWAVE
419
SPECTRUM OF CH,OD
II. EXPERIMENTAL
DETAILS
The spectrum was observed using two spectrometers. In the frequency region between 14 and 18 GHz, the computer-controlled spectrometer with a 3-m-long X-band waveguide cell at the National Chemical Laboratory for Industry was used, while between 18 and 92 GHz a conventional 106kHz Stark modulated spectrometer with a 120-cm-long K-band waveguide cell was used. Appropriate Varian and OKI klystrons were used as a source. The sample of CH,OD was obtained from Tokyo Chemical Industry and was used without further purification. The observations were made at room temperature. The estimated accuracy of measured frequencies is kO.05 MHz. III. THEORY
The zeroth-order Hamiltonian for CH,OD can be expressed by considering two rigid mutually rotating groups, subjected to a threefold hindering potential. The Hamiltonian in the internal axis system may be written as
HRAsum,
(1)
H Tar = FP2, + (l/2) V,( 1 - cos 3r),
(2)
H =
H~or
+
H~syrn
+
with H R sym =
(l/2)@ + C)(P% + P”,) + AP;,
(3)
and H RAsvm
=
(WV3
-
c)(p:
-
p:)
+
Dab(PaPb
+
pbpa),
(4)
where H,,, is the torsional part of the Hamiltonian, HR Symis the rotational Hamiltonian for the rigid symmetric top, and H RASymis the part of the rotational Hamiltonian where the second term arises because the internal axes do not coincide with the i>rincipal axes. The constants in Eqs. (2) and (4) are given in Ref. (5).2 The moments of inertia are calculated in a molecular axis system with the origin at the center of mass, the a axis parallel to the methyl top axis, and c axis perpendicular to the COD plane. Za2 is the moment of inertia of the methyl top about its axis, I,, is defined as I, = I,, + Zaz, and Z&,is the product of inertia about the a and b axes. P, = -iti(day) is the torsional angular momentum where y is the angle of internal rotation between the methyl and OD groups. IV. ANALYSIS OF THE SPECTRUM
A general description of the torsion-rotation spectrum of methanol is given by Lees and Baker (5). The notation we use follows that of Lees et al. (6) for A torsional levels and of Gerry et al. (7) for E torsional levels. The A levels with K # 0 are split by molecular asymmetry into K-type doublets, which we denote by A’. The observed spectrum was analyzed using the perturbation treatment of Kivelson (8) and Kirtman (9). Initially, the u-type spectrum was analyzed and the observed constants were used to predict high-Z, u-type transitions. These high-J, u-type transitions were combined with the observed b-type P- and R-branch transitions 2 There is a misprint in the definition of p in Ref. (5). The corrected one is p = I,#[ (IJ,
- 1%).
+ Z:B)1’2/
420
KAUSHIK,
TAKAGI, AND MATSUMURA TABLE I
K = 1, A Doublet Transitions J-value
3
vobs (MHz)
v (MHZ) cal
6160.87(=)
4
13600.16
of CH,OD (MHZ) "obs - "cal
6160.94
-0.07
13600.08
0.08
5
20396.67
20396.59
0.08
6
28547.81
28547.72
0.09
7
38049.06
38049.11
-0.05
8
48894.00
48994.13
-0.13
(a) Calculated from the combination relation of observed transitions.
to give Q-branch origins. Finally, the Q-branch origins were used to calculate the torsional parameters and barrier height.
4.1. a-Type Transitions Since CH,OD is a slightly asymmetric top, these transitions follow a nearly symmetric rotator pattern with the groups at multiples of (B + C). Most of these transitions have been reported by Lees and Baker (5). In the present work all the TABLE II a-Type Molecular Parameters of CHsOD (MHz) B+C 2
22711.90 f 0.25 -65.14 i 0.24
KV
-2.605 f 0.019
GV
-0.200 + 0.025
Lv
0.196 + 0.025
DJK
0.0478 + 0.0080
DJ b
(a) ab
676.2 * 5.4
(B-c) 2 v=o
724.59 * 0.35
(B-C)
713.32 ?:0.40
(B-C)
721.47 ?:0.40
T-
2
v=l
v=2
(a) Constant fixed to Lees and Baker's
(5) value.
