A new analysis and additional measurements of the millimeter and submillimeter spectrum of methanol

JOURNAL

OF MOLECULAR

SPECTROSCOPY

108,42-57

(1984)

A New Analysis and Additional Measurements of the Millimeter and Submillimeter Spectrum of Methanol ERIC HERBST, J. K. MESSER, FRANK C. DE LUCIA Department of Physics, Duke University, Durham, North Carolina 27706 AND PAUL HELMINGER Department of Physics, University of South Alabama, Mobile, Alabama 36688 Over 100 new spectral linesof gas-phase methanol in the millimeter and submillimeter region (viz. 150-1000 GHz) corresponding to rotational transitions in the two lowest torsional states have been measured and assigned. Some of these lines have been combined with spectral lines measured by previous investigators below 1000 GHz into a global data set consisting of 470 lines involving transitions with J d 8 and u, (torsional quantum number) c 2, and then analyzed via a nonlinear least-squares procedure. The analysis involves supplementing the standard IAM Hamiltonian with a number of new distortion and “interaction” constants. Direct diagonalization has been employed in preference to an earlier perturbation scheme. The quality of the least-squares fit compares favorably with the previous quantum mechanical approach. 0 I984 Academic Press. Inc. I. INTRODUCTION The rotational-torsional spectrum of methanol, one of the simplest asymmetric rotors with internal rotation, has been studied by a large number of investigators in both the microwave and infrared regions of the spectrum. Among the early microwave studies are those of Hughes et al. (I), Venkataswarlu et al. (2), Dreizler and Rudolph (j), and Rudolph et al. (4). In 1968, Lees and Baker (5) measured an extensive number of both a-type and b-type spectral lines at frequencies up to 200 GHz. During the 1970’s, some high-resolution (6, 7) and interstellar studies (8) of methanol spectra in the microwave were undertaken, while Johnston and Srivastawa (9) and Johnston et al. (10) reported laser Stark measurements in the 8OO-GHz region. More recently, methanol spectra involving torsionally excited states have been reported in the Orion interstellar source (II, 12), and dipole moment mesurements along both a and b axes were accurately measured in the laboratory via microwave Stark spectroscopy ( 13) and ir-microwave double resonance (14). In 198 1, Pickett et al. (15) published 126 new spectral lines of methanol in the region 200-850 GHz involving transitions in the ground torsional state. Finally, Sastry et al. (16) have measured and assigned many transitions at frequencies up to 400 GHz involving the first three torsional states of methanol. Most of their measurements were accomplished in our laboratory. 0022-2852184 $3.00 Copyright 0

1984 by Academic Press. Inc.

All rights of reproduction in any form resewed.

42

SUBMILLIMETER

SPECTRUM

OF METHANOL

43

In addition to these experimental studies, advances have been made in the theoretical understanding of the rotational-torsional spectrum of methanol. Early work by Dennison and co-workers (I 7-19) led to an understanding of the general features of the spectrum. The detailed features of the spectrum were treated by Kivelson (20, 21), Nishikawa (22), Hecht and Dennison (23, and Swan and Strandberg (24). Refinements to the detailed theory were made by Kirtman (23, and were utilized in spectral analysis by Kwan and Dennison (26) and Lees and Baker (5). These latter authors applied the detailed theory in a systematic manner to their millimeter data. They fit u-type and b-type spectra separately, and treated asymmetry and torsional effects via perturbation theory. In order to fit the b-type spectra, Lees and Baker (5) included infrared data in their analysis. The accuracy of their approach (5, 16, 27) is often sufficient to assign spectral lines, but does not approach the quality of least-squares fits to normal, semirigid asymmetric top data, where agreement between observed and calculated frequencies is customarily ~100 kHz. The purpose of this paper is twofold. First, a number of new millimeter and submillimeter lines of methanol involving the two lowest torsional states are reported. The measured lines were selected for study based on Fortrat diagrams that showed which were the most salient transitions not yet studied in this frequency region with angular momentum J < 15. Second, these lines and those of previous investigators have been combined into a global data set which includes 470 transitions involving J G 8 and o1 d 2. The data set has been analyzed via an essentially nonperturbative diagonalization procedure involving an extended IAM (“internal axis method”) Hamiltonian. Our least-squares fit to this data set has a root-mean-square deviation of 1.2 MHz and, although better than the earlier perturbative approach, is still not comparable in quality with customary analyses of semirigid molecules. II. EXPERIMENTAL

DETAILS

The measurements of methanol spectral lines have been accomplished with standard millimeter and submillimeter techniques, described elsewhere in literature (28, 29). All measurements were made with phase-locked klystrons lock-in detection techniques. The data were collected, processed, and measured a computer.

our the and via

III. THEORY

The internal axis method (IAM) has been employed with identical phase conventions to those of Lees and Baker (5). The Hamiltonian used by these authors has been supplemented with a variety of new distortion and “interaction” constants. Contained in Table I, this Hamiltonian can be divided into rotation (fi&, torsion (Z&J, and distortion and “interaction” terms (fi&. The torsional Hamiltonian is not completely independent of the rotational Hamiltonian, but rather contains a dependence on p,, the angular momentum along the inertial a (figure) axis. Other parameters in the Hamiltonian expression listed in Table I are the effective rotation constants A, B, C, Dab, and F; the angular momentum operators Js2, pif, and pf;

44

HERBST ET AL. TABLE I Rotation-Torsion

G= ii rot =

Hamiltonian’

iirot + citors+ hdist +(B+C)($b2+$c2)

+ Asa

+ %(B-C) (6b2-6c2)

,.,. t Dab(P,Pb fi tars A

=F(;

Hdist

=

Aa2

:2cg

- D,F2 tk;

3a

v

t 4V3(1-cos3y)

:f'p,A2 v

(1-cos3y)

(; + P';~ )3 t k,($Y Y

t P;,)~

+ p?',) x

(1-cos3y)

62(eb2-6c2)

(;;b2Sc2)

tc2

($b2-~c2)(l-cos3y)

[

+HP .. %2hJs4(?b2 Ka + 62(6,2

notation

replaced basis

reference

by 6 y + I+

+ ,+a)2

+ 4)2(1-cos3Y)

A kb2-q

+

~b2qSa2)

1

(Gy + &)26b2

+ H P6 t HJKe4ea2

- Gc2)

