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Laser Stark spectroscopy of the ν4 band of CH3C15N: Fermi resonance with 3ν83
JOURNAL OF MOLECULAR SPECTROSCOPY
103,26-40 (1984)
Laser Stark Spectroscopy of the u4 Band of CH3C15N: Fermi Resonance with 3~; AK~HIRO MITO, JUN SAKAI, AND MIKIO KATAYAMA Department of Pure and Applied Sciences, College of General Education. University of Tokyo, Komaba, Meguro-ku, Tokyo 153. Japan
Laser Stark spectra for the v4 band of CH$?N have been measured by using CO2 and N20 lasers. AImost 650 resonances have been assigned to about 140 ro-vibrational transitions with S =Z34 and K =Z 11.An anomaly of the rotational structure around K = 7 has been proved to be due to a Fermi interaction by analyzing each K subband separately. Observed data have been fitted to a model which includes LQ-~Y~Fermi coupling by the method of least squares. The standard deviation of observed from calculated frequencies is 4.6 MHz. Molecular constants derived are also listed. INTRODUCTION
Acetonitrile and its isotopic species have been extensively studied by using a variety of spectroscopic techniques. The ground-state microwave spectrum of CHjC”N has been investigated by Bauer et al. (1, 2). The spectrum has recently been remeasured accurately by Demaison et al. (3) and highly precise rotational constants are determined. Microwave spectra have also been analyzed for the vg (2) and 2~~ (4, 5) excited vibrational states. These rotational transitions in the u8 = 0, 1, and 2 states have been reanalyzed by Careless and Kroto (6) and by Bauer et al. (7), and the vibrational dependence of the rotational constants has been obtained. As for the v4 state, the microwave spectrum with K < 6 has been analyzed by Bauer and Godon (8). The infrared spectrum of the v4 band has been measured with moderate resolution by Duncan et al. (9), and the band origin has been determined from the Q-branch maximum. No rotational analyses, however, have been reported for this band. Recently, the v4 band of CHjC14N has been studied by Rackley et al. (10) and Igarashi et al. (11) by means of laser Stark spectroscopy. Rackley et al. analyzed the spectra with K < 7 and fitted them to a model which includes v4-v7 Coriolis coupling. Igarashi et al. analyzed the spectra with K < 10 and attributed the perturbation around K = 7 lines to the Fermi interaction between u4 and 3~;. The assignment of the spectrum with K = 7 by Rackley et al. is also different from that by Igarashi el al. It is necessary to examine the v4band of various isotopic species in order to determine the major perturbation in the v4 band of acetonitrile. Duncan et al. (9) have discussed the possibility of Fermi resonance between v4 and 3~; by studying the fundamental vibration frequency displacements on isotopic substitution. They estimated the absolute value of the interaction matrix elements 1W4gg3 to be 25 cm-‘. Igarashi et al. (II), however, determined lW4,,,l = 0.38 cm-‘. Since the discussion by Duncan et al. was based on the small amounts of discrepancies 0022-2852184 $3.00 Copyright Q 1984 by Academic Press, Inc. All nghts of reproduci,on I” any form resewed.
26
LASER
STARK
SPECTROSCOPY
OF CH3C’5N
27
between the calculated and observed isotopic shifts (0.2-0.4 cm-‘), it is considered desirable to determine the band origins of various isotopic species with higher resolution. In this study, laser Stark spectroscopy .was applied to the v4 band of CH3C”N. Before the analysis of the whole band, each K subband was analyzed separately. This subband analysis was very useful for clarifying the effects of perturbations involved. EXPERIMENTAL
DETAILS
The sample of CH,C15N was obtained from Merck Sharp & Dohme of Canada. The isotopic purity ensured was 95% or greater. The sample was used without further purification. Laser Stark spectra of the v4band were measured using a flowing gas laser, operated on “CO2 regular band P(40) to P(60), Ol’l-[ 11’0, 03’01 hot band P( 11) to P(34), 00°2-[ 10’1, 02’11 sequence band P(4 1) to P(49), and N20 P( 12) to P(40) around 10.6 pm. We also observed the spectra using a sealed gas laser operating on i3C02 R(2) to R(22), P(4) to P( 16) and ‘3C’802 P( 12) to P(34) around 10.6 pm. The regular band frequencies of COZ, 13C02, and ‘3C’802 lasers were taken from the recent measurements of Freed et al. (12). The frequencies of CO2 hot band were taken from Whitford et al. (13) and Monchalin et al. (14). Its frequencies of sequence band were taken from Siemsen et al. (15). The frequencies of N20 laser were taken from Whitford et al. (16). Gas pressures of the sample in an absorption cell were typically about a few milliTorr, and the measurements were made at room temperature. The Stark field of up to 28 kV/cm was used in this study. The amplitude of Stark moduration was about 100 V/cm for most of the measurements. The electric field strength was calibrated by using the Stark effect of CH3F (I 7). The accuracy of the voltage measurement was about 0. l%, and the resonances, whose Stark shifts were larger than 10 GHz, were omitted from the analysis. Most of spectra were observed in the parallel polarization, resulting in the selection rule AA4 = 0. Several spectra for low J transitions were observed in the perpendicular polarization corresponding to the AM = + 1 selection rule. A representative spectrum with I( = 7 is shown in Fig. 1. ANALYSIS
(A) Subband Analysis In the course of the assignment of the spectrum, an anomaly was found around K = 7 lines. Presumably, an interaction with another energy level nearby may produce the irregular spectrum. In order to know the nature of the perturbations involved, we made the analysis of each K subband before the interpretation of the whole band. The subband origin z&, and the effective rotational constant B& of the v4 state were determined by the least squares method, and their dependences on K were used as a criterion of perturbations (18). Each Stark shifted transition frequency was calculated by setting up and diagonalizing the upper- and lower-state Hamiltonians, and was fitted to each laser frequency. The Hamiltonian for the present system is described as H=H,+H,,
(1)
28
MITO, SAKAI, AND KATAYAMA C H3C15N Vbband
FIG. 1. Laser Stark spectrum of v4 band of CH$?N taken with the CO2 hot band P(25) laser line near 906 cm-‘. AM = 0 transitions of QP6(9), aP,(9), and QPs(9) are observed.
H,, denotes the unperturbed Hamiltonian of the symmetric top, and its nonvanishing matrix elements are (~4, J, KtHobt, J, K) = z&, + B&J’(J’ + 1) - (D;)effJ’z(J’ + 1)’ - (D;&J’(J’ (G.S., J, KIH,IG.S.,
+ l)K’,
(2)
J, K) = B”J”(J” + 1) - D[;J”2(J” + 1)2 - DL;,J”(J” + 1)K2
+ H;J”3(J” + 1)3 + Hl;KJ”2(J” + 1)2K2 + HbJ”(J”
+ 1)K4,
(3)
where J-independent terms are absorbed in I&, . The matrix elements of Hs, the Stark term, are expressed as (u, J, K MHsb, J, 4 M) = -PL,EKMI[J(J + (0, J, K Mffsb,
l)l,
(4)
J - 1, K M) = (pVE/J)[(J2
- K2)(J2 - M2)/(2J
- 1)(2J + 1)]“2,
(5)
where E is the electric field strength and pclvis the dipole moment in the given state v. The constants in the ground state, B”, DI;, DI;K, H;, HI;K, and Hb, were constrained to the microwave values of Demaison et al. (3). Those in the v4 state, (D’& and were assumed to be equal to 0; and D :KK,respectively. Consequently, v&i,, WIK~T, Bbff, and the upper- and lower-state dipole moments were included as parameters in the fit. Truncation limits for Stark effects were the same as those in the analysis of the band system in the next subsection. If a band is not perturbed by any interaction, the following expressions are obtained: &,, = v. + (A’ - A” - B’ + B”)K2 - (DZ - D;)K4,
(6)
BL.n = B’ - (D>K - D[;K)K2.
(7)
Figure 2 shows the relation between the &, values obtained for each K subband and K, and the B&values are plotted against K2 as shown in Fig. 3. For simplicity,
LASER STARK SPECTROSCOPY (cm-‘1
vsubo
.O.O0555LK*
OF CH$?N
29
-7.5.10‘7KL
911.72
I 911.71
91169%
’ 1
’ 2
’ 3
’ 4
’ 5
’ 6
7
’ 8
! 9
’ 10K
FIG. 2. K subband origin I&, + 0.005554K’ - 7.5 X lo-‘K4 plotted as a function of K. Figure shows another vibrational energy level crosses between K = 7 and 8. Error bars represent 2.5 times standard deviations.
u$,~ + 0.005554K’
- 7.5 X 1O-7 K4
(8)
is used for v$, in Fig. 2. The values of the dipole moments obtained for different K with each other within their experimental errors. The upper- and the lower-state dipole moment of K = 10 subband were fixed to each mean value of K < 9, because only a few resonances with K = 10 could be observed. Figure 2 shows clearly that another vibrational energy level crosses between K = 7 and 8, and its energy level at K < 7 is higher than that of the v4 level. A comparison of these figures demonstrates clearly that the value of r&i, in Fig. 2 is more affected than that of & in Fig. 3, but an irregularity of the Bkff values around K = 7, 8 is still observed as shown in Fig. 3. If the perturbation is caused by a J-dependent interaction, the deviation of B& at K = 8 has the opposite sign to that at K = 7. Figure 3 shows, however, that both values of B& at K = 7, 8 are larger than the expected values on the straight line. These facts indicate that the perturbation is evidently due to the Fermi interaction with the higher vibrational energy level (a), and that the rotational constant B of the perturbing state is larger than that of the u4 state (b). The 3~2 state were coincident
Betf’
(cm-‘) 0.29617
@
=I;
I
t
122z32 h2
52
6?
72
82
92
10ZK2
FIG. 3. Effective rotational constant B& plotted as a function of K’. An anomaly is shown at K = 7 and 8. Error bars represent 2.5 times standard deviations.
30
MITO, SAKAI, AND KATAYAMA
is considered to be the best candidate for the perturbing state, because the state satisfies the above (a,b) conditions. The 3~; vibrational state includes nearly degenerate Al and A2 states, one of which has the same symmetry as the v4 (A,) state. The rotational energy levels are coupled each other by Coriolis interaction about the symmetric axis except for K = 0. As discussed by Hougen (19), if the vibrational splitting between the A, and A2 states is much smaller than the magnitude of the Coriolis interaction, their rotational energy levels are conveniently considered to be similar to those arising from a degenerate E vibronic state. This condition is satisfied in the present case, because the energy splitting of A, - A2 is possibly within a few cm-‘, being much smaller compared with the value of 2A{KZ N 200 cm-’ at K = 7, where the interaction investigated in the present article has an important role as demonstrated by our experimental results. Since the splitting is not known experimentally but is assumed to be small, the vibrational splitting between Al and A2 states is completely neglected in the present analysis. We calculated the unperturbed energy levels of v4 and 3~; states for the case of J = 0. The calculation was made on the following assumptions: the rotational constants B and A of both states were equal to the ground-state values (3); A[ was equal to the value obtained by microwave absorption (7); and the v4 band origin was equal to the subband origin of K = 0. By adjusting the 3vg3band origin to the value of about 1120 cm-’ as estimated for CH3C4N by Duncan et al. (9), we obtained Fig. 4, where the energy levels are plotted as a function of K. Figure 4 indicates that relatively large Coriolis term of 2A{Kl N 27.6K (cm-‘) gives rise to the crossing of their rotational levels around K = 7, although the 3~: vibrational level separates from the v4 level by about 200 cm-‘. (B) Analysis of the v4-3~: Band System Having examined the effect of the interaction involved in the v4 band, we subsequently analyzed the v4-3~: band system in which the Fermi interaction was taken into account. Nonvanishing matrix elements of Hamiltonian are expressed:
CH3C"N E(cm-') 1500-
0
/
12
3
4
5
6
7
6
9 IO
FIG. 4. Unperturbed energy levels of the vq and 3~: states for the case of J = 0, which are plotted against K. The energy difference AE between vq and Kl > 0 is about 8.8 cm-’ at K = 7.
