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Fourier spectroscopy of the OD infrared spectrum. Merge of electronic, vibration-rotation, and microwave spectroscopic data
JOURNAL
OF
MOLECULAR
SPECTROSCOPY
87, 196-218 (1981)
Fourier Spectroscopy of the OD Infrared Spectrum. Merge of Electronic, Vibration-Rotation, and Microwave Spectroscopic Data C. AMIOT~ Laboratoire
de Physique Molkculaire et d’optique Atmosphkrique, Campus d’orsay, 91405 Orsay Cedex, France
B&iment 221
I
AND
J.-P. MAILLARD Observatoire
de Meudon,
Laboratoire
AND
J. CHAUVILLE
du Telescope
Infrarouge,
92190Meudon, France
The OD infrared spectrum, emitted in a flame of deuterium and oxygen, has been recorded for the first time in the 2-pm spectral range with a Fourier Transform spectrometer. A simultaneous fit of the ir 2-0, 3- 1, 4-2, 5-3, 3-0, 4-l vibration-rotation bands, of the uv data (O-O, l-l, 2-2, O-l bands of the A%+ + XV transition) and of the microwave data, gives accurate molecular constants for the ground-state vibrational levels up to v = 5. The classical “unique perturber approach” and the effective Hamiltonian of Brown for W states, have been successively used for the reduction ofthe spectroscopic data. I. INTRODUCTION
The hydroxyl radical has been intensively studied because it is involved in a wide variety of chemical and physical systems. It has been detected in interstellar gas clouds by radio-astronomy (I ) and it is commonly observed in astrophysical sources, some of which are masers (2). The short-lived transient OH plays an important role in the chemistry of the interstellar clouds (3). Numerous investigations were performed in different spectral regions. The hydroxyl radical was the first short-lived molecule to be investigated in the microwave region. Dousmanis ef al. (4) detected the transitions between A-doublet components of both spin components (Q2, J = 2.5 to 5.5 and 2113,2,J = 5.5 to 8.5) in the spectra of the OD, 160H, and ‘*OH molecules located in the 7.5-40-GHz region. The gas-phase E.P.R. spectra of OD and OH were observed by Radford (5,6). Magnetic moments generated by spin-uncoupling were strong enough to allow the observation of transitions involving the 2111,2component. Accurate E.P.R. measurements of the