MICROWAVE
SPECTRUM TABLE
OF CH,OD
421
III
Observed a-Type Transitions of CH,OD (MHz)
v=o
v=2
V=l
Transition
lo-O0
A+
Zo-lo A
+
Zl-l1 A
'ohs
Vobs-vcal
45359.40(a)
-0.02
45266.3Zta)
-0.19
45193.74(a)
-1.78
90705.81(a)
-0.12
90534.53(a)
-0.46
90386.35(a)
-2.75
0.39
9ll2o.50(a)
4.18
91064.2ZCa)
-0.08
89707.61(=)
-0.08
92075.51(a)
Zl-l1 A+
89355.10(@
0.39
30-20 A+
136026.40
-0.21
31-21 A
138101.53
0.67
32-22 A
+
'ohs
"ohs-"al
89961.64(=) 135806.92
4.18 -0.50
"obs
Vobs-vcal
135576.86
-1.96
136102.82
0.73
135663.76(b)
-27.63
135528.06
-1.31
32-22 A
136055.46
0.51
135652.7ZCb1
-26.51
135526.43
0.19
40-30 A+
181308.30
-0.28
-0.59
180764.21
1.46
41-31 A
184113.18
0.91
41-31 A+
178673.89
1.69
42-32 A+
181507.14
1.14
180875.33(b)
-35.76
180701.68
-2.56
42-32 A
181388.97
0.79
180847.82(b)
-32.90
180697.36
0.96
43-33 A
181428.24
0.43
181046.09
43-33 A+
181428.24
1.03
181046.09
lo-O0 E
45344.16(')
181085.21
0.12
45260.02(")
4.22 4.70 -0.20
45190.13(a)
0.07 0.21
zo-lo E
9O669.98(a)
1.22
90514.92(a)
-1.08
90379.72(a)
Zl-ll E
90743.56(')
-0.09
90487.27(a)
-7.57
90368.92(")
1.15
2_l-l_l E
90703.65(")
-0.59
90500.49(a)
2.52
90381.11(')
-6.20
30-20 E
135958.38
3.53
31-21 E
136171.61
-0.96
3_1-2_l E
135972.50
-1.56
32-22 E
136098.96
-3.63
135764.85
3_2-2_2 E
136107.60
0.03
135894.26
40-30 E
181191.27
8.27
180990.87
135760.11
-2.79
135568.97
1.21
135552.04
1.98
6.80
135587.02
6.66
-5.62
180756.34
2.15
180733.23
2.79
-2.50
41-31 E
181666.31
-2.60
4_l-3_1 E
181142.85
-3.48
42-32 E
181486.11
-6.50
181024.22
-3.28
180806.46
-7.25
181126.40
-2.07
180776.29
10.27
180712.52
-7.53
4-2-3-z E
181504.50
0.13
43-33 E
181451.29
-2.48
4_3-3_3 E
181428.24
1.02
(a)
Present measureIrent.
(b) Frequencies not included in the least square fit.
= 2 t 1 transitions in the three torsional states (V = 0, 1, 2) have been measured. The J = 1 + 0 transitions have also been measured with a better accuracy. In addition, five transitions between K-type doublets with K = 1 have also been
J
422
KAUSHIK,
TAKAGI, AND MATSUMURA TABLE IV
CH,OD Q-Branch Series Transition Frequencies’“) (MHz) 1+0 A
J-value
(b'
I+0 E
2cl E
110188.86
(0.03)(d)
110262.64
(0.04)
18957.95
CO.071
18991.67
(0.03)
110475.76(-0.12)
196586.65
(0.02)
19005.64(-0.04)
140175.20(-0.011
110950.75
(0.031
196406.57
(0.011
143741.65
110846.30
(0.18)
196053.82(-0.03)
(0.01)
(0.01)
113350.80(-0.43) 115674.45 159437.60
the
ib) Observed (c) present Cd) The
E
196659.35(-0.02)
137370.45
(al All
-I+0
(0.00)
frequencies by Lees
except
and Baker
195459.89
(0.01)
(0.38)
119025.80(-0.12)
(cl have
been
and assigned
18957.17(-0.11) 18792.97(-0.08) 18454.76
(0.04)
17888.64
(0.19) (=)
17O56.86(-O.1O)(c)
measured
by Lees
in the present
and
Baker
I?).
study.
measurement.
figures
in parentheses
are
the difference
between
observed
and
calculated
frequencies.