LASER
STARK
SPECTROSCOPY
OF CH3C?N
31
(u,, J, KIHOIv4, J, K) = v. + B’J’(J’ + 1) + (A’ - B’)K’ - D;J”(J’ (G.S., =
J, KIHoIG.S., B”J”(J” -
+
-
B”)K2
-
DI;J”?(J”
+
1)2 -
&,,(J”
+
])K’
+ H;J”‘(J” + 1)3 + HI;KJ”‘(J” + 1)‘K’ + HkJJ”(J”
+ 1)K4,
(3v8, J, K, 1 = +31H013u,, J, K, 1 = -t3) = v. + BJ’(J’ + 1) + (A - B)K’ - 2A{Kl+
elements
of the Fermi
interaction
(v41H013vs, 1 = *3)
(10) (11)
&‘(J’
+ 1)KI + qKK31
- DJJ”(J’ + 1)’ - D,,J’(J’ The matrix
(9)
J, K)
1) + (A”
D;K4
+ 1)2 - D;KJ’(Jr + l)K* - DkK4,
+ 1)K2 - DKK4.
(11)
terms are = kV4888.
(12)
Those of the Stark effect term are the same as in the subband analysis. Because of Stark interaction of AJ = + 1 type, the matrix is infinite in size. We used fixed truncation limits, truncating at J,,,,, = J + 5 for J > 3 or J,,,,, = 7 for J < 3, and at Jmin = J - 7 for IKI or IMI < J - 7. This truncation introduced no appreciable errors in the calculations and the results were the same as the case that J,,, = J + 4 and Jmin = J - 6. The maximum size of the matrix was 39 X 39, because 1~~)was connected to both /3vs, I = +3) and 13us, f = -3) by the Fermi interaction. The constants in the ground state, B”, D;, DL;K.HI;, Hj;K, and HkJ;,, were constrained to the microwave values of Demaison et al. (3), and A” was constrained to the value of Mast-i et al. (20). The constant Dk was also constrained to the value of Duncan et al. (9). The vibrational A, - A2 splitting of 3~: was neglected, as mentioned in the subband analysis. The constants in the 3ui state, A{, DJ, DJk., and were constrained to the values which were calculated from the microwave values (us, 2~) of Bauer d al. (7). The constants were the same as those calculated from the values of Careless and Kroto (6). The value of nK was arbitrarily fixed to zero, because any data was not obtained. Those of A and DK were fixed to the ground-state values. The dipole moment was constrained to the value which was determined for the 3~; state of CH3C14N by Igarashi et al. (II). Consequently, the ground-state dipole moment, all of the u4-state constants, the 3~; band origin, and rotational constant B were included as parameters in the fit. The weights of the resonances for each ro-vibrational transition, which were observed with one laser line and under the same AM selection rule, were given so that their total was unity. The total of 644 observed Stark resonances, which were assigned to 139 transitions, were analyzed by the least squares method and the molecular constants determined in the final fit are presented in Table I. A complete list of the data included in the fit, together with residues, is given in Table II. The spectra observed by using the CO2 regular band P(56) or hot band P(23) laser line were eliminated from the analysis because the laser lines overlap each other. For several high J transitions which were very close to the laser lines, their A4 components were not separated. We calculated the sum of the spectral shapes of the qJ,
32
MITO, SAKAI, AND KATAYAMA TABLE I Molecular Constants of CH,C”N (In units of cm-’ except for dipole moments in Debye) Microwave
vO
Ground state
3V63
911.712306(531a
1113.57(10)
B
0.29616430(53)
A
5.2400031(35)
0.29616415 (e)
[
AS
[
0.30013(66)
lb
( 5.247 4.60
(f)
1
1.1919(52)x10-7
1.187x10-7 (e)
[ 1.274~10-~ I lg)
DJK
5.791(13)x10-6
5.774x10-6
[ 5.707x10-6
DK
9.3947(38)x10-5
[
9.47x1O-5
I
(j) If)
ig)
DJ
(e)
0.297607334
[ 5.247 1
1 (gl
I
(hl
[
1.193t3x10-7
[
5.63867X10S6 I (j)
1
(j)
( 9.47x10-5 1
(h)
"J
I 0.0
lj)
RJK
[ 2.97x1O-11 1
Ij)
HKJ
[
(jl
'IJ
1 1.247~10-~
'IK
I 0.0 I
u
3.9354(7)
(C)
[ 3.87 1
I (g) (d)
(c,i)
I
2.40~10-~~ 3.9256(7)
1
(Cl
I"148881 0.3908(15)
(d) Arbitrarily fixed to zero.
a. Errors in parenthese are 2.5 times standard deviations in units of the last significant figure.
(e) Ref. (a).
b. Quantities in square brackets are fixed values.
(gl Ref. (1,.
(h) Ref. (2).
(c)
(i) Ref. (11) -*
(j) Ref. (1).
Absolute uncertainties for dipole moments are 0.1%.
(fl Ref. (=I.
individual A4 components and derived the electric field strength of the first A4 component by fitting the calculated spectrum pattern to the observed. The calculations were made by the approximation of the first- and the second-order Stark effects, because higher-order corrections were negligible. The electric field strengths determined with this procedure are indicated in Table II by asterisks. DISCUSSION
The vibration-rotation parameters given in Table I are determined with great accuracy. The observed data can be reproduced with the standard deviation of 4.6 MHz. This is considered to be a proof that the model (~~-3~2Fermi interaction) used in this analysis is adequate. It may be noted that the K subband analysis was also useful in laser Stark spectroscopy for the examination of such an accidentally perturbed band. For comparison, the microwave values of rotational constants for the u4 state are given in Table I (8). The rotational B and centrifugal distortion constants DJ and DJK obtained are in good agreement with their microwave values. The 3~: rotational constant of B = 0.30013 + 0.00066 cm-’ obtained is in good agreement with the calculated value of B = 0.30024 which is extrapolated from the v8 and 2v8 microwave values (7). We also made the analysis of the band system, in which A r was included in the fit. The derived constant A{ = 4.73 + 0.74 cm-‘, although not determined
LASER STARK SPECTROSCOPY
33
OF CH,C”N
TABLE II Observed Stark Resonances of CH,C”N
Transitiona
M’
+
co2
M”
O-C,MHZl’
E,“,Crnl
Laser
co2
P(40)=924.97398c -23 QR 5(231
945
Pt42,=922.91429 OR 4(19) 19
2480
P1461=918.71833 -12 QR 81121 -10 QR 91121 -7 -6 -4 -3 QR10112, 10 9
19924 24067 3175 3731 5537 7456 16112 17803
ld
l
OP
51101
QP
61101
4.8
-1.2
5.1 16.5 1.8 3.9 -1.5 -0.3 -9.0 -0.6
P16Ol=903.21177 QP 91131 12 11 10 9
8 7 12
UP101131 P,48)=916.58177 -8 QR 6( 81 -7 -6 -5 *87!8) -8 -7 -6 -5 -4 -3 -8 QR 81 81
17341 19993 23496 28619 6320 7241
-11.1 4.5 0.3 3.9 -2.7 -3.0
8478
-3.9
10264 12982 17930 463
*
-0.3 -3.0 6.0 -0.6
P,50,=914.41928 QR314l -4 -3 QR414, -4 -3 -2
13912 19067 7638 10576 18375
-14.4 -0.9 -16.5 -15.3 -3.0
P1541=910.01585 0 QP 01 3) -1 QP II 3) QP2l3) -2
21506 15598 5708
1.5 3.6 12.6
28678 7942 9079 12744
8.7 -2.4 -2.4 0.6
8353 9504 11059 16417 7775 8769 10105 11899 18619 17258
-5.7 -1.5 -1.8 -5.4 0.3 4.5 1.8 0.6 -4.2 -0.6
18141 21673 27001 20510 25326 8469 10195 17426 8416 lOiOl
0.6 -3.9 2.7 4.2 9.3 -3.0 -5.1 -3.9 -0.9 -4.8
P,58,=905.50659 QP 31101 QP 4tlOl
8 7 6 4 ? 2 12 0
71 91
4 3 1 8
3
4
P,l4,=915.62774 QR3l6l -6 -5 -4 -1 -2 0
OR 41 61
-1
-6 -5 -3 -2 -1
a.
QR
b.
O-C
c.
Laser
d.
+ denotes
51231
-3 -2
means
laser
15
-----
co2
laser
_
Hot
P(lll=918.25807 QR 7(111 -11 -IO -9 -8 QR 8,111 -9 -8 -7 -6 -5 QR 9(111 9 8 7 6
QR
54 9)
QR 6( 9)
-1
-6 -5 -4 9
P1221=908.48736 QPl(5) 3 QP 2( 51 4 3 4 3 2 10 4 QP 3( 51 3 2 4 3 2 10 4 4 QP 4( 5) 3 2 1 3 2
2706 3095 3637 4351 5435 11820 13561
0.3 0.0 -3.0 -1.2 -0.3 2.1 -1.2
15976 17429 19148 21187 23784 27077 605 *
-3.3 1.5 3.6 -1.2 3.6 8.1 0.6
Band
13144 14472 16085 18187 2968 3368 3858 4497 5400 13675 15312 17426 20197
P(121=917.35000 QR 3( 91 -6 -7 QR4(9) -8 -6 -5 -5 -6 -4 -5 0
6 8 7
OR 6( 9)
QR
l,a*er
-8 -7 -6 -5 -4 -8 -7
2
3 2 1
3 2 1 5
2 1
frequency
minuscalculated in cm-l.
transition
unresolved
M-components;
see
text.
-3.3
-4.2 -6.6 0.3 -3.3 0.6 1.5 0.6 -0.3 -4.2 0.3 0.3 0.6
23944 15247 20310 24364 11379 12567 21324 2712 3294 4120 7425
4.5 -2.1 -1.2 0.6 -4.2 -1.5 0.0 -3.6
28082 19422 25388 13441 16239 20379 27506 12251 15882 22200 8219 9856 12151 15840 24262 7307 9505 13319 20960 5830 7160
13.8 -8.1 6.9 -14.4 13.2 9.3 20.7 -14.4 -9.3 0.0 -5.7 -5.4 -8.1 3.9 6.0 -21.9 -10.8 -9.3 -6.9 1.2 -3.3
AK = 0, &J = tl, K = 5, and J = 23.
frequency
-----
frequency.