+ HKJs2sa4

t hJK B2p"a2(Pb2 - kc2) [

+ h&4(Bb2

-2 (fb2 - PC )(B, + pQ4

follows

Y t PP,,

t k56a2(1-cos3Y)

1 J

- Gc2)

- 6c2,q

+

t L"P&P

+ k2Ga2(:Y

t k,(GY

- I$&2

(GY + pQ2

C

a

+ pQ2

+ G$Y + ~6,)

- DKca4 -2A5

+ c3

t 4v6(l-cos6Y)

A 2 + kja3($Y - DJKP, 1

t k6$a(6y

+ c1

An t PbP,)

5 except

The difference

+

- fc2)

+

'1,2 - Q62]

(BY t pQ4(Bb2

that

their

is due

,. PYhas

1

- Bc2)

been

to a difference

in

set.

the torsional angular momentum operator pY,, where y is the torsional angle; the torsional potential constants VJ and Vh which describe the height of the cos 37 and cos 67 contributions to the torsional potential; the centrifugal distortion constants DJ, DJK, DK, &, &, HJ, HJK, HKJ, HK, hJ, h.,K, and hK; the “interaction” constants F,, fu, G,, L,, k,, k2, k,, k4, kg, k6, k,, CI, ~2, and ~3, which describe the strength of various interactions between the rigid body angular momenta, the torsional angular momentum, and the torsional potential energy; and the unitless parameter p which is a function of several moments of inertia (5). The “interaction” constants cl, c2, c3, and a variety of centrifugal distortion constants are used here for the first time. The new “interaction” constants describe interactions between the torsional quantities Pt and cos 37 and the operator expression ai - pf , which is related to the rigid body asymmetry. The essence of the IAM approach is the removal of the strong coupling between the angular momentum for rigid body rotation and that associated with internal (torsional) rotation (30). This is a big advantage and, as shall be seen below, leads to relatively unimportant matrix elements off-diagonal in torsional state. This

SUBMILLIMETER

SPECTRUM

OF METHANOL

45

advantage is achieved at the expense of a slight complication in the torsional problem-instead of a simple kinetic energy term involving torsional angular momentum P7 in Ej,,,, the term contains the mixed angular momentum expression p? + ppa,, which leads to the complication that the torsional Hamiltonian must be reevaluated for different values of K, the eigenvalue of pa,. It is to be noted that the Hamiltonian in Table I appears to be somewhat different from that of Lees and Baker (5) in terms containing FT. These authors utilized a Hamiltonian that has p, in expressions where our Hamiltonian has p7 + ppQ. Most terms with p7 + pp= can be reduced to ones with pY only by suitable manipulation of the basis set used for solving the problem. This manipulation, involving a definition of single-valuedness, has been done by Lees and Baker (5) whereas we, as Amano (14), have preferred to keep the more complicated expressions to indicate more overtly the residual coupling between &,, and the rigid body rotation. The overall Hamiltonian is best evaluated in stages. First, &,, is evaluated in a product basis set comprised of free rotor torsional eigenfunctions of pY = -ia& and eigenfunctions IK) of pa,:

IKka)= & IK) exp(W + dr), where u = 1, 0, - 1 and k is any integer. The eigenvalues of pY are simply 3k + u. Because of the threefold symmetry of the torsional problem, basis functions of different c do not mix. In addition, because [fit,,,

(2)

Rx1= 0,

basis functions of different K do not mix either. The resulting Hamiltonian matrix for each value of CJand K contains diagonal terms, and terms off-diagonal in k by +I and +2 units. The matrix is formally infinite in size, but it was found that diagonalization of a 2 1 X 2 1 matrix (- 10 < k < 10) is sufficient to ensure the needed accuracy in the energies of the lowest torsional states. The resulting torsional eigenfunctions can be written as IKv)

= &

K) ,,,

A%?, exp(G3k +

4rh

(3)

where u, = 0, 1, 2, 3,. . - is the torsional vibrational quantum number and the A$& are the expansion coefficients or eigenvector elements. The notation for these coefficients is that of Lin and Swalen (30). States with u = 0 are labeled A whereas states with u = + 1 and - 1 are labeled El and E2, respectively. For A torsional states, there is a degeneracy between +K levels while for E states there is a degeneracy between El, K and Ez, -K levels. We can thus refer to El and E2 levels as E levels where the sign of K is that appropriate for E, . The rotational and distortion Hamiltonian (fir,, + Ijdist) is then evaluated in the basis set IJZCu,a) = IJK)IKv,a), (4) where IJK) is the remaining factor of the symmetric top eigenfunction with total angular momentum J. The total matrix elements (including the diagonal torsional

HERBST ET AL.

46

energy contribution) obtained in this representation are shown in Table II. Note that matrix elements off-diagonal in o, occur for those elements with AK = + 1, and t-2. Matrix elements off-diagonal in u, also occur for selected AK = 0 terms of TABLE II Matrix Elements of Rotation-Torsion Hamiltonian Basis

Set:

~JKv~o>

IKvt~>

=

=

IJK>IKv~u>

exp(ipk+o]v);

= &IK>k_;!OA;;::

E;tR2

+ $

(B+C)F(J+l)-Kq

+ AK2

0 = 1,0,-l

+ J(J+l)

{ ITv+fv

J(J+l)]

t

K.‘J~

K.Vt

- DJKKZ

tk3K

- OJJ(J+l)}

K,"t 2 i (A3k+o) (3k+o+pK)

+ klK3

A;;;;l)+c

+ P(k+l)+c+~~2)]

K,"t 2 1 (A 3k+o) (3k+o+pK) k

+ LvK

+ k2K2

K,"t 2 ; (A3k+o) (3k+o+pK)2

K,v + k4 ; (A3kt;)2(3k+o+oK)4

[ (A;;:;)2(3k+o+i,K)3

+ k5K2(1-i

K.“t

2 (A3kto ) (3k+o+pK)'

) + Gv l

x ('-i A3(k+l)+oA3k+o

A:;:,$

- DKK4

+ k6K 1

+

K*"t 2 (A3k+o) (3kto+pK)

HJp(J+1f13

+ HKJ J(J+1)K4

+ HJK J2(J+1)2K2

+ HKK6


V;W

= ~~~


vi">

=

JJ(J+i)