measured. The observed frequencies of these transitions are given in Table I. Unlike the other isotopes of CH30H the frequencies of these transitions cannot be expressed by (l/2)@ - C)J(J
+ 1)(X = +1, u = 0, u = O/K = -1, z) = 0, u = O),
(5)
where (KwIK’v’~‘) are the overlap integrals between the indicated states. This arises because of the fact that the contribution of the asymmetry parameter Dab to these frequencies is sufficiently large for this molecule. The D,,, was fixed to the value reported by Lees and Baker (5), while (B - C)/2 was determined from the observed frequencies of the 2,-l, A+ and 21-1, A- transitions. Once (B - C)/2 and Dab values are known, the frequencies of the K-type doublet transitions with K = 1 can be calculated. However, there is small difference between observed and calculated values at high J. This difference which arises because of the centrifugal distortion effect can be fitted to v&X + YJ(J + l)] where X and Y are constants analogous to the centrifugal distorsion constants (10) dWx and dwJ. The agreement between observed and calculated frequencies is shown in Table I and the values of X and Y obtained are x = (0.738 + 0.052) x 10-4 TABLE V Q-Branch Expansion Coefficients of CH,OD (MHz) Coefficient
"0
I+0 A
133236.24
a
0.396
b
-0.00134
2*1 E
I*0 E
t 0.04 f 0.002 f 0.00003
110158.23 0.148 -0.04709
t 0.22 t 0.016 * 0.00022
196647.66 -1.689 -0.00023
-l*O
? 0.05 f 0.005 f 0.00011
18923.05 -0.946 -0.04266
E
+ 0.10 t 0.007 ? 0.00009
MICROWAVE
423
SPECTRUM OF CH,OD TABLE VI
CH,OD b-Type Transitions (MHz) Transition
" obs
Transition
11-20 A+
41861.43
l_l-Oo E
64302.16
40-31 A+
52098.82
11-Z. E
19518.79
42-51 A
83903.30
2o-l_l E
71711.91
63498.66
22-31 E
60487.65
52-61 A
+
u
obs
S2-61 A
34537.32
30-21 E
25695.84
62-71 A+
23407.52
32-41 E
14920.43
63-72 A+
82040.93
3_2-4_l E
88340.24
63-72 A
83534.60
40-31 E
70715.45
71-62 A
15467.91
4_2-5_l E
43658.76
73-02 A+
36018.48
51-42 E
30839.20
73-82 A
38510.10
61-52 E
76868.83
8l-72 A+
15720.99
63-72 E
85003.12
81-72 A
66100.09
7-l-6-2 E
43945.92
73-82 E
39246.81
8-l-7-2 E
86510.22
and Y = -(0.766 The frequencies the relation
of the u-type,
+ 0.012) x 10-5.
AJ = 1, AK = 0 transitions
were then fitted to
TABLE VII CH,OD Q-Branch Origins (MHz) K'+K
PO
'ohs
estimated Uncertainty
'cal
'ohs - veal
A
133236
1
133211.6
24.4
2+1 A
320788
3.5
320851.3
-63.3
3+2 A
400520
47
400492.0
28.0
l+O E
110158
1
110160.3
-2.3
2+1 E
196647
1
196617.2
29.8
3~2 E
403003
77
402944.4
58.6
-1+0 E
18923
1
18935.2
-12.2
269285
27
269278.8
6.2
-2+-l E
424
KAUSHIK,
TAKAGI, AND MATSUMURA TABLE VIII
Rotational Constants of CH,OD
I?I+l,K+J,K
-
A
110125.46 MHz
B
23436.49 MHz
F
C
21987.31 MHz
p
~~~
876.2
MHz
522825.16 MHz 0.69979
2(J + 1)[(1/2)(B + C) + F”(1 - cos 3y)
vasYm =
+Gr(P$)
+ &K(PY)
- D.,,#]
- 405(5 + 1)3, (6)
where vaSymis the asymmetry contribution to the frequency (see below for its definition). Thus obtained a-type parameters along with the (B - C)/2 values of ground and excited torsional states are given in Table II. The agreement between observed and calculated frequencies of these transitions is shown in Table III. 4.2. b-Type Transitions (a) Q-Branch series. Three series of E species, i.e., K = 1 + 0 E, 2 * 1 E, and - 1 t 0 E have been reported by Lees and Baker (5). We have added two more transitions to the - 1 t 0 E series. By using the observed frequencies of the li-2,, A+ and 4,-31 A+ transitions, four transitions of K = 1 + 0 A series were definitely assigned. These transition frequencies were reported by Lees and Baker (5) but left unassigned. The frequencies of Q-branch series transitions can be fitted to the relation vobs -
vasym = v. +
aJ(J + 1) + bJ2(J + 1)2,
(7)
where v. is the Q-branch origin and v,,~,,,comes from the expectation value ( HR A,m) which has been obtained by diagonalyzing the matrix for Hamiltonian (1). The TABLE IX Barrier Height and Inertial ConstantP’
of CH,OD
Parameter "3
man
365.88
I
1.41237
* 0.09
m-1
370.28
t 0.00026
amuA2
1.39507
m-1
and Dennison
366.25
aI&2
? 0.05
c*-1
1.41344
f 0.00018
mb2
3.21387
f 0.00042
&x2
=1 I
3.21461
f 0.00046
mu;;2
'b
21.53354
f 0.00055
a~&~
21.5370
t 0.0018
amb2
Ic
22.98489
t 0.00063
a&,*
22.9951
f 0.0020
am~2
I ab
0.8051
f 0.0049
amIz2
0.8050
f 0.0051
amG2
0.0390
2 0.0014
emu;;2
0.0630
f 0.0027
a&'
3.22593
a&2
=2
A(lc-lb-lal)
(a) Conversion (b) Taken
factor
from Table
= 505376
MHz
I of reference
mJ2. 11; using
1 am
= 1.66043
x10
-24
gm.