i:: -3.6
34
MITO, SAKAI,
AND
KATAYAMA
TABLE II-Continued Transition
M’
+
M”
-6
E,“,Crni
O-CIHHZl
3452 3449 3127 3902 5126 3837 5293 7868
-3.3 -0.3 2.7 0.6 -3.6 -0.3 -1.5 1.2 -2.4
4 4 3 4 3 2 -5 -5 -3
22935 18970 24207 17222 21730 28819 23219 14426 27558
3.0 6.3 4.8 15.9 8.1 -7.5 15.6 -3.6 6.3
P(16)=913.88037 QR2(3) -3 -2 QR3(3) -3 -2
14035 20179 6755 11164
2.4 -4.5 -4.8 -1.8
P(17)=913.11803 QR O( 1) fl QR l( 1) 1 0
16869 8882 17109
1.8 20.7 0.0
P(20)=910.31020 ?l QP Of 2) t1 0 ?I t2 QP l( 21 1 0 10 0 -1 12
16019 13952 26814 7821 15779 5486 10207 15252
-6.9 2.7 30.0 -14.1 -5.1 -12.9 -15.3 -1.5
2 2 1 -3
20972 13555 20104 16511
-25.5 -14.7 -22.2 17.1
6 5 4
-9 -8
14922 17744 21910 9074 10057 11287 14973 17836 1786 2043 2369 2837 4697 6900 1593 1804 2072 2403 2848 4167 5022 6336 8658 6153 8259
-3.9 -5.4 3.6 -0.9 -4.5 -5.7 0.0 -2.7 2.1 3.0 0.0 0.0 2.1 1.5 1.2 5.1 7.8 4.5 -2.1 6.9 6.6 5.1 -2.1 3.6 0.6
P(26)=904.76597 10 QP 51111 7 6 5
19661 28026 18245
3.3 8.7 16.5
QR5(6)
2279
-4
0 QR
-1
6( 6)
5 4 3 0 7 6
P(15)=914.85382 QR 2( 4) QR 3( 4) QR 4( 4)
QR 4( 5, QR5(5)
1 6 5
Transition
M’ +
QP 3( 4,
QP
61 91
6 5 4 2 10 QP
71 91
QP 81 91
5 4 3 1 8 7 6 5 3 2
5 4 3 2 10 -6
4 3 2 1
-5
-4 -3 -8 -7
0-c
(MHZ)
9256 12947 14723
-3.9 -3.9 3.9
22340 25146 28624 18369 21340 25449 17368 23720 11364 13544 16777 21841 9147 10523 2689 3144 3762 6175 2003 2237 2533 2927 3447 4205 7260 16014 8040 8577
-0.9 15.9 9.0 -0.3 0.6 5.1 -5.4 5.1 -3.3 -3.9 3.3 3.9 -5.4 -7.2 -6.3 -2.7 -3.3 -3.6 0.0 0.0 -0.3 1.5 -0.6 -0.3 0.3 3.3 -1.5 -1.2
27494 21352 24345 15703 17277 19158 21525 24604 11273 12848
21.0 -2.7 7.8 0.0 5.4 0.9 2.4 14.1 -8.1 -6.0
-9
24755
-7.5
P(28)=902.86734 QP 6114) 13 11 9 7 QP 7(14) -13 -12 -11 -10 -9 -8 -7 QP 8(14, -8
13287 15718 19133 24676 6641 7234 7856 8683 9659 10834 12408 27589
-2.7 -0.6 -6.3 -0.3 5.1 0.6 4.8 0.6 0.0 3.0 1.8 -0.6
17913 19629 21572 24027 26926 7900 8572 9329 10264 11431 12872 20504
-4.2 2.7 I.2 5.1 -1.2 2.7 1.5 3.6 3.6 1.8 I.2 3.0
P(241=906.63929 QP3181 6 5 4 QP 4( 81 7 6 5 4 2 QP 51 81 6 5 4 3 4 3 7 QP 61 81 6 5 3 6 5 4 3 2 10 QP 7( 8) -4 -2 -7
P(21)=909.57909 QP II 31 QP 21 31
MX’ E (“/cm)
10 0 -1 4 5
5 4 3
3 1
3 2
5 4 3 2 1
-8
0
1
P(25)=905.95028 QP4(9, 6 QP 5( 9) 8 7 7 6 5 4 3 QP 6( 9) 8 7
QP
9(12)
P(29)=902.23148 12 QP 6(15) 11 10 9
8
QP
7(15)
-13 -12 -11 -10 -9
QP
8(15)
-13
-8
5
6 5 4 3 2
LASER STARK
SPECTROSCOPY
OF CH#?N
35
TABLE II-Continued Transition QP
QP
M’ +
cc111
7111)
QP
8,111
QP
9111)
6 5 4 10 11 9 10 -10 -9 -10 -8 -9 -5 -10 -11 -9 -8 -3 -2
P(271=904.10214 QP 5112) QP 6,121
QP QP
M”
7
6 11 10 9 8 7
6 8 7 6 5 3 -11 -11 -10 -9
7(121 81121
-8
QP
9112)
QR
9(14,
7 6 5 4 2
-7 -7 -6 -6 -5 -5 -4 -11 -12 -10 -11 -10
E(V/cml
O-CIMHz)
11150 13363 16618 13201 16402 5801 14332 19146 24619 23642 23570 26692 27459
i8079 15046 16549 18336 20589 23491 27361 12347 13367 14512 15913 19695 585 8644 9511 10571 11958 13675 7651 8314 9130 17030 20823 22172
-1.2 0.9 1.5 -1.8 -0.9 2.4 0.6 1.5 1.z -9.9 -13.8 -11.4 -0.9
*
7.5 4.8 6.3 2.1 0.9 1.8 5.1 -3.9 0.3 -3.6 -2.7 -2.1 0.0 -0.6 0.6 2.4 -3.9 -0.3 3.3 6.3 4.5 -0.6 0.3 -3.6
P(301=900.94336 QP 6(171
QP
7(17)
P,3l,=900.33828 QP 6(18)
0.9 1.8 -3.6 10.5 3.6
QRlO(14,
8 6
22661 25613 5949 7955 9658 3379 3767 4216 4798 17722 23331
-0.6 7.8 0.0 -0.3 7.8 4.2 1.2 4.5 6.9 13.8 3.6
OR
Et101
QR
9(10)
22 il 2 1 0 2 1 0
9732 25937 3218 6366 26883 2481 4515 12743
14.4 6.0 11.1 15.3
-5 10
8
P(49,=913.51203 QR 0, 2, @R
1(
2)
QR
2(
21
_____ R(
2,=915.73396 *R 2, 6) OR
3(
6)
QR
41
6)
13CO*
-3 -2 -6 -5 -4 3
Laser
17482 24687 1607 1956 2444 5964
13 12 11 10 9 8
12634 13806 15077 16632 18460 20743
-12.0 -6.3 -5.7 -3.9 -5.1 -6.6
1.5 -1.8
1559 26691 28235
f
-4.2 -5.7 -3.9
P(33)=898.42251 QP 6(211
-20
5091
*
-8.1
P(34,=897.01908 QP 7(23l
22
1691
*
---
-I(201 8120)
CO2
Laser
sequence
Band
0.0 ---
P(41,=921.87024 QF! 3(17l P(431=919.81854 QR 8(14l QR 9(14)
R(
8)=920.21948 QR 3,141 QR
4114)
R(22)=929.99305 QR 6133) P,
P,
P,
3.3 3.0 -4.8 0.0 0.0 0.3
-5.1 0.6 7.5 6.0 -3.3 0.0 -0.3
-19 -18 -17
OP QP
;:: 8.1 10.2
____.
22879 24482 26334 28346 10900 lil8B 13937 16204 19560
P(32)=898.99396
-17
4754
-14 -9 -8
27320 4880 5520
13 6278 8836 18527 19947 26502
-7 -5 13 12 9
16 15 14 13 -9 -8 -7 -6 -5
4)=910.27796 QP 0, 2) QP II 21
6)=908.67515 QP OI 51 QP
II
51
QP
21
51
*P
3,
51
QP
4,
51
8)=907.05284 QP 5( 71 QP
61
7)
P(10)=905.41104 QP 4(101
CO*
*
-8.7
-12.0 1.2 3.3
l,a.ser
-8 -7 11 10
21718 24386 12185 13410
4.8 -1.8 0.0 0.3
33
4712
-1.5
+I 1 0
17396 8938 17145
1.8 -18.6 -12.3
t4 i3 4 3 2 4 2 1 -3 -2 -1 -3 -2
17935 27108 5145 6970 11029 955 1927 3849 1927 2916 6134 4411 6970
0.0 3.3 -3.0 -3.0 0.0 -3.9 -1.8 -2.1 -1.8 -1.z 2.1 -0.3 -9.9
2 5 4
24438 28738 16376 19298 23426
17.4 15.3 2.4 -0.3 7.5
9
25519
10.2
6
MITO,
36
SAKAI,
AND KATAYAMA
TABLE II-Continued Transition
M' + 6 5 4 5 4 3
QR SC 6)
OR
RI
6( 61
41=917.24878 5, 91
QR
-9
-8 -7
QR619l
QR
-8 -7 -5 -4 9 8 7 8 9 7
71 91
QR 8( 91 QR 91 91
RI 6)=918.74396 QR 91121
M" E[V/cmi
O-CIMHz)
I
Transition.
6776 8080 9996 12160 14902 19092 26060
2.4 3.3 3.3 -1.8 -3.6 -3.9 -4.8
QP
5110)
QP
6110)
19460 21923 25147 7691 8778 12389 15587 4454 5006 5711 11422 18597 23512
-1.8 -1.2 4.8 0.9 -3.3 -1.2 -3.0 3.0 3.0 3.3 -3.6 -13.8 -4.2
QP QP
71101 81101
2850 3202 3663 4288 5131 6382
2.4 2.7 2.1 0.0 0.6 1.2
9 8 6 4
;: 9 8 7 6
0.6 -2.1 -0.9 6.9 4.2 5.4 0.9 4.5
P116)=916.81456 QR 3C 8) -8 -7 -6 -5 QR 4( 8) -7 -5 -3 8 QR 5( 8) 7 6 5 4 8 QR 61 81 6 4 3 QR 7( 81 6 5
17656 20061 23266 27811 6322 8855 15012 2663 3078 3580 4296 5423 9527 12616 18518 24089 21797 25826
1.8 -3.0 -4.2 5.1 -3.3 -3.9 8.7 7.8 0.6 2.1 1.2 -6.0 -2.4 -3.6 0.3 -4.5 -1.5 -17.1
-6.0 -0.9 0.3 -6.3 -2.4 0.9 -2.4 -5.4 -5.4 1.5 -2.7 -6.6 -4.8
P1121=903.74974 QP l(131 -12 QP 2,13, -9
9382
21937
-0.9 -2.7
P(14)=902.06895 QP 9115) -9 -8 -7
5384 6053 6917
1.5 2.1 2.7
QP 9(10)
P(16)=900.36865 -17 QP 61181 _____
2
QR
31 5)
QR
41 5)
OR SC 51
3 2 5 3 2
P(20)=913.64451 22 OR 01 2) 2 QR II 2)
18440 24994 20911 6368 8018 16341 11996 17499 8684 14033 22307
22697 12174
2966
13c1802
-9.6 -5.4 -8.7 13.2 5.7 -2.7 3.3 0.3 12.9 -6.0 -2.1
-18.9 10.2
LaSer
P(12)=919.89443 QR 8(14) -13 -12
P(30)=905.32296 QP 5(10) QP 6(10)
*
-3.3
_____
10236 11102
4.5 5.4
Laser
9 8 7 6 5 6 5 4 3 -4 -3 -9 -6 -4
26924 16406 18706 21708 25851 4426 5302 6566 8705 7167 9700 11482 17611 27877
12.6 0.0 3.9 4.2 8.1 -2.4 -1.8 -5.4 -2.4 -3.9 -3.9 3.0 -1.8 -4.8
Pl32)=903.59029 QP 4(13) 11 10 QP 51131 11 10 9 QP 6(13) -8 -7 -5
25294 27825 6460 7084 7898 13401 15367 21565
4.8 2.7 -0.3 -2.4 -0.3 -3.6 -6.9 -7.2
QP
7LlO)
QP
8(1Ot
QP
9(10)
P(34)=901.83469 QP 11161 15 -----
P(181=915.24082 QR 0, 5) f5 f4 2 QR 1( 5) QR 2( 51 5 4
O-C(MHzI
13061 14704 19526 2671 3024 3472 4024 4797 5979 9554 15819 18638 22051
13c1802
10907 13323 17179 5343 6542 7344 8423 9770
QR 7(11)
M" ElV/cml
9 8 6 9 8 7 6 5 4 -7 -7 -6 -8
13~180~laser P1141=918.36575 -11 QR 6(11) -9
M' +
N20
5717 Laser
*
2.7
----_
P,12)=928.61661 QR 41301 -30
6107
*
4.2
P1161.925.09696 QR 2(23l -23
6932
l
1.2
P(lEl=923.31713 -20 QR 6(20)
5279
*
-8.4
P(191=922.42221 QR 3,181 18
6433
'
-0.6
P,20,=921.52398 QR 81171 -17 QR 9(17) 14
15250 20152
7.5 9.0
LASER
STARK
SPECTROSCOPY
OF CH$?‘N
37
TABLE II-Continued Transition
M' +
C'R 2( 21
M" ElV/cml
1 2 1 0
20629 8256 13192 24334
0-CfMHZl -6.6 10.5 3.6 -30.0
P(24)=910.38402 r1 QP O( 2) 1 QP II 2)
12566
0
1228,
-12.6 6.9 -9.0
QP O( 5)
0
QP I( 5) QP2(5)
-1 -4 -1 -2
20304 23604 13955 4208 16268 10162
-2.1 -3.6 -1.2 0.9 -1.8 2.7
6 6 5 4
26103 17794 20967 25406
19.5 -4.2 2.1 14.1
10 9 8 7
14719 16371 18315 20867
1.8 -5.4 1.2 -1.2
4 9 8 7
23046 25758 5234 ,508 1,769 ,105 ,945 9054 12742 15794 19619 22012 25110
15.9 5.1 -9.0 -6.3 -0.6 -1.8 3.9 6.0 -5.7 -2.4 5.1 2.4 -9.3
8 6 8 7 8 -9 -8 -7 -6 -5 -4
26555 27814 22543 2571, 25241 6482 ,312 8398 9836 11969 15262
-11.4 -11.4 -9.0 -11.4 -11.1 -9.9 -9.0 -6.0 -9.3 0.3 4.2
Transition
M' +
M" E(V/Crn) 0-C(HHZ)
13
21778
P(21,=920.62242 -15 QR 6(15)
2601
2.4
'
1.5
P(22)=919.71754 5185
PR 2(13) OR 3(13)
13 11 10 8
933 18329 20277 25601
0.0
4.5 0.9 -2.7
P,26)=908.71977 ?1
QP
3( 51
QP 5( 7) QP 6( 7)
QR 91121
P,24)=91,.89,83 -9 QR 4,101 -8 -10 OR 51101 -7 -3 9 QR 6(101 8
QR
,(lO)
P,25)=916.98301 QR II 8) QR 3( 8) QR 4( 8) QR QR
5( 8) Y( 9)
P(23)=918.80935 QR 7(121 -10 -9 -8 QR 8(12l -11 -10 -9 -R
-;
QR
QR
9(12)
5( 51
;;
-2 5
P128)=914.21869 QR 11 31 QR
21 31
QR
31 3)
18180 21319 25963 8978 1052, 12770 16253 22634 968 1139 1383 1731 2352 3564 7811
4.5 -3.3 11.1 -7.2 -8.4 -3.6 -2.1 2.4 -7.5 -4.8 -0.6 -1.2 3.9 2.1 0.6
P,2,)=915.14344 QR 2, 51 -4 -2 -3 -4
11854 2224, ,070
-4.8 0.9 -4.5
