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Laser stark spectroscopy of the ν4 + ν8 − ν8 band of CH3C15N: Fermi resonances with 4ν84, 4ν82, and (ν7 + ν8)2
JOURNALOFMOLECULARSPECTROSCOPY
105,410-424(1984)
Laser Stark Spectroscopy of the v4 + v8 - vg Band of CH3C15N: Fermi Resonances with 4vi, 4~;) and (v, + v8)2 AK~HIRO MITO, JUN SAKAI, AND
MIKIO
KATAYAMA
Department of Pure and Applied Sciences, College of General Education, Universityof Tokyo, Komaba, Meguro-ku, Tokyo 153, Japan Laser Stark spectra for the v4 + Y*- Y*parallel band of CH&“N were measured by using CO2 and N20 lase.rs in the IO-pm region. About 300 resonances have been assigned to 102 rovibrational transitions with J’ =Z16 and -9 < kl < +9. Anomalies observed around kl = -6 and +8 were proved to be due to the Fermi interactions with 4~1 and 4v:, respectively. Another Fermi interaction with (v, + us)* was necessary to account for the anomaly around kl = -6. Observed data were analyzed by the method of least squares, and precise molecular constants have been obtained. INTRODUCTION
In our previous paper, the v4 fundamental band of CH3C”N has been studied by laser Stark spectroscopy, and the Fermi interaction between the u4 and 3~: states has been analyzed (I). In this paper, we report the analysis of the v4 + vs - us hot band in the same lo-pm region. The main purpose of the present study is to examine perturbations in the u4 + us state, since the similar Fermi resonances are expected with 4~; and 4u;f. The infrared spectra of this band have been measured by several workers with low or moderate resolution for 14Nspecies (2, 3). Sakai et al. have analyzed the rotational structure by laser Stark spectroscopy (4). As for “N species, no data about this band have been reported as far as the authors know. The microwave spectrum for the vs state has been measured by Bauer and Maes (5). The dipole moment of this state has also been measured (6). The v4 + vs state lies near 1300 cm-‘, and the vg, v7 + vs, and v3 states lie in the region between about 1300 and 1500 cm-‘. The vg band is known to be perturbed by a Fermi interaction with v7 + vs and a Coriolis interaction with v3 (7, 8). Matsuura et al. have recently analyzed this band system of 14N with high resolution, and have also found some local perturbations which remain unexplained (9). The determination of the precise molecular constants of the u4 + vs - vs band will be useful in investigating in more detail the above Fermi and Coriolis interacting band system. The vibrational energy-level diagram for CH3CL5N is shown in Fig. 1. Several possible interactions which have been discussed in previous papers are outlined in the diagram. EXPERIMENTAL
DETAILS
The sample of CH3C15N was obtained from Merck Sharp & Dohme of Canada. Stark spectra were measured by using the CO* and N20 laser lines, and their frequencies 0022-2852184 $3.00 Copwt 0 1984 by Academic All ri&hts of reproduction
410 Press, Inc.
in any form rewwd.
LASER STARK SPECTROSCOPY
411
OF CH3C”N
FIG. 1. Vibrational energy level diagram for CH3C”N. The solid lines show Fermi broken lines Coriolis interactions.
resonances,and the
were taken from Refs. (10-14). The electric field strength was calibrated by using the Stark effect of CH3F (IS), and the accuracy was about 0.1%. Other experimental details were described in Ref. (I). OBSERVED SPECTRA
Both the upper and lower states of the v4 + v8 - us band are doubly degenerate E states. The observed band was a parallel band with selection rules Al = 0 and Ak = 0, and the appearance of the spectra was similar to the v4 fundamental band, except that most of transitions (K # 0) split into doublets with kl > 0 and kl < 0. By using the usual energy expression of symmetric top, the splitting of J + AJ - J transition is given by 4[(&-‘) - (&+“)IK - 2(& - &))K3 - 2[s;(J + AJ)(J + AJ + 1) - llI;J(J+ 1)JK.
(1)
For the lines with K < 4, the observed spacing of the doublets were almost linearly dependent on K, but only slightly dependent on J, showing that the first term in Eq. (1) was predominant. The typical magnitude of the splitting was about 25K MHz. An example of observed Stark spectra is given in Fig. 2, where the doublet structure
I 0
11
I
5
(kV/cm)
10
FIG. 2. Laser Stark spectrum (Ah4 = 0) of CH3Ci5N taken with the N20 P(28) laser line near 914 cm-’ showing kl splittings of QP,(4) and Q&(4) transitions in the v4 + Y,, - vs band. Strong signal above 10 kV/cm is due to the fundamental transition.
MITO, SAKAI, AND KATAYAMA
412
of QP3(4) is clearly shown. The lines with kl = +2 were only partially resolved in the P branch, but more clearly resolved in the R branch owing to the favorable contribution of the third term in Eq. ( 1). The lines with kl = f 1 were not resolved in our Dopplerbroadened spectra at all. The sign of kl was determined by taking into account the intensity ratio of the doublet, which was calculated from the Boltzmann factors of the lower levels and from the statistical weights. Each higher-frequency component (at zero field) was assigned to kl > 0 and each lower component to kl < 0. The characteristic patterns of the doublets were useful in the assignment of K values for K < 4. On the other hand, the splittings were no longer expressed by Eq. (1) for the lines with K > 5. The spacing between kl = +5 and -5 was about 300 - 400 MHz, which was more than twice as large as the expected value of 125 MHz. Furthermore, even the signs of splittings were reversed for kl = *6, f7, and +8. These results suggested the existence of some perturbations. We assigned the total of 324 resonances to 102 rovibrational transitions with J’ =S 16 and -9 G kl i +9. ANALYSIS
(A) Subband Analysis In order to study the nature of the perturbations involved, the subband origin, &,, and the effective rotational constant of the upper state, BLrr, were determined for each subband, and their kl dependences were examined in the same manner as Ref. (I). Each Stark-shifted transition frequency was calculated by setting up and diagonalizing the upper- and lower-state energy matrices and was fitted to each laser frequency. The Hamiltonian for the present system is described as H = Ho + Hs,
(2)
where H,, denotes the unperturbed Hamiltonian of the symmetric top, and its diagonal matrix elements are (~4 + us, 1, J, klHh
+
US,
1,
J, k) = &
+ &J’(J’
- (D;&J’(J’
+ 1) - (D;),,TJ’~(J’ + 1)2 + l)k2 + (o$nJ’(J’ + I)kl,
(3)
+ l)k2 + $J”(J” + l)kl,
(4)
(h3, 1, J, k~f&h’s, 1, J, k) = B”J”(J” + 1) - Dy2(J”
+ 1)2 - &J”(J”
where all of the J-independent terms are absorbed in &, . O&diagonal matrix elements such as the Al = Ak = +2 interaction were neglected. The matrix elements of Hs, the Stark term, are expressed as (u, J, K MIHsb, J, K M) = -P,J=WJ(J
+
111,
(5)
(v, J, K MIHsb, J - 1, K M) = (p&/J)[(J2 - K2)(J2 - M2)/(2J - 1)(2J + 1)]“2,
(6)
where E is the electric field strength and p, is the dipole moment of a given vibrational
LASER STARK SPECTROSCOPY
OF CH,Ci5N
413
state 2). The constants in the Vs state, B”, 05, D[;K, and 7; were constrained to the microwave values of Bauer et al. (16). Those in the u4 + u8 state, (D&, (U&r, and (v&-r were assumed to be equal to D;, D L;k, and ol;, respectively. The upper- and lower-state dipole moments were fixed to the values 3.917 and 3.908 Debye, respectively. If a band is not perturbed by any interaction, the following expressions are obtained: V;“b= V()+ (A’ - A” - B’ + B”)k2 - 2((A51’- (A[)“)kf - (D:, - D;)k4 + (& - 7&k% B& = B’ - (D;K - DI;K)k2+ (?f/ - ?$)kl.
(7) (8)
The values of & and B& are plotted against kl in Figs. 3 and 4, respectively. For simplicity, &, + 6.273 X 10-3k2 - 5.0 X 10-4kl - 7.6 X lo-‘k4 (9) is used for &, in Fig. 3. Figure 3 shows clearly that other vibrational energy levels cross between kl = +8 and +9, and between kl = -5 and -6; and their energies at kl = +8 and -5 are higher than that of v4 + u*. If the perturbations are caused by J-dependent interactions, the deviations of B& at kl = +9 and -6 have the opposite signs to those at kl = +8 and -5, respectively. Figure 4 shows, however, that all of the B& at these kl are larger than the expected value on the line (a), which indicates that the perturbations are due to Fermi interactions and that the rotational constants B of the perturbing states are larger than that of v4 + vg. These results are quite similar to the case of the v4 band (Z), where the Fermi interaction between v4 and 3~: has been revealed. The Fermi interaction is caused by an effective Hamiltonian term of the form k48M&:+
(10)
+ K-)/2,
where qk is the ladder operator defined by Oka (I 7). In the present case, (v4 + @i (E) is coupled to 4vg2 (E) and 4vt4 (E) by this term with matrix elements W’ = 3”2k48g8/2 and W” = 3”2k4888, respectively. The values of k, where the level crossings occur, are estimated as follows. Duncan et al. estimated VAband origin to (Cd,
9,6,6_
1
vwb0+6.273.10-3k2-50dO-Lkl-76r10-7k4
916.6 I I1 I I I1 I I ,/,,,,,, 1 2 3 4 5 6 7 6 9 -9-6-7-64-4-3-2-10
k
FIG. 3. Subband origin ufub+ 6.213 X IO-‘k2 - 5.0 X IO-“kl7.6 X IO-‘k4 as a function of kl. Figure shows that other vibrational energy levels cross between kl = +8 and +9, and between kl = -5 and -6.
414
MITO, SAKAI, AND KATAYAMA
(cm-11
0.29720 -
B&f i
-9 -8 -7 -6 -5-L -3 -2 -1 0 1 2 3 4 5 6 7 8 9
kl
FIG. 4. Effective rotational constant B& as a function of kl. Anomalies are shown around kl = -6 and kl = +8. Error bars represent 2.5 times standard deviations.
362.10 cm-’ and observed the 2~: band at 7 11.55 cm-’ (28). Bauer et al. determined the anharmonic COtWant ggg = 5.62 Cm-’ (Z6). Using these values, we deduce wg = 357.19 cm-’ and x& = -0.705 cm -I, from which we can estimate the vibrational energies of 4~; and 4~: to be 1440 and 1507 cm-‘, respectively. The band origin of vg is about 9 16.75 cm-’ so that the v4 + vE state lies about 1279 cm-’ "4 + % above the ground state. Thus, neglecting the vibrational dependence of the constants A, B, and A&, the energy differences between the interacting levels (in cm-‘) are approximately written by be
E(~Y;~) - E((v4 + Ye)+‘)= 161 f 6A&gk,
(11)
E(4vg4) - E((v4 + v~)“) = 228 T 6/f{&.
(12)
Using the microwave value of A& = 4.60 cm-’ (26), Eqs. (11) and (12) predict the crossings between the pairs of levels at k = T5.8 and at k = k8.3, respectively. Since these estimations agree well with the results of the subband analysis, it seems quite reasonable to assume that the perturbation around kl = -6 is due to the Fermi resonance with 4~: and that around kl = +8 is due to the resonance with 4~:. Consequently, all of the data were analyzed in the manner similar to that described in the next subsection. The Fermi interactions were taken into account by introducing two independent parameters IV (interaction with 4~:) and IV” (interaction with 4~:). Indeed, satisfactory fit was obtained with a standard deviation of 6.7 MHz, but the determined anharmonic constants, lk48881= 0.522 f 0.002 cm-’ from IV and lk488sI= 0.429 ? 0.002 cm-’ from IV”, were inconsistent with each other. Since the latter is comparable to the value of 0.45 1 f 0.002 cm-’ obtained from the resonance between v4 and 3~:, it is the perturbation around kl = -6 that is not correctly treated by the present model. The obtained value of interaction constant which is larger than the expected one suggests that the perturbation is caused by cooperative interactions with 4~: and another energy level. (B) Analysis of the u4 + v8 - 4vg, (q + us)’ Fermi Interacting Band System We assumed that (v, + ys)2 (E) was the perturbing state, because it is expected to cross the u4 + v8 level around kl = -6. By considering the appearance of &, in Fig.
LASER STARK SPECTROSCOPY
415
OF CH?(?N
3, both 4~: and (v, + Y~)~levels must cross between kl = -5 and -6. The Fermi interaction between (vq + us)*’ and (v7 + Q,)+~is caused by effective Hamiltonian of the form k4,8sq.&,+q;+ + q,-&)/2. (13) In addition to the three direct Fermi couplings considered above, three other Fermi interactions between the perturbing states are also possible. Among them, the interaction between (Q + Q2 and 4vz2 was included in the analysis. The same type interaction between Y: and 3~: was studied by several workers (18-21). The corresponding part of the Hamiltonian is &&q,+q8+&
+ 47-48-4;+)/2.
