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The high resolution infrared spectrum of the 2ν2 + ν3 and ν1 + ν2 + ν3 bands of 14N16O2
JOURNAL
OF MOLECULAR
The
High
SPECTROSCOPY
Resolution
Infrared
v1 +v,
Vibration
(1977)
66,47X-492
+
V~
Spectrum
v3
and
Bands of 14N1602
ond Vibration-Rotation Constants Ground State of 14N160 2 WALTER
of the 2~, +
J. LAFFERTY
of the Electronic
AND ROBERT L. SAMS
Nalional Bureau of Standards, Washington, D. C. 20234 The A-type bands, 2~9 + ~8 and VI + YS+ ~3, with band centers at 3092 and 3638 cm-‘, respectively, of rrNrBO~have been measured with resolution of 0.03 cm-r or better. Spectroscopic constants have been derived for the upper states of both bands. Infrared determined band constants have been combined with laser-excited resonance fluorescence data to obtain a set of vibration and vibration-rotation constants for the ground state of r4Nr60p. INTRODUCTION
Because of political and social concerns, much effort has been expended in recent years in the study of all regions of the nitrogen dioxide spectrum. In the infrared region all fundamental bands have been recorded under high resolution and precise band centers and rovibration constants have been obtained (1-7). A number of overtone and combination bands have also been studied with high resolution spectrometers (6, S-12). Much information on the electronic ground state of NOs recently has become available from laser-excited fluorescence studies. The data from such studies are much less precise than infrared measurements and are quite limited (generally only two or three lines per band are available), but these data have proven to be invaluable in the determination of ground state vibration-rotation constants, since high quantum vibrational levels of Al states are observed which are not accessible by infrared absorption studies. In the latest and most comprehensive of these studies, Bist and Brand (13) (references to previous fluorescence work can be found in this paper) report the observation of some 70 fluorescence lines. We recently have recorded under high resolution the spectrum of two A-type bands, 2vz + v) and VI + v2 + ~3, and one B-type band, vi + ~2. These bands were chosen for study in order to improve the precision of certain anharmonic constants, particularly those involving the bending vibration. In this paper we report the spectra and spectroscopic constants obtained for the two A-type bands. The analysis of the more complex B-type band will be reported in a subsequent paper. The spectroscopic constants obtained have been included with all available data-both from previous infrared studies and fluorescence studies-and fit to obtain improved estimates of anharmonic and vibration-rotation constants. Although this fit is somewhat empirical, the constants obtained will be useful in the prediction of unobserved levels in the NOr molecule. 478 Copyright _4U rights
@ 1977 by Academic of reproduction
Press.
in any form
Inc. reserved.
ISSN
0022-2852
480
LAFFERTY
AND SAMS
FIG. 2. Compressed scan of the Y, f Ye+ ~3 band of IN’*OZ taken at 15 Torr pressure with a 36 m
path. The subband origins are indicated.
difhculty in the analysis of the spectrum since they could be readily identified and overlapping with the NOz spectrum was not severe. These combination bands are quite weak. It was necessary to record the 2vz + va spectrum with a total absorbing path of 39 m and 10 Torr pressure. A 35 m path and 15 Torr pressure were used in the study of the JQ f p2 + YSband. A compressed scan of the 2~2 -I- v) band is given in Fig. 1 while the VI + v2 f ~3 band is shown in Fig. 2. BAND DESCRIPTION
AND DATA TREATMENT
Both of these combination bands have large values of A’-A”. As a result the origins of the subbands are considerably displaced from the band origin. This is illustrated in Fig. 1 for the 2~2 + yg band for which A’-A” - 0.5 cm-l. As a result the bands are practically featureless. Since the rotational constants of both bands could be estimated from previously estimated a! values (6), the line assignment for the lower K, subbands proved to be straightforward.
INFRARED
SPECTRUM
OF lrN1eOz
481
The assignment of the higher K, subbands proved to be more complicated since the higher K, states are perturbed by XI’ Coriolis interactions with nearby states. The matrix element governing such a resonance is (&, N, VilH[ K, f
1, N, Vj) = W[N(N
+ 1) - X,(X,
f
l)]$
(1)
and W is a complicated function of harmonic and anharmonic force constants (16). These interactions, which take place between vibrational states of A 1 and & vibrational symmetry, are found in all observed A-type bands of NO2 between levels with quantum numbers ~1~3~3 and 01, v2 + 2, v3 - 1. Because of the AK, f 1 restriction, the large difference in the A values of both states and the weak coupling constant, the shifts are small, and generally quite local, affecting only two or three subbands. For weak interactions such as these, the net effect of the perturbation is to slightly change the fi of the subbands involved in the resonance. Perturbation shifts in the ~1 + y2 + y3 band are small. The K, = 3 and 4 levels lie close to and are perturbed by the K, = 4 and 5 levels of the ~1 + 3v2 state. The line assignment was straightforward and could be checked with combination differences. In the lower K, subbands where the combination differences are not strongly K, dependent, an additional check is provided by fitting the lines of the subbands concerned to a polynomial and comparing the subband center with a value of the subband center computed from the constants obtained from the unperturbed segments of the band. Table
I. Spectroscopic
Constants
of the 2x12 +
~3 and V, + "2 + "3
Bands of 14N1602 in cm-'. __----
--_
B
V, + V2 t V3
2v2 + "3 ____-------
__--_
8.0023657(65)a
b’4i”
0.50651(26)a
0.22805(27)a
0.43370797(97)
B'-R"
-0.0029236(25)
-0.0051020(57)
@'_C"
-0.0045104(20)
0.41044536(161) 2.6881(13)
x 10
1.9499(64)
x 10
3.0068(83)
x 10
4.13(41)
-3 -5
x 10
2.946(27)
x 10
1.97(14) x 10
-8 -6
-3
1.084(24) x 10
-7.77(38) y 1O-6
0; - "i
-2.14(22) x 10
A;( - 6;
4.18(58) x 10
6r; - s;
8.9(55) x 10
H;-H;;
-6
1.13(17) x 10
-10
3.1(13) x 10
Hr;K-HiiK
-5
-9
1.085(82) x lO-5
b
%n-%
-3
-3
1.60(20) x 1O-8
6.17(70) x 10-g
-8
-3.7(10) ,: 10-10
-0.0063900(50)
1.357(27) x 10
- h;;K
%K -7
x 10-6
3.179(41)
Ai - Ai;
3.99(39) x 10-7
5.07(71) " 10-8
b
b
5.3(18) x lo-l3
Hr; - H;;
b
b
2.2(1.4) ‘x lo-l3
hi; - hi
b
b
h; - hi
b
b
- L;
b
9.18(88) j: 1O-8
-7.8(26)
x lO-8
3.55(16) x 10
-9 Lk
-.-_____
\'O
3092.4812(4)
3637.8430(7)
a
The uncertainties in the last digits are given in parenthesis standard deviation.
b
upper state constant constrained
at ground state value.