-1 4
P(30)=912.35929 QR O( 0)
9.0 8.4 12.0 -2.1 -0.9 -1.5 -1.8 0.0 1.8 5.4
11724 13243
2.7 -3.9
17911 26298 12509 1,649 10368 14335 2179:
-4.2 -5.7 -0.3 6.3 16.2 3.q -1.2
2,448 2421, 15409 8029 519, 8646 17190
19.8 5.4 -7.2 -8.4 -4.8 -4.8 -0.6
3902 6121
-4.8 17.1
5861 1105 5314 24525
-2.1 -4.5 3.0 0.6
-3 -3
2,221 14685
-2.1 0.6
3 4 3 4 3 2 1 4 3 2 i
23015 8755 11592 4104 5411 ,922 14097 925 1238 1843 3493
1.5 -3.9 -7.5 -3.0 -5.1 -1.5 -2.7 -6.0 -2.1 -0.3 -0.6
5 4 -6 -6
19395 23458 29023 26405
-24.3 -15.3 9.0 8.1
3 2 3 2 3 2 1
P(29)=913.29064 '1 0 QR 0, 21 -1 QR If 2, 0 -1 -2 QR2(21 -1 -2 0 -1 -3 -2
0
!l
0
P(32).910.48668 tl QP 01 21 1 QP II 2) 0 -1 pt331=909.54543
QP 2( 41 QP3(41
P126)=916.06488 -7 QR 5( 7) -6 -5 QR 6( 7, -7 -6 -5 -4 -3 QR ,( 7, -7 -6 -5 -4 -3 -* -1
19993 22239 25104 4107 4528 5028 566lI 6491 7605 13382
P(34l=908.60088
QP l( 51 QP 2( 51 QP
31 51
QP
41 51
P(351=907.65304 QP 51 61 QP 41 71 QP5(7)
MITO, SAKAI, AND KATAYAMA
38
TABLE II-Continued Transition
M'
+
0 QR
3C
51
M" -1
12509 2902
-5.4
3653 7370 2617 4124 996 1258 1685 2476 1098 1416 4098 6624 7656
-1.z -4.5 -5.1 -1.8 3.9 -0.6 -3.6 1.2 4.2 1.8 -5.4 4.5 -1.2
-3 -1 5 4 3 2
12 0
1 5 3
-1
0
N20 QP 71 9) QP El 91
0.0
-4 -2 -2 0
5( 5)
O-CWHz)
-5
QR 4( 5)
OR
E(V/cml
TransitIon
QP
31 8)
QP 41 81
QP
71 8,
P1371=905.74748 QP 7C 91
Laser
QP 7,11, QP
9t11,
P,391=903.82875 QPlOilZl
c
E(V/cmi
O-CLMHz1
7 6 5 6 5 4 -7 -5 -4
19679 22934 27555 12074 14432 17915 8866 12655 16219
0.3 -0.9 8.4 -2.1 -2.7 -3.0 3.6 3.9 0.3
8
21299
-8.1
N20
7 8 7 6
24161 14040 15971 18413
-2.1 -5.1 5.4 -2.7
8 7 6 5 -9 -8 -9
3541 4049 4705 5645 10236 11531 26410
-3.0 -2.4 -4.2 -3.6 -1.5 -0.6 4.5
8
2612
-1.5
QPlO112)
M"
Laser
7 6 5 4 -10 -9 -8
2960 3515 4206 5189 11024 12287 13881
-5.1 4.5 4.2 -0.3 1.2 6.6 5.7
P(401=902.86445 QP 6(141 13 QP 7(14) -11 -10 -9 -8 -7
14012 7120 7841 8732 9823 11213
-3.6 0.6 0.0 -1.5 -1.Z 0.3
QP11,12, Pl38)=904.78976 QP 61111
M'
P136)=906.70191
very accurately, was consistent with the assumed value A{ = 4.60 cm-’ of Bauer et al. (7). We note that the parameter 3~; band origin is strongly dependent on the other constants of 3~:, especially on the values of A{ and A. The error quoted in Table I does not include the uncertainty which comes from the uncertainties of the assumed constants. As seen in Fig. 4, the energy differences between v4 and Kl < 0 of the 3~; are larger than 200 cm-’ at any K. The perturbation appeared in the rotational energy of the u4 state can be well explained without taking the Fermi interaction with KI < 0 into account. Its effect is only to reduce the u4 band origin by about 20 MHz without affecting other rotational constants of u4. To determine the vibrational frequency of v4 from which the effect of the Fermi interaction with 3~: is completely removed, the Fermi interaction with Kl < 0 was included in the analysis. In the present study, no lines in the 3~: band could be assigned. This band is presumably very weak and has not been observed in any isotopic species of acetonitorile. From derived constants, the unperturbed energy difference between v4 and 3~; state is calculated to be about 8.8 cm-’ at K = 7, which is much larger than the Fermi interaction parameter of 0.39 cm-‘. Consequently, the intensity borrowed from the u4 band amounts to only 0.2% of the corresponding v4 line even at K = 7. For CH3C14N, some workers (10,21) have discussed the x-y type Coriolis interaction between v4 and v, states. Figure 3. however, shows that the Bh values plotted against K* fall on the straight line, except for the values at K = 7, 8. This linearity satisfies the relation between Bke and K2 in Eq. (7) which holds for the case without any perturbation. It seems that the effect is too small to be detected in the Stark spectra for the v4 band, even if the band is perturbed by the Coriolis interaction. The poor fit around K = 7 observed by Moskienko and Dyubko (22) in the u4 microwave
LASER STARK SPECTROSCOPY OF CHxC”N
39
spectrum at high J for 14Nis presumably due to the v4-3yi Fermi interaction, although Rackley et al.explained the cause with the Coriolis interaction which transferred the Fermi resonance in v7 (10). Duncan et ul. (9) have examined the isotopic shifts on vs and u4bands of acetonitrile, and discussed the possibility of the uq-2ug and u~-~Y:Fermi resonances. They estimated the Fermi resonance parameters, 1W4g~l= 30 cm-’ and 1W’QWJ~ = 25 cm-‘, for CH$N species. As pointed out by Duncan et al., because of the parallel nature of the v4 and 2~: bands, the Fermi resonance is absorbed in conventional anharmonicity effects. As for j W48881 = 25 cm- ‘, they were unsure as to whether such an interaction parameter was physically possible between a fundamental and a ternary overtone, and only the Fermi resonance with 2~: was taken into account for force field refinement calculations. In fact, IIP’,,,,I = 0.39 cm-’ is obtained for 15N in this study, and the value of 0.38 cm-’ is obtained for 14N by Igarashi et al. (II). From these data, the possibility of such a large parameter is excluded. It should be noted that the infrared value of the u4 band origin for CH3C”N reported by Duncan et al. is smaller by 0.50 cm-’ than our value and the isotopic shift is larger by 0. I3 cm- ‘. such a large parameter is excluded. It should be noted that the infrared value of the u4 band origin for CH3C”N reported by Duncan et al. is smaller by 0.50 cm-’ than our value and the isotopic shift is larger by 0.13 cm-‘. The frequency measurements of N20 laser by Whitford et al. (16) were limited to the P( 15) line in the lower frequency side, and most of the laser frequencies used in the present study were calculated by extrapolation. Stark resonances obtained by using P(32) to P(40) lines were analyzed with zero weight at the initial stage. It was proved, however, that the data were consistent with the data measured by other laser lines in the same spectral region. Since no systematic deviation was found in these data, they were incorporated in the final analysis. The Stark shifted frequencies for nine resonances, observed using the P(53) laser line of the CO2 sequence band, were uniformly higher by 30 MHz than the value calculated by Siemsen et al. (15) and these data were excluded from the analysis. To confirm this observation, we measured the laser Stark spectrum of CH3C’4N using the same laser line and also found the equal amount of deviations. Therefore, their frequency of the P(53) laser line presumably includes the errors of about 30 MHz. ACKNOWLEDGMENT 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 Center, University of Tokyo. RECEIVED:
April
26, 1983 REFERENCES
1. A. BAUER, A. MO&S, AND S. MAES, C. R. Acad. Sci. Paris Ser. 3. 264, 941-943 (1967). 2. A. BAUER AND S. MAES. J. Phys. (Paris) 30, 169-180 (1969). 3. J. DEMAISON, A. DUBRULLE, D. BOLJCHER,AND J. BURIE, J. Mol. Spectrosc. 76, l-16 (1979). 4. A. BAUER, J. Mol. Spectrosc. 40, 183-206 (1971). 5. A. BAUER AND S. MAES, J. Mol. Spectrosc. 40, 207-216 ( 1971). 6. A. J. CARELESS AND H. W. KROTO, J. Mol. Spectrosc. 57, 189-197 (1975). 7. A. BAUER, G. TARRAGO, AND A. REMY, J. Mol. Spectrosc. 58, I1 1-124 (1975).
40
MITO, SAKAI, AND KATAYAMA
8. A. BAUERAND M. GOWN, Canad. J. Phys. 53, 1154-1156 (1975). 9. J. L. DUNCAN,D. C. MCKEAN,F. TULLINI,G. D. NIVELLINI,ANDJ. PEREZPEI~A,J. Mol. Spectrosc. 69, 123-140 (1978). 10. S. A. RACKLEY,R. J. BUTCHER,M. R~MHELD,S. M. FREUND,AND T. OKA, J. Mol. Spectrosc. 92, 203-217 (1982). II. I. IGARASHI,J. SAKAI,H. FUJIMA,AND M. KATAYAMA,Symposium on Molecular Structure,Kyoto, October 1981. 12. C. FREED,L. C. BRADLEY,AND R. G. O’DONNELL,IEEE J. Quantum Electron. QE-16, 1195-1206
(1980). 13. B. G. WHITFORD,K. J. SIEMSEN,AND J. REID, Opt. Commun. 22, 261-264 (1977). 14. J. -P. MONCHALIN,M. J. KELLY, J. E. THOMAS,N. A. KURNIT,AND A. JAVAN,J. Mol. Spectrosc. 64,491-494 (1977). 15. K. J. SIEMSEN ANLIB. G. WHITFORD,Opt. Commun. 22, 11-16 (1977). 16. B. G. WHITFORD,K. J. SIEMSEN, H. D. RICCIUS, AND R. G. HANES,Opt. Commun. 14,70-74 (1975). 17. S. M. FREUND,G. DUXBURY,M. R~MHELD,J. T. TIEDJE,AND T. OKA,J. Mol. Spectrosc. 52, 3857 (1974). 18. H. MATSUURAAND T. SHIMANOUCHI, J. Mol. Spectrosc. 60, 93-110 (1976). 19. J. T. HOLJGEN, J. Chem. Phys. 38, 1167-1173 (1963). 20. F. N. MASRI,J. L. DUNCAN,AND G. K. SPEIRS,J. Mol. Spectrosc. 47, 163-178 (1973). 21. S. KONLXIAND W. B. PERSON,J. Mol. Spectrosc. 52,287-300 (1974). 22. M. V. MOSKIENKO AND S. F. D~BKO, Izv. Vyssh. Uchebn. Zaved. Radiojiz. 21,95 l-954 (1978).