(14)
The remaining two interactions, 4vt4 - 4uz2 and 4vg4 - (v, + Q)“, were neglected because both were higher order (A/ = ?6). The I-resonance interactions (Ak = AZ = t2) in the upper and lower states were also included in the analysis. This interaction is significant in the microwave spectra of the vg state (5) because of the small value of A - B - A{ (~0.35 cm-‘). An almost equal contribution is expected to the rotational energy levels of the v4 + Ig state. Other off-diagonal interactions in k were neglected, as in Ref. (16). The energies of the upper and lower levels were obtained by direct diagonalization of the energy matrices. The Hamiltonian is described as H=z&+H,+H,+Hs,
(15)
where Hr and HI denote the Fermi and f-resonance interactions, respectively. Because of the Stark term Hs, the energy matrix includes off-diagonal elements in J. The size of the submatrix which is diagonal in J is 2 X 2 in the lower state. The submatrix in the upper state is 8 X 8 in size, and represents the two Fermi-coupled level systems (4 X 4) coupled by the I-resonance interaction. Diagonal elements of unperturbed Hamiltonian are (II, 1, J, klH&,
1, J, k) = v. + BJ(J + 1) + (A - B)k2 - 2A{kl+ + sKk31 - DJJ2(J + 1)2 - D,,J(J
s_,J(J + 1)kf
+ l)k2 - DKk4,
(16)
where v is a given vibrational state. The matrix elements of the Fermi interaction terms are following:
(V4
(v4
+
v8,
f =
+11H,14 Vg, 1 = +2)
= 3”2k,888/2,
(17)
(v4
+
Y8,
1 =
+1IHFj4Y8, 1 = f4)
= 3”2k,888,
(18)
&3,
1 =
fllf&
= (1/2)“2k4788,
(19)
= (3/2)“2k,,,,.
(20)
+
(4&3, 1 = +21H&,
+
Y,3,
1 =
+2)
+ Vg, 1 = +2)
The Fermi interaction constants, W’ and W”, are expressed by the single parameter kd8@ as given by Eqs. ( 17) and ( 18) respectively. The matrix elements of /-resonance interactions are (u4 + v8, 1, J, kjH,Iu4 + v,3, 1 f 2, J, k ?I 2) = -(q,,/2)[J(J
+ 1) - k(k f 1)]1’2[J(J + 1) - (k * l)(k f 2)]“2,
(21)
416
MITO, SAKAI, AND KATAYAMA
(vg, I, J, k(H,(v8, If
2, J, k f 2)
= -(q8/2)[J(J + 1) - k(k f l)]“‘[J(J + 1) - (k f l)(k f 2)]1’2. (22) The matrix elements of the Stark term are the same as in the subband analysis. The energy matrix was truncated at J,,.,,, = J + 5 for J 3 3 or Jmax = 7 for J -c 3, and at Jmin = J - 7 for IKI or IMI < J - 7. The maximum size of the matrix was 104 X 104 because of the Stark term which was off diagonal in J. The constants in the v8 state, B, AS; DJ, DJK, ll~, and @ were constrained to the microwave values of Bauer et al. (16). The constants A and DK were taken from Masri et al. (22) and Duncan et al. (18), respectively. The value of qIKwas arbitrarily fixed to zero, because no data was obtained. The constants in the 4~s state, B, DJ, DJK, and qJ, were calculated from the microwave values (v8, 2~~) of Bauer et al. (16), and the other rotational constants were fixed to the v8 state values. The v7 + Yg constants, B, A, and A{ were calculated from the infrared values of Matsuura et al. (9). The constants DJ, DJK, and DK were fixed to the us values. Those of tJ and qIK were arbitrarily fixed to zero. The dipole moments of the perturbing states, 4~s and v7 + v8, were calculated from the relations
where cl0 = 3.9256 Debye was the ground state value (I). The coefficient of the vibrational dependence Ap7 was taken from the result of CH3C14N by Igarashi et al. (29), and Ap8 was determined in this analysis. The Fermi parameter k7,,, was fixed to the value of Igrashi et al. The l-type doubling constant q4* in the v4 + v8 state was not well determined (6.8( 19) X 10m4cm-‘), and was finally assumed to be equal to that in the v8state. The value of nKwas fixed to zero for the same reason. Consequently, the v8 State dipole moment, all Of the v4 + VSState Constants except qIKand &g, the 4~s and (v7 + vS)~band origins, and three Fermi interaction parameters were included as parameters in the fit. The observed resonances were equally weighted with unity. Because of the mutual Fermi interactions between three close-lying levels around kl = -6 of v4 + v8, two different sets of constants were obtained depending on whether the sign of the product, k4,,, - k4788- k7888, was positive (+) or negative (-). The standard deviations were 6.7 MHz for (+) and 6.6 MHz for (-). The molecular constants determined in the final fit are presented in Table I. The constants of v4 + v8are listed only for (-), because they agreed with those for (+) within experimental errors. A complete list of the data included in the fit, together with residues, is given in Table II. The zero-field transition frequencies of the v4 + vE - v8 band obtained by subtracting the Stark shifts from the laser frequencies are also given in Table III. DISCUSSION
Among the obtained parameters, only the band origin of 4~; - vg has different values beyond the experimental uncertainties depending on the sign of the product k 4888 - k4788- kTsE8.From the vibrational energy differences between 4~; and 4~;) the anharmonic constant &$8was calculated to be 5.49 cm-’ for (-) and 5.98 cm-’ for (+). Bauer et al. have analyzed the I-resonance effect between the 2~; and 2~: states
LASER STARK SPECTROSCOPY
417
OF CH3C15N
TABLE IA Molecular Constants of CH3C’5N (in cm-‘, except for dipole moments in Debye) 4 ‘.’
4Q2
*4,
4+“8
[
F,
II.;.47ti6h5(27ia
P
5.2.3929117(95)
[
5.247
A-
4.53974601761
[
4.60
1.33125)
[
1.304.10--’
'.4r,5,96,.10-6
I
1.734
‘.4orlDlll.1o-5
I
9.47’10-5
1.314114l~10-5
[
1.259,10-1
L’J T'JK GK
“J
‘IK
[ n.0
‘1
j
.10-’
Id
5.6?1f,,i0-4
le
errors 1”
units
in
parentheses of
the
are
last
lb.
[ ( .29837
10-6
ICI
3.856
1.44
1e
[
i.??R.lo-’
1e
[ ~.hi43.10_6
[ I .”
lP
I I’.0
standard
deviat:ons
figures. fixed
values.
moments
are
If
“’
, c5.6141.1’l-F/’
]P lg
j
9.47
-lC-L’
[ l.?:i.li,-c,
Id
[
il.”
1”
:I
Ill
, =>.6?16.lri-4
Id
91?
[
, _’
:?
[ ,.??R.:,l-:
If
1 ‘1.47.10-5
1’
times
h. Q”antlt>es I” square brackets are I-. AbscJlut‘, uncertainties for dipole
I 5.24: 1 4.60
Ih
I
1g
, ,,.?9RZnl~,-
Ih
j “.I> I d
[ 0.0
signlflcant
‘.8
lh
[ c ,268
f
le
I’!
2.5
I”
0.3010328
[ 0.0
[
3.91h3(13)c
I
a.
0.3010875,
1 I-
?+.‘*
j(/
?.Q”7’,I’I“
lC
d.
Arhltrarlly
e.
Ref.
1161.
flxed f.
Re=F.
1”
zc’ro. I?‘).
4.
RCf.
(Is,.
h.
R-f.
(0,.
_
0.1%.
by microwave spectroscopy and have obtained ggg = 5.62 cm-’ (16) which is close to the value for (-). The small discrepancy may be attributed to the fact that the 08 dependences of A and A{ have been neglected in both analyses, but the discrepancy between (+) and microwave values seems to be too large. The product of the anharmonic potential constants is therefore concluded to have the negative sign. The unperturbed sublevel energies (J = 0) of the uq + vg, hi, 4vi, and (q + Vg)z TABLE IB
4+“8
-
4 ,‘84 48
.’
-‘R
, 7+‘.‘81 2-
a.
j-1
91h.748Rn(lll
,8
“8
and
h
/+,
k4888.k4;RR-k7888,
!~,6:?4RRZ(*:~~
11411.6’6(32l
114O.hI4li2)
:0:4,7:i2ii
lfl6R.HI141)
104i.!1,14,
1II44.i(1~I
denote
the
r,gns
see
tvxt.
‘uf
th+
i’rodurt,
418
MITO, SAKAI, AND KATAYAMA TABLE II Stark Resonances of the v4 + v8 - vg Band of CH,C”N Transitiona
M' + M" E(V/cn)
P(42)=922.91429C QR-5110) -9 QR+5(10) -8 -5 QR-6(10) 10 9 QR+6(10) 8
QP+6(
P(44)=920.82912 QR+2( 6) 6 QR-3( 61 6 5 QR+3( 6) 5 4 QR-41 6) 7 6 QR+4( 6) 6 5 12 QR-51 6) 5 4 OR+51 6) 3 QR+6( 6) 6 4 QR+7l 7) -7
2122 6446 7710 7000 8751 19685 9123 10884 10866 15916 19548 23088 15585 22383 20960
1.8 -4.5 -1.2 1.8 -0.3 -5.4 -0.9 1.2 -7.2 10.8 -0.3 -5.1 3.9 -9.3 -2.4
P(50)=914.41928 QP-3( 4) -3 -2 QP*3( 4) -3 -2
7015 11656 6894 11399
11.1 4.2 11.4 13.8
P(52)=912.23070 QP-41 7) 5 4 6 QP+4( 7) 5 4 2 6 QP-5( 7) 5 4 2 4 3 2 5 QP+5( 7) 4 3 4 2 6 5 QP-6( 7) 4 2 2
20919 25801 17998 21387 15481 21507 9156 10908 13458 24491 7859 9115 10873 11838 14672 19023 8562 11814 19867 6133 7588 14022 6118
-12.9 10.2 1.5 3.6 -12.9 9.0 -11.4 -9.3 -6.3 10.2 -0.3 -3.3 3.3 -20.4 3.6 14.1 2.4 1.5 -0.6 -12.6 -11.1 -12.3 0.3
~~-5~10)
3 1
3 2 1
3 1 7
1
means AK = 0,
b.
0 - C is laser frequency Laser
d.
l
frequency
7)
M”
6 5 3 2 5 4 3
-----
co2
E(V/cm)
0-C(MHz)
4 3 2
3411 4079 6641 9585 2574 2933 3413
Laser Hot Band -----
1681 2571
0.6 0.6
P(14)=915.62774 0 QP O( 2)
9632
5.7
P(16J.913.88037 QP-2( 5) -4 QP+2( 5) -4 QP-3( 5) -4 -3 QP+3( 5) -4 -3 QP-4( 5) -3
26571 26285 16778 22941 16538 22621 20830
-8.7 -13.8 -8.4 -9.9 6.9 3.9 10.8
P(17)=913.11803 QP-3( 6) -4 -2 QP+3( 6) -4 -2 QP-4( 6) -5 -3 -2 -5 -6 QP+4( 6) -5 -3 -2 -3 -2 -2 -1 -5 -6 0 1 QP-5( 6) -5 -6 QP+S( 6) -4 -3 -5 -6
7561 15557 7241 14917 8110 14001 23067 16240 7825 13498 22131 7194 8873 15642 16992 20470 12474 17634 19240
5.7 -3.6 11.7 0.0 7.8 12.9 -1.2 -4.2 5.7 9.0 -2.4 -3.6 -2.7 -1.5 -3.9 -0.3 10.5 3.0 -0.6
P(20)=910.31020 9 QP+7(10) 8 7 6 5 QP-8(10) -4
2649 2980 3408 3979 4755 12902
-1.8 -1.5 -0.3 0.9 -0.3 4.2
18091 22403 25513
15.9 2.4 7.8
P(21)=909.57909 QP*7(11) 10 8
minus calculated
M COmpOnentS:
-8.7 -7.8 -9.3 -6.9 -1.2 -2.7 -2.7
P(12)=917.35000 0 QR 01 0) *1 0
transition
in cm-l.
unresolved
+
AJ = +I, ~2 = -5, and 3" = 10.
c.
denotes
M’
co2 Laser
7607 2.7 12434 -0.6 19895 -4.5 77q ._ ld 15.9 4530 0.9 5096 a..3 5822 0.0 -9.0 18318 -8.1 20539 -12.6 23396
9 8 7
a.
Transition
Laser
co2
QR+7(10)
O-C(MHzIh
see Ref.