__-_and are one
.I
.I
7
I
:
L
:
i
_
./ . I,
_i L
, /; ,:
,.
_
n . . ,,
,1
ii_,.>
-,,.>-:-
_‘^-
‘_:“-
,,.
:.:r-
“Ii,., Ld..,
.,
.“-
-
:I -, . ii -
3 . 2
Lr“
: :
..j”.L ,
;i-
iii-c*,> .,___.“_ :,.;-
=..“.“7’
\
&,
.,I
.,
1>1,:.:-
r
‘,(:.L
..
*,,,---
-I.,‘:-
:<‘.:.:-
I.::.,-
rI
-,.:_.._;.,.,_ II
L
__ JI
ri
Li
: I
i(
36
38
10
Ii
L”
-
-
-
34
-
-
32
-
2*
30
-
a
4
4
a
4
4
4
4
4
4
26
-
-
4
4
5’1
-
-
0
LB
22
-
4
:
3
3
3
:
-
10 1. I6
-
-
27
21
-
-
19 17
23
--
IAILL
IIICONIINUEOl
484
LAFFERTY TABLE
AND SAMS IIICONlINtlED)
Since only the B and C rotational constants are to a good approximation affected by the resonance, both origins should be in agreement. Subbands with K, = 0 through 7 could readily be assigned. The lines of the higher K, subbands are weak and considerably overlapped especially at lower N’s, however, and only fragments of these lines were useful for fitting purposes. The 2~ + vg band is crossed by two vibrational states, however. The K, = 4 levels of this band fall very close to the K, = 5 levels of 4vz while the K, = 5 levels of 2~ are nearly coincident with the K, = 6 level of 2v2 i- v3. As a result assignment of the higher K, subbands proved to be somewhat difficult. Again these subbands are weak and badly blended ; in fact the P series are doubled by spin splitting, and only fragments of these subbands are assigned. Indeed, no definite assignment could be made of the K, = 4 subband at all. Fragments of a series with anomalously large spin splitting were initially assigned to lines of this subband, but a check using combination differences was not conclusive and served only to verify the N assignment. A polynomial fit to the lines observed in the series gave VBub= 3099.847 f 0.009 cm-‘. Using the band constants derived from the K, = 0, 1,2, and 3 subbands a value of v#,& = 3100.34 cm-l is obtained as an estimate of the origin of this subband. The discrepancy of 0.49 cm-l rules out the assignment of this series to the K, = 4 subband. A calculation using the vibrationrotation constants derived below indicates that the origin of the AK = +l, K'h = 4 subband of the 4~ vibrational band falls close to 3099.72 cm-r. Since it is the upper state of this transition which is responsible for the perturbation in 2~2 + ~3, it is likely that this series in fact belongs to 4vz and that the intensity of the series is enhanced by the resonance. The spin splitting of this series is much larger than what would appear in an A-type subband and on the order of what one would expect from a perpendicular band, and adds further evidence in favor of this assignment. A large number of weak and blended lines remain unassigned in this region. No doubt the perturbed K, = 4 series of 2v2 + v3 is to be found amongst these. Since these weak bands are badly fragmented and since the perturbing states have not been completely observed, no attempt was made to quantitatively account for the perturbations. SufIicient portions of both bands are unperturbed, however, so that reliable estimates of the band origins and rotational constants can be obtained. The fitting procedure and Hamiltonian used have been described previously (1, 6, II, 12). The molecular constants obtained are listed in Table I. The ground state constants used
INFRARED
SPECTRUM
OF 1sN’60z
485
in the fitting are very slightly different from those reported previously since combination differences to higher K, levels have been recently obtained from the VI+ v2 band and a slightly improved set of ground state rotational constants has been obtained. In fitting the vr + v2 + v3 band the lines from the K, = 0,1, 2, 5, 6, and 7 subbands have been included, while, because of the extensive perturbations, only the lines of the K, = 0, 1,2, and 3 subbands were included in the 2~2 + VI fittings. The spectroscopic constants obtained are listed in Table I, while the observed and calculated unperturbed line frequencies are given in Tables II and III. Aside from the perturbed subbands very few spin-split lines were observed in both of these A-type bands. There are two reasons for this : (1) Because of the AK = 0 selection rule in an A-type band, splittings in such bands are inherently small; and (2) the low N lines of the higher K, subbands where the splitting is largest are weak and thus badly blended. Since the spin-splitting data of the unperturbed states are so sparse, we have made no attempt to obtain the spin-rotation parameters. DETERMINATION
OF VIBRATIONAL
AND VIBRATION-ROTATION
CONSTANTS
Since data from several new vibrational levels have recently become available from infrared studies including data on the v1 fundamental (7), it was felt worthwhile to redetermine the vibrational and vibration-rotational constants of NO*. Our approach differs from that of Bist and Brand (13) in that all available data from infrared studies including vibrational band centers, the rotational constants, and the Ax distortion constant were fit simultaneously with the visible resonance fluorescence line shifts. In addition, in the fitting we have included an empirical term to account for the DarlingDennison resonance between the overtone and combination levels of the two stretching modes. In fitting the combined data the following equations were used. The infrared determined band centers were fit to the usual equations V =
C
W”iVi i
The A rotational
constants A VI,V2IW
+
C
C i
determined -
XqijViVj
+
C
j>i
C
directly
C
PijkVjVjVk.
for each infrared
band were fit to
dAiVi + C C yO*ijViVj.