7

- ~5~

K.Vt

- K(K+~)

(KS)

J(J+l)

B2+(Kk2)2]

- $

x 1 A k 3k+o

Krl ,v ’ t

A3k+a

ir -

+ hJ J’(J+l)’

+ #

+

g4+(K?2)4]j

[ A:;;;

(3k+o+p(K?2))2]

K,V + A3k+;

+ g _

A;;:;;f,o)j

+ (3k+o+p(K?2))4]

$

A:;;;"

K,Vt 1 A 3k+o ik

c3 k +TIA

1

+ $

(J+l)

J(J+l)~*+(K+2)~

+ 2

A;;:;';

[( 3k+o+pK)

K+2,v; *3k+o

:;:,t A:;;;Vt

-

i A;;:;

- 'i ; (A;;;:l)+o

x

K(K?l)llS(~+l)

[( 3k+o+pK)4

- (K?l)(K?2fl

A:;:;Yt

2

SUBMILLIMETER

SPECTRUM

OF METHANOL

47

Ijdist. These have not been included in the present treatment for reasons discussed below. In effect therefore, these terms of Ijdist are treated by first-order perturbation theory. The included elements off-diagonal in Us can be divided into two classes: those that are nonzero because of nonzero torsional overlaps of the type and those that are nonzero because of nonzero terms that involve Cz_,, &,A?;% the expansion coefficients Av+, in more complex expressions. The latter terms stem from the Hamiltonian “interaction” constants cl, c2, and c3 (Table I). Details of matrix element evaluation can be found in Lees and Baker (5) and Lin and Swalen (30). A direct diagonalization procedure has been utilized to determine the rotationaltorsional eigenvalues and eigenfunctions. Matrix elements connecting Av, = 0, + 1, and k2 were included. Because data for vt = 0, 1, 2 were used in the analysis, matrices containing vl = 0, 1, 2, 3, and 4 were required for each value of J considered. The dimension of the rotational-torsional matrix for a given value of J is then [(2J + 1) X 51 X [(2J + 1) X 51. The diagonalized rotational-torsional A states (a = 0) can be classified as “+” or “-” (5, J9), where the designations “Y’ refer respectively to the IJKv,O) t IJ, -K, vtO) and jJK&O) T IJ, -K, vtO) linear combinations of basis set functions for K even and K odd. These descriptions do not refer to the overall parities of the levels which are +(- l)J+y. Strongly allowed transitions for methanol in the absence of torsional (v,) changes are A levels: +- c* i AJ = 0 (~30) +-+-++IAJI= 1 E levels: AJ = 0 IAJI = 1

IAKI = 0, 1 IAK~=OJ [AK1 = 1 [AK/ = 0, I,

(5)

where the K quantum number is, of course, an exact one only in the absence of asymmetry. A nonlinear least-squares treatment has been utilized in an attempt to fit a large number of rotational-torsional transitions of methanol in the microwave, millimeter, and submillimeter regions of the spectrum. All transitions utilized do not involve changes in vt. The number of observed spectral lines of methanol with Av, = 0 below 1 THz in frequency that have been measured to high accuracy (~1 MHz) and assigned is near 700. These lines can be divided into three major distinct classes: a-type R-branch transitions (AK = 0, A J = 1); 6-type Q-branch transitions (AK = kl, AJ = 0); and b-type R- and P-branch transitions (AK = 1, AJ = fl). In addition, there are some K-doubling (AK = AJ = 0 + - -) transitions at low frequencies and one reported AK = -3 Q-branch series (16). The Q-branch transitions, most of which involve t.+ = 0 only, are grouped into closely spaced series of lines. Some Q-branch series have been studied up to J = 25-30 whereas a-type transitions have been measured up to J = 8 only. In deciding what transitions to include in our analysis, we were motivated by several factors. These included the desirability of checking certain ambiguous assignments by loop methods if possible (5) or by error curve analyses, the need to exclude certain lines which previous theoretical treatments and ours could not reproduce to within 5 GHz, and cost. Eventually, it was decided to include 470 lines with J < 8 subject to the above

48

HERBST ET AL.

criteria. These 470 lines, consisting of 241 A transitions and 229 E transitions, involve the lowest three torsional levels (u, = 0, 1, 2). All lines measured in this laboratory with J d 8 have been included in the data set. IV. RESULTS AND DISCUSSION

The experimental lines fit by our analysis are listed in Tables III and IV, along with residuals and references to the original investigators. Uncertainties in the frequencies measured in this work are ?50 kHz. Other uncertainties are as noted by past investigators, except that all uncertainties less than *50 kHz are set at this value. The overall root-mean-square deviation of the fit, 1.18 MHz, was obtained by varying 21 out of 34 constants in the analysis and fixing the others either at zero or at values obtained by Lees and co-workers (5, 27). Parameters determined by this procedure are listed in Table V. Agreement with previous determinations (2, 5, 27) is quite good, with our standard deviations being somewhat smaller. Lees and co-workers (5, 27) obtained the “Kirtman interaction” constants /cl-k7 and the potential energy parameter Va by including infrared data in their fit. (See also Kwan and Dennison (26).) In our fit, we were able to vary k, , k3, k,, b, and V6 independently, but obtained large uncertainties in these parameters and did not improve the quality of the analysis. We were not able to vary kz, k5, and k7 at all. Therefore, these eight parameters were fixed at previous values obtained via the simultaneous infrared and millimeter analysis which included transitions with Av, # 0 (5, 27). Values for the constants BK, CI, ~2, ~3, HJK, HKI, HK, and hK have been obtained for the first time. The use of the interaction constants cl, c2, and c3 is necessary to reproduce the torsional state variation in the molecular asymmetry. The parameter 6J, HJ, hJ, hJK, and fu were set at zero; their inclusion lowers the root-mean-square deviation of the fit only marginally. The advantage of the IAM method is that the matrix elements off-diagonal in u, do not play a significant role in the analysis. This advantage has been checked by simple elimination of the Au, = &l, &2 matrix elements from our analysis. The resulting root-mean-square deviation of the fit rises only to 1.7 MHz, although selected excited torsional state lines are fit much more poorly. Our nonlinear least-squares fit to the microwave, millimeter, and submillimeter data with J < 8, u, < 2 is significantly more accurate and coherent than previous nonphenomenological approaches (5, 27) which utilize pertubation theory and are not global in scope. However, we have not been able to fit the spectral lines to the normal - lOO-kHz accuracy customary for most molecular rotation spectra. Given the nature of our technique, it is probable that the discrepancy between theory and experiment is due to shortcomings in the IAM Hamiltonian utilized and/or the exclusion of the fidirt matrix elements diagonal in K but off-diagonal in u,. These matrix elements will be included in future work but it must be noted that, without the infrared data used by Lees and Baker (5) the constants multiplying most of the relevant terms (k,-k,) are not important to nor accurately determined by our analysis. It is unlikely that off-diagonal elements containing these constants will affect the present millimeter analysis significantly. The phenomenological approach of Pickett et al. (15) to the analysis of ground torsional state spectra results in a fit that is significantly tighter than ours. These