103,26-40 (1984)
Laser Stark Spectroscopy of the u4 Band of CH3C15N: Fermi Resonance with 3~; AK~HIRO MITO, JUN SAKAI, AND MIKIO KATAYAMA Department of Pure and Applied Sciences, College of General Education. University of Tokyo, Komaba, Meguro-ku, Tokyo 153. Japan
Laser Stark spectra for the v4 band of CH$?N have been measured by using CO2 and N20 lasers. AImost 650 resonances have been assigned to about 140 ro-vibrational transitions with S =Z34 and K =Z 11.An anomaly of the rotational structure around K = 7 has been proved to be due to a Fermi interaction by analyzing each K subband separately. Observed data have been fitted to a model which includes LQ-~Y~Fermi coupling by the method of least squares. The standard deviation of observed from calculated frequencies is 4.6 MHz. Molecular constants derived are also listed. INTRODUCTION
Acetonitrile and its isotopic species have been extensively studied by using a variety of spectroscopic techniques. The ground-state microwave spectrum of CHjC”N has been investigated by Bauer et al. (1, 2). The spectrum has recently been remeasured accurately by Demaison et al. (3) and highly precise rotational constants are determined. Microwave spectra have also been analyzed for the vg (2) and 2~~ (4, 5) excited vibrational states. These rotational transitions in the u8 = 0, 1, and 2 states have been reanalyzed by Careless and Kroto (6) and by Bauer et al. (7), and the vibrational dependence of the rotational constants has been obtained. As for the v4 state, the microwave spectrum with K < 6 has been analyzed by Bauer and Godon (8). The infrared spectrum of the v4 band has been measured with moderate resolution by Duncan et al. (9), and the band origin has been determined from the Q-branch maximum. No rotational analyses, however, have been reported for this band. Recently, the v4 band of CHjC14N has been studied by Rackley et al. (10) and Igarashi et al. (11) by means of laser Stark spectroscopy. Rackley et al. analyzed the spectra with K < 7 and fitted them to a model which includes v4-v7 Coriolis coupling. Igarashi et al. analyzed the spectra with K < 10 and attributed the perturbation around K = 7 lines to the Fermi interaction between u4 and 3~;. The assignment of the spectrum with K = 7 by Rackley et al. is also different from that by Igarashi el al. It is necessary to examine the v4band of various isotopic species in order to determine the major perturbation in the v4 band of acetonitrile. Duncan et al. (9) have discussed the possibility of Fermi resonance between v4 and 3~; by studying the fundamental vibration frequency displacements on isotopic substitution. They estimated the absolute value of the interaction matrix elements 1W4gg3 to be 25 cm-‘. Igarashi et al. (II), however, determined lW4,,,l = 0.38 cm-‘. Since the discussion by Duncan et al. was based on the small amounts of discrepancies 0022-2852184 $3.00 Copyright Q 1984 by Academic Press, Inc. All nghts of reproduci,on I” any form resewed.
26
LASER
STARK
SPECTROSCOPY
OF CH3C’5N
27
between the calculated and observed isotopic shifts (0.2-0.4 cm-‘), it is considered desirable to determine the band origins of various isotopic species with higher resolution. In this study, laser Stark spectroscopy .was applied to the v4 band of CH3C”N. Before the analysis of the whole band, each K subband was analyzed separately. This subband analysis was very useful for clarifying the effects of perturbations involved. EXPERIMENTAL
DETAILS
The sample of CH,C15N was obtained from Merck Sharp & Dohme of Canada. The isotopic purity ensured was 95% or greater. The sample was used without further purification. Laser Stark spectra of the v4band were measured using a flowing gas laser, operated on “CO2 regular band P(40) to P(60), Ol’l-[ 11’0, 03’01 hot band P( 11) to P(34), 00°2-[ 10’1, 02’11 sequence band P(4 1) to P(49), and N20 P( 12) to P(40) around 10.6 pm. We also observed the spectra using a sealed gas laser operating on i3C02 R(2) to R(22), P(4) to P( 16) and ‘3C’802 P( 12) to P(34) around 10.6 pm. The regular band frequencies of COZ, 13C02, and ‘3C’802 lasers were taken from the recent measurements of Freed et al. (12). The frequencies of CO2 hot band were taken from Whitford et al. (13) and Monchalin et al. (14). Its frequencies of sequence band were taken from Siemsen et al. (15). The frequencies of N20 laser were taken from Whitford et al. (16). Gas pressures of the sample in an absorption cell were typically about a few milliTorr, and the measurements were made at room temperature. The Stark field of up to 28 kV/cm was used in this study. The amplitude of Stark moduration was about 100 V/cm for most of the measurements. The electric field strength was calibrated by using the Stark effect of CH3F (I 7). The accuracy of the voltage measurement was about 0. l%, and the resonances, whose Stark shifts were larger than 10 GHz, were omitted from the analysis. Most of spectra were observed in the parallel polarization, resulting in the selection rule AA4 = 0. Several spectra for low J transitions were observed in the perpendicular polarization corresponding to the AM = + 1 selection rule. A representative spectrum with I( = 7 is shown in Fig. 1. ANALYSIS
(A) Subband Analysis In the course of the assignment of the spectrum, an anomaly was found around K = 7 lines. Presumably, an interaction with another energy level nearby may produce the irregular spectrum. In order to know the nature of the perturbations involved, we made the analysis of each K subband before the interpretation of the whole band. The subband origin z&, and the effective rotational constant B& of the v4 state were determined by the least squares method, and their dependences on K were used as a criterion of perturbations (18). Each Stark shifted transition frequency was calculated by setting up and diagonalizing the upper- and lower-state Hamiltonians, and was fitted to each laser frequency. The Hamiltonian for the present system is described as H=H,+H,,
(1)
28
MITO, SAKAI, AND KATAYAMA C H3C15N Vbband
FIG. 1. Laser Stark spectrum of v4 band of CH$?N taken with the CO2 hot band P(25) laser line near 906 cm-‘. AM = 0 transitions of QP6(9), aP,(9), and QPs(9) are observed.
H,, denotes the unperturbed Hamiltonian of the symmetric top, and its nonvanishing matrix elements are (~4, J, KtHobt, J, K) = z&, + B&J’(J’ + 1) - (D;)effJ’z(J’ + 1)’ - (D;&J’(J’ (G.S., J, KIH,IG.S.,
+ l)K’,
(2)
J, K) = B”J”(J” + 1) - D[;J”2(J” + 1)2 - DL;,J”(J” + 1)K2
+ H;J”3(J” + 1)3 + Hl;KJ”2(J” + 1)2K2 + HbJ”(J”
+ 1)K4,
(3)
where J-independent terms are absorbed in I&, . The matrix elements of Hs, the Stark term, are expressed as (u, J, K MHsb, J, 4 M) = -PL,EKMI[J(J + (0, J, K Mffsb,
l)l,
(4)
J - 1, K M) = (pVE/J)[(J2
- K2)(J2 - M2)/(2J
- 1)(2J + 1)]“2,
(5)
where E is the electric field strength and pclvis the dipole moment in the given state v. The constants in the ground state, B”, DI;, DI;K, H;, HI;K, and Hb, were constrained to the microwave values of Demaison et al. (3). Those in the v4 state, (D’& and were assumed to be equal to 0; and D :KK,respectively. Consequently, v&i,, WIK~T, Bbff, and the upper- and lower-state dipole moments were included as parameters in the fit. Truncation limits for Stark effects were the same as those in the analysis of the band system in the next subsection. If a band is not perturbed by any interaction, the following expressions are obtained: &,, = v. + (A’ - A” - B’ + B”)K2 - (DZ - D;)K4,
(6)
BL.n = B’ - (D>K - D[;K)K2.
(7)
Figure 2 shows the relation between the &, values obtained for each K subband and K, and the B&values are plotted against K2 as shown in Fig. 3. For simplicity,
LASER STARK SPECTROSCOPY (cm-‘1
vsubo
.O.O0555LK*
OF CH$?N
29
-7.5.10‘7KL
911.72
I 911.71
91169%
’ 1
’ 2
’ 3
’ 4
’ 5
’ 6
7
’ 8
! 9
’ 10K
FIG. 2. K subband origin I&, + 0.005554K’ - 7.5 X lo-‘K4 plotted as a function of K. Figure shows another vibrational energy level crosses between K = 7 and 8. Error bars represent 2.5 times standard deviations.
u$,~ + 0.005554K’
- 7.5 X 1O-7 K4
(8)
is used for v$, in Fig. 2. The values of the dipole moments obtained for different K with each other within their experimental errors. The upper- and the lower-state dipole moment of K = 10 subband were fixed to each mean value of K < 9, because only a few resonances with K = 10 could be observed. Figure 2 shows clearly that another vibrational energy level crosses between K = 7 and 8, and its energy level at K < 7 is higher than that of the v4 level. A comparison of these figures demonstrates clearly that the value of r&i, in Fig. 2 is more affected than that of & in Fig. 3, but an irregularity of the Bkff values around K = 7, 8 is still observed as shown in Fig. 3. If the perturbation is caused by a J-dependent interaction, the deviation of B& at K = 8 has the opposite sign to that at K = 7. Figure 3 shows, however, that both values of B& at K = 7, 8 are larger than the expected values on the straight line. These facts indicate that the perturbation is evidently due to the Fermi interaction with the higher vibrational energy level (a), and that the rotational constant B of the perturbing state is larger than that of the u4 state (b). The 3~2 state were coincident
Betf’
(cm-‘) 0.29617
@
=I;
I
t
122z32 h2
52
6?
72
82
92
10ZK2
FIG. 3. Effective rotational constant B& plotted as a function of K’. An anomaly is shown at K = 7 and 8. Error bars represent 2.5 times standard deviations.
30
MITO, SAKAI, AND KATAYAMA
is considered to be the best candidate for the perturbing state, because the state satisfies the above (a,b) conditions. The 3~; vibrational state includes nearly degenerate Al and A2 states, one of which has the same symmetry as the v4 (A,) state. The rotational energy levels are coupled each other by Coriolis interaction about the symmetric axis except for K = 0. As discussed by Hougen (19), if the vibrational splitting between the A, and A2 states is much smaller than the magnitude of the Coriolis interaction, their rotational energy levels are conveniently considered to be similar to those arising from a degenerate E vibronic state. This condition is satisfied in the present case, because the energy splitting of A, - A2 is possibly within a few cm-‘, being much smaller compared with the value of 2A{KZ N 200 cm-’ at K = 7, where the interaction investigated in the present article has an important role as demonstrated by our experimental results. Since the splitting is not known experimentally but is assumed to be small, the vibrational splitting between Al and A2 states is completely neglected in the present analysis. We calculated the unperturbed energy levels of v4 and 3~; states for the case of J = 0. The calculation was made on the following assumptions: the rotational constants B and A of both states were equal to the ground-state values (3); A[ was equal to the value obtained by microwave absorption (7); and the v4 band origin was equal to the subband origin of K = 0. By adjusting the 3vg3band origin to the value of about 1120 cm-’ as estimated for CH3C4N by Duncan et al. (9), we obtained Fig. 4, where the energy levels are plotted as a function of K. Figure 4 indicates that relatively large Coriolis term of 2A{Kl N 27.6K (cm-‘) gives rise to the crossing of their rotational levels around K = 7, although the 3~: vibrational level separates from the v4 level by about 200 cm-‘. (B) Analysis of the v4-3~: Band System Having examined the effect of the interaction involved in the v4 band, we subsequently analyzed the v4-3~: band system in which the Fermi interaction was taken into account. Nonvanishing matrix elements of Hamiltonian are expressed:
CH3C"N E(cm-') 1500-
0
/
12
3
4
5
6
7
6
9 IO
FIG. 4. Unperturbed energy levels of the vq and 3~: states for the case of J = 0, which are plotted against K. The energy difference AE between vq and Kl > 0 is about 8.8 cm-’ at K = 7.