(1).
frequency.
LASER STARK
SPECTROSCOPY
419
OF CHf_“N
TABLE II-Continued Transition co2
QP-8 Ill)
M' + M" E(V/cm)
0-C(MHz)
Transition
QR+J(
6421 8045 9145 11909 21911 2797 3100 3493 4604
0.6 8.4 3.6 -0.3 4.2 -14.4 -12.0 -12.6 -1.5
P(22)=908.48736 7 QP-6(13) 9 QP+6(13) -12 QP-7(13) -11 -10 -9 -8 -4 -12 QP+7(131 -11 -9 -8
28474 14443 4315 4646 5153 5713 6415 12834 7712 8436 10302 11671
14.7 12.6 -9.0 -0.3 -5.4 -3.9 -2.4 2.1 0.9 -2.1 0.3 -7.2
--- CO2 Laser Sequence
Band ---
11)
QP+9
11)
P(41)=921.87024 -7 Q&3( 8) -6 QR+31
8)
QR+4(
8)
QR-5(
8)
QR+5(
8)
1,' -5 -3 7 6 5 4
P(43)=919.81854 4 QR-2( 4) 3 4 QR+2( 4) 3 4 QR-3( 4) 3 2 4 QR+3( 4) 3 2 3 QR-4 4) QR+4 4 4i 3 2
---__-
R(10)=921.67529 QR-71 8) -8
8)
4 3 2
1515 2000 2951
-2.4 -0.6
P( 4)=910.27796 QP-6(10) 8 QP+6110) 8 6 QP-7(10) 7 6 5 QPt7(10) 9 0 7 5 4 QP-8110) -7 -6 -5 -4 QP+3(101 -6
25460 21716 28568 10864 12647 15114 6460 7246 8260 11491 14210 2911 3395 4039 5053 25951
-2.4 a.7 1.8 -5.4 -0.6 6.0 0.6 -1.8 -2.7 1.2 -0.3 0.9 2.1 9.3 11.7 -8.1
14875 18695 20265 7057 7794 8610
16.2 -5.4 -6.9 7.5 4.5 9.9
P( 8)=907.05284 QP-8(15) QP+8(15) QPtP(15)
15857 18425 23946 3996 4812 8038 8551 9945 8974 11161
-3.6 -4.2 0.3 -3.9 -2.4 -2.4 4.2 5.7 -10.5 -10.5
16278 21367 16017 21003 14143 18198 25218 13858 17835 24775 17414 13355 17005 22980
-0.6 -7.2 10.5 11.4 -10.8 4.2 -6.0 -3.6 13.5 -3.3 3.9 0.3 4.8 -0.3
13C02 Laser ------
R( 8)=920.21948 -5 OR-2( 5) -3 QR+2( 5) -2 5 QR+3( 51 4 3 QR-4( 5) 2 3 QR+4( 5) 2 3 QR-5( 51 4 QR+5( 51 3
3323 6241 9272 928 1190 7765 11175 6988 10167 12751 8843 11449
340 *
0-C(MHz)
13c02 Laser
Laser Hot Band 10 8 7 -9 -5 -10 -9 -8 -6
QP+8
M' + M" E(V/cm)
-0.6 1.8 5.1 5.7 -1.2 -0.6 8.7 0.9 -3.3 0.3 0.3 4.2
3.6
__-_-
10 8 -12 -11 -10 -9
-3.9
13 C 1802 Laser -----
P(10)=921.40060 7 QR-2( 7) 7 QR+2( J) 7 QR-3( 7) 6 5 6 QR+3( 7) 5 7 QR+4( J) 6
9191 11000 8267 9927 11342 13236
-6.6 -5.1 -12.0 -5.4 -1.5 -3.9 -4.5 0.6 -6.6
P(20)=913.64451 4 QP-3( 5) 2 4 QP+3( 5) 2 QP-4( 5) -2 QP+4( 5) -4
2161 4224 2349 4583 1899 717
-4.5 -7.8 5.1 1.2 0.6 4.8
P(24)=910.38402 QP-5110) 9 8 7 6 7 QP+5(10) 6 QP+6(10) 8 7 QP-7(10) -9 -8 QP+7(10) -8 -7
15709 17653 20140 23458 22033 25624 5543 6397 4001 4547 6851 7888
0.9 2.1 3.6 9.0 5.1 6.9 -6.9 4.8 3.3 -6.0 0.9 -7.2
--_-_
N20
P(191.922.42221 QR+4( 91 -6 OR-51 91 5 9 QR+Si 91 8
2931 * 2122 * 7916
Laser
__---
10698 11786 4190 4644
-6.0 1.8 -3.9 7.2
420
MITO,
SAKAI,
AND
KATAYAMA
TABLE II-Continued Transition
M' + M" E(V/cm)
9) 9)
19296 5651 6606 8031 10136 7501 8705
P(21)=920.62242 QR-4( 6) -6 -5 -4 QR+4( 6) -6 -5 -4 QR-5( 6) -6 -5 -3 QR+5( 6) -6 -4 -3 P(22)=919.71754 QR-2( 41 4 QR+2( 41 4 3 2 QR-3( 4) 4 3 2 QR+3l 4) 4 QR-4( 4) 2 0
4)
1
2 0
1
M' + M" E(V/cm)
0-C(MHz)
N20 Laser 5341 17333
7 7
P(20)=921.52398 QR+7( 8) -6 QR-8( 8) -7 -6 -5 -4 QR+B( 8) 7 6
QR+4(
Ikansition
Laser
N20
QR+5( QR+6(
0-C(MHz)
1.8 -2.7
7.8 6.6 3.3 14.1 3.9 4.2 5.1
12584 15233 19257 13277 16072 20334 4231 5088 8655 5384 8138 11181
-0.9 9.3 11.1 -8.4 1.5 4.5 -5.7 -7.8 -11.1 -5.7 -16.8 0.9
6289 6005 8009 11906 6790 8887 12806 6517 14233 9805 13667 9403
2.1 11.1 5.1 6.0 -2.1 4.8 -1.2 -3.9 -4.5 -4.8 0.6 0.9
12548 19067 9012 13168 5468 6863 7308 9679 14188 4241 7378 1972 3294 952 1220 8083 7710 8585 19912 11090
5.1 9.3 3.0 1.8 -8.7 -0.9 -5.4 -0.6 5.7 -1.5 -4.5 0.9 4.5 8.1 1.5 -1.8 -1.2 6.9 -3.3 0.3
17880 21771 13554 16065 19603
4.5 1.8 -1.2 3.6 0.3
11452 12940 14733 13618 15551 18152 21765 2177 2844 4367 603 * 6430 7330 8550 9226
-6.6 1.2 -5.1 -0.3 -1.5 0.0 -0.6 -2.1 1.5 -1.8 2.4
P(33)=909.54543 9 QP+7(11) 9 QP-8(11) fi QP+B(ll) -10 -9 -8 -10 -11 QP-9(11) -4
25200 11779 17434 6507 7233 8150 12808 5303
11.4 9.3 6.3 -3.0 -1.8 -1.8 4.8 -2.4
P(34)=908.60088 QP-4(13) 12 9 QP+4(13) 10
18988 25430 23913
4.2 6.9 4.5
P(35)=907.65304 QP-B(14) 12 10 QP+8114) -11 -10 -9
17829 21380 10080 11128 12308
-12.3 -8.4 -1.8 -5.7 1.2
QP+3(
7)
QP-4(
7)
QP+4(
7)
QP-5(
7)
QP+5(
7)
QP-6(
7)
QP+6(
7)
12306 12509
-0.3 5.7
P(241=917.89783 0 QR O( 1) 0
6076 20334
-14.4 -2.7
P(26)=916.06488 0 QP O( 1) 0 fl
4811 7700
-13.2 -0.6
P(28)=914.21869 QP-3( 4) 3 2 1 10 -1 -2 QP+3( 4) 3 2 1 10 -1 -2
3153 4598 8064 3694 12243 3306 4792 8354 3837 12591
-12.3 -7.5 -8.7 -6.6 -4.2 9.9 5.1 -0.3 -0.6 1.8
P(30)=912.35929 QP-3( 7) 4 10 6 7 QP+3( 7) 6 5 4
17875 18559 23264 12267 14712 18320
1.5 -5.4 -3.6 5.1 10.2 11.7
2 3 2
2 10
1 4 3 2
4 3 10 -5 -3 -5 -4 -3 -6 -7 -4 -2 -6 -7
P(31)=911.42463 QP-7( 8) 5 4 QP+7( '3) 6 5 4 P(32)=910 QP-4(10
QP+4(10
QP-5(10)
QP+5(10) QP-6(10)
P(23)=918.80935 QR-3( 3) -3 QR+3( 3) -3
3 10
48668 9 8 7 B 7 6 5 -4 -3 -2 9 -8 -7
-a QP+6(10)
-9
P(37)=905.74748 QP+9(17) -16 -16 -15
1149 * 738 l
-0.9
3.6 6.3 5.7
1.2 7.2
LASER STARK SPECTROSCOPY
OF CH#?N
TABLE 111 Zero-Field Transition Frequencies for the v4 + v8 - us Band of CH#.?N
Transitiona QR+7(101 QR-6(10) QR+6(10) OR-5(10) QR+S(lOl QR+6( 91 QR-5( 9) QR+5( 91 QR+4( 9) QR-8( 81 QR+8( 81 QR-7( 8) QR+7( 81 QR*7( 8) QR-5( 81 QR+i( 81 QR+4( 8) QR-31 8) QR+3( 8) QR+7( 7) QR+4( 71 QR-31 7) QR+3( 71 QR-2( 7) QR+2( 71 QR+6( 61 QR-5( 61 OR-St 61 QR+S( 61 QR+S( 61 QR-41 6) QR-4( 6) QR+4( 6) QR+4i 6) QR-3( 6) QR+3( 6) QR+2( 6) QR-5( 5) QR+5( 5) QR-4( 5) QR+4( 51 QR+3( 5) QR+Zl 5) QR-2( 51 QR-41 4) QR-41 4) OR+41 4) QR+4( 4) QR-3( 4) OR-3( 4) QR+3( 4) OR+31 4) QR-21 4) QR-2( 4) QR+2( 41
a.
v, (cm-l) 922.79972 922.90970
922.89015 922.94758 922.96235 922.32520 922.38301 922.39752 922.45537 921.58112 921.44799 921.67873 921.66766 921.66800 921.81564 921.82922 921.88747 921.92741 921.93231 921.09712 921.31655 921.35662 921.36117 921.38980 921.39282 920.61317 920.67187 920.67143 920.68487 920.68479 920.73631 920.73671 920.7427s 920.74280 920.78309 920.78743 920.81909 920.09543 920.10849 920.16020 920.16606 920.21069 920.24230 920.23959 919.58087 919.58058 919.58653 919.58650 919.62703 919.62718 919.63099 919.63079 919.65991 919.66011 919.66281
Laser(cm-l)d Shlft(MHzlb 0-C(MHz)' C P42 922.91429 -9.9 3434.6 922.91429 137.7 15.6 922.91429 0.4 723.8 922.91429 -998.1 3.0 -2.6 922.91429 -1440.7 -2.8 N P19 922.42221 2908.1 2.0 922.42221 1175.1 922.42221 740.1 1.7 922.42221 -994.0 -6.1 6.9 N P20 921.52398 -1713.0 4.7 921.52398 2278.0 C' RlO 921.67529 3.5 -103.1 -2.3 921.67529 228.6 N P20 921.52398 7.7 -4317.5 5.2 CS P41 921.87024 1636.9 921.87024 1229.8 -10.6 -2.9 921.87024 -516.5 -3.8 921.87024 -1714.0 921.87024 -1860.9 0.4 -2.3 c P44 920.82912 -8034.4 -3.0 C" PlO 921.40060 2519.7 -6.2 1318.6 921.40060 -4.2 921.40060 1182.2 -6.5 921.40060 323.8 -5.1 921.40060 233.3 -2.8 C P44 920.82912 6474.0 920.82912 4714.1 5.4 -1469.2 -8.0 N P21 920.62242 -5.0 4324.5 C P44 920.82912 -7.3 -1869.9 N P21 920.62242 -5.4 2782.5 C P44 920.82912 6.6 -3426.3 N P21 920.62242 -2.3 2589.3 C P44 920.82912 -0.7 -3609.0 N P21 920.62242 1379.9 -2.9 c P44 920.82912 0.7 C P44 920.82912 1249.7 1.8 300.6 920.82912 0.4 3718.8 C' R8 920.21948 3327.5 2.3 920.21948 4.0 920.21948 1777.1 -1.3 1601.5 920.21948 2.4 920.21948 263.5 3.4 -684.1 920.21948 -602.9 -0.5 920.21948 4.0 CS P43 919.81854 7125.2 -4.6 4105.9 N P22 919.71754 1.7 CS P43 919.81854 6955.4 3928.4 0.7 N P22 919.71754 -4.1 5741.3 CS P43 919.81854 2708.9 0.4 N P22 919.71754 2.2 CS P43 919.81854 5622.5 -3.8 2600.6 N P22 919.71754 -3.9 4755.7 CS P43 919.81854 2.1 N P22 919.71754 1721.8 10.9 CS P43 919.81854 4668.7
QR+7(10) means AK = 0, AJ = +l, KZ = +l. and J" = 10.
b. The average of the Stark shifts of the M-components. c. 0 - C 1s ", minus the calculated zero-field frequency by using the constants in Table I. d. C, CH, and CS denote CO2 laser regular, hot, and sequence band, respectively. laser.