SUBMILLIMETER

SPECTRUM OF METHANOL TABLE III

Methanol A Transitions “TORSIGMA J” KUPU c-0 0 ”

1 2 0 0 0 0 0 1 1 0 0

v 1 1 1 2 2 2 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1

z” 2 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 2 2 2 2 2

J‘ Kr.PL FRBOUENCYIMHZ, 1 1 0 0

0

+

1 0

+ +

0

+

0 0

0

+

0

2 0 21+ 21+ Zl2 2 2 2 0 1 11t 1 lIO 1 1+ 1 i0 1 1 if 1 I0 1 1 It 1 l1+ 1 11 3 0 31t 3 1 313 2 3 2 3 2 3 2 2 0 21+ 2 1 2 2 2 2 2 0 2 1+ 2 1 2 2 2 2 2 0 2 I 2 I 2 n 2 1 2 I 2 I 2 2 2 2 2 2 2 1 2 1 4 0 4 1 4 1+ 4 1 4 2 4 2 4 3 4 3 4 2 4 2 3 0 3 1 3 1 3 2 3 3 3 3 3 0 3 1+ 3 1 3 2 3 2 3 3 3 3 3 0 3 1 3 1 3 2 3 2

+

+

+ +

+

+

+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + -

303366.890

834.267 48372.456 482S7.490 48132.120 350905.119 3cI4208.350 2SO2.778 484004.740 481504.232 553763.582 554052.056 96741.420 95314.290 97582.830 96513.660 36396.010 96588.600 96383.130 96183.670 96553.780 398446.920 -205791.270 S,3084.700 -457367.889 -457463.899 305473.520 soos.321 485263.263 480263.321 251905.812 251917.050 553624.453 SS4202.988 145103.230 143865.730 146368.300 145133.460 145124.410 144768.200 144583.820 144878.580 144728.700 144728.700 144571.970 144281.780 144827.610 445571.414 -156602.420 629140.493 626626.302 -335133.513 397039.090 397041.410 -403035.s34 -409323.292 3C7165.940 8341.640 486940.837 478633.272 251866.579 251300.435 636420.231 636420.231 553437.476 554402.514 193454.330 191810.490 135146.760 193488.030 133471.520 193471.520 193019.870 192778.520 133163.330 192363.47" 192965.530 132963.470 192363.470 lY2757.650 132370.480 133098.290 132613.090 192613.090

0.078 0.019 -0.067

1.221 1.569 0.674 0.500 -0.384 -0.440 -0.596

0.20s -O.ZBl 0.323 -0.360 -0.436 -0.145

-0.171 0.882 1.242 0.826 -0.965

-0.143 -0.132 -0.174 1.724 1.531 0.809 -0.746 -2.266 -2.412 -O.ZBB 0.442 0.258 -0.311 0.313 0.023 0.095 -0.525 -0.546 -0.234 -0.220 -0.946 -0.300

1.419 I.625 0.436 -0.515 0.535 -0.343 0.836 -2.407 -2.386 -0.251 -0.468 1.741 2.090 1.098 -1.124 -1.465 -1.625

6.028 6.158 -D.lB4 0.637 0.283 -0.260 0.250 -0.006 0.825 0.714 -0.796 -0.603 -0.389 -O.YlB -0.674 0.539 0.537 -0.369 1.931

2.242 0.440 0.435

49

50

HERBST

ET AL.

TABLE III-Continued VTOR SIGMA 2

2 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1

1 2 2 2 2 2 2 2 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 : 0 0 i 1 1 1 1 1 1 2 2 2 2 2

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 : 0 0 0 0 0 0 0 0

0 0 0 0 0 0

JU

KU PU <--

9

3

+<--

9 4 9

3 1 0

t t

9 9 4 4 4 9 9 9 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6

2 2 1 1 2 2 2 2 1 1 2 2 3 3 4 9 1 1 0 1 1 2 2 3 3 9 9 0 1 1 2 2 3 3 0 1 1 2 2 3 3 1 0 2 2 I 1 2 2 1 1 2 2 3 3 9 1 1 0 f 1 2 2 3 3 9 4 5 5 0 1 1 2 2 3 3 0 1 1 2 2

+ <--<-+<--<-+<--<-t <--<-- <--<--<-t<-- <-tc-- (-t c-- <-t<-t<-t<--<-t<--c-tc--<-t<--<-+<-t<-- <-t<-- (-t<--<-t<-t<-- (-+<-- (-t<--<-t<-t<-+<--<-t<--<-+<--<--<--<--<-t<--<-t <-t<--<-+<-+ <-t<-- <-t<-- <-t<-- <-+ <-- <-+<-- <-t<-t <-- <-t<--<-+ <--<-t <-t <--<-+ <--<--

<--

c-<--

JL 3 3 3 3

KL PL 3

+

3 0

+

1

+

3 1 313 2 3 2 3 3t 3 3 3 1t 3 1 5 ot 5 1t 51t 515 2t 5 2 5 3t 5 3 5 2t 5 2 4 ot 9 1t 919 2t 9 2 9 3 9 3 9 9 9 9 9 ot 9 1t 919 2 9 2 9 3 9 3 9 ot 91+ 9 l9 2t 9 2 9 3 9 3 4 ot 91t 9 1+ 919 2t 9 2 91t 916 ot 61+ 6 1t 6 1 6 2t 6 2 6 3 6 2t 6 2 5 ot 51t 515 2 5 2 5 3t 5 3 5 4 5 9 5 5 5 5 5 ot 5 1+ 515 2 5 2 5 3 5 3 5 0 5 1 5 1 5 2 5 2