A000 = -C
(1)
j>ik>j
i
z
(2)
i i>j
The vibrational changes in the A rotational constants are quite large for NOz, and as might be expected, the higher-order y OAijViViterms are necessary in the expansion. We have averaged the B and C rotational constants observed for each level and fit these averages to the expression
&.%03-
Boo0=
-c CPjvj. *
Higher terms were not required in this case. Finally the centrifugal distortion constants, AK, were found to exhibit unusually large changes. These changes can be fit, at least to first order, to the equation Avlo~e3~_ AooOx= -c
pivie I
(4)
IABLE III OF THE 2v2
+“S BAND
IN
OBSERVED ANDCALCULAlED WAVENUYBLRS
(CM-‘)
lMLE
IlllCONllNUtOI
LAFFERTY
488
AND SAMS
In the above equations it was assumed that the changes in the Watson rotational constants are equal to the changes in the actual rotational constants. The resonance fluorescence frequency shifts as reported by Bist and Brand (23) for a given vibrational state is the frequency of a “fictitious” Q-branch transition from the vibrational ground state to the vibrational level in question having the indicated iV and K, rotational quantum numbers. To within the measurement error the frequency shift for a given line is given by AV = &“iVi + F ,& $iiVG’j + 2 >Gi kFj
y”djkvivjvk
-
C
Q’~+‘P~
+
CpOS4avi
i
-Ca^‘i(N(N
+
l)
-
K’a)Vi
+
q
,IEi
TnAijViVjK2a,
(5)
where all the parameters have been previously defined. Spin-splitting effects in these AK = 0 transitions will be quite small and have been ignored. Although NO2 is an asymmetric rotor, the effects of the molecular asymmetry on the shifts of the K, = 4 and the K, = 5 states will be negligible. A small correction has been made for this effect for the shifts measured for the K, = 1 states. The NO, molecule has CZa symmetry, and Darling-Dennison resonance terms must be considered. The matrix elements which control this resonance are (Vl,
82,
33,
IHI
Vl
-
2,
v2,
113
+
2)
=
(Y/2)[(Vl
-
l>Vl(V2
+
1)
(22
+
31’
(6)
INFRARED
Table
IV.
This paper 1325.325(55)b 750.141(22) 1633.860(51)
Vibration
and Vibration-Rotation
Bist and Branda
489
in cm-' for x0*
Constants
This paper
Bist and Branda
"?A
-0.0835(22)b
-0.0844(83)
750.18(3)
no* 2
-0.3577(18)
-0.3544(42)
1633.12(36)
,o* 3
0.2313(15)
Y;;
Q.0038(11)
0.0034(14)
0.01433(71)
0.0152(27)
-5.471(32)
-5.836(33)
-0.469(15)
-0.497(5)
-17.062(51)
-16.34(12)
y;; oA y33 oA '12 1
-6.340(93)
-29.549(52)
-29.03(54)
-11.399(20)
-11.36(3)
___
y';'j oA '23
-0.07(2)
.068(11)
0.07(3)
-1.146(31)
+0.34(5)
___
Gl 82 e3 aOS
-1.75(5)
28.50(20)
b
OF 14N1602
1325.64(60)
-6.433(23)
aRef.
SPECTRUM
1
c
0.00374(75)
0.0235(37)
0.0309(15) -0.0140(13)
-0.018(7)
-0.0203(16)
-0.022(5)
-0.000209(19)
c
-0.000866(23)
c
0.000234(26)
c
0.002450(12)
aoB
0.000482(11)
E”;
0.002707(12)
c
c
c
(!_2).
Uncertainties
'Not determined
are one standard deviation. in Ref.
(13).
where y is the Darling-Dennison coupling constant. This well-known resonance (17) which occurs between overtone and combination levels involving the two stretching vibrations is quite weak in NO2 since the two stretching vibrations are separated by about 300 cm-r. In fact Bist and Brand (13) did not consider Darling-Dennison contributions in fitting their data and absorbed the resonance effects in the higher order cubic terms, YijkViVivk.In this study we have chosen to include, albeit in a somewhat empirical manner, the Darling-Dennison contributions, at least with regard to the vibrational terms. Effects of the resonance on the rotational constants have been ignored. The problem with treating this resonance for the higher vibrational levels is that for the most part only one of the levels in a resonance diad or triad has been observed, and the shifts due to the perturbation are highly correlated with shifts arising from normal anharmonic terms. Fortunately, since the perturbations are weak, we have used an iterative expansion method. Using the first term from a binomial expansion, the for any resonating diad is given by perturbation shift, 8a1.20a:.1-~,az,or+2, Y2 (D16Y1D2D3 :v1-2.W.V3f2
=
f
l)V1(Q + I>(% + 2) (7)
-
4
-@'v,--2.w,va+z -
Eav,,vt,w
>
'
where the Eo are the unperturbed energy levels of the two states in question, In the fitting this term was included with the appropriate sign initially using an estimate of
"1 "2 "3
N
Ka
A.&*
"Ca1c
ob* -ca,c
ASS'd. lincert
Ref. NO.
0
1
0
5
5
758.5
758.43
0.07
0.3
13
0
2
"13
1
1499.1
1499.00
0.10
0.3
0
2
0
5
5
1516.7
1516.64
0.06
0.3
13
"
3
013
1
2246.8
2247.14
-0.34
0.3
0
3
0
5
5
2274.9
2274.62
0.28
0.3
13
0
4
013
1
2994.0
2994.37
-0.37
0.3
O
4
O
5
5
3032.5
3032.39
0.11
0.3
13
0
5
013
1
3739.6
3740.69
-1.09
a
II 5
0
5
5
3790.0
3789.93
0.07
0.3
13
10
013
1
1319.4
1319.50
-0.10
0.3 0.3
0
6
0
5
5
4547.2
4547.26
-0.06
0.3
13
11
013
1
2063.7
2063.05
0.05
0
7
0
5
5
5304.5
5304.36
0.14
0.3
13
12
013
1
2805.7
2805.70
0.00
0.3
0
8
0
5
5
6061.5
6061.24
0.26
0.3
13
13
"13
1
3547.6
3547.43
0.17
".3
"10
0
5
5
7577.0
7574.34
2.66
a
13
2
011
0
5
5
8336.0
8330.56
5.44
a
13
010
1"
0
"
"13
5
5
1321.6
1321.89
-0.29
0.3
13
0
5
5
2074.3
2074.66
-0.36
0.3
13
"3084
12055
2826.5
2827.21
-0.71
0.3
13
i) 6
13055
3579.3
3579.53
-0.23
0.3
13
2
4332.2
4331.64
0.56
0.3
13
21"
5083.8
5083.52
0.28
0.3
13
2
2""
110
14
0
5
5
15055
0
0
on
2626.6
2626.64
-n.04
0.3
4
755.4
755.3R
0.02
0.3
8
4
1510.3
1510.27
O."3
0.3
2264.7
2264.69
0.01
0.3
*
4
4524.5
4525.07
-0.57
0.3
R
4
2629.9
2629.fm
0.02
0.3
II 4
3373.5
3373.35
cl.15
0.3
4
4116.1
4116.34
-0.24
0.3
5
5
2631.7
2631.61
0.09
0.3
13
2
3
0
R
4
4858.6
4R5R.86
-0.26
0.7
5
5
3379.0
3378.70
0.30
0.3
13
0
0
2
R
4
3194.1
3194.1"
0.00
0.3
0
5
5
4125.4
4125.56
-0.16
0.3
13
01284
3924.9
3926.05
-1.15
0.3
4
0
5
5
5618.3
5618.61
-0.31
0.3
13
0
4656.5
4657.53
-1.03
0.3
5
0
5
5
6364.2
6364.80
-0.60
0.3
13
10284
4454.2
4454.17
0.03
0.3
711*.2
7110.77
-0.57
0.3
13
11284
5179.4
5180.25
-0.85
a a
2
0
2
Ill
2
2
2 2
0
26055 0
0.54
0.3
13
0
5
2
8
4
6849.8
6849.09
-1.29
6
5
4670.7
4670.22
0.48
0.3
13
0
6
2
8
4
7577.0
7578.65
-1.65
a
5
5
5411.4
5411.36
0.04
0.3
13
010
750.0
750.04
-0.04
0.3
a
13