LASER
STARK
SPECTROSCOPY
OF CH3C?N
31
(u,, J, KIHOIv4, J, K) = v. + B’J’(J’ + 1) + (A’ - B’)K’ - D;J”(J’ (G.S., =
J, KIHoIG.S., B”J”(J” -
+
-
B”)K2
-
DI;J”?(J”
+
1)2 -
&,,(J”
+
])K’
+ H;J”‘(J” + 1)3 + HI;KJ”‘(J” + 1)‘K’ + HkJJ”(J”
+ 1)K4,
(3v8, J, K, 1 = +31H013u,, J, K, 1 = -t3) = v. + BJ’(J’ + 1) + (A - B)K’ - 2A{Kl+
elements
of the Fermi
interaction
(v41H013vs, 1 = *3)
(10) (11)
&‘(J’
+ 1)KI + qKK31
- DJJ”(J’ + 1)’ - D,,J’(J’ The matrix
(9)
J, K)
1) + (A”
D;K4
+ 1)2 - D;KJ’(Jr + l)K* - DkK4,
+ 1)K2 - DKK4.
(11)
terms are = kV4888.
(12)
Those of the Stark effect term are the same as in the subband analysis. Because of Stark interaction of AJ = + 1 type, the matrix is infinite in size. We used fixed truncation limits, truncating at J,,,,, = J + 5 for J > 3 or J,,,,, = 7 for J < 3, and at Jmin = J - 7 for IKI or IMI < J - 7. This truncation introduced no appreciable errors in the calculations and the results were the same as the case that J,,, = J + 4 and Jmin = J - 6. The maximum size of the matrix was 39 X 39, because 1~~)was connected to both /3vs, I = +3) and 13us, f = -3) by the Fermi interaction. The constants in the ground state, B”, D;, DL;K.HI;, Hj;K, and HkJ;,, were constrained to the microwave values of Demaison et al. (3), and A” was constrained to the value of Mast-i et al. (20). The constant Dk was also constrained to the value of Duncan et al. (9). The vibrational A, - A2 splitting of 3~: was neglected, as mentioned in the subband analysis. The constants in the 3ui state, A{, DJ, DJk., and were constrained to the values which were calculated from the microwave values (us, 2~) of Bauer d al. (7). The constants were the same as those calculated from the values of Careless and Kroto (6). The value of nK was arbitrarily fixed to zero, because any data was not obtained. Those of A and DK were fixed to the ground-state values. The dipole moment was constrained to the value which was determined for the 3~; state of CH3C14N by Igarashi et al. (II). Consequently, the ground-state dipole moment, all of the u4-state constants, the 3~; band origin, and rotational constant B were included as parameters in the fit. The weights of the resonances for each ro-vibrational transition, which were observed with one laser line and under the same AM selection rule, were given so that their total was unity. The total of 644 observed Stark resonances, which were assigned to 139 transitions, were analyzed by the least squares method and the molecular constants determined in the final fit are presented in Table I. A complete list of the data included in the fit, together with residues, is given in Table II. The spectra observed by using the CO2 regular band P(56) or hot band P(23) laser line were eliminated from the analysis because the laser lines overlap each other. For several high J transitions which were very close to the laser lines, their A4 components were not separated. We calculated the sum of the spectral shapes of the qJ,
32
MITO, SAKAI, AND KATAYAMA TABLE I Molecular Constants of CH,C”N (In units of cm-’ except for dipole moments in Debye) Microwave
vO
Ground state
3V63
911.712306(531a
1113.57(10)
B
0.29616430(53)
A
5.2400031(35)
0.29616415 (e)
[
AS
[
0.30013(66)
lb
( 5.247 4.60
(f)
1
1.1919(52)x10-7
1.187x10-7 (e)
[ 1.274~10-~ I lg)
DJK
5.791(13)x10-6
5.774x10-6
[ 5.707x10-6
DK
9.3947(38)x10-5
[
9.47x1O-5
I
(j) If)
ig)
DJ
(e)
0.297607334
[ 5.247 1
1 (gl
I
(hl
[
1.193t3x10-7
[
5.63867X10S6 I (j)
1
(j)
( 9.47x10-5 1
(h)
"J
I 0.0
lj)
RJK
[ 2.97x1O-11 1
Ij)
HKJ
[
(jl
'IJ
1 1.247~10-~
'IK
I 0.0 I
u
3.9354(7)
(C)
[ 3.87 1
I (g) (d)
(c,i)
I
2.40~10-~~ 3.9256(7)
1
(Cl
I"148881 0.3908(15)
(d) Arbitrarily fixed to zero.
a. Errors in parenthese are 2.5 times standard deviations in units of the last significant figure.
(e) Ref. (a).
b. Quantities in square brackets are fixed values.
(gl Ref. (1,.
(h) Ref. (2).
(c)
(i) Ref. (11) -*
(j) Ref. (1).
Absolute uncertainties for dipole moments are 0.1%.
(fl Ref. (=I.
individual A4 components and derived the electric field strength of the first A4 component by fitting the calculated spectrum pattern to the observed. The calculations were made by the approximation of the first- and the second-order Stark effects, because higher-order corrections were negligible. The electric field strengths determined with this procedure are indicated in Table II by asterisks. DISCUSSION
The vibration-rotation parameters given in Table I are determined with great accuracy. The observed data can be reproduced with the standard deviation of 4.6 MHz. This is considered to be a proof that the model (~~-3~2Fermi interaction) used in this analysis is adequate. It may be noted that the K subband analysis was also useful in laser Stark spectroscopy for the examination of such an accidentally perturbed band. For comparison, the microwave values of rotational constants for the u4 state are given in Table I (8). The rotational B and centrifugal distortion constants DJ and DJK obtained are in good agreement with their microwave values. The 3~: rotational constant of B = 0.30013 + 0.00066 cm-’ obtained is in good agreement with the calculated value of B = 0.30024 which is extrapolated from the v8 and 2v8 microwave values (7). We also made the analysis of the band system, in which A r was included in the fit. The derived constant A{ = 4.73 + 0.74 cm-‘, although not determined
LASER STARK SPECTROSCOPY
33
OF CH,C”N
TABLE II Observed Stark Resonances of CH,C”N
Transitiona
M’
+
co2
M”
O-C,MHZl’
E,“,Crnl
Laser
co2
P(40)=924.97398c -23 QR 5(231
945
Pt42,=922.91429 OR 4(19) 19
2480
P1461=918.71833 -12 QR 81121 -10 QR 91121 -7 -6 -4 -3 QR10112, 10 9
19924 24067 3175 3731 5537 7456 16112 17803
ld
l
OP
51101
QP
61101
4.8
-1.2
5.1 16.5 1.8 3.9 -1.5 -0.3 -9.0 -0.6
P16Ol=903.21177 QP 91131 12 11 10 9
8 7 12
UP101131 P,48)=916.58177 -8 QR 6( 81 -7 -6 -5 *87!8) -8 -7 -6 -5 -4 -3 -8 QR 81 81
17341 19993 23496 28619 6320 7241
-11.1 4.5 0.3 3.9 -2.7 -3.0
8478
-3.9
10264 12982 17930 463
*
-0.3 -3.0 6.0 -0.6
P,50,=914.41928 QR314l -4 -3 QR414, -4 -3 -2
13912 19067 7638 10576 18375
-14.4 -0.9 -16.5 -15.3 -3.0
P1541=910.01585 0 QP 01 3) -1 QP II 3) QP2l3) -2
21506 15598 5708
1.5 3.6 12.6
28678 7942 9079 12744
8.7 -2.4 -2.4 0.6
8353 9504 11059 16417 7775 8769 10105 11899 18619 17258
-5.7 -1.5 -1.8 -5.4 0.3 4.5 1.8 0.6 -4.2 -0.6
18141 21673 27001 20510 25326 8469 10195 17426 8416 lOiOl
0.6 -3.9 2.7 4.2 9.3 -3.0 -5.1 -3.9 -0.9 -4.8
P,58,=905.50659 QP 31101 QP 4tlOl
8 7 6 4 ? 2 12 0
71 91
4 3 1 8
3
4
P,l4,=915.62774 QR3l6l -6 -5 -4 -1 -2 0
OR 41 61
-1
-6 -5 -3 -2 -1
a.
QR
b.
O-C
c.
Laser
d.
+ denotes
51231
-3 -2
means
laser
15
-----
co2
laser
_
Hot
P(lll=918.25807 QR 7(111 -11 -IO -9 -8 QR 8,111 -9 -8 -7 -6 -5 QR 9(111 9 8 7 6
QR
54 9)
QR 6( 9)
-1
-6 -5 -4 9
P1221=908.48736 QPl(5) 3 QP 2( 51 4 3 4 3 2 10 4 QP 3( 51 3 2 4 3 2 10 4 4 QP 4( 5) 3 2 1 3 2
2706 3095 3637 4351 5435 11820 13561
0.3 0.0 -3.0 -1.2 -0.3 2.1 -1.2
15976 17429 19148 21187 23784 27077 605 *
-3.3 1.5 3.6 -1.2 3.6 8.1 0.6
Band
13144 14472 16085 18187 2968 3368 3858 4497 5400 13675 15312 17426 20197
P(121=917.35000 QR 3( 91 -6 -7 QR4(9) -8 -6 -5 -5 -6 -4 -5 0
6 8 7
OR 6( 9)
QR
l,a*er
-8 -7 -6 -5 -4 -8 -7
2
3 2 1
3 2 1 5
2 1
frequency
minuscalculated in cm-l.
transition
unresolved
M-components;
see
text.
-3.3
-4.2 -6.6 0.3 -3.3 0.6 1.5 0.6 -0.3 -4.2 0.3 0.3 0.6
23944 15247 20310 24364 11379 12567 21324 2712 3294 4120 7425
4.5 -2.1 -1.2 0.6 -4.2 -1.5 0.0 -3.6
28082 19422 25388 13441 16239 20379 27506 12251 15882 22200 8219 9856 12151 15840 24262 7307 9505 13319 20960 5830 7160
13.8 -8.1 6.9 -14.4 13.2 9.3 20.7 -14.4 -9.3 0.0 -5.7 -5.4 -8.1 3.9 6.0 -21.9 -10.8 -9.3 -6.9 1.2 -3.3
AK = 0, &J = tl, K = 5, and J = 23.
frequency
-----
frequency.