+ t -

-

+ + -

+ + -

+ -

-

-

+ + + -

t + + t + -

FREPUENCY(MHZ) 132733.990 132733.990 992278.713 -107Ol3.850 678785.955 673795.931 -293963.990 -285111.150 -58399.990 -58923.010 -360661.433 -361236.976 309290.900 12511.000 989036.955 976605.192 251811.882 251890.901 636393.568 636393.568 553201.597 559651.031 291791.430 239796.250 293915.830 291887.700 291892.320 291832.950 291832.950 291806.510 291806.510 291267.880 290960.560 291441.29O 291192.810 291196.350 291198.290 241198.290 290938.990 290954.850 291369.120 290757.910 290757.910 290916.160 290916.160 538570.582 -5,032.920 728862.523 720991.236 -297228.693 -239683.390 -312247.359 -313203.928 311852.690 17513.391 991550.827 974196.319 251738.520 251895.728 636363.893 552915.356 559947.981 ~.011~.6bb 287670.835 292672.890 290269.150 290189.690 290189.510 230190.590 290161.190 290161.190 290195.090 230195.090 289511.110 283139.050 289710.460 289919.030 289920.290 289429.750 289929.750 283119.820 288533.690 289624.280 288897.110 288897.110

RESIOUAL(MHZ) -1.630 -1.630 -0.099 0.099 0.759 -0.769 -0.869 1.009 2.280 2.939 -0.172 -1.092 1.571 2.002 1.199 -1.929 -0.989 -0.753 3.67, 9.197 -0.005 0.839 0.345 -0.017 0.115 -0.185 0.037 1.133 0.743 -0.995 -0.999 -1.039 -0.437 -0.498 -0.613 -0.705 0.862 0.856 -0.538 2.627 2.523 0.716 0.686 -1.983 -1.983 -0.339 0.694 0.693 -1.237 -1.019 1.085 -0.393 -1.330 0.965 1.578 0.818 -1.522 1.116 0.290 1.698 0.259 0.558 O.i3J 0.901 -0.309 -0.329 0.003 1.039 1.028 -1.195 -1.192 -1.378 -1.378 -1.953 -0.218 -0.688 -0.388 -0.533 1.389 1.967 -0.752 3.389 2.777 1.099

1.097

REFERENCE

g : 9 f f

a a a

f’ f a 1 f f

e,= e,= e

f’ f e,= e,= e,= =,a e,= e,= e,= e,= e,= a a

a a a a a

a a

a a a

a

f” f” f =,a e,= f f =,a

F f =,a

=,a

1 f =,a =,a a =.a =.a =.= =.a =,a =,a =,a =,a a a a a a a a a a a a =

SUBMILLIMETER

SPECTRUM

51

OF METHANOL

TABLE III-Continued VTOR SIGMA

2 2 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0

u 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0

a 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0

u 0 0 0 0 0 0 1 1

JU KU PU

<--

JL

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 cl 0 0 0 0 0 0 0 0 0 0 0 0

KL PL

5 5 5 5 5 5 5

3 3 0 1 1 2 2

+ + + + -

5 5 5 5 7 7 7 7 7 7 7 7 7 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 8 8 8 8 8 8 9 8 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7

3 3 1 1 o 1+ 1+ I2 2 3 3 2 o 1 1 2 2 3 3 4 4 5 5 0 1 1 2 2 2 3 3 1 1 o 1+ 1 2 2 3 3 2 o 1 1 2 2 3 3 4 4 5 5 o 1 2 2 2 2 3 3 4 4 1 1

+ + +

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + -

--___

E c d

e

Ref Ref _ _

16 7

Ref. Ref.

2 15

Her.

b

f g n 1

i

This Ref.

work 5

Ref. Ref. Ref.

27 4 1

FREWENCY(MHZ)

2s9ue7.370

289087.370 584449.713 779380.507 766710.345 -201445:590 -183853.000 38452.690 38293.500 -263793.856 -265224.400 314859.550 23347.530 494481.683 471420.477 251641.667 251923.631 636337.419 636333.470 555291.142 33e4co.681 335582.005 341415.500 338639.939 338512.762 338540.795 338543.204 339512.762 338512.762 338486.337 338486.337 629921.337 44069.490 830349.412 -156127.700 -132621.940 590277.696 86903.060 86615.760 -215302.201 -217299.202 318318.793 497828.231 468293.771 251517.262 251984.702 636311.690 636304.355 555680.931 386681.920 383477.880 390141.730 387oi4.800 386824.430 386885,540 386890.120 386e59.820 386859.820 386820.010 386820.010 674990.423 95169.440 -111289.620 -80993.160 638523.496 638817.830 135376.760 134896.960 -249451.911 -249443,402 -166773.278 -169427.231

RESIDUALlHHZ)

-1.049 -1.049 -0.552 0.469 -1.100 -0.460 0.559 0.062 0.987 -0.316 -1.337 -0.171 0.335 -0.126 -1.350 2.754 1.406 -0.185 -0.249 -0.244 0.235 0.925 -1.012 -0.560 -0.118 1.128 1.196 -0.770 -0.758 -1.518 -1.518 0.365 0.936 -0.691 0.824 -0.206 2.178 -1.595 -0.121 -0.157 -0.921 -2.277 -1.984 -0.745 5.141 2.611 -2.018 -0.919 -1.852 0.125 1.795 -1.414 -1.032 -0.062 1.182 I.080 -0.675 -0.641 -1.682 -1.682 I.812 0.171 3.318 -1.690 4.117 2.663 -4.061 -1.405 1.352 1.260 cl.130 0.175

REFERENCE

52

HERBST

ET AL.