02
0.3
13
0
0.3
13
14
0.60
0.3
13
2
0
1.48
0.3
13
2
I"
-0.03
0.3
73
2
2
-0.12
0.3
13
0
0
a
13
-0.07
0.3
-0.06
0.3
3
2
3
4
0
5
5
6893.3
6892.96
0.34
3
5
0
5
5
7633.0
7633.42
-0.42
5
5
5949.4
5948.84
0.56
5
5
6684.8
6684.20
5
5
7215.5
7214.02
5
5
8465.0
8465.03
5
5
3190.4
3190.52
5
5
3924.7
3923.71
0.99
5
5
4451.1
4451.17
1
749.9
749.96
2
5
IO
6
IO
0
0
0
2
012 10
2 1
013
4
3928.86
10
4
8
3929.4
3
410
2
5
0
0
2
5
3
a
2
1 8
31
3
0
3,
1499.1
1499.17
-0.07
0.3
0
3,
2247.2
2247.39
-".19
0.3
0
3
4288.7
4S.9.00
-0.30
0.3
0
31
2627.5
2627.47
0.03
0.3
1
3
1
3364.2
3364.68
-".4R
0.3
0
3
1
41OO.S
4100.98
-0.18
0.3
2
3
1
3200.9
3200.94
-0.04
0.3
01231
3928."
392K.16
-0.16
0.3
13
12031
28"6.,
2806.28
-0.18
0.3
13
13031
3547.7
1548 1"
-0.40
0.3
the energy level separation, and the fitting was iterated until no significant change in the standard deviation was obtained. In the case of the few levels which were components of resonating triads, onIy the lowest of the IeveIs was observed, and Eq. (7) appears to provide an adequate approximation for the resonance shift. The rotational constants, of course, will also be affected by the resonance, but the changes in these constants will also be quite small. We have made no attempt in this work to account for this. All resonance effects for rotational constants have been absorbed into the higher terms. In fitting simultaneously these data of differing sources and highly varying precision, careful consideration must be paid to properly weighting each datum. We have assigned
INFRARED
obs
"I "2 "3
0
1
0
100 o
01
2
0
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0
ob< -talc
RSS'd. ""cert.
Ref. NO.
OF “N”Oz
749.649
749.672
-0.023
0.005
6
I
1319.194
1319.854
-0.060
0.010
7
11
0
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1616.861
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0.005
1
3
2627.337
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0.005
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2906.074
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0
4119.938
4179.900
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0
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01
491
abs "1 "2 "3
0
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CalC
SPECTRUM
2
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talc
-talc
Arc'd. RPf. Ilncert. N".
0
89.0
87.3
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310.97
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3201.443
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Infrared (0' -VK) T lo4 _.__._._._..__-
Infrared (O'_-_EJ'jm ,lS3_
6.84
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-1.82
fl.48
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-0.469
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a
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b
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3
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in fitting and W. J. Lafferty, to be published
each datum a probable uncertainty. This uncertainty was taken as f0.3 cm-1 for the resonance fluorescence shifts. Although the standard deviations cited for the infrared band centers are usually better than 0.001 cm-‘, we have assigned much larger uncertainties to these data because of unknown absolute frequency errors. The A, B, and AK constants were assigned uncertainties equal to three times the standard deviation cited for these constants. The weight assigned to each datum was calculated by squaring the reciprocal of its estimated uncertainty. In such a fitting scheme if proper uncertainties have been assigned and if the model to be fit is reasonable, the standard deviation will be close to unity. If the derived standard deviation differs substantially from unity, either the fitting model is not entirely adequate or the individual weights have been improperly estimated. The constants obtained in this fitting are listed in Table IV. For comparison the constants obtained by Bist and Brand are also included. The overall standard deviation
LAFFEKTY
492
ANL, SAMS
of the fitting is 3.1, much larger than would be expected from a perfect fitting. A glance at the observed and calculated values given in Table V indicates that the resonance fluorescence data are very well fit. On the other hand, the fit of the higher precision infrared data is less satisfactory. The A, constants are the major cont.ributors to the large standard deviation. These, no doubt, are rather poorly determined and very sensitive to local resonance effects. In addition, the A and B rotational constants have not been corrected for the effect of Darling-Dennison resonance effects and some of the difficulty in fitting these constants may stem from this effect. The vibration and vibration-rotation constants obtained in this work agree for the most part rather well with those derived by Bist and Brand (13). More high resolution infrared data have become available since their work, however, and when these data are fit simultaneously with the visible data, the uncertainties of the derived constants are considerably improved. In addition since a Darling-Dennison resonance term has also been included in the fitting, two of the higher-order vibrational y terms can be excluded from the fitting. It is necessary, however, to retain two of these terms in the fitting. One of these, the y133z~1”*3 term, appears to be unduly large. This serves to illustrate the limitations of perturbation theory when applied to the NO2 molecule as pointed out earlier by Hardwick and Brand (18). ACKNOWLEDGMENTS We are indebted to Sidney Kirschner for diagnosing a problem in the asymmetric rotor fitting program used in this study. We are also indebted to AldCe Cabana and Michel Laurin for communicating to us the results of their study of the ~1 band. RECEIVED:
April 1.5, 1977 REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 1.5. 16. 17. 18.
A. V. V. S. S.
CABANA, M. LAURIN, C. P~PIN, AND W. J. LAFFERTY, J. Mol. Spectrosc. DANA, Rev. Phys. Appl.