C' and C" denote 13C02 and 13C1802
N denotes N20 laser.
P42 is the P(421 laser 11ne.
421
422
MITO,
SAKAI,
AND
KATAYAMA
TABLE III-Continued Transition QR+2( 4) QR-3( 3) QR+3( 3) QR 0( 1) QR O( 0) QP O( 1) QP 0( 2) QP-3( 4) QP-31 4) QP+3( 4) QP+3( 4) QP-21 5) QP+21 5) QP-31 5) QP-3( 5) QP+31 5) QP+3( 5) QP-4( 5) QP-4( 5) QP+4( 5) QP-3( 6) QP+3( 6) QP-4( 61 QP+4( 61 QP-5( 6) QP+5( 61 QP-3( 7) QP+3( 7) QP-4( 7) QP-4( 7) QP+4( 71 QP+4( 7) QP-5( 7) QP-5( 7) QP+5( 71 QP+S( 7) QP-6( 71 QP-6( 7) QP+6( 71 QP+6( 7) QP-7( 8) QP+7( 8) QP-4(10) QP+4(10) QP-5(10) QP-5(10) QP+5(10) QP+5llO) QP-6110) QP-6(10) QP+6110) QP+6(10) QP+6llo) QP-7(10) QP-7(10) QP+7(10) QP+7(10) QP*7(10) QP-8(10) QP-8(10) QP+B(lO) QP+7(11) QP+7(11) QP-8(11) QP-8111) QP+8(111 QP+8(11) QP-9(111 QP+9(11) QP-4(13)
v, lcn~-~) 919.66269
919.04479 919.04853 917.93016 917.33921 916.14782 915.54837 914.28200 914.28148 914.28447 914.28416 913.70516 913.70632 913.67310 913.67320 913.67578 913.67571 913.62839 913.62805 913.63189 913.06223 913.06448 913.01702 913.02046 912.95377 912.96387 912.44804 912.45038 912.40285 912.40284 912.40629 912.40634 912.33997 912.33980 912.34981 912.34965 912.30382 912.30357 912.27935 912.27912 911.59209 911.57480 910.54351 910.54672 910.48090 910.48105 910.49032 910.49045 910.44563 910.44546 910.42032 910.42010 910.42032 910.35008 910.35013 910.33257 910.33266 910.33266 910.25623 910.25628 910.11528 909.70762 909.70771 909.63104 909.63116 909.49337 909.49328 909.52639 909.55386 908.65868
Shift(MHz) 0-ClMHzl 1644.3 -7058.2 -7170.5 -969.3 323.4 -2486.6 2379.5 4115.6 -1882.4 4041.4 -1962.8 5252.8 5218.0 6213.8 -860.1 6133.3 -935.2 7554.2 493.6 378.4 1672.8 1605.4 3028.1 2925.0 4924.5 4621.7 -2660.5 -2730.8 -1305.9 -5160.7 -1408.9 -5265.5 579.2 -3270.6 284.2 -3566.2 1663.0 -2184.6 2396.5 -1451.6 -5020.4 -4502.0 -1703.8 -1800.0 173.4 -2909.0 -109.3 -3190.6 1230.6 -5021.4 1989.3 -1081.7 -4267.7 1017.6 -2163.5 1542.3 -673.4 -1640.0 1618.1 649.8 4877.0 -3853.3 -4865.1 -1557.4 -2570.2 2569.9 1563.4 570.9 756.5 -1732.7
7.4 -0.3 5.8 -8.5 0.6 -6.9 5.8 7.7 -7.8 12.5 3.2 -8.8 -13.7 -9.1 -6.1 5.4 3.1 10.9 0.6 4.8 1.1 5.8 3.8 0.1 -0.1 4.4 -2.4 8.3 -1.2 -1.4 -1.2 0.3 2.9 -2.3 4.7 0.1 -1.8 -9.3 1.4 -5.6 3.0 0.9 -3.3 -0.5 -0.7 4.1 2.3 6.0 2.7 -2.6 5.6 -1.1 5.4 -1.5 -0.0 -3.2 -0.6 -0.6 4.2 6.0 -8.2 8.7 11.5 4.2 7.9 2.0 -0.5 -2.4 -10.1 5.7
Laser(cm-1) N N N CH N CH c N c N CH C" CH C" CH C" CH
N C N C N C N C N C N C N N C" N C" N C' N C" C' C" C' C" CH C' CH C' CH N CH N CH N CH N
P22 919.71754 P23 918.80935 918.80935 P24 917.89783 P12 917.35000 P26 916.06488 Pl4 915.62774 P50 914.41928 P28 914.21869 P50 914.41928 P28 914.21869 P16 913.88037 913.88037 913.88037 P20 913.64451 P16 913.88037 P20 913.64451 P16 913.88037 P20 913.64451 913.64451 P17 913.11803 913.11803 913.11803 913.11803 913.11803 913.11803 P30 912.35929 912.35929 912.35929 P52 912.23070 P30 912.35929 P52 912.23070 P30 912.35929 P52 912.23070 P30 912.35929 P52 912.23070 P30 912.35929 P52 912.23070 P30 912.35929 P52 912.23070 P31 911.42463 911.42463 P32 910.48668 910.48668 910.48668 P24 910.38402 P32 910.48668 P24 910.38402 P32 910.48668 P4 910.27796 P32 910.48668 P24 910.38402 P4 910.27796 P24 910.38402 P4 910.27796 P24 910.38402 P20 910.31020 P4 910.27796 P20 910.31020 P4 910.27796 910.27796 P21 909.57909 P33 909.54543 P21 909.57909 P33 909.54543 P21 909.57909 P33 909.54543 909.54543 P21 909.57909 P34 908.60088
states calculated from the constants (-) are plotted against k in Fig. 5, showing the level crossings between the v4 + v8 and perturbing states. The appearance of energy levels for (+) is almost similar to Fig. 5, except that 4~; is shifted lower by 5.8 cm-‘.
LASER STARK SPECTROSCOPY
423
OF CH3C15N
TABLE III-Continued Transltlon
QPi4113) QP-6113) QP+6(13) QP-7(13) VP+71131 UP-8(141 QP+8l141 QP-8(15) QP+8(151 QP19115) ap+91171
“,
(cm-l)
Shlft(MHzl 0-C(MHz)
908.66150 908.56189 908.53'555 908.46550 908.44794 907.73755 907.61004 907.10071 906.97657 907.02513 905.74305
-1817.2 -2234.4 -1444.8 655.5 1181.8 -2533.5 1289.3 -1435.2 2286.6 830.7 132.7
4.5 14.3 12.1 -3.2 -2.0 -10.4 -2.1 -1O.R -6.8 7.4 4.1
Laserlcm-1) 908.60088 CH P22 908.48736 908.48736 908.48736 908.48736 N P35 907.65304 907.65304 c ' PB 907.05284 907.05284 907.05284 N P37 905.74748
Although two perturbing states cross the (vq + v$’ state between k = i5 and ~6 in both cases, the relative positions of 4~:~ and (v, + @* are different. The crossing of 4~8”~and (u7 + @* is expected between k = ~6 and T7 for (-), as shown in Fig. 5, whereas it is predicted between k = T5 and ~6 for (+). Because of the Fermi interaction between them, (v, + i+J2must be perturbed in different manners depending on the choice of the signs. Further evidence of the sign may, therefore, be obtained by studying the (v7 + v~)~combination band or (y7 + Q)* - VAhot band with high resolution. As discussed before, the observed splitting of kf doublet for K < 4 is almost linearly dependent on K and, if unperturbed, is expressed by the first term of Eq. (1). From the determined constants Ar and Ar, the magnitude of the splitting is estimated to be 30K MHz, which agrees with the observed value of 25K MHz. This means that the effect of the Fermi interactions on the splitting is small for K i 4. Though the strong Fermi resonance between (v7 + vs)’ and vg has been observed (7-9), it is neglected in the present study. This contribution is effectively absorbed - vs. in the determined anharmonic constant k 4788and the band origin (v7 + ZG&* From Table I, the values of 4 and a: are calculated to be 0.007709( 10) and 0.001437(3) cm-‘, respectively. These values are in satisfactory agreement with those determined from the fundamental band; 4 = 0.006997(4) and cy? = 0.001443(l) cm-’ (1). The decrease of the dipole moment is 0.46% from ground state to v8, and 0.48% from u4 to v4 + Yg. These values are in good agreement, and their decreases against 2)sshow parallel nature. Messer and Roberts have observed a similar decrease
13001200 ”
”
”
”
I’
-10-9-6-7-6-5-4-3-2-l
”
”
”
”
’ ”
0 1 2 3 4 5 6 7 6 910
fk
FIG. 5. Unperturbed energy levels of the u4 + us, 4ui, 44, and (Y, + Y# states for J = 0.
plotted
againstk
MITO,
424
SAKAI,
AND
KATAYAMA
using the Stark effect on the (.I, K) = (2, 0) - ( 1, 0) pure rotational transitions (6), but the present values are more precise. ACKNOWLEDGMENTS This work was supported in part by a grant in aid for Scientific Research from the Ministry of Education. Calculations in the present work were carried out at the Computer Centre, University of Tokyo. RECEIVED:
January 26, 1984 REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. II. 12. 13. 14. IS. 16. 17. 18.
A. MITO, J. SAKAI, AND M. KATAYAMA, J. Mol. Spectrosc. 103, 26-40 (1984). F. W. PARKERAND A. H. NIELSEN,J. Mol. Spectrosc. 1, 107-123 (1957). 1. NAKAGAWA AND T. SHIMANOUCHI,Spectrochim. Acta 18, 5 13-539 (1962). J. SAKAI, 1. IGARASHI,AND M. KATAYAMA, 45th Annual Meeting of the Chemical Society of Japan, 1982. A. BAUER AND S. MAES, J. Phys. (Paris) 30, 169-180 (1969). J. K. ME~SERAND J. A. ROBERTS,J. Mol. Spectrosc. 96, 351-352 (1982). J. L. DUNCAN, D. ELLIS, AND I. J. WRIGHT, Mol. Phys. 20, 673-685 (1971). H. MATSUURA, Bull. Chem. Sot. Japan 44, 2379-2381 (1971). H. MATSUURA, N. KUBOTA, AND H. MURATA, Chem. Lett. 1509-1512 (1982). C. FREED,L. C. BRADLEY,AND R.G. O’DONNELL, IEEE J. Quantum Electron. 16, 1195-1206 (1980). B. G. WHITFORD, K. J. SIEMSEN,AND J. REID, Opt. Commun. 22, 261-264 (1977). J.-P. MONCHALIN,M. J. KELLY, J. E. THOMAS, N. A. KURNIT, AND A. JAVAN, J. Mol. Spectrosc. 64, 491-494 (1977). K. J. SIEMSENAND B. G. WHITFORD, Opt. Commun. 22, 11-16 (1977). B. G. WHITFORD, K. J. SIEMSEN,H. D. RICCIUS,AND R. G. HANES, Opt. Commun. 14,70-74 (1975). S. M. FREUND, G. DUXBURY, M. R~MHELD, J. T. TIEDJE,AND T. OKA, J. Mol. Spectrosc. 52, 3857 (1974). A. BAUER, G. TARRAGO, AND A. REMY, J. Mol. Spectrosc. 58, 111-124 (1975). T. OKA, J. Chem. Phys. 47, 5410-5426 (1967). J. L. DUNCAN, D. C. MCKEAN, F. TULLINI,G. D. NIVELLINI,AND J. PEREZ PERA, J. Mol. Spectrosc.
69, 123-140 (1978). 19. I. IGARASHI,J. SAKAI, H. FLJJIMA,AND M. KATAYAMA, Symposium on Molecular Structure, Kyoto, October I98 1. 20. S. A. RACKLEY, R. J. BUTCHER,M. RUMHELD, S. M. FREUND, AND T. OKA, J. Mol. Spectrosc. 92, 203-217 (1982). 21. Y. MORI, T. NAKAGAWA, AND K. KUCHITSU,to be published, 22. F. N. MASRI, J. L. DUNCAN, AND G. K. SPEIRS,J. Mol. Spectrosc. 47, 163-178 (1973).