authors varied 104 coefficients of polynomial power series to fit 270 lines involving J d 20 and K d 6 to a root-mean-square deviation of - 100 kHz. Their method involves a fraction of the computational effort involved in ours but is not quantum mechanical in origin. Utilizing our determined parameters, and their uncertainties and correlations, we have predicted the frequencies and estimated uncertainties of all 2538 CHJOH transitions involving J d 10 and u, d 2. These predictions are available from the authors. Many of the predicted transitions lie at frequencies greater than 1 THz, and have not been studied at high accuracy in the laboratory. Of those predictions that can be compared with experimental measurements, the agreement is generally within l-10 MHz. These lines were excluded from our data set because of their high values of J (J = 9 or lo), because we could not use error curve techniques to check assignments, or because error curve techniques showed the assignments to be ambiguous. In addition, Sastry et al. (16) have recently assigned a series of methanol lines in the range 10 l- 114 GHz to the K = -2 - 1, E, u, = 0 Q-branch series. This AK = -3 series was not included in our fit, but is well predicted by our analysis. There are some serious disagreements between our predicted values and experimental assignments. Johnston and Srivastawa (9) and Johnston et al. (10) have published zero-field frequencies of the K = 6 - 5, E, ut = 0 Q-branch series obtained via laser Stark spectroscopy using the 337~pm HCN laser. These frequencies, accurate to 3-10 MHz, are not predicted well by our results. For example, the line at 890 445 MHz is assigned to the J = 6 transition, whereas our predicted value for this frequency is 890 304 MHz, with a predicted uncertainty of 15 MHz. In general, there are 2 loo-MHz discrepancies for the higher J members of this series. Since this represents a substantial extrapolation, this is not an unexpected result. Sastry et al. (16) have assigned a series of lines from 25 to 40 GHz originally measured by Hughes et al. (I) to the K = 9 - 8, Af, t+ = 1 Q-branch series. Our frequency predictions for the J = 9 and J = 10 lines of this series differ by 1.4 and 2.1 GHz from the experimental values with the assignments of Sastry et al. (16). If the theory is at fault, the above two sets of discrepancies are probably due to the fact that high-K transitions are involved, whereas these are noticeably deficient in our data set. The final major discrepancy between prediction and experimental assignment involves a series of b-type P- and R-branch lines assigned by Sastry et al. (16) to K = 2 * 3, E, vt = 1 transitions. An example is the J = 6 - 7, K = 3 - 2 transition, predicted to lie at 22098 MHz, which is assigned to a line at 27227 MHz. Discrepancies of 5 GHz also exist between the J = 5 - 6, K = 3 - 2; - 3; and J = 10 - 9, K = 2 - 3 J=8+7,K=2+-3;J=9+-8,K=2 assignments and predictions. Again, this branch represents an extrapolation from the data set used in the analysis, and more work is needed to understand and resolve these discrepancies. It must be reiterated, however, that our global treatment of the CH30H microwave, millimeter, and submillimeter data is capable of fitting almost 500 transitions of this species involving o, = 0, 1, 2 and J < 8 to a root-mean-square deviation of - 1.2 MHz, and of predicting the great majority of transitions involving these

SUBMILLIMETER

SPECTRUM

OF METHANOL

TABLE IV Methanol E Transitions .___

157270.700

165050.130 189689.570 48377.090 48247.850 48178.000 -108893.940 -141441.280 157276.040 165061.140 24934.380 96739.390 96744.580 96755.510 96501.660 96493.590 96492.200 96391.090 96355.550 96334.990 520179.066 254015.340 -60531.420 261805.710 -68305.630 1216E9.850 -93196.710 423468.663 157272.470 165099.310 24928.700 530647.27? 189692.150 145126.370 145097.470 145093.750 145131.880 145126.370 144728.700 144750.200 144736.300 144734.520 144733.320 144583.910 :44E?e.'i60 144499.760 144579.860 568566.054 302369.900 -12178.600 310193.000 -19967.300 170060.630 120197.520 675773.439 -44955.810 334426.590 524947.234 423538.258 157246.100 165190.530 24933.470 530610.288 189694.330 193488.990 193511.210 193441.620 193415.370 193506.600 193511.210 193474.330 192952.700 132962.100 lE12996.CI30 192974.360 192972.080 192973.650 192957.680 192756.310 192773.580 192702.240 192661.130 192768.140

-0.292

0.454 -0.799 0.219 0.202 ii.005 0.162 1.401 -0.3Cl3 0.650 -0.308 0.235 0.074 3.251 0.188 -0.193 -0.225 -0.596 0.656 0.315 2.053 -0.158 0.417 0.714 -0.400 -0.097 1.235 1.438 -0.407 0.956 -0.563 1.633 -1.464 -0.135 cl.333 0.078 0.344 0.258 -0.774 0.283 -0.389 -0.282 -1.225 -0.855 0.9:: 0.542 -1.251 1.692 -0.115 0.606 0.974 -0.482 -0.169 0.672 1.683 1.115 -1.826 -3.391 0.839 -0.726 1.145 -0.823 0.991 -1.459 -0.211 -0.195 0.409 cl.211 0.410 -0.010 -0.543 -1.369 -0.879 0.418 -0.453 -0.499 -1.710 1.877 3.036 -1.089 I.222 0.721 -1.528

53

54

HERBST

ET AL.

TABLE IV-Continued VTOR

SIGMA

0 0 0 0 0 0 0 0 0 0 1 0 * 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 :

2 2

2 2 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 2

2 2 2 2 0

0 0

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

JU

KU PU

4

-1

4

-2

4

0

4

-1

4 4 4 4 4 4 4

1 0 2 1 3 2 0

5

-4

5

-2

5 5 5 5 5

0 1 2 3

<--

--

(__

--

<__

--

<--

--

(_-

--------

<-<-<-<-<-<-<--

--

(--

--

(_-

-----

<-<-<-<--

o--<--

5

-4

--

(-_

.j

-3

--

(-_

5

-2

--

(--

5

-1

_-

(--

5 0 -- <-5 1 -- <-5 z--c-5 3 -- c-5 4 -- <-.j -3 -- (-V -2 -- (__ 5 -1 -- (__ 5 0 -- <-5 1 -- <-5 2 -- <-5 3 -- <-5 -2 -- (-5 -1 __ (-_ 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6

0 1 2 -3 -1 -2 0 -1 1 2 1 3 2 1 0 -4 -2

6 6 6 6 6 6 6 6 6

0 -- <-1 -- <-2 -- <-3 -- <--5 -- (__ -4 -- (__ -3 -- (__ -2 -- (_-1 -- (_0 -- (_1 -- <-2--<-3--<-4 -- (_5 -- <--3 -- (--2 -- (__ -1 -- (-0 -- <-1 -- <-2 -- (-3 -- <--2 -- (_-