i:: -3.6
34
MITO, SAKAI,
AND
KATAYAMA
TABLE II-Continued Transition
M’
+
M”
-6
E,“,Crni
O-CIHHZl
3452 3449 3127 3902 5126 3837 5293 7868
-3.3 -0.3 2.7 0.6 -3.6 -0.3 -1.5 1.2 -2.4
4 4 3 4 3 2 -5 -5 -3
22935 18970 24207 17222 21730 28819 23219 14426 27558
3.0 6.3 4.8 15.9 8.1 -7.5 15.6 -3.6 6.3
P(16)=913.88037 QR2(3) -3 -2 QR3(3) -3 -2
14035 20179 6755 11164
2.4 -4.5 -4.8 -1.8
P(17)=913.11803 QR O( 1) fl QR l( 1) 1 0
16869 8882 17109
1.8 20.7 0.0
P(20)=910.31020 ?l QP Of 2) t1 0 ?I t2 QP l( 21 1 0 10 0 -1 12
16019 13952 26814 7821 15779 5486 10207 15252
-6.9 2.7 30.0 -14.1 -5.1 -12.9 -15.3 -1.5
2 2 1 -3
20972 13555 20104 16511
-25.5 -14.7 -22.2 17.1
6 5 4
-9 -8
14922 17744 21910 9074 10057 11287 14973 17836 1786 2043 2369 2837 4697 6900 1593 1804 2072 2403 2848 4167 5022 6336 8658 6153 8259
-3.9 -5.4 3.6 -0.9 -4.5 -5.7 0.0 -2.7 2.1 3.0 0.0 0.0 2.1 1.5 1.2 5.1 7.8 4.5 -2.1 6.9 6.6 5.1 -2.1 3.6 0.6
P(26)=904.76597 10 QP 51111 7 6 5
19661 28026 18245
3.3 8.7 16.5
QR5(6)
2279
-4
0 QR
-1
6( 6)
5 4 3 0 7 6
P(15)=914.85382 QR 2( 4) QR 3( 4) QR 4( 4)
QR 4( 5, QR5(5)
1 6 5
Transition
M’ +
QP 3( 4,
QP
61 91
6 5 4 2 10 QP
71 91
QP 81 91
5 4 3 1 8 7 6 5 3 2
5 4 3 2 10 -6
4 3 2 1
-5
-4 -3 -8 -7
0-c
(MHZ)
9256 12947 14723
-3.9 -3.9 3.9
22340 25146 28624 18369 21340 25449 17368 23720 11364 13544 16777 21841 9147 10523 2689 3144 3762 6175 2003 2237 2533 2927 3447 4205 7260 16014 8040 8577
-0.9 15.9 9.0 -0.3 0.6 5.1 -5.4 5.1 -3.3 -3.9 3.3 3.9 -5.4 -7.2 -6.3 -2.7 -3.3 -3.6 0.0 0.0 -0.3 1.5 -0.6 -0.3 0.3 3.3 -1.5 -1.2
27494 21352 24345 15703 17277 19158 21525 24604 11273 12848
21.0 -2.7 7.8 0.0 5.4 0.9 2.4 14.1 -8.1 -6.0
-9
24755
-7.5
P(28)=902.86734 QP 6114) 13 11 9 7 QP 7(14) -13 -12 -11 -10 -9 -8 -7 QP 8(14, -8
13287 15718 19133 24676 6641 7234 7856 8683 9659 10834 12408 27589
-2.7 -0.6 -6.3 -0.3 5.1 0.6 4.8 0.6 0.0 3.0 1.8 -0.6
17913 19629 21572 24027 26926 7900 8572 9329 10264 11431 12872 20504
-4.2 2.7 I.2 5.1 -1.2 2.7 1.5 3.6 3.6 1.8 I.2 3.0
P(241=906.63929 QP3181 6 5 4 QP 4( 81 7 6 5 4 2 QP 51 81 6 5 4 3 4 3 7 QP 61 81 6 5 3 6 5 4 3 2 10 QP 7( 8) -4 -2 -7
P(21)=909.57909 QP II 31 QP 21 31
MX’ E (“/cm)
10 0 -1 4 5
5 4 3
3 1
3 2
5 4 3 2 1
-8
0
1
P(25)=905.95028 QP4(9, 6 QP 5( 9) 8 7 7 6 5 4 3 QP 6( 9) 8 7
QP
9(12)
P(29)=902.23148 12 QP 6(15) 11 10 9
8
QP
7(15)
-13 -12 -11 -10 -9
QP
8(15)
-13
-8
5
6 5 4 3 2
LASER STARK
SPECTROSCOPY
OF CH#?N
35
TABLE II-Continued Transition QP
QP
M’ +
cc111
7111)
QP
8,111
QP
9111)
6 5 4 10 11 9 10 -10 -9 -10 -8 -9 -5 -10 -11 -9 -8 -3 -2
P(271=904.10214 QP 5112) QP 6,121
QP QP
M”
7
6 11 10 9 8 7
6 8 7 6 5 3 -11 -11 -10 -9
7(121 81121
-8
QP
9112)
QR
9(14,
7 6 5 4 2
-7 -7 -6 -6 -5 -5 -4 -11 -12 -10 -11 -10
E(V/cml
O-CIMHz)
11150 13363 16618 13201 16402 5801 14332 19146 24619 23642 23570 26692 27459
i8079 15046 16549 18336 20589 23491 27361 12347 13367 14512 15913 19695 585 8644 9511 10571 11958 13675 7651 8314 9130 17030 20823 22172
-1.2 0.9 1.5 -1.8 -0.9 2.4 0.6 1.5 1.z -9.9 -13.8 -11.4 -0.9
*
7.5 4.8 6.3 2.1 0.9 1.8 5.1 -3.9 0.3 -3.6 -2.7 -2.1 0.0 -0.6 0.6 2.4 -3.9 -0.3 3.3 6.3 4.5 -0.6 0.3 -3.6
P(301=900.94336 QP 6(171
QP
7(17)
P,3l,=900.33828 QP 6(18)
0.9 1.8 -3.6 10.5 3.6
QRlO(14,
8 6
22661 25613 5949 7955 9658 3379 3767 4216 4798 17722 23331
-0.6 7.8 0.0 -0.3 7.8 4.2 1.2 4.5 6.9 13.8 3.6
OR
Et101
QR
9(10)
22 il 2 1 0 2 1 0
9732 25937 3218 6366 26883 2481 4515 12743
14.4 6.0 11.1 15.3
-5 10
8
P(49,=913.51203 QR 0, 2, @R
1(
2)
QR
2(
21
_____ R(
2,=915.73396 *R 2, 6) OR
3(
6)
QR
41
6)
13CO*
-3 -2 -6 -5 -4 3
Laser
17482 24687 1607 1956 2444 5964
13 12 11 10 9 8
12634 13806 15077 16632 18460 20743
-12.0 -6.3 -5.7 -3.9 -5.1 -6.6
1.5 -1.8
1559 26691 28235
f
-4.2 -5.7 -3.9
P(33)=898.42251 QP 6(211
-20
5091
*
-8.1
P(34,=897.01908 QP 7(23l
22
1691
*
---
-I(201 8120)
CO2
Laser
sequence
Band
0.0 ---
P(41,=921.87024 QF! 3(17l P(431=919.81854 QR 8(14l QR 9(14)
R(
8)=920.21948 QR 3,141 QR
4114)
R(22)=929.99305 QR 6133) P,
P,
P,
3.3 3.0 -4.8 0.0 0.0 0.3
-5.1 0.6 7.5 6.0 -3.3 0.0 -0.3
-19 -18 -17
OP QP
;:: 8.1 10.2
____.
22879 24482 26334 28346 10900 lil8B 13937 16204 19560
P(32)=898.99396
-17
4754
-14 -9 -8
27320 4880 5520
13 6278 8836 18527 19947 26502
-7 -5 13 12 9
16 15 14 13 -9 -8 -7 -6 -5
4)=910.27796 QP 0, 2) QP II 21
6)=908.67515 QP OI 51 QP
II
51
QP
21
51
*P
3,
51
QP
4,
51
8)=907.05284 QP 5( 71 QP
61
7)
P(10)=905.41104 QP 4(101
CO*
*
-8.7
-12.0 1.2 3.3
l,a.ser
-8 -7 11 10
21718 24386 12185 13410
4.8 -1.8 0.0 0.3
33
4712
-1.5
+I 1 0
17396 8938 17145
1.8 -18.6 -12.3
t4 i3 4 3 2 4 2 1 -3 -2 -1 -3 -2
17935 27108 5145 6970 11029 955 1927 3849 1927 2916 6134 4411 6970
0.0 3.3 -3.0 -3.0 0.0 -3.9 -1.8 -2.1 -1.8 -1.z 2.1 -0.3 -9.9
2 5 4
24438 28738 16376 19298 23426
17.4 15.3 2.4 -0.3 7.5
9
25519
10.2
6
MITO,
36
SAKAI,
AND KATAYAMA
TABLE II-Continued Transition
M' + 6 5 4 5 4 3
QR SC 6)
OR
RI
6( 61
41=917.24878 5, 91
QR
-9
-8 -7
QR619l
QR
-8 -7 -5 -4 9 8 7 8 9 7
71 91
QR 8( 91 QR 91 91
RI 6)=918.74396 QR 91121
M" E[V/cmi
O-CIMHz)
I
Transition.
6776 8080 9996 12160 14902 19092 26060
2.4 3.3 3.3 -1.8 -3.6 -3.9 -4.8
QP
5110)
QP
6110)
19460 21923 25147 7691 8778 12389 15587 4454 5006 5711 11422 18597 23512
-1.8 -1.2 4.8 0.9 -3.3 -1.2 -3.0 3.0 3.0 3.3 -3.6 -13.8 -4.2
QP QP
71101 81101
2850 3202 3663 4288 5131 6382
2.4 2.7 2.1 0.0 0.6 1.2
9 8 6 4
;: 9 8 7 6
0.6 -2.1 -0.9 6.9 4.2 5.4 0.9 4.5
P116)=916.81456 QR 3C 8) -8 -7 -6 -5 QR 4( 8) -7 -5 -3 8 QR 5( 8) 7 6 5 4 8 QR 61 81 6 4 3 QR 7( 81 6 5
17656 20061 23266 27811 6322 8855 15012 2663 3078 3580 4296 5423 9527 12616 18518 24089 21797 25826
1.8 -3.0 -4.2 5.1 -3.3 -3.9 8.7 7.8 0.6 2.1 1.2 -6.0 -2.4 -3.6 0.3 -4.5 -1.5 -17.1
-6.0 -0.9 0.3 -6.3 -2.4 0.9 -2.4 -5.4 -5.4 1.5 -2.7 -6.6 -4.8
P1121=903.74974 QP l(131 -12 QP 2,13, -9
9382
21937
-0.9 -2.7
P(14)=902.06895 QP 9115) -9 -8 -7
5384 6053 6917
1.5 2.1 2.7
QP 9(10)
P(16)=900.36865 -17 QP 61181 _____
2
QR
31 5)
QR
41 5)
OR SC 51
3 2 5 3 2
P(20)=913.64451 22 OR 01 2) 2 QR II 2)
18440 24994 20911 6368 8018 16341 11996 17499 8684 14033 22307
22697 12174
2966
13c1802
-9.6 -5.4 -8.7 13.2 5.7 -2.7 3.3 0.3 12.9 -6.0 -2.1
-18.9 10.2
LaSer
P(12)=919.89443 QR 8(14) -13 -12
P(30)=905.32296 QP 5(10) QP 6(10)
*
-3.3
_____
10236 11102
4.5 5.4
Laser
9 8 7 6 5 6 5 4 3 -4 -3 -9 -6 -4
26924 16406 18706 21708 25851 4426 5302 6566 8705 7167 9700 11482 17611 27877
12.6 0.0 3.9 4.2 8.1 -2.4 -1.8 -5.4 -2.4 -3.9 -3.9 3.0 -1.8 -4.8
Pl32)=903.59029 QP 4(13) 11 10 QP 51131 11 10 9 QP 6(13) -8 -7 -5
25294 27825 6460 7084 7898 13401 15367 21565
4.8 2.7 -0.3 -2.4 -0.3 -3.6 -6.9 -7.2
QP
7LlO)
QP
8(1Ot
QP
9(10)
P(34)=901.83469 QP 11161 15 -----
P(181=915.24082 QR 0, 5) f5 f4 2 QR 1( 5) QR 2( 51 5 4
O-C(MHzI
13061 14704 19526 2671 3024 3472 4024 4797 5979 9554 15819 18638 22051
13c1802
10907 13323 17179 5343 6542 7344 8423 9770
QR 7(11)
M" ElV/cml
9 8 6 9 8 7 6 5 4 -7 -7 -6 -8
13~180~laser P1141=918.36575 -11 QR 6(11) -9
M' +
N20
5717 Laser
*
2.7
----_
P,12)=928.61661 QR 41301 -30
6107
*
4.2
P1161.925.09696 QR 2(23l -23
6932
l
1.2
P(lEl=923.31713 -20 QR 6(20)
5279
*
-8.4
P(191=922.42221 QR 3,181 18
6433
'
-0.6
P,20,=921.52398 QR 81171 -17 QR 9(17) 14
15250 20152
7.5 9.0
LASER
STARK
SPECTROSCOPY
OF CH$?‘N
37
TABLE II-Continued Transition
M' +
C'R 2( 21
M" ElV/cml
1 2 1 0
20629 8256 13192 24334
0-CfMHZl -6.6 10.5 3.6 -30.0
P(24)=910.38402 r1 QP O( 2) 1 QP II 2)
12566
0
1228,
-12.6 6.9 -9.0
QP O( 5)
0
QP I( 5) QP2(5)
-1 -4 -1 -2
20304 23604 13955 4208 16268 10162
-2.1 -3.6 -1.2 0.9 -1.8 2.7
6 6 5 4
26103 17794 20967 25406
19.5 -4.2 2.1 14.1
10 9 8 7
14719 16371 18315 20867
1.8 -5.4 1.2 -1.2
4 9 8 7
23046 25758 5234 ,508 1,769 ,105 ,945 9054 12742 15794 19619 22012 25110
15.9 5.1 -9.0 -6.3 -0.6 -1.8 3.9 6.0 -5.7 -2.4 5.1 2.4 -9.3
8 6 8 7 8 -9 -8 -7 -6 -5 -4
26555 27814 22543 2571, 25241 6482 ,312 8398 9836 11969 15262
-11.4 -11.4 -9.0 -11.4 -11.1 -9.9 -9.0 -6.0 -9.3 0.3 4.2
Transition
M' +
M" E(V/Crn) 0-C(HHZ)
13
21778
P(21,=920.62242 -15 QR 6(15)
2601
2.4
'
1.5
P(22)=919.71754 5185
PR 2(13) OR 3(13)
13 11 10 8
933 18329 20277 25601
0.0
4.5 0.9 -2.7
P,26)=908.71977 ?1
QP
3( 51
QP 5( 7) QP 6( 7)
QR 91121
P,24)=91,.89,83 -9 QR 4,101 -8 -10 OR 51101 -7 -3 9 QR 6(101 8
QR
,(lO)
P,25)=916.98301 QR II 8) QR 3( 8) QR 4( 8) QR QR
5( 8) Y( 9)
P(23)=918.80935 QR 7(121 -10 -9 -8 QR 8(12l -11 -10 -9 -R
-;
QR
QR
9(12)
5( 51
;;
-2 5
P128)=914.21869 QR 11 31 QR
21 31
QR
31 3)
18180 21319 25963 8978 1052, 12770 16253 22634 968 1139 1383 1731 2352 3564 7811
4.5 -3.3 11.1 -7.2 -8.4 -3.6 -2.1 2.4 -7.5 -4.8 -0.6 -1.2 3.9 2.1 0.6
P,2,)=915.14344 QR 2, 51 -4 -2 -3 -4
11854 2224, ,070
-4.8 0.9 -4.5