105,410-424(1984)
Laser Stark Spectroscopy of the v4 + v8 - vg Band of CH3C15N: Fermi Resonances with 4vi, 4~;) and (v, + v8)2 AK~HIRO MITO, JUN SAKAI, AND
MIKIO
KATAYAMA
Department of Pure and Applied Sciences, College of General Education, Universityof Tokyo, Komaba, Meguro-ku, Tokyo 153, Japan Laser Stark spectra for the v4 + Y*- Y*parallel band of CH&“N were measured by using CO2 and N20 lase.rs in the IO-pm region. About 300 resonances have been assigned to 102 rovibrational transitions with J’ =Z16 and -9 < kl < +9. Anomalies observed around kl = -6 and +8 were proved to be due to the Fermi interactions with 4~1 and 4v:, respectively. Another Fermi interaction with (v, + us)* was necessary to account for the anomaly around kl = -6. Observed data were analyzed by the method of least squares, and precise molecular constants have been obtained. INTRODUCTION
In our previous paper, the v4 fundamental band of CH3C”N has been studied by laser Stark spectroscopy, and the Fermi interaction between the u4 and 3~: states has been analyzed (I). In this paper, we report the analysis of the v4 + vs - us hot band in the same lo-pm region. The main purpose of the present study is to examine perturbations in the u4 + us state, since the similar Fermi resonances are expected with 4~; and 4u;f. The infrared spectra of this band have been measured by several workers with low or moderate resolution for 14Nspecies (2, 3). Sakai et al. have analyzed the rotational structure by laser Stark spectroscopy (4). As for “N species, no data about this band have been reported as far as the authors know. The microwave spectrum for the vs state has been measured by Bauer and Maes (5). The dipole moment of this state has also been measured (6). The v4 + vs state lies near 1300 cm-‘, and the vg, v7 + vs, and v3 states lie in the region between about 1300 and 1500 cm-‘. The vg band is known to be perturbed by a Fermi interaction with v7 + vs and a Coriolis interaction with v3 (7, 8). Matsuura et al. have recently analyzed this band system of 14N with high resolution, and have also found some local perturbations which remain unexplained (9). The determination of the precise molecular constants of the u4 + vs - vs band will be useful in investigating in more detail the above Fermi and Coriolis interacting band system. The vibrational energy-level diagram for CH3CL5N is shown in Fig. 1. Several possible interactions which have been discussed in previous papers are outlined in the diagram. EXPERIMENTAL
DETAILS
The sample of CH3C15N was obtained from Merck Sharp & Dohme of Canada. Stark spectra were measured by using the CO* and N20 laser lines, and their frequencies 0022-2852184 $3.00 Copwt 0 1984 by Academic All ri&hts of reproduction
410 Press, Inc.
in any form rewwd.
LASER STARK SPECTROSCOPY
411
OF CH3C”N
FIG. 1. Vibrational energy level diagram for CH3C”N. The solid lines show Fermi broken lines Coriolis interactions.
resonances,and the
were taken from Refs. (10-14). The electric field strength was calibrated by using the Stark effect of CH3F (IS), and the accuracy was about 0.1%. Other experimental details were described in Ref. (I). OBSERVED SPECTRA
Both the upper and lower states of the v4 + v8 - us band are doubly degenerate E states. The observed band was a parallel band with selection rules Al = 0 and Ak = 0, and the appearance of the spectra was similar to the v4 fundamental band, except that most of transitions (K # 0) split into doublets with kl > 0 and kl < 0. By using the usual energy expression of symmetric top, the splitting of J + AJ - J transition is given by 4[(&-‘) - (&+“)IK - 2(& - &))K3 - 2[s;(J + AJ)(J + AJ + 1) - llI;J(J+ 1)JK.
(1)
For the lines with K < 4, the observed spacing of the doublets were almost linearly dependent on K, but only slightly dependent on J, showing that the first term in Eq. (1) was predominant. The typical magnitude of the splitting was about 25K MHz. An example of observed Stark spectra is given in Fig. 2, where the doublet structure
I 0
11
I
5
(kV/cm)
10
FIG. 2. Laser Stark spectrum (Ah4 = 0) of CH3Ci5N taken with the N20 P(28) laser line near 914 cm-’ showing kl splittings of QP,(4) and Q&(4) transitions in the v4 + Y,, - vs band. Strong signal above 10 kV/cm is due to the fundamental transition.
MITO, SAKAI, AND KATAYAMA
412
of QP3(4) is clearly shown. The lines with kl = +2 were only partially resolved in the P branch, but more clearly resolved in the R branch owing to the favorable contribution of the third term in Eq. ( 1). The lines with kl = f 1 were not resolved in our Dopplerbroadened spectra at all. The sign of kl was determined by taking into account the intensity ratio of the doublet, which was calculated from the Boltzmann factors of the lower levels and from the statistical weights. Each higher-frequency component (at zero field) was assigned to kl > 0 and each lower component to kl < 0. The characteristic patterns of the doublets were useful in the assignment of K values for K < 4. On the other hand, the splittings were no longer expressed by Eq. (1) for the lines with K > 5. The spacing between kl = +5 and -5 was about 300 - 400 MHz, which was more than twice as large as the expected value of 125 MHz. Furthermore, even the signs of splittings were reversed for kl = *6, f7, and +8. These results suggested the existence of some perturbations. We assigned the total of 324 resonances to 102 rovibrational transitions with J’ =S 16 and -9 G kl i +9. ANALYSIS
(A) Subband Analysis In order to study the nature of the perturbations involved, the subband origin, &,, and the effective rotational constant of the upper state, BLrr, were determined for each subband, and their kl dependences were examined in the same manner as Ref. (I). Each Stark-shifted transition frequency was calculated by setting up and diagonalizing the upper- and lower-state energy matrices and was fitted to each laser frequency. The Hamiltonian for the present system is described as H = Ho + Hs,
(2)
where H,, denotes the unperturbed Hamiltonian of the symmetric top, and its diagonal matrix elements are (~4 + us, 1, J, klHh
+
US,
1,
J, k) = &
+ &J’(J’
- (D;&J’(J’
+ 1) - (D;),,TJ’~(J’ + 1)2 + l)k2 + (o$nJ’(J’ + I)kl,
(3)
+ l)k2 + $J”(J” + l)kl,
(4)
(h3, 1, J, k~f&h’s, 1, J, k) = B”J”(J” + 1) - Dy2(J”
+ 1)2 - &J”(J”
where all of the J-independent terms are absorbed in &, . O&diagonal matrix elements such as the Al = Ak = +2 interaction were neglected. The matrix elements of Hs, the Stark term, are expressed as (u, J, K MIHsb, J, K M) = -P,J=WJ(J
+
111,
(5)
(v, J, K MIHsb, J - 1, K M) = (p&/J)[(J2 - K2)(J2 - M2)/(2J - 1)(2J + 1)]“2,
(6)
where E is the electric field strength and p, is the dipole moment of a given vibrational
LASER STARK SPECTROSCOPY
OF CH,Ci5N
413
state 2). The constants in the Vs state, B”, 05, D[;K, and 7; were constrained to the microwave values of Bauer et al. (16). Those in the u4 + u8 state, (D&, (U&r, and (v&-r were assumed to be equal to D;, D L;k, and ol;, respectively. The upper- and lower-state dipole moments were fixed to the values 3.917 and 3.908 Debye, respectively. If a band is not perturbed by any interaction, the following expressions are obtained: V;“b= V()+ (A’ - A” - B’ + B”)k2 - 2((A51’- (A[)“)kf - (D:, - D;)k4 + (& - 7&k% B& = B’ - (D;K - DI;K)k2+ (?f/ - ?$)kl.
(7) (8)
The values of & and B& are plotted against kl in Figs. 3 and 4, respectively. For simplicity, &, + 6.273 X 10-3k2 - 5.0 X 10-4kl - 7.6 X lo-‘k4 (9) is used for &, in Fig. 3. Figure 3 shows clearly that other vibrational energy levels cross between kl = +8 and +9, and between kl = -5 and -6; and their energies at kl = +8 and -5 are higher than that of v4 + u*. If the perturbations are caused by J-dependent interactions, the deviations of B& at kl = +9 and -6 have the opposite signs to those at kl = +8 and -5, respectively. Figure 4 shows, however, that all of the B& at these kl are larger than the expected value on the line (a), which indicates that the perturbations are due to Fermi interactions and that the rotational constants B of the perturbing states are larger than that of v4 + vg. These results are quite similar to the case of the v4 band (Z), where the Fermi interaction between v4 and 3~: has been revealed. The Fermi interaction is caused by an effective Hamiltonian term of the form k48M&:+
(10)
+ K-)/2,
where qk is the ladder operator defined by Oka (I 7). In the present case, (v4 + @i (E) is coupled to 4vg2 (E) and 4vt4 (E) by this term with matrix elements W’ = 3”2k48g8/2 and W” = 3”2k4888, respectively. The values of k, where the level crossings occur, are estimated as follows. Duncan et al. estimated VAband origin to (Cd,
9,6,6_
1
vwb0+6.273.10-3k2-50dO-Lkl-76r10-7k4
916.6 I I1 I I I1 I I ,/,,,,,, 1 2 3 4 5 6 7 6 9 -9-6-7-64-4-3-2-10
k
FIG. 3. Subband origin ufub+ 6.213 X IO-‘k2 - 5.0 X IO-“kl7.6 X IO-‘k4 as a function of kl. Figure shows that other vibrational energy levels cross between kl = +8 and +9, and between kl = -5 and -6.
414
MITO, SAKAI, AND KATAYAMA
(cm-11
0.29720 -
B&f i
-9 -8 -7 -6 -5-L -3 -2 -1 0 1 2 3 4 5 6 7 8 9
kl
FIG. 4. Effective rotational constant B& as a function of kl. Anomalies are shown around kl = -6 and kl = +8. Error bars represent 2.5 times standard deviations.
362.10 cm-’ and observed the 2~: band at 7 11.55 cm-’ (28). Bauer et al. determined the anharmonic COtWant ggg = 5.62 Cm-’ (Z6). Using these values, we deduce wg = 357.19 cm-’ and x& = -0.705 cm -I, from which we can estimate the vibrational energies of 4~; and 4~: to be 1440 and 1507 cm-‘, respectively. The band origin of vg is about 9 16.75 cm-’ so that the v4 + vE state lies about 1279 cm-’ "4 + % above the ground state. Thus, neglecting the vibrational dependence of the constants A, B, and A&, the energy differences between the interacting levels (in cm-‘) are approximately written by be
E(~Y;~) - E((v4 + Ye)+‘)= 161 f 6A&gk,
(11)
E(4vg4) - E((v4 + v~)“) = 228 T 6/f{&.
(12)
Using the microwave value of A& = 4.60 cm-’ (26), Eqs. (11) and (12) predict the crossings between the pairs of levels at k = T5.8 and at k = k8.3, respectively. Since these estimations agree well with the results of the subband analysis, it seems quite reasonable to assume that the perturbation around kl = -6 is due to the Fermi resonance with 4~: and that around kl = +8 is due to the resonance with 4~:. Consequently, all of the data were analyzed in the manner similar to that described in the next subsection. The Fermi interactions were taken into account by introducing two independent parameters IV (interaction with 4~:) and IV” (interaction with 4~:). Indeed, satisfactory fit was obtained with a standard deviation of 6.7 MHz, but the determined anharmonic constants, lk48881= 0.522 f 0.002 cm-’ from IV and lk488sI= 0.429 ? 0.002 cm-’ from IV”, were inconsistent with each other. Since the latter is comparable to the value of 0.45 1 f 0.002 cm-’ obtained from the resonance between v4 and 3~:, it is the perturbation around kl = -6 that is not correctly treated by the present model. The obtained value of interaction constant which is larger than the expected one suggests that the perturbation is caused by cooperative interactions with 4~: and another energy level. (B) Analysis of the u4 + v8 - 4vg, (q + us)’ Fermi Interacting Band System We assumed that (v, + ys)2 (E) was the perturbing state, because it is expected to cross the u4 + v8 level around kl = -6. By considering the appearance of &, in Fig.
LASER STARK SPECTROSCOPY
415
OF CH?(?N
3, both 4~: and (v, + Y~)~levels must cross between kl = -5 and -6. The Fermi interaction between (vq + us)*’ and (v7 + Q,)+~is caused by effective Hamiltonian of the form k4,8sq.&,+q;+ + q,-&)/2. (13) In addition to the three direct Fermi couplings considered above, three other Fermi interactions between the perturbing states are also possible. Among them, the interaction between (Q + Q2 and 4vz2 was included in the analysis. The same type interaction between Y: and 3~: was studied by several workers (18-21). The corresponding part of the Hamiltonian is &&q,+q8+&
+ 47-48-4;+)/2.