6 6 6 6 6 6 6 6 6 6 6 6 6 6 6

-1

__

0 1 2

6 6 6

----------------_ --

<-<-<-(__ (__ (__ <-(_<-<-<-<-<-<-<-(-(_-

(-_

----

<-<-<--

6

-3

--

(_-

6

-1

-_

<--

6

-2

--

(--

JL KL PL

FREPUENCY(MH2)

3 -2 -3 -1 -3 -1 -3 o-3 o-3 l-3 l-3 2-3 2-3 3-3 l-5 -3 -5 -1 -5 -1 -5 o--

-230027.060 616979.384 350687.730 36169.240 358605.800 26316.030 218440.050 168577.860 724121.576 -337135.873 382666.474 524908.133 423675.155 157178.970 165363.440 24959.080 530549.271 189696.750 241813.257 241852.352 241904.119 241767.224 241700.219 241679.073 241904.407 241843.646 241829.646 241179.900 241187.400 241238.160 241205.990 241203.690 241210.680 241166.530 240936.730 240358.800 240869.490 240817.940 240952.070 -283094.900 -181771.050 665442.450 398946.230 84521.210 407069.553 266838.130 216945.600 772453.803 -288705.567 51509.280 430900.319 524860.820 423912.696 157048.620 165678.770 25018.140 530454.695 290117.815 290162.430 290209.700 290307.563 290069.824 289939.477 230248.762 290307.563 290213.238 290183.210 290138.890 2SV399.590 289402.490 289475.610 289429.120 2394*7.600 289443.930 289355.020 289111.350 289138.820

5 5 5 4 4 4

l-2-l--4 --3 --2 --

4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 6 6 6 6 6 6 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

-1 -0 -l-2-3-4--3 --2 --1 -o-l-2-3--2 --1 -o-1-2--4 --2 --I --1 -o-o-l-2-*-3-o-l--3 --1 --1 -O-1 -2--5 --4 --3 --2 --1 -o-l-2-3 -4-5--3 --2 --1 -o-1-2-3--2 --

5 -1 5 0 5 l-5 2 5 -4 5 -2 5 -1

-------

289031.290

288969.290 289130.620 -234698.450 -133605.500

RESIDUAL(MHZ)

-1.046 1.354 -0.307 0.907 1.256 -0.775 -0.433 0.934 1.053 -1.449 -1.953 -1.734 0.070 -0.948 1.222 -1.033 0.299 -1.440 1.290 -0.373 -0.296 0.474 0.370 0.338 -O.OES -0.523 -0.667 -1.243 -0.610 0.518 -0.572 -0.531 -2.038 1.464 3.925 -1.470 1.441 0.811 -1.744 3.000 -0.380 0.615 -0.437 1.286 1.493 -0.656 1.219 0.336 -0.764 0.908 -2.092 0.350 -0.922 -0.937 0.905 -1.113 -0.556 -1.750 1.430 -0.637 -0.113 0.675 0.689 0.328 -0.011 -0.615 -1.114 1.662 -0.998 -0.608 0.521 -1.221 -0.594 -1.825 0.481 4.871 -1.675 1.691 1.029 -1.826 1.020 ^ .^_ “.‘ldb

-0.297

REFERENCE

: e

c e c e e d d d d f

a a c f t,.

foe f,S

f.e f.e f,e f,e f,C

f,e e e e e P

e e e

e e P

e e .i d h d

e e d

f,e : d f a a ;

fre f,t f.e f,a f,e f,e f,e f,C

f,c ::: c e P I? P

e e e e e e c e

f’

SUBMILLIMETER

SPECTRUM

TABLE IV-Continued

-VTOR

SIGMA

0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

:, 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1

: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

JU KU

PU

<--

JL KL

PL

FREQUENCYtMHZI 132890.790 455618.116

124569.970 315266.830 265289.650 820762.501 -240241.502 99730.900 479126.480 524804.969 156828.520 166169.210 25124.880 530316.196 338456.439 338504.099 338559.926 338722.940

338344.628 33E124.502 338614.999 338721.630 338583.195 338530.249 338475.290 -186300.950 -85567.970 762635.948 181296.030 504293.685 172445.950 363739.820 313596.840 869037.809

-191733.050 147343.630 527342.624 524740.167 424857.263 156488.950 166898.650 25294.410 530123.294 189700.490

--

55

OF METHANOL

386788.660 386837.700 386901.950 387153.550 386587.270 386247.660 386977.140

387146.560 386953.820 386869.410 386802.300 -137903.060 -37703.720 811445.210 229758.760 553146.296 -143163.500

196146.210 57s547.119

RESIDUALtMHZ) 1.559 1.463

-0.600 -0.857 1.329

-0.324 -0.104 0.896 -2.051

2.800 -0.647 -0.093 -1.045 -1.502 -1.536 1.355 -1.118 -0.564 0.793 1.057 0.115 0.074 -0.808 -1.511 1.441

-1.526 l.El3 -1.174 1.752 0.936 0.369 -0.989 1.209 -1.444 0.645 1.002 -2.271 5.510 -4.168 0.176

-2.147 -0.765 -2.459 -2.054 -1.021 1.713 -1.549 -0.884 0.979 1.763 -0.250 -0.080 -0.876 -2.114 0.869 -4.391 3.276 -2.511 1.637 -0.398 1.557 1.138 -2.427

REFERENCE a d a e e d f,e : d a a P fre fre f,e f.e fre f.e fre f.e fre f,e f.e a : : a e e d a : d f a e c f a e e e e e e e e e e e a c d : a :

-._ a b

c d

Ref. Ref. Rd. This

5 2 1 work

e f 9 h

Ref. Ref. Ref. Ref.

16 15 4 6

torsional quantum numbers and J G 10 to l-10 MHz. Predicted frequencies should be of use to radioastronomers, especially for excited torsional states not treated by Pickett et at. (15). Future work will be in the direction of improving our analysis and including higher J, K data in the fit.

56

HERBST ET AL. TABLE V Rotation, Torsion, Distortion, and Interaction Constants of CH30H constant (MHz unless noted)

Present value a

Other Values b

A

127630.7538(1583)

B

24684.1785(2751)

24676.6’.

2462gd

C

23765.3680(2738)

23772.8’.