MICROWAVE
SPECTRUM TABLE
OF CH,OD
425
X
Stark Shift of CH,OD Transitions’“’
Transition
20-10 A
+
21-11 A+ 2-1-l-l E
Observed Shifttb)
Calculated Shift (b)
(-0.129 + 0.184 M2,E2
(-0.1308 + 0.1860 M2)E2
(-1.042 + 3.305
(-1.0415 + 3.3052 M2,E2
M2)&2
0.1374 M&
0.138 M&
(a) The Stark field was calibrated on the basis of u(OCS) = 0.71521 D given by Muenter
(13).
(b) In units of 10m5 MHz (volt/cm)-2 for 20-10 A+ and 21-11 A+ and MHz (volt/cm)
-1
for 2-l-l-l E.
usual empirical relation i+,bs= v,, + a.Z(.Z + 1) + b.Z2(J + 1)2 (5) is not used here because vaSymis so large for CH30D that this relation does not give a good fit for higher J. The differences (v&s - vasy,,,)are fit by Eq. (7). Unlike the constants yo, a, and b used by Lees and Baker (S), our constants do not contain contribution from HR Asym- The observed frequencies are given in Table IV and the coefficients v,, a, and b are given in Table V. (b) P and R branches. Twenty-eight randomly spaced P- and R-branch transitions have been observed in the frequency region studied and have been assigned using the Stark effect measurements. The frequencies of these transitions are given in Table VI.
4.3. Extrapolation
of Q-Branch Origins
In order to obtain torsional parameters it is necessary to have as many Q-branch origins as possible, which are the v. values in Eq. (7). Besides the four Q-branch origins obtained directly from Q-branch series, the method of Gerry et al. (7) was followed to extrapolate the Q-branch origins from b-type P- and R-branch transitions. The eight Q-branch origins with their estimated uncertainties are given in Table VII. The Q-branch origins thus obtained were fitted to V, and the inertial constants I,, andI,, with each Q-branch origin weighted by the inverse square of its estimated uncertainty. The standard deviation of the fit was 19.8 MHz. The comparison between observed and calculated Q-branch origins is shown in Table VII. Although several higher-order torsional terms contribute to the Q-branch origin (5) this method gives fairly accurate values of Vt, Zal, and I,,. The rotational constants and the inertial constants obtained as a result of analysis are given in Tables VIII and IX, respectively. For comparison the inertial constants obtained by Lees and Baker (5) and the torsional constants obtained by Kwan and Dennison (11) have also been included in Table IX. Because of the fact that the data used by Lees and Baker were not sufficient to determine the torsional constants well, our torsional constants differ considerably from their constants.
426
KAUSHIK,
TAKAGI,
AND MATSUMURA
However, our constants agree closely with those of Kwan and Dennison, who took every higher-order term in their analysis. V. DIPOLE MOMENT
The components of dipole moment pa and & of CHBOD were determined from the Stark effect measurements of the 2,- 1, A+ and 20-l,, A+ transitions, which have relatively large Stark effects. The observed Stark shifts of the 2,,-lo A+ and 2,- 1, A+ transitions, which have second-order Stark effects of the form (A + BW) it?, were fitted to pz and &. The dipole moment components obtained are pa = 0.833 ? 0.008 D and &, = 1.488 ‘_ 0.015 D. These pa and ,..&b values were used to calculate the Stark shifts of M = + 1 components of the 2-r- 1-r E transition taking the effect of the D&.&b term (12) into consideration. The calculated Stark shift shows a good agreement with the observed shift. The observed and calculated shifts are given in Table X. It should be noted that the a axis in the internal axis system is tilted from the methyl axis by an angle of tan-l (Dab/B) (4, 14, 15). The value of dipole moment cr. = 1.705 + 0.017 D for CHBOD can be compared with that of CH30H (p = 1.69 D) reported by earlier workers (12). The difference in pa and ,..&bvalues from those of CH,OH (CL,,= 0.885 D, pI = 1.44 D) can be explained by the rotation of inertial axes with respect to the molecular frame when the hydrogen atom is replaced by the deuterium atom. ACKNOWLEDGMENTS The authors thank Professors T. Kojima and E. Hirota for their helpful criticism of the manuscript. This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education. RECEIVED:
June 4, 1979 REFERENCES
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