(14)
The remaining two interactions, 4vt4 - 4uz2 and 4vg4 - (v, + Q)“, were neglected because both were higher order (A/ = ?6). The I-resonance interactions (Ak = AZ = t2) in the upper and lower states were also included in the analysis. This interaction is significant in the microwave spectra of the vg state (5) because of the small value of A - B - A{ (~0.35 cm-‘). An almost equal contribution is expected to the rotational energy levels of the v4 + Ig state. Other off-diagonal interactions in k were neglected, as in Ref. (16). The energies of the upper and lower levels were obtained by direct diagonalization of the energy matrices. The Hamiltonian is described as H=z&+H,+H,+Hs,
(15)
where Hr and HI denote the Fermi and f-resonance interactions, respectively. Because of the Stark term Hs, the energy matrix includes off-diagonal elements in J. The size of the submatrix which is diagonal in J is 2 X 2 in the lower state. The submatrix in the upper state is 8 X 8 in size, and represents the two Fermi-coupled level systems (4 X 4) coupled by the I-resonance interaction. Diagonal elements of unperturbed Hamiltonian are (II, 1, J, klH&,
1, J, k) = v. + BJ(J + 1) + (A - B)k2 - 2A{kl+ + sKk31 - DJJ2(J + 1)2 - D,,J(J
s_,J(J + 1)kf
+ l)k2 - DKk4,
(16)
where v is a given vibrational state. The matrix elements of the Fermi interaction terms are following:
(V4
(v4
+
v8,
f =
+11H,14 Vg, 1 = +2)
= 3”2k,888/2,
(17)
(v4
+
Y8,
1 =
+1IHFj4Y8, 1 = f4)
= 3”2k,888,
(18)
&3,
1 =
fllf&
= (1/2)“2k4788,
(19)
= (3/2)“2k,,,,.
(20)
+
(4&3, 1 = +21H&,
+
Y,3,
1 =
+2)
+ Vg, 1 = +2)
The Fermi interaction constants, W’ and W”, are expressed by the single parameter kd8@ as given by Eqs. ( 17) and ( 18) respectively. The matrix elements of /-resonance interactions are (u4 + v8, 1, J, kjH,Iu4 + v,3, 1 f 2, J, k ?I 2) = -(q,,/2)[J(J
+ 1) - k(k f 1)]1’2[J(J + 1) - (k * l)(k f 2)]“2,
(21)
416
MITO, SAKAI, AND KATAYAMA
(vg, I, J, k(H,(v8, If
2, J, k f 2)
= -(q8/2)[J(J + 1) - k(k f l)]“‘[J(J + 1) - (k f l)(k f 2)]1’2. (22) The matrix elements of the Stark term are the same as in the subband analysis. The energy matrix was truncated at J,,.,,, = J + 5 for J 3 3 or Jmax = 7 for J -c 3, and at Jmin = J - 7 for IKI or IMI < J - 7. The maximum size of the matrix was 104 X 104 because of the Stark term which was off diagonal in J. The constants in the v8 state, B, AS; DJ, DJK, ll~, and @ were constrained to the microwave values of Bauer et al. (16). The constants A and DK were taken from Masri et al. (22) and Duncan et al. (18), respectively. The value of qIKwas arbitrarily fixed to zero, because no data was obtained. The constants in the 4~s state, B, DJ, DJK, and qJ, were calculated from the microwave values (v8, 2~~) of Bauer et al. (16), and the other rotational constants were fixed to the v8 state values. The v7 + Yg constants, B, A, and A{ were calculated from the infrared values of Matsuura et al. (9). The constants DJ, DJK, and DK were fixed to the us values. Those of tJ and qIK were arbitrarily fixed to zero. The dipole moments of the perturbing states, 4~s and v7 + v8, were calculated from the relations
where cl0 = 3.9256 Debye was the ground state value (I). The coefficient of the vibrational dependence Ap7 was taken from the result of CH3C14N by Igarashi et al. (29), and Ap8 was determined in this analysis. The Fermi parameter k7,,, was fixed to the value of Igrashi et al. The l-type doubling constant q4* in the v4 + v8 state was not well determined (6.8( 19) X 10m4cm-‘), and was finally assumed to be equal to that in the v8state. The value of nKwas fixed to zero for the same reason. Consequently, the v8 State dipole moment, all Of the v4 + VSState Constants except qIKand &g, the 4~s and (v7 + vS)~band origins, and three Fermi interaction parameters were included as parameters in the fit. The observed resonances were equally weighted with unity. Because of the mutual Fermi interactions between three close-lying levels around kl = -6 of v4 + v8, two different sets of constants were obtained depending on whether the sign of the product, k4,,, - k4788- k7888, was positive (+) or negative (-). The standard deviations were 6.7 MHz for (+) and 6.6 MHz for (-). The molecular constants determined in the final fit are presented in Table I. The constants of v4 + v8are listed only for (-), because they agreed with those for (+) within experimental errors. A complete list of the data included in the fit, together with residues, is given in Table II. The zero-field transition frequencies of the v4 + vE - v8 band obtained by subtracting the Stark shifts from the laser frequencies are also given in Table III. DISCUSSION
Among the obtained parameters, only the band origin of 4~; - vg has different values beyond the experimental uncertainties depending on the sign of the product k 4888 - k4788- kTsE8.From the vibrational energy differences between 4~; and 4~;) the anharmonic constant &$8was calculated to be 5.49 cm-’ for (-) and 5.98 cm-’ for (+). Bauer et al. have analyzed the I-resonance effect between the 2~; and 2~: states
LASER STARK SPECTROSCOPY
417
OF CH3C15N
TABLE IA Molecular Constants of CH3C’5N (in cm-‘, except for dipole moments in Debye) 4 ‘.’
4Q2
*4,
4+“8
[
F,
II.;.47ti6h5(27ia
P
5.2.3929117(95)
[
5.247
A-
4.53974601761
[
4.60
1.33125)
[
1.304.10--’
'.4r,5,96,.10-6
I
1.734
‘.4orlDlll.1o-5
I
9.47’10-5
1.314114l~10-5
[
1.259,10-1
L’J T'JK GK
“J
‘IK
[ n.0
‘1
j
.10-’
Id
5.6?1f,,i0-4
le
errors 1”
units
in
parentheses of
the
are
last
lb.
[ ( .29837
10-6
ICI
3.856
1.44
1e
[
i.??R.lo-’
1e
[ ~.hi43.10_6
[ I .”
lP
I I’.0
standard
deviat:ons
figures. fixed
values.
moments
are
If
“’
, c5.6141.1’l-F/’
]P lg
j
9.47
-lC-L’
[ l.?:i.li,-c,
Id
[
il.”
1”
:I
Ill
, =>.6?16.lri-4
Id
91?
[
, _’
:?
[ ,.??R.:,l-:
If
1 ‘1.47.10-5
1’
times
h. Q”antlt>es I” square brackets are I-. AbscJlut‘, uncertainties for dipole
I 5.24: 1 4.60
Ih
I
1g
, ,,.?9RZnl~,-
Ih
j “.I> I d
[ 0.0
signlflcant
‘.8
lh
[ c ,268
f
le
I’!
2.5
I”
0.3010328
[ 0.0
[
3.91h3(13)c
I
a.
0.3010875,
1 I-
?+.‘*
j(/
?.Q”7’,I’I“
lC
d.
Arhltrarlly
e.
Ref.
1161.
flxed f.
Re=F.
1”
zc’ro. I?‘).
4.
RCf.
(Is,.
h.
R-f.
(0,.
_
0.1%.
by microwave spectroscopy and have obtained ggg = 5.62 cm-’ (16) which is close to the value for (-). The small discrepancy may be attributed to the fact that the 08 dependences of A and A{ have been neglected in both analyses, but the discrepancy between (+) and microwave values seems to be too large. The product of the anharmonic potential constants is therefore concluded to have the negative sign. The unperturbed sublevel energies (J = 0) of the uq + vg, hi, 4vi, and (q + Vg)z TABLE IB
4+“8
-
4 ,‘84 48
.’
-‘R
, 7+‘.‘81 2-
a.
j-1
91h.748Rn(lll
,8
“8
and
h
/+,
k4888.k4;RR-k7888,
!~,6:?4RRZ(*:~~
11411.6’6(32l
114O.hI4li2)
:0:4,7:i2ii
lfl6R.HI141)
104i.!1,14,
1II44.i(1~I
denote
the
r,gns
see
tvxt.
‘uf
th+
i’rodurt,
418
MITO, SAKAI, AND KATAYAMA TABLE II Stark Resonances of the v4 + v8 - vg Band of CH,C”N Transitiona
M' + M" E(V/cn)
P(42)=922.91429C QR-5110) -9 QR+5(10) -8 -5 QR-6(10) 10 9 QR+6(10) 8
QP+6(
P(44)=920.82912 QR+2( 6) 6 QR-3( 61 6 5 QR+3( 6) 5 4 QR-41 6) 7 6 QR+4( 6) 6 5 12 QR-51 6) 5 4 OR+51 6) 3 QR+6( 6) 6 4 QR+7l 7) -7
2122 6446 7710 7000 8751 19685 9123 10884 10866 15916 19548 23088 15585 22383 20960
1.8 -4.5 -1.2 1.8 -0.3 -5.4 -0.9 1.2 -7.2 10.8 -0.3 -5.1 3.9 -9.3 -2.4
P(50)=914.41928 QP-3( 4) -3 -2 QP*3( 4) -3 -2
7015 11656 6894 11399
11.1 4.2 11.4 13.8
P(52)=912.23070 QP-41 7) 5 4 6 QP+4( 7) 5 4 2 6 QP-5( 7) 5 4 2 4 3 2 5 QP+5( 7) 4 3 4 2 6 5 QP-6( 7) 4 2 2
20919 25801 17998 21387 15481 21507 9156 10908 13458 24491 7859 9115 10873 11838 14672 19023 8562 11814 19867 6133 7588 14022 6118
-12.9 10.2 1.5 3.6 -12.9 9.0 -11.4 -9.3 -6.3 10.2 -0.3 -3.3 3.3 -20.4 3.6 14.1 2.4 1.5 -0.6 -12.6 -11.1 -12.3 0.3
~~-5~10)
3 1
3 2 1
3 1 7
1
means AK = 0,
b.
0 - C is laser frequency Laser
d.
l
frequency
7)
M”
6 5 3 2 5 4 3
-----
co2
E(V/cm)
0-C(MHz)
4 3 2
3411 4079 6641 9585 2574 2933 3413
Laser Hot Band -----
1681 2571
0.6 0.6
P(14)=915.62774 0 QP O( 2)
9632
5.7
P(16J.913.88037 QP-2( 5) -4 QP+2( 5) -4 QP-3( 5) -4 -3 QP+3( 5) -4 -3 QP-4( 5) -3
26571 26285 16778 22941 16538 22621 20830
-8.7 -13.8 -8.4 -9.9 6.9 3.9 10.8
P(17)=913.11803 QP-3( 6) -4 -2 QP+3( 6) -4 -2 QP-4( 6) -5 -3 -2 -5 -6 QP+4( 6) -5 -3 -2 -3 -2 -2 -1 -5 -6 0 1 QP-5( 6) -5 -6 QP+S( 6) -4 -3 -5 -6
7561 15557 7241 14917 8110 14001 23067 16240 7825 13498 22131 7194 8873 15642 16992 20470 12474 17634 19240
5.7 -3.6 11.7 0.0 7.8 12.9 -1.2 -4.2 5.7 9.0 -2.4 -3.6 -2.7 -1.5 -3.9 -0.3 10.5 3.0 -0.6
P(20)=910.31020 9 QP+7(10) 8 7 6 5 QP-8(10) -4
2649 2980 3408 3979 4755 12902
-1.8 -1.5 -0.3 0.9 -0.3 4.2
18091 22403 25513
15.9 2.4 7.8
P(21)=909.57909 QP*7(11) 10 8
minus calculated
M COmpOnentS:
-8.7 -7.8 -9.3 -6.9 -1.2 -2.7 -2.7
P(12)=917.35000 0 QR 01 0) *1 0
transition
in cm-l.
unresolved
+
AJ = +I, ~2 = -5, and 3" = 10.
c.
denotes
M’
co2 Laser
7607 2.7 12434 -0.6 19895 -4.5 77q ._ ld 15.9 4530 0.9 5096 a..3 5822 0.0 -9.0 18318 -8.1 20539 -12.6 23396
9 8 7
a.
Transition
Laser
co2
QR+7(10)
O-C(MHzIh
see Ref.
(1).
frequency.