23761

0 ab

-77.6655(4671)

F(cm-')

27.63354173(3533)

o(unitless)

0.8097451117(1452)

v3ccm-1) V6(cm-l) F"

373.0839507(9174) -O.EO(fixed) -71.43105(2521)

127597C,127603d

-7B.2(5.0) 27.6266’ 0.809739’ 373.10(9) -0.80(12) -71.637(50)

-3.535184(2482)

-3.5012(27)

L"XlO2

4.01084(30762)

6.78(51)

DJxlo*

4.9768(284)

4.92(20)

2.86082(3103)

2.864(58)

6"

DJKXlOl OK kl k2 k3 k4 k5 k6 k7 65 6K Cl c2

1.058349(23160) -3.8(fixed) -BO.O(fixed)

-80(3)

-132,0(fixed)

-132(4)

-249.0(fixed)

-249(7)

16l.O(fixed)

161(23)

884.0(fixed)

884(4000)

O.O(fixed)

-0.75071(11932) -1.22722(9944) 1.1392(2378) -1.4695(6582)

"J 4 HJKXlO

-2.8164(4998)

HKX102 hJ hJK hKx102 f”

O(fixed)

O.O(fixed)

C3X102

4 HKJXIO

1.27(6) -3.8(1.1)

O.O(fixed)

9.42500(1.66993) -1.071236(92898) O.O(fixed) O.O(fixed) -5.92119(87581) O.O(fixed)

'Uncertainties in parentheses represent lo deviations. Number of

listed

significant figures for each constant is necessary to reproduce calculated frequencies to l-10 kHz. bReferences (5) and (27) unless otherwise noted. 'Taken from canbinations of constants of references(5) and (27). dReference (2).

SUBMILLIMETER

SPECTRUM

OF METHANOL

57

V. ACKNOWLEDGMENTS We acknowledge the support of NASA via Grant NAGW-189 and AR0 via Grant DAAG 29-83-K0078 for our laboratory program. E.H. wishes to thank the National Science Foundation for support of his theoretical work via Grants AST-8020321 and AST-8312270. Finally, helpful comments by the referee are acknowledged with appreciation. RECEIVED:

May 4, 1984 REFERENCES

1. R. H. HUGHES,W. E. GOOD, AND D. K. COLES,Phys. Rev. A 84, 4 18-425 ( 195 1). 2. P. VENKATESWARLU, H. D. EDWARDS,AND W. GORDY, J. Chem. Phys. 23, 1195-l 199 (195%; 3. 4. 5. 6. 7. 8. 9. 10. Il. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.

24. 25. 26. 27. 28. 29. 30.

P. VENKATESWARLU AND W. G~RDY, J. Chem. Phys. 23, 1200-1202 (1955). H. DREIZLERAND H. D. RUDOLPH,Z. Naturforsch. A 15, 1013-1014 (1960). H. D. RUDOLPH,H. DREIZLER,AND W. MAIER, Z. Natutfbrsch. A 15, 274-275 (1960). R. M. LEESAND J. G. BAKER,J. Chem. Phys. 48, 5299-53 18 (1968). J. E. M. HEUVELAND A. DYMANUS,J. Mol. Spectrosc. 45, 282-292 (1973). H. E. REDFORD,Astrophys. J. 174, 207-208 (1972). B. ZUCKERMAN,B. E. TURNER,D. R. JOHNSON,P. PALMER,AND M. MORRIS,Astrophys. J. 177, 60 l-607 ( 1972). L. H. JOHNSTONAND R. R. SRIVASTAWA,J. Mol. Spectrosc. 61, 147-149 (1976). L. H. JOHNSTON,P. R. SRIVASTAWA,AND R. M. LEES,J. Mol. Spectrosc. 84, l-40 (1980). F. J. LOVAS, R. D. SUENRAM,L. E. SNYDER,J. M. HOLLIS,AND R. M. LEES,Astrophys. J. 253, 149-153 (1982). J. M. HOLLIS,F. J. L~VAS, R. D. SUENRAM,P. R. JEWELL,AND L. E. SNYDER,Astrophys. J. 264, 543-545 (1983). K. V. L. N. SASTRY,R. M. LEES,AND J. VAN DER LINDE,J. Mol. Spectrosc. 88,228-230 (1981). T. AMANO,J. Mol. Spectrosc. 88, 194-206 ( 198 1). H. M. F%x~‘r-r, E. A. COHEN,D. E. BRINZA,AND M. M. SCHAEFER, J. Mol. Spectrosc. 89,542-547 (1981). K. V. L. N. SASTRY,R. M. LEES,AND F. C. DE LUCIA,J. Mol. Spectrosc. 103, 486-494 (1984). J. S. K~CHLERAND D. M. DENNISON,Phys. Rev. 57, 1006-1021 (1940). D. G. BURKHARDAND D. M. DENNISON,Phys. Rev. 84,408-417 (195 I). E. V. IVASHAND D. M. DENNISON,J. Chem. Phys. 21, 1804-1816 (1953). D. KIVELSON,J. Chem. Phys. 22, 1733-1739 (1954). D. KIVELSON,J. Chem. Phys. 23,2236-2243 (1955). T. NISHIKAWA,J. Phys. Sot. Japan 11,781 (1956). K. T. HECHTAND D. M. DENNISON,J. Chem. Phys. 26,48-69 (1957). P. R. SWANAND M. W. P. STANDBERG, J. Mol. Spectrosc. 1, 333-378 (1957). B. KIRTMAN,J. Chem. Phys. 37,2516-2539 (1962). Y. Y. KWAN AND D. M. DENNISON,J. Mol. Spectrosc. 43,291-3 19 (1972). R. M. LEES,F. J. LQVAS,W. H. KIRCHHOFF,AND D. R. JOHNSON,J. Phys. Chem. Ref: Data Ser. 2,205-214 (1973). F. C. DE LUCIA,in “Molecular Spectroscopy, Modern Research” (K. Narahari Rao, Ed.), Vol 2, pp. 69-92, Academic Press, New York, 1976. P. HELMINGER,J. K. MESSER,AND F. C. DE LUCIA,Appl. Phys. Lett. 42, 309-310 (1983). C. C. LIN AND J. D. SWALEN,Rev. Mod. Phys. 31, 841-890 (1959).