-1 4
P(30)=912.35929 QR O( 0)
9.0 8.4 12.0 -2.1 -0.9 -1.5 -1.8 0.0 1.8 5.4
11724 13243
2.7 -3.9
17911 26298 12509 1,649 10368 14335 2179:
-4.2 -5.7 -0.3 6.3 16.2 3.q -1.2
2,448 2421, 15409 8029 519, 8646 17190
19.8 5.4 -7.2 -8.4 -4.8 -4.8 -0.6
3902 6121
-4.8 17.1
5861 1105 5314 24525
-2.1 -4.5 3.0 0.6
-3 -3
2,221 14685
-2.1 0.6
3 4 3 4 3 2 1 4 3 2 i
23015 8755 11592 4104 5411 ,922 14097 925 1238 1843 3493
1.5 -3.9 -7.5 -3.0 -5.1 -1.5 -2.7 -6.0 -2.1 -0.3 -0.6
5 4 -6 -6
19395 23458 29023 26405
-24.3 -15.3 9.0 8.1
3 2 3 2 3 2 1
P(29)=913.29064 '1 0 QR 0, 21 -1 QR If 2, 0 -1 -2 QR2(21 -1 -2 0 -1 -3 -2
0
!l
0
P(32).910.48668 tl QP 01 21 1 QP II 2) 0 -1 pt331=909.54543
QP 2( 41 QP3(41
P126)=916.06488 -7 QR 5( 7) -6 -5 QR 6( 7, -7 -6 -5 -4 -3 QR ,( 7, -7 -6 -5 -4 -3 -* -1
19993 22239 25104 4107 4528 5028 566lI 6491 7605 13382
P(34l=908.60088
QP l( 51 QP 2( 51 QP
31 51
QP
41 51
P(351=907.65304 QP 51 61 QP 41 71 QP5(7)
MITO, SAKAI, AND KATAYAMA
38
TABLE II-Continued Transition
M'
+
0 QR
3C
51
M" -1
12509 2902
-5.4
3653 7370 2617 4124 996 1258 1685 2476 1098 1416 4098 6624 7656
-1.z -4.5 -5.1 -1.8 3.9 -0.6 -3.6 1.2 4.2 1.8 -5.4 4.5 -1.2
-3 -1 5 4 3 2
12 0
1 5 3
-1
0
N20 QP 71 9) QP El 91
0.0
-4 -2 -2 0
5( 5)
O-CWHz)
-5
QR 4( 5)
OR
E(V/cml
TransitIon
QP
31 8)
QP 41 81
QP
71 8,
P1371=905.74748 QP 7C 91
Laser
QP 7,11, QP
9t11,
P,391=903.82875 QPlOilZl
c
E(V/cmi
O-CLMHz1
7 6 5 6 5 4 -7 -5 -4
19679 22934 27555 12074 14432 17915 8866 12655 16219
0.3 -0.9 8.4 -2.1 -2.7 -3.0 3.6 3.9 0.3
8
21299
-8.1
N20
7 8 7 6
24161 14040 15971 18413
-2.1 -5.1 5.4 -2.7
8 7 6 5 -9 -8 -9
3541 4049 4705 5645 10236 11531 26410
-3.0 -2.4 -4.2 -3.6 -1.5 -0.6 4.5
8
2612
-1.5
QPlO112)
M"
Laser
7 6 5 4 -10 -9 -8
2960 3515 4206 5189 11024 12287 13881
-5.1 4.5 4.2 -0.3 1.2 6.6 5.7
P(401=902.86445 QP 6(141 13 QP 7(14) -11 -10 -9 -8 -7
14012 7120 7841 8732 9823 11213
-3.6 0.6 0.0 -1.5 -1.Z 0.3
QP11,12, Pl38)=904.78976 QP 61111
M'
P136)=906.70191
very accurately, was consistent with the assumed value A{ = 4.60 cm-’ of Bauer et al. (7). We note that the parameter 3~; band origin is strongly dependent on the other constants of 3~:, especially on the values of A{ and A. The error quoted in Table I does not include the uncertainty which comes from the uncertainties of the assumed constants. As seen in Fig. 4, the energy differences between v4 and Kl < 0 of the 3~; are larger than 200 cm-’ at any K. The perturbation appeared in the rotational energy of the u4 state can be well explained without taking the Fermi interaction with KI < 0 into account. Its effect is only to reduce the u4 band origin by about 20 MHz without affecting other rotational constants of u4. To determine the vibrational frequency of v4 from which the effect of the Fermi interaction with 3~: is completely removed, the Fermi interaction with Kl < 0 was included in the analysis. In the present study, no lines in the 3~: band could be assigned. This band is presumably very weak and has not been observed in any isotopic species of acetonitorile. From derived constants, the unperturbed energy difference between v4 and 3~; state is calculated to be about 8.8 cm-’ at K = 7, which is much larger than the Fermi interaction parameter of 0.39 cm-‘. Consequently, the intensity borrowed from the u4 band amounts to only 0.2% of the corresponding v4 line even at K = 7. For CH3C14N, some workers (10,21) have discussed the x-y type Coriolis interaction between v4 and v, states. Figure 3. however, shows that the Bh values plotted against K* fall on the straight line, except for the values at K = 7, 8. This linearity satisfies the relation between Bke and K2 in Eq. (7) which holds for the case without any perturbation. It seems that the effect is too small to be detected in the Stark spectra for the v4 band, even if the band is perturbed by the Coriolis interaction. The poor fit around K = 7 observed by Moskienko and Dyubko (22) in the u4 microwave
LASER STARK SPECTROSCOPY OF CHxC”N
39
spectrum at high J for 14Nis presumably due to the v4-3yi Fermi interaction, although Rackley et al.explained the cause with the Coriolis interaction which transferred the Fermi resonance in v7 (10). Duncan et ul. (9) have examined the isotopic shifts on vs and u4bands of acetonitrile, and discussed the possibility of the uq-2ug and u~-~Y:Fermi resonances. They estimated the Fermi resonance parameters, 1W4g~l= 30 cm-’ and 1W’QWJ~ = 25 cm-‘, for CH$N species. As pointed out by Duncan et al., because of the parallel nature of the v4 and 2~: bands, the Fermi resonance is absorbed in conventional anharmonicity effects. As for j W48881 = 25 cm- ‘, they were unsure as to whether such an interaction parameter was physically possible between a fundamental and a ternary overtone, and only the Fermi resonance with 2~: was taken into account for force field refinement calculations. In fact, IIP’,,,,I = 0.39 cm-’ is obtained for 15N in this study, and the value of 0.38 cm-’ is obtained for 14N by Igarashi et al. (II). From these data, the possibility of such a large parameter is excluded. It should be noted that the infrared value of the u4 band origin for CH3C”N reported by Duncan et al. is smaller by 0.50 cm-’ than our value and the isotopic shift is larger by 0. I3 cm- ‘. such a large parameter is excluded. It should be noted that the infrared value of the u4 band origin for CH3C”N reported by Duncan et al. is smaller by 0.50 cm-’ than our value and the isotopic shift is larger by 0.13 cm-‘. The frequency measurements of N20 laser by Whitford et al. (16) were limited to the P( 15) line in the lower frequency side, and most of the laser frequencies used in the present study were calculated by extrapolation. Stark resonances obtained by using P(32) to P(40) lines were analyzed with zero weight at the initial stage. It was proved, however, that the data were consistent with the data measured by other laser lines in the same spectral region. Since no systematic deviation was found in these data, they were incorporated in the final analysis. The Stark shifted frequencies for nine resonances, observed using the P(53) laser line of the CO2 sequence band, were uniformly higher by 30 MHz than the value calculated by Siemsen et al. (15) and these data were excluded from the analysis. To confirm this observation, we measured the laser Stark spectrum of CH3C’4N using the same laser line and also found the equal amount of deviations. Therefore, their frequency of the P(53) laser line presumably includes the errors of about 30 MHz. ACKNOWLEDGMENT 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 Center, University of Tokyo. RECEIVED:
April
26, 1983 REFERENCES
1. A. BAUER, A. MO&S, AND S. MAES, C. R. Acad. Sci. Paris Ser. 3. 264, 941-943 (1967). 2. A. BAUER AND S. MAES. J. Phys. (Paris) 30, 169-180 (1969). 3. J. DEMAISON, A. DUBRULLE, D. BOLJCHER,AND J. BURIE, J. Mol. Spectrosc. 76, l-16 (1979). 4. A. BAUER, J. Mol. Spectrosc. 40, 183-206 (1971). 5. A. BAUER AND S. MAES, J. Mol. Spectrosc. 40, 207-216 ( 1971). 6. A. J. CARELESS AND H. W. KROTO, J. Mol. Spectrosc. 57, 189-197 (1975). 7. A. BAUER, G. TARRAGO, AND A. REMY, J. Mol. Spectrosc. 58, I1 1-124 (1975).
40
MITO, SAKAI, AND KATAYAMA
8. A. BAUERAND M. GOWN, Canad. J. Phys. 53, 1154-1156 (1975). 9. J. L. DUNCAN,D. C. MCKEAN,F. TULLINI,G. D. NIVELLINI,ANDJ. PEREZPEI~A,J. Mol. Spectrosc. 69, 123-140 (1978). 10. S. A. RACKLEY,R. J. BUTCHER,M. R~MHELD,S. M. FREUND,AND T. OKA, J. Mol. Spectrosc. 92, 203-217 (1982). II. I. IGARASHI,J. SAKAI,H. FUJIMA,AND M. KATAYAMA,Symposium on Molecular Structure,Kyoto, October 1981. 12. C. FREED,L. C. BRADLEY,AND R. G. O’DONNELL,IEEE J. Quantum Electron. QE-16, 1195-1206
(1980). 13. B. G. WHITFORD,K. J. SIEMSEN,AND J. REID, Opt. Commun. 22, 261-264 (1977). 14. J. -P. MONCHALIN,M. J. KELLY, J. E. THOMAS,N. A. KURNIT,AND A. JAVAN,J. Mol. Spectrosc. 64,491-494 (1977). 15. K. J. SIEMSEN ANLIB. G. WHITFORD,Opt. Commun. 22, 11-16 (1977). 16. B. G. WHITFORD,K. J. SIEMSEN, H. D. RICCIUS, AND R. G. HANES,Opt. Commun. 14,70-74 (1975). 17. S. M. FREUND,G. DUXBURY,M. R~MHELD,J. T. TIEDJE,AND T. OKA,J. Mol. Spectrosc. 52, 3857 (1974). 18. H. MATSUURAAND T. SHIMANOUCHI, J. Mol. Spectrosc. 60, 93-110 (1976). 19. J. T. HOLJGEN, J. Chem. Phys. 38, 1167-1173 (1963). 20. F. N. MASRI,J. L. DUNCAN,AND G. K. SPEIRS,J. Mol. Spectrosc. 47, 163-178 (1973). 21. S. KONLXIAND W. B. PERSON,J. Mol. Spectrosc. 52,287-300 (1974). 22. M. V. MOSKIENKO AND S. F. D~BKO, Izv. Vyssh. Uchebn. Zaved. Radiojiz. 21,95 l-954 (1978).