59, 13 (1976).
9, 711 (1974).
DANA AND J. C. FONTANELLA,Nom. Rev. Opt. 4, 237 (1973). C. HURLOCK, W. J. LAFFERTY, AND K. NARAHARI RAO, J. Mol. Spectrosc. 50, 246 (1974). C. HURLOCK, K. NARAHARI RAO, L. A. WELLER, AND P. K. L. YIN, J. Mol. Spectrosc. 48, 372 (1974). A. CABANA, M. LAURIN, W. J. LAFEERTY, AND R. L. SAMS, Cm. J. Phys. 53, 1902 (1975). A. CABANA AND M. LAURIN, private communication. M. D. OLMAN AND C. D. HAUSE, J. Mol. Spectrosc. 26, 241 (1968). R. E. BLA~IK AND C. D. HAUSE, J. Mol. Spectrosc. 34, 478 (1970). R. E. BLANK, M. D. OLMAN, AND C. D. HAUSE, J. Mol. Spectrosc. 33, 109 (1970). W. J. LAFFERTY AND R. L. SAMS, Mol. Phys. 28, 861 (1974). R. L. SAMS AND W. J. LAFFERTY, J. Mol. Spectrosc. 56, 399 (1975). H. D. BIST AND J. C. D. BRAND, J. Mol. Spectrosc. 62, 60 (1976). A. G. MAKI, J. Mol. Spectrosc. 47, 217 (1973). A. GIACCHETTI,R. W. STANLEY, AND R. ZALWAS, J. Opt. Sot. Amer. 60, 474 (1970). J. K. G. WATSON, private communication. B. T. DARLING AND D. M. DENNISON, Phys. Rev. 57, 128 (1940). J. L. HARDWICK AND J. C. D. BRAND, Can. J. Phys. 54, 80 (1976).
OF MOLECULAR
The
High
SPECTROSCOPY
Resolution
Infrared
v1 +v,
Vibration
(1977)
66,47X-492
+
V~
Spectrum
v3
and
Bands of 14N1602
ond Vibration-Rotation Constants Ground State of 14N160 2 WALTER
of the 2~, +
J. LAFFERTY
of the Electronic
AND ROBERT L. SAMS
Nalional Bureau of Standards, Washington, D. C. 20234 The A-type bands, 2~9 + ~8 and VI + YS+ ~3, with band centers at 3092 and 3638 cm-‘, respectively, of rrNrBO~have been measured with resolution of 0.03 cm-r or better. Spectroscopic constants have been derived for the upper states of both bands. Infrared determined band constants have been combined with laser-excited resonance fluorescence data to obtain a set of vibration and vibration-rotation constants for the ground state of r4Nr60p. INTRODUCTION
Because of political and social concerns, much effort has been expended in recent years in the study of all regions of the nitrogen dioxide spectrum. In the infrared region all fundamental bands have been recorded under high resolution and precise band centers and rovibration constants have been obtained (1-7). A number of overtone and combination bands have also been studied with high resolution spectrometers (6, S-12). Much information on the electronic ground state of NOs recently has become available from laser-excited fluorescence studies. The data from such studies are much less precise than infrared measurements and are quite limited (generally only two or three lines per band are available), but these data have proven to be invaluable in the determination of ground state vibration-rotation constants, since high quantum vibrational levels of Al states are observed which are not accessible by infrared absorption studies. In the latest and most comprehensive of these studies, Bist and Brand (13) (references to previous fluorescence work can be found in this paper) report the observation of some 70 fluorescence lines. We recently have recorded under high resolution the spectrum of two A-type bands, 2vz + v) and VI + v2 + ~3, and one B-type band, vi + ~2. These bands were chosen for study in order to improve the precision of certain anharmonic constants, particularly those involving the bending vibration. In this paper we report the spectra and spectroscopic constants obtained for the two A-type bands. The analysis of the more complex B-type band will be reported in a subsequent paper. The spectroscopic constants obtained have been included with all available data-both from previous infrared studies and fluorescence studies-and fit to obtain improved estimates of anharmonic and vibration-rotation constants. Although this fit is somewhat empirical, the constants obtained will be useful in the prediction of unobserved levels in the NOr molecule. 478 Copyright _4U rights
@ 1977 by Academic of reproduction
Press.
in any form
Inc. reserved.
ISSN
0022-2852
480
LAFFERTY
AND SAMS
FIG. 2. Compressed scan of the Y, f Ye+ ~3 band of IN’*OZ taken at 15 Torr pressure with a 36 m
path. The subband origins are indicated.
difhculty in the analysis of the spectrum since they could be readily identified and overlapping with the NOz spectrum was not severe. These combination bands are quite weak. It was necessary to record the 2vz + va spectrum with a total absorbing path of 39 m and 10 Torr pressure. A 35 m path and 15 Torr pressure were used in the study of the JQ f p2 + YSband. A compressed scan of the 2~2 -I- v) band is given in Fig. 1 while the VI + v2 f ~3 band is shown in Fig. 2. BAND DESCRIPTION
AND DATA TREATMENT
Both of these combination bands have large values of A’-A”. As a result the origins of the subbands are considerably displaced from the band origin. This is illustrated in Fig. 1 for the 2~2 + yg band for which A’-A” - 0.5 cm-l. As a result the bands are practically featureless. Since the rotational constants of both bands could be estimated from previously estimated a! values (6), the line assignment for the lower K, subbands proved to be straightforward.