LASER STARK
SPECTROSCOPY
419
OF CHf_“N
TABLE II-Continued Transition co2
QP-8 Ill)
M' + M" E(V/cm)
0-C(MHz)
Transition
QR+J(
6421 8045 9145 11909 21911 2797 3100 3493 4604
0.6 8.4 3.6 -0.3 4.2 -14.4 -12.0 -12.6 -1.5
P(22)=908.48736 7 QP-6(13) 9 QP+6(13) -12 QP-7(13) -11 -10 -9 -8 -4 -12 QP+7(131 -11 -9 -8
28474 14443 4315 4646 5153 5713 6415 12834 7712 8436 10302 11671
14.7 12.6 -9.0 -0.3 -5.4 -3.9 -2.4 2.1 0.9 -2.1 0.3 -7.2
--- CO2 Laser Sequence
Band ---
11)
QP+9
11)
P(41)=921.87024 -7 Q&3( 8) -6 QR+31
8)
QR+4(
8)
QR-5(
8)
QR+5(
8)
1,' -5 -3 7 6 5 4
P(43)=919.81854 4 QR-2( 4) 3 4 QR+2( 4) 3 4 QR-3( 4) 3 2 4 QR+3( 4) 3 2 3 QR-4 4) QR+4 4 4i 3 2
---__-
R(10)=921.67529 QR-71 8) -8
8)
4 3 2
1515 2000 2951
-2.4 -0.6
P( 4)=910.27796 QP-6(10) 8 QP+6110) 8 6 QP-7(10) 7 6 5 QPt7(10) 9 0 7 5 4 QP-8110) -7 -6 -5 -4 QP+3(101 -6
25460 21716 28568 10864 12647 15114 6460 7246 8260 11491 14210 2911 3395 4039 5053 25951
-2.4 a.7 1.8 -5.4 -0.6 6.0 0.6 -1.8 -2.7 1.2 -0.3 0.9 2.1 9.3 11.7 -8.1
14875 18695 20265 7057 7794 8610
16.2 -5.4 -6.9 7.5 4.5 9.9
P( 8)=907.05284 QP-8(15) QP+8(15) QPtP(15)
15857 18425 23946 3996 4812 8038 8551 9945 8974 11161
-3.6 -4.2 0.3 -3.9 -2.4 -2.4 4.2 5.7 -10.5 -10.5
16278 21367 16017 21003 14143 18198 25218 13858 17835 24775 17414 13355 17005 22980
-0.6 -7.2 10.5 11.4 -10.8 4.2 -6.0 -3.6 13.5 -3.3 3.9 0.3 4.8 -0.3
13C02 Laser ------
R( 8)=920.21948 -5 OR-2( 5) -3 QR+2( 5) -2 5 QR+3( 51 4 3 QR-4( 5) 2 3 QR+4( 5) 2 3 QR-5( 51 4 QR+5( 51 3
3323 6241 9272 928 1190 7765 11175 6988 10167 12751 8843 11449
340 *
0-C(MHz)
13c02 Laser
Laser Hot Band 10 8 7 -9 -5 -10 -9 -8 -6
QP+8
M' + M" E(V/cm)
-0.6 1.8 5.1 5.7 -1.2 -0.6 8.7 0.9 -3.3 0.3 0.3 4.2
3.6
__-_-
10 8 -12 -11 -10 -9
-3.9
13 C 1802 Laser -----
P(10)=921.40060 7 QR-2( 7) 7 QR+2( J) 7 QR-3( 7) 6 5 6 QR+3( 7) 5 7 QR+4( J) 6
9191 11000 8267 9927 11342 13236
-6.6 -5.1 -12.0 -5.4 -1.5 -3.9 -4.5 0.6 -6.6
P(20)=913.64451 4 QP-3( 5) 2 4 QP+3( 5) 2 QP-4( 5) -2 QP+4( 5) -4
2161 4224 2349 4583 1899 717
-4.5 -7.8 5.1 1.2 0.6 4.8
P(24)=910.38402 QP-5110) 9 8 7 6 7 QP+5(10) 6 QP+6(10) 8 7 QP-7(10) -9 -8 QP+7(10) -8 -7
15709 17653 20140 23458 22033 25624 5543 6397 4001 4547 6851 7888
0.9 2.1 3.6 9.0 5.1 6.9 -6.9 4.8 3.3 -6.0 0.9 -7.2
--_-_
N20
P(191.922.42221 QR+4( 91 -6 OR-51 91 5 9 QR+Si 91 8
2931 * 2122 * 7916
Laser
__---
10698 11786 4190 4644
-6.0 1.8 -3.9 7.2
420
MITO,
SAKAI,
AND
KATAYAMA
TABLE II-Continued Transition
M' + M" E(V/cm)
9) 9)
19296 5651 6606 8031 10136 7501 8705
P(21)=920.62242 QR-4( 6) -6 -5 -4 QR+4( 6) -6 -5 -4 QR-5( 6) -6 -5 -3 QR+5( 6) -6 -4 -3 P(22)=919.71754 QR-2( 41 4 QR+2( 41 4 3 2 QR-3( 4) 4 3 2 QR+3l 4) 4 QR-4( 4) 2 0
4)
1
2 0
1
M' + M" E(V/cm)
0-C(MHz)
N20 Laser 5341 17333
7 7
P(20)=921.52398 QR+7( 8) -6 QR-8( 8) -7 -6 -5 -4 QR+B( 8) 7 6
QR+4(
Ikansition
Laser
N20
QR+5( QR+6(
0-C(MHz)
1.8 -2.7
7.8 6.6 3.3 14.1 3.9 4.2 5.1
12584 15233 19257 13277 16072 20334 4231 5088 8655 5384 8138 11181
-0.9 9.3 11.1 -8.4 1.5 4.5 -5.7 -7.8 -11.1 -5.7 -16.8 0.9
6289 6005 8009 11906 6790 8887 12806 6517 14233 9805 13667 9403
2.1 11.1 5.1 6.0 -2.1 4.8 -1.2 -3.9 -4.5 -4.8 0.6 0.9
12548 19067 9012 13168 5468 6863 7308 9679 14188 4241 7378 1972 3294 952 1220 8083 7710 8585 19912 11090
5.1 9.3 3.0 1.8 -8.7 -0.9 -5.4 -0.6 5.7 -1.5 -4.5 0.9 4.5 8.1 1.5 -1.8 -1.2 6.9 -3.3 0.3
17880 21771 13554 16065 19603
4.5 1.8 -1.2 3.6 0.3
11452 12940 14733 13618 15551 18152 21765 2177 2844 4367 603 * 6430 7330 8550 9226
-6.6 1.2 -5.1 -0.3 -1.5 0.0 -0.6 -2.1 1.5 -1.8 2.4
P(33)=909.54543 9 QP+7(11) 9 QP-8(11) fi QP+B(ll) -10 -9 -8 -10 -11 QP-9(11) -4
25200 11779 17434 6507 7233 8150 12808 5303
11.4 9.3 6.3 -3.0 -1.8 -1.8 4.8 -2.4
P(34)=908.60088 QP-4(13) 12 9 QP+4(13) 10
18988 25430 23913
4.2 6.9 4.5
P(35)=907.65304 QP-B(14) 12 10 QP+8114) -11 -10 -9
17829 21380 10080 11128 12308
-12.3 -8.4 -1.8 -5.7 1.2
QP+3(
7)
QP-4(
7)
QP+4(
7)
QP-5(
7)
QP+5(
7)
QP-6(
7)
QP+6(
7)
12306 12509
-0.3 5.7
P(241=917.89783 0 QR O( 1) 0
6076 20334
-14.4 -2.7
P(26)=916.06488 0 QP O( 1) 0 fl
4811 7700
-13.2 -0.6
P(28)=914.21869 QP-3( 4) 3 2 1 10 -1 -2 QP+3( 4) 3 2 1 10 -1 -2
3153 4598 8064 3694 12243 3306 4792 8354 3837 12591
-12.3 -7.5 -8.7 -6.6 -4.2 9.9 5.1 -0.3 -0.6 1.8
P(30)=912.35929 QP-3( 7) 4 10 6 7 QP+3( 7) 6 5 4
17875 18559 23264 12267 14712 18320
1.5 -5.4 -3.6 5.1 10.2 11.7
2 3 2
2 10
1 4 3 2
4 3 10 -5 -3 -5 -4 -3 -6 -7 -4 -2 -6 -7
P(31)=911.42463 QP-7( 8) 5 4 QP+7( '3) 6 5 4 P(32)=910 QP-4(10
QP+4(10
QP-5(10)
QP+5(10) QP-6(10)
P(23)=918.80935 QR-3( 3) -3 QR+3( 3) -3
3 10
48668 9 8 7 B 7 6 5 -4 -3 -2 9 -8 -7
-a QP+6(10)
-9
P(37)=905.74748 QP+9(17) -16 -16 -15
1149 * 738 l
-0.9
3.6 6.3 5.7
1.2 7.2
LASER STARK SPECTROSCOPY
OF CH#?N
TABLE 111 Zero-Field Transition Frequencies for the v4 + v8 - us Band of CH#.?N
Transitiona QR+7(101 QR-6(10) QR+6(10) OR-5(10) QR+S(lOl QR+6( 91 QR-5( 9) QR+5( 91 QR+4( 9) QR-8( 81 QR+8( 81 QR-7( 8) QR+7( 81 QR*7( 8) QR-5( 81 QR+i( 81 QR+4( 8) QR-31 8) QR+3( 8) QR+7( 7) QR+4( 71 QR-31 7) QR+3( 71 QR-2( 7) QR+2( 71 QR+6( 61 QR-5( 61 OR-St 61 QR+S( 61 QR+S( 61 QR-41 6) QR-4( 6) QR+4( 6) QR+4i 6) QR-3( 6) QR+3( 6) QR+2( 6) QR-5( 5) QR+5( 5) QR-4( 5) QR+4( 51 QR+3( 5) QR+Zl 5) QR-2( 51 QR-41 4) QR-41 4) OR+41 4) QR+4( 4) QR-3( 4) OR-3( 4) QR+3( 4) OR+31 4) QR-21 4) QR-2( 4) QR+2( 41
a.
v, (cm-l) 922.79972 922.90970
922.89015 922.94758 922.96235 922.32520 922.38301 922.39752 922.45537 921.58112 921.44799 921.67873 921.66766 921.66800 921.81564 921.82922 921.88747 921.92741 921.93231 921.09712 921.31655 921.35662 921.36117 921.38980 921.39282 920.61317 920.67187 920.67143 920.68487 920.68479 920.73631 920.73671 920.7427s 920.74280 920.78309 920.78743 920.81909 920.09543 920.10849 920.16020 920.16606 920.21069 920.24230 920.23959 919.58087 919.58058 919.58653 919.58650 919.62703 919.62718 919.63099 919.63079 919.65991 919.66011 919.66281
Laser(cm-l)d Shlft(MHzlb 0-C(MHz)' C P42 922.91429 -9.9 3434.6 922.91429 137.7 15.6 922.91429 0.4 723.8 922.91429 -998.1 3.0 -2.6 922.91429 -1440.7 -2.8 N P19 922.42221 2908.1 2.0 922.42221 1175.1 922.42221 740.1 1.7 922.42221 -994.0 -6.1 6.9 N P20 921.52398 -1713.0 4.7 921.52398 2278.0 C' RlO 921.67529 3.5 -103.1 -2.3 921.67529 228.6 N P20 921.52398 7.7 -4317.5 5.2 CS P41 921.87024 1636.9 921.87024 1229.8 -10.6 -2.9 921.87024 -516.5 -3.8 921.87024 -1714.0 921.87024 -1860.9 0.4 -2.3 c P44 920.82912 -8034.4 -3.0 C" PlO 921.40060 2519.7 -6.2 1318.6 921.40060 -4.2 921.40060 1182.2 -6.5 921.40060 323.8 -5.1 921.40060 233.3 -2.8 C P44 920.82912 6474.0 920.82912 4714.1 5.4 -1469.2 -8.0 N P21 920.62242 -5.0 4324.5 C P44 920.82912 -7.3 -1869.9 N P21 920.62242 -5.4 2782.5 C P44 920.82912 6.6 -3426.3 N P21 920.62242 -2.3 2589.3 C P44 920.82912 -0.7 -3609.0 N P21 920.62242 1379.9 -2.9 c P44 920.82912 0.7 C P44 920.82912 1249.7 1.8 300.6 920.82912 0.4 3718.8 C' R8 920.21948 3327.5 2.3 920.21948 4.0 920.21948 1777.1 -1.3 1601.5 920.21948 2.4 920.21948 263.5 3.4 -684.1 920.21948 -602.9 -0.5 920.21948 4.0 CS P43 919.81854 7125.2 -4.6 4105.9 N P22 919.71754 1.7 CS P43 919.81854 6955.4 3928.4 0.7 N P22 919.71754 -4.1 5741.3 CS P43 919.81854 2708.9 0.4 N P22 919.71754 2.2 CS P43 919.81854 5622.5 -3.8 2600.6 N P22 919.71754 -3.9 4755.7 CS P43 919.81854 2.1 N P22 919.71754 1721.8 10.9 CS P43 919.81854 4668.7
QR+7(10) means AK = 0, AJ = +l, KZ = +l. and J" = 10.
b. The average of the Stark shifts of the M-components. c. 0 - C 1s ", minus the calculated zero-field frequency by using the constants in Table I. d. C, CH, and CS denote CO2 laser regular, hot, and sequence band, respectively. laser.