INFRARED
SPECTRUM
OF lrN1eOz
481
The assignment of the higher K, subbands proved to be more complicated since the higher K, states are perturbed by XI’ Coriolis interactions with nearby states. The matrix element governing such a resonance is (&, N, VilH[ K, f
1, N, Vj) = W[N(N
+ 1) - X,(X,
f
l)]$
(1)
and W is a complicated function of harmonic and anharmonic force constants (16). These interactions, which take place between vibrational states of A 1 and & vibrational symmetry, are found in all observed A-type bands of NO2 between levels with quantum numbers ~1~3~3 and 01, v2 + 2, v3 - 1. Because of the AK, f 1 restriction, the large difference in the A values of both states and the weak coupling constant, the shifts are small, and generally quite local, affecting only two or three subbands. For weak interactions such as these, the net effect of the perturbation is to slightly change the fi of the subbands involved in the resonance. Perturbation shifts in the ~1 + y2 + y3 band are small. The K, = 3 and 4 levels lie close to and are perturbed by the K, = 4 and 5 levels of the ~1 + 3v2 state. The line assignment was straightforward and could be checked with combination differences. In the lower K, subbands where the combination differences are not strongly K, dependent, an additional check is provided by fitting the lines of the subbands concerned to a polynomial and comparing the subband center with a value of the subband center computed from the constants obtained from the unperturbed segments of the band. Table
I. Spectroscopic
Constants
of the 2x12 +
~3 and V, + "2 + "3
Bands of 14N1602 in cm-'. __----
--_
B
V, + V2 t V3
2v2 + "3 ____-------
__--_
8.0023657(65)a
b’4i”
0.50651(26)a
0.22805(27)a
0.43370797(97)
B'-R"
-0.0029236(25)
-0.0051020(57)
@'_C"
-0.0045104(20)
0.41044536(161) 2.6881(13)
x 10
1.9499(64)
x 10
3.0068(83)
x 10
4.13(41)
-3 -5
x 10
2.946(27)
x 10
1.97(14) x 10
-8 -6
-3
1.084(24) x 10
-7.77(38) y 1O-6
0; - "i
-2.14(22) x 10
A;( - 6;
4.18(58) x 10
6r; - s;
8.9(55) x 10
H;-H;;
-6
1.13(17) x 10
-10
3.1(13) x 10
Hr;K-HiiK
-5
-9
1.085(82) x lO-5
b
%n-%
-3
-3
1.60(20) x 1O-8
6.17(70) x 10-g
-8
-3.7(10) ,: 10-10
-0.0063900(50)
1.357(27) x 10
- h;;K
%K -7
x 10-6
3.179(41)
Ai - Ai;
3.99(39) x 10-7
5.07(71) " 10-8
b
b
5.3(18) x lo-l3
Hr; - H;;
b
b
2.2(1.4) ‘x lo-l3
hi; - hi
b
b
h; - hi
b
b
- L;
b
9.18(88) j: 1O-8
-7.8(26)
x lO-8
3.55(16) x 10
-9 Lk
-.-_____
\'O
3092.4812(4)
3637.8430(7)
a
The uncertainties in the last digits are given in parenthesis standard deviation.
b
upper state constant constrained
at ground state value.
__-_and are one
.I
.I
7
I
:
L
:
i
_
./ . I,
_i L
, /; ,:
,.
_
n . . ,,
,1
ii_,.>
-,,.>-:-
_‘^-
‘_:“-
,,.
:.:r-
“Ii,., Ld..,
.,
.“-
-
:I -, . ii -
3 . 2
Lr“
: :
..j”.L ,
;i-
iii-c*,> .,___.“_ :,.;-
=..“.“7’
\
&,
.,I
.,
1>1,:.:-
r
‘,(:.L
..
*,,,---
-I.,‘:-
:<‘.:.:-
I.::.,-
rI
-,.:_.._;.,.,_ II
L
__ JI
ri
Li
: I
i(
36
38
10
Ii
L”
-
-
-
34
-
-
32
-
2*
30
-
a
4
4
a
4
4
4
4
4
4
26
-
-
4
4
5’1
-
-
0
LB
22
-
4
:
3
3
3
:
-
10 1. I6
-
-
27
21
-
-
19 17
23
--
IAILL
IIICONIINUEOl
484
LAFFERTY TABLE
AND SAMS IIICONlINtlED)
Since only the B and C rotational constants are to a good approximation affected by the resonance, both origins should be in agreement. Subbands with K, = 0 through 7 could readily be assigned. The lines of the higher K, subbands are weak and considerably overlapped especially at lower N’s, however, and only fragments of these lines were useful for fitting purposes. The 2~ + vg band is crossed by two vibrational states, however. The K, = 4 levels of this band fall very close to the K, = 5 levels of 4vz while the K, = 5 levels of 2~ are nearly coincident with the K, = 6 level of 2v2 i- v3. As a result assignment of the higher K, subbands proved to be somewhat difficult. Again these subbands are weak and badly blended ; in fact the P series are doubled by spin splitting, and only fragments of these subbands are assigned. Indeed, no definite assignment could be made of the K, = 4 subband at all. Fragments of a series with anomalously large spin splitting were initially assigned to lines of this subband, but a check using combination differences was not conclusive and served only to verify the N assignment. A polynomial fit to the lines observed in the series gave VBub= 3099.847 f 0.009 cm-‘. Using the band constants derived from the K, = 0, 1,2, and 3 subbands a value of v#,& = 3100.34 cm-l is obtained as an estimate of the origin of this subband. The discrepancy of 0.49 cm-l rules out the assignment of this series to the K, = 4 subband. A calculation using the vibrationrotation constants derived below indicates that the origin of the AK = +l, K'h = 4 subband of the 4~ vibrational band falls close to 3099.72 cm-r. Since it is the upper state of this transition which is responsible for the perturbation in 2~2 + ~3, it is likely that this series in fact belongs to 4vz and that the intensity of the series is enhanced by the resonance. The spin splitting of this series is much larger than what would appear in an A-type subband and on the order of what one would expect from a perpendicular band, and adds further evidence in favor of this assignment. A large number of weak and blended lines remain unassigned in this region. No doubt the perturbed K, = 4 series of 2v2 + v3 is to be found amongst these. Since these weak bands are badly fragmented and since the perturbing states have not been completely observed, no attempt was made to quantitatively account for the perturbations. SufIicient portions of both bands are unperturbed, however, so that reliable estimates of the band origins and rotational constants can be obtained. The fitting procedure and Hamiltonian used have been described previously (1, 6, II, 12). The molecular constants obtained are listed in Table I. The ground state constants used
INFRARED
SPECTRUM
OF 1sN’60z
485
in the fitting are very slightly different from those reported previously since combination differences to higher K, levels have been recently obtained from the VI+ v2 band and a slightly improved set of ground state rotational constants has been obtained. In fitting the vr + v2 + v3 band the lines from the K, = 0,1, 2, 5, 6, and 7 subbands have been included, while, because of the extensive perturbations, only the lines of the K, = 0, 1,2, and 3 subbands were included in the 2~2 + VI fittings. The spectroscopic constants obtained are listed in Table I, while the observed and calculated unperturbed line frequencies are given in Tables II and III. Aside from the perturbed subbands very few spin-split lines were observed in both of these A-type bands. There are two reasons for this : (1) Because of the AK = 0 selection rule in an A-type band, splittings in such bands are inherently small; and (2) the low N lines of the higher K, subbands where the splitting is largest are weak and thus badly blended. Since the spin-splitting data of the unperturbed states are so sparse, we have made no attempt to obtain the spin-rotation parameters. DETERMINATION
OF VIBRATIONAL
AND VIBRATION-ROTATION
CONSTANTS
Since data from several new vibrational levels have recently become available from infrared studies including data on the v1 fundamental (7), it was felt worthwhile to redetermine the vibrational and vibration-rotational constants of NO*. Our approach differs from that of Bist and Brand (13) in that all available data from infrared studies including vibrational band centers, the rotational constants, and the Ax distortion constant were fit simultaneously with the visible resonance fluorescence line shifts. In addition, in the fitting we have included an empirical term to account for the DarlingDennison resonance between the overtone and combination levels of the two stretching modes. In fitting the combined data the following equations were used. The infrared determined band centers were fit to the usual equations V =
C
W”iVi i
The A rotational
constants A VI,V2IW
+
C
C i
determined -
XqijViVj
+
C
j>i
C
directly
C
PijkVjVjVk.
for each infrared
band were fit to
dAiVi + C C yO*ijViVj.
A000 = -C
(1)
j>ik>j
i
z
(2)
i i>j
The vibrational changes in the A rotational constants are quite large for NOz, and as might be expected, the higher-order y OAijViViterms are necessary in the expansion. We have averaged the B and C rotational constants observed for each level and fit these averages to the expression
&.%03-
Boo0=
-c CPjvj. *
Higher terms were not required in this case. Finally the centrifugal distortion constants, AK, were found to exhibit unusually large changes. These changes can be fit, at least to first order, to the equation Avlo~e3~_ AooOx= -c
pivie I
(4)
IABLE III OF THE 2v2
+“S BAND
IN
OBSERVED ANDCALCULAlED WAVENUYBLRS
(CM-‘)
lMLE
IlllCONllNUtOI
LAFFERTY
488
AND SAMS
In the above equations it was assumed that the changes in the Watson rotational constants are equal to the changes in the actual rotational constants. The resonance fluorescence frequency shifts as reported by Bist and Brand (23) for a given vibrational state is the frequency of a “fictitious” Q-branch transition from the vibrational ground state to the vibrational level in question having the indicated iV and K, rotational quantum numbers. To within the measurement error the frequency shift for a given line is given by AV = &“iVi + F ,& $iiVG’j + 2 >Gi kFj
y”djkvivjvk
-
C
Q’~+‘P~
+
CpOS4avi
i
-Ca^‘i(N(N
+
l)
-
K’a)Vi
+
q
,IEi
TnAijViVjK2a,
(5)
where all the parameters have been previously defined. Spin-splitting effects in these AK = 0 transitions will be quite small and have been ignored. Although NO2 is an asymmetric rotor, the effects of the molecular asymmetry on the shifts of the K, = 4 and the K, = 5 states will be negligible. A small correction has been made for this effect for the shifts measured for the K, = 1 states. The NO, molecule has CZa symmetry, and Darling-Dennison resonance terms must be considered. The matrix elements which control this resonance are (Vl,
82,
33,
IHI
Vl
-
2,
v2,
113
+
2)
=
(Y/2)[(Vl
-
l>Vl(V2
+
1)
(22
+
31’
(6)
INFRARED
Table
IV.
This paper 1325.325(55)b 750.141(22) 1633.860(51)
Vibration
and Vibration-Rotation
Bist and Branda
489
in cm-' for x0*
Constants
This paper
Bist and Branda
"?A
-0.0835(22)b
-0.0844(83)
750.18(3)
no* 2
-0.3577(18)
-0.3544(42)
1633.12(36)
,o* 3
0.2313(15)
Y;;
Q.0038(11)
0.0034(14)
0.01433(71)
0.0152(27)
-5.471(32)
-5.836(33)
-0.469(15)
-0.497(5)
-17.062(51)
-16.34(12)
y;; oA y33 oA '12 1
-6.340(93)
-29.549(52)
-29.03(54)
-11.399(20)
-11.36(3)
___
y';'j oA '23
-0.07(2)
.068(11)
0.07(3)
-1.146(31)
+0.34(5)
___
Gl 82 e3 aOS
-1.75(5)
28.50(20)
b
OF 14N1602
1325.64(60)
-6.433(23)
aRef.
SPECTRUM
1
c
0.00374(75)
0.0235(37)
0.0309(15) -0.0140(13)
-0.018(7)
-0.0203(16)
-0.022(5)
-0.000209(19)
c
-0.000866(23)
c
0.000234(26)
c
0.002450(12)
aoB
0.000482(11)
E”;
0.002707(12)
c
c
c
(!_2).
Uncertainties
'Not determined
are one standard deviation. in Ref.
(13).
where y is the Darling-Dennison coupling constant. This well-known resonance (17) which occurs between overtone and combination levels involving the two stretching vibrations is quite weak in NO2 since the two stretching vibrations are separated by about 300 cm-r. In fact Bist and Brand (13) did not consider Darling-Dennison contributions in fitting their data and absorbed the resonance effects in the higher order cubic terms, YijkViVivk.In this study we have chosen to include, albeit in a somewhat empirical manner, the Darling-Dennison contributions, at least with regard to the vibrational terms. Effects of the resonance on the rotational constants have been ignored. The problem with treating this resonance for the higher vibrational levels is that for the most part only one of the levels in a resonance diad or triad has been observed, and the shifts due to the perturbation are highly correlated with shifts arising from normal anharmonic terms. Fortunately, since the perturbations are weak, we have used an iterative expansion method. Using the first term from a binomial expansion, the for any resonating diad is given by perturbation shift, 8a1.20a:.1-~,az,or+2, Y2 (D16Y1D2D3 :v1-2.W.V3f2
=
f
l)V1(Q + I>(% + 2) (7)
-
4
-@'v,--2.w,va+z -
Eav,,vt,w
>
'
where the Eo are the unperturbed energy levels of the two states in question, In the fitting this term was included with the appropriate sign initially using an estimate of
"1 "2 "3
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Ka
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6
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5618.3
5618.61
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4656.5
4657.53
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6364.2
6364.80
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10284
4454.2
4454.17
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the energy level separation, and the fitting was iterated until no significant change in the standard deviation was obtained. In the case of the few levels which were components of resonating triads, onIy the lowest of the IeveIs was observed, and Eq. (7) appears to provide an adequate approximation for the resonance shift. The rotational constants, of course, will also be affected by the resonance, but the changes in these constants will also be quite small. We have made no attempt in this work to account for this. All resonance effects for rotational constants have been absorbed into the higher terms. In fitting simultaneously these data of differing sources and highly varying precision, careful consideration must be paid to properly weighting each datum. We have assigned
INFRARED
obs
"I "2 "3
0
1
0
100 o
01
2
0
11 3
0
ob< -talc
RSS'd. ""cert.