C' and C" denote 13C02 and 13C1802
N denotes N20 laser.
P42 is the P(421 laser 11ne.
421
422
MITO,
SAKAI,
AND
KATAYAMA
TABLE III-Continued Transition QR+2( 4) QR-3( 3) QR+3( 3) QR 0( 1) QR O( 0) QP O( 1) QP 0( 2) QP-3( 4) QP-31 4) QP+3( 4) QP+3( 4) QP-21 5) QP+21 5) QP-31 5) QP-3( 5) QP+31 5) QP+3( 5) QP-4( 5) QP-4( 5) QP+4( 5) QP-3( 6) QP+3( 6) QP-4( 61 QP+4( 61 QP-5( 6) QP+5( 61 QP-3( 7) QP+3( 7) QP-4( 7) QP-4( 7) QP+4( 71 QP+4( 7) QP-5( 7) QP-5( 7) QP+5( 71 QP+S( 7) QP-6( 71 QP-6( 7) QP+6( 71 QP+6( 7) QP-7( 8) QP+7( 8) QP-4(10) QP+4(10) QP-5(10) QP-5(10) QP+5(10) QP+5llO) QP-6110) QP-6(10) QP+6110) QP+6(10) QP+6llo) QP-7(10) QP-7(10) QP+7(10) QP+7(10) QP*7(10) QP-8(10) QP-8(10) QP+B(lO) QP+7(11) QP+7(11) QP-8(11) QP-8111) QP+8(111 QP+8(11) QP-9(111 QP+9(11) QP-4(13)
v, lcn~-~) 919.66269
919.04479 919.04853 917.93016 917.33921 916.14782 915.54837 914.28200 914.28148 914.28447 914.28416 913.70516 913.70632 913.67310 913.67320 913.67578 913.67571 913.62839 913.62805 913.63189 913.06223 913.06448 913.01702 913.02046 912.95377 912.96387 912.44804 912.45038 912.40285 912.40284 912.40629 912.40634 912.33997 912.33980 912.34981 912.34965 912.30382 912.30357 912.27935 912.27912 911.59209 911.57480 910.54351 910.54672 910.48090 910.48105 910.49032 910.49045 910.44563 910.44546 910.42032 910.42010 910.42032 910.35008 910.35013 910.33257 910.33266 910.33266 910.25623 910.25628 910.11528 909.70762 909.70771 909.63104 909.63116 909.49337 909.49328 909.52639 909.55386 908.65868
Shift(MHz) 0-ClMHzl 1644.3 -7058.2 -7170.5 -969.3 323.4 -2486.6 2379.5 4115.6 -1882.4 4041.4 -1962.8 5252.8 5218.0 6213.8 -860.1 6133.3 -935.2 7554.2 493.6 378.4 1672.8 1605.4 3028.1 2925.0 4924.5 4621.7 -2660.5 -2730.8 -1305.9 -5160.7 -1408.9 -5265.5 579.2 -3270.6 284.2 -3566.2 1663.0 -2184.6 2396.5 -1451.6 -5020.4 -4502.0 -1703.8 -1800.0 173.4 -2909.0 -109.3 -3190.6 1230.6 -5021.4 1989.3 -1081.7 -4267.7 1017.6 -2163.5 1542.3 -673.4 -1640.0 1618.1 649.8 4877.0 -3853.3 -4865.1 -1557.4 -2570.2 2569.9 1563.4 570.9 756.5 -1732.7
7.4 -0.3 5.8 -8.5 0.6 -6.9 5.8 7.7 -7.8 12.5 3.2 -8.8 -13.7 -9.1 -6.1 5.4 3.1 10.9 0.6 4.8 1.1 5.8 3.8 0.1 -0.1 4.4 -2.4 8.3 -1.2 -1.4 -1.2 0.3 2.9 -2.3 4.7 0.1 -1.8 -9.3 1.4 -5.6 3.0 0.9 -3.3 -0.5 -0.7 4.1 2.3 6.0 2.7 -2.6 5.6 -1.1 5.4 -1.5 -0.0 -3.2 -0.6 -0.6 4.2 6.0 -8.2 8.7 11.5 4.2 7.9 2.0 -0.5 -2.4 -10.1 5.7
Laser(cm-1) N N N CH N CH c N c N CH C" CH C" CH C" CH
N C N C N C N C N C N C N N C" N C" N C' N C" C' C" C' C" CH C' CH C' CH N CH N CH N CH N
P22 919.71754 P23 918.80935 918.80935 P24 917.89783 P12 917.35000 P26 916.06488 Pl4 915.62774 P50 914.41928 P28 914.21869 P50 914.41928 P28 914.21869 P16 913.88037 913.88037 913.88037 P20 913.64451 P16 913.88037 P20 913.64451 P16 913.88037 P20 913.64451 913.64451 P17 913.11803 913.11803 913.11803 913.11803 913.11803 913.11803 P30 912.35929 912.35929 912.35929 P52 912.23070 P30 912.35929 P52 912.23070 P30 912.35929 P52 912.23070 P30 912.35929 P52 912.23070 P30 912.35929 P52 912.23070 P30 912.35929 P52 912.23070 P31 911.42463 911.42463 P32 910.48668 910.48668 910.48668 P24 910.38402 P32 910.48668 P24 910.38402 P32 910.48668 P4 910.27796 P32 910.48668 P24 910.38402 P4 910.27796 P24 910.38402 P4 910.27796 P24 910.38402 P20 910.31020 P4 910.27796 P20 910.31020 P4 910.27796 910.27796 P21 909.57909 P33 909.54543 P21 909.57909 P33 909.54543 P21 909.57909 P33 909.54543 909.54543 P21 909.57909 P34 908.60088
states calculated from the constants (-) are plotted against k in Fig. 5, showing the level crossings between the v4 + v8 and perturbing states. The appearance of energy levels for (+) is almost similar to Fig. 5, except that 4~; is shifted lower by 5.8 cm-‘.
LASER STARK SPECTROSCOPY
423
OF CH3C15N
TABLE III-Continued Transltlon
QPi4113) QP-6113) QP+6(13) QP-7(13) VP+71131 UP-8(141 QP+8l141 QP-8(15) QP+8(151 QP19115) ap+91171
“,
(cm-l)
Shlft(MHzl 0-C(MHz)
908.66150 908.56189 908.53'555 908.46550 908.44794 907.73755 907.61004 907.10071 906.97657 907.02513 905.74305
-1817.2 -2234.4 -1444.8 655.5 1181.8 -2533.5 1289.3 -1435.2 2286.6 830.7 132.7
4.5 14.3 12.1 -3.2 -2.0 -10.4 -2.1 -1O.R -6.8 7.4 4.1
Laserlcm-1) 908.60088 CH P22 908.48736 908.48736 908.48736 908.48736 N P35 907.65304 907.65304 c ' PB 907.05284 907.05284 907.05284 N P37 905.74748
Although two perturbing states cross the (vq + v$’ state between k = i5 and ~6 in both cases, the relative positions of 4~:~ and (v, + @* are different. The crossing of 4~8”~and (u7 + @* is expected between k = ~6 and T7 for (-), as shown in Fig. 5, whereas it is predicted between k = T5 and ~6 for (+). Because of the Fermi interaction between them, (v, + i+J2must be perturbed in different manners depending on the choice of the signs. Further evidence of the sign may, therefore, be obtained by studying the (v7 + v~)~combination band or (y7 + Q)* - VAhot band with high resolution. As discussed before, the observed splitting of kf doublet for K < 4 is almost linearly dependent on K and, if unperturbed, is expressed by the first term of Eq. (1). From the determined constants Ar and Ar, the magnitude of the splitting is estimated to be 30K MHz, which agrees with the observed value of 25K MHz. This means that the effect of the Fermi interactions on the splitting is small for K i 4. Though the strong Fermi resonance between (v7 + vs)’ and vg has been observed (7-9), it is neglected in the present study. This contribution is effectively absorbed - vs. in the determined anharmonic constant k 4788and the band origin (v7 + ZG&* From Table I, the values of 4 and a: are calculated to be 0.007709( 10) and 0.001437(3) cm-‘, respectively. These values are in satisfactory agreement with those determined from the fundamental band; 4 = 0.006997(4) and cy? = 0.001443(l) cm-’ (1). The decrease of the dipole moment is 0.46% from ground state to v8, and 0.48% from u4 to v4 + Yg. These values are in good agreement, and their decreases against 2)sshow parallel nature. Messer and Roberts have observed a similar decrease
13001200 ”
”
”
”
I’
-10-9-6-7-6-5-4-3-2-l
”
”
”
”
’ ”
0 1 2 3 4 5 6 7 6 910
fk
FIG. 5. Unperturbed energy levels of the u4 + us, 4ui, 44, and (Y, + Y# states for J = 0.
plotted
againstk
MITO,
424
SAKAI,
AND
KATAYAMA
using the Stark effect on the (.I, K) = (2, 0) - ( 1, 0) pure rotational transitions (6), but the present values are more precise. ACKNOWLEDGMENTS This work was supported in part by a grant in aid for Scientific Research from the Ministry of Education. Calculations in the present work were carried out at the Computer Centre, University of Tokyo. RECEIVED:
January 26, 1984 REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. II. 12. 13. 14. IS. 16. 17. 18.
A. MITO, J. SAKAI, AND M. KATAYAMA, J. Mol. Spectrosc. 103, 26-40 (1984). F. W. PARKERAND A. H. NIELSEN,J. Mol. Spectrosc. 1, 107-123 (1957). 1. NAKAGAWA AND T. SHIMANOUCHI,Spectrochim. Acta 18, 5 13-539 (1962). J. SAKAI, 1. IGARASHI,AND M. KATAYAMA, 45th Annual Meeting of the Chemical Society of Japan, 1982. A. BAUER AND S. MAES, J. Phys. (Paris) 30, 169-180 (1969). J. K. ME~SERAND J. A. ROBERTS,J. Mol. Spectrosc. 96, 351-352 (1982). J. L. DUNCAN, D. ELLIS, AND I. J. WRIGHT, Mol. Phys. 20, 673-685 (1971). H. MATSUURA, Bull. Chem. Sot. Japan 44, 2379-2381 (1971). H. MATSUURA, N. KUBOTA, AND H. MURATA, Chem. Lett. 1509-1512 (1982). C. FREED,L. C. BRADLEY,AND R.G. O’DONNELL, IEEE J. Quantum Electron. 16, 1195-1206 (1980). B. G. WHITFORD, K. J. SIEMSEN,AND J. REID, Opt. Commun. 22, 261-264 (1977). J.-P. MONCHALIN,M. J. KELLY, J. E. THOMAS, N. A. KURNIT, AND A. JAVAN, J. Mol. Spectrosc. 64, 491-494 (1977). K. J. SIEMSENAND B. G. WHITFORD, Opt. Commun. 22, 11-16 (1977). B. G. WHITFORD, K. J. SIEMSEN,H. D. RICCIUS,AND R. G. HANES, Opt. Commun. 14,70-74 (1975). S. M. FREUND, G. DUXBURY, M. R~MHELD, J. T. TIEDJE,AND T. OKA, J. Mol. Spectrosc. 52, 3857 (1974). A. BAUER, G. TARRAGO, AND A. REMY, J. Mol. Spectrosc. 58, 111-124 (1975). T. OKA, J. Chem. Phys. 47, 5410-5426 (1967). J. L. DUNCAN, D. C. MCKEAN, F. TULLINI,G. D. NIVELLINI,AND J. PEREZ PERA, J. Mol. Spectrosc.
69, 123-140 (1978). 19. I. IGARASHI,J. SAKAI, H. FLJJIMA,AND M. KATAYAMA, Symposium on Molecular Structure, Kyoto, October I98 1. 20. S. A. RACKLEY, R. J. BUTCHER,M. RUMHELD, S. M. FREUND, AND T. OKA, J. Mol. Spectrosc. 92, 203-217 (1982). 21. Y. MORI, T. NAKAGAWA, AND K. KUCHITSU,to be published, 22. F. N. MASRI, J. L. DUNCAN, AND G. K. SPEIRS,J. Mol. Spectrosc. 47, 163-178 (1973).