Ref. NO.
OF “N”Oz
749.649
749.672
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0.005
6
I
1319.194
1319.854
-0.060
0.010
7
11
0
1616.852
1616.861
-0.015
0.005
1
3
2627.337
2627.343
-0.006
0.005
6
110
1
3637.843
3637.865
-0.022
0.005
this work
0
10
1
5437.540
5437.568
-0.028
0.015
9
0
0
2906.074
2906.025
0.049
0.010
8
2
0
4119.938
4179.900
0.038
0.010
8
0
11 0
01
491
abs "1 "2 "3
0
101 2
CalC
SPECTRUM
2
ohs
talc
-talc
Arc'd. RPf. Ilncert. N".
0
89.0
87.3
1.7
1.2
1
228.05
228.48
0.43
0.78
this work this work
7
506.51
504.68
1.83
0.78
490.26
490.23
0.03
0.12
b
310.97
372.03
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0.72
6
1
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0.07
0.33
1
0
182.10
182.26
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0.24
6
123.89
124.26
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0.30
12
2
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0.33
11
1
-148.5
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9
3
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8.7
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1
10
3
5984.705
5984.705
0.000
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8
0
0"
2
3201.443
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0.001
0.005'
11
10
3
4754.209
4754.209
0.000
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6
3
2063.118
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0.025
0.005
b
10
1
2355.152
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0.012
0.005
12
2
1
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1
3092.48,
3092.475
0.006
0.005
thi* work
0"
3
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9
0
o
110 01 0
2
0
0
Infrared (0' -VK) T lo4 _.__._._._..__-
Infrared (O'_-_EJ'jm ,lS3_
6.84
8.66
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11.02,
10.752
0.275
0.057
b
6
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5.53
6.33
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1
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6
111
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this work
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this work
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1
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b
II
-0.469
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0.029
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0
2
0
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01
a
Not included
b
R. L. Sam
3
R
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in fitting and W. J. Lafferty, to be published
each datum a probable uncertainty. This uncertainty was taken as f0.3 cm-1 for the resonance fluorescence shifts. Although the standard deviations cited for the infrared band centers are usually better than 0.001 cm-‘, we have assigned much larger uncertainties to these data because of unknown absolute frequency errors. The A, B, and AK constants were assigned uncertainties equal to three times the standard deviation cited for these constants. The weight assigned to each datum was calculated by squaring the reciprocal of its estimated uncertainty. In such a fitting scheme if proper uncertainties have been assigned and if the model to be fit is reasonable, the standard deviation will be close to unity. If the derived standard deviation differs substantially from unity, either the fitting model is not entirely adequate or the individual weights have been improperly estimated. The constants obtained in this fitting are listed in Table IV. For comparison the constants obtained by Bist and Brand are also included. The overall standard deviation
LAFFEKTY
492
ANL, SAMS
of the fitting is 3.1, much larger than would be expected from a perfect fitting. A glance at the observed and calculated values given in Table V indicates that the resonance fluorescence data are very well fit. On the other hand, the fit of the higher precision infrared data is less satisfactory. The A, constants are the major cont.ributors to the large standard deviation. These, no doubt, are rather poorly determined and very sensitive to local resonance effects. In addition, the A and B rotational constants have not been corrected for the effect of Darling-Dennison resonance effects and some of the difficulty in fitting these constants may stem from this effect. The vibration and vibration-rotation constants obtained in this work agree for the most part rather well with those derived by Bist and Brand (13). More high resolution infrared data have become available since their work, however, and when these data are fit simultaneously with the visible data, the uncertainties of the derived constants are considerably improved. In addition since a Darling-Dennison resonance term has also been included in the fitting, two of the higher-order vibrational y terms can be excluded from the fitting. It is necessary, however, to retain two of these terms in the fitting. One of these, the y133z~1”*3 term, appears to be unduly large. This serves to illustrate the limitations of perturbation theory when applied to the NO2 molecule as pointed out earlier by Hardwick and Brand (18). ACKNOWLEDGMENTS We are indebted to Sidney Kirschner for diagnosing a problem in the asymmetric rotor fitting program used in this study. We are also indebted to AldCe Cabana and Michel Laurin for communicating to us the results of their study of the ~1 band. RECEIVED:
April 1.5, 1977 REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 1.5. 16. 17. 18.
A. V. V. S. S.
CABANA, M. LAURIN, C. P~PIN, AND W. J. LAFFERTY, J. Mol. Spectrosc. DANA, Rev. Phys. Appl.
59, 13 (1976).
9, 711 (1974).
DANA AND J. C. FONTANELLA,Nom. Rev. Opt. 4, 237 (1973). C. HURLOCK, W. J. LAFFERTY, AND K. NARAHARI RAO, J. Mol. Spectrosc. 50, 246 (1974). C. HURLOCK, K. NARAHARI RAO, L. A. WELLER, AND P. K. L. YIN, J. Mol. Spectrosc. 48, 372 (1974). A. CABANA, M. LAURIN, W. J. LAFEERTY, AND R. L. SAMS, Cm. J. Phys. 53, 1902 (1975). A. CABANA AND M. LAURIN, private communication. M. D. OLMAN AND C. D. HAUSE, J. Mol. Spectrosc. 26, 241 (1968). R. E. BLA~IK AND C. D. HAUSE, J. Mol. Spectrosc. 34, 478 (1970). R. E. BLANK, M. D. OLMAN, AND C. D. HAUSE, J. Mol. Spectrosc. 33, 109 (1970). W. J. LAFFERTY AND R. L. SAMS, Mol. Phys. 28, 861 (1974). R. L. SAMS AND W. J. LAFFERTY, J. Mol. Spectrosc. 56, 399 (1975). H. D. BIST AND J. C. D. BRAND, J. Mol. Spectrosc. 62, 60 (1976). A. G. MAKI, J. Mol. Spectrosc. 47, 217 (1973). A. GIACCHETTI,R. W. STANLEY, AND R. ZALWAS, J. Opt. Sot. Amer. 60, 474 (1970). J. K. G. WATSON, private communication. B. T. DARLING AND D. M. DENNISON, Phys. Rev. 57, 128 (1940). J. L. HARDWICK AND J. C. D. BRAND, Can. J. Phys. 54, 80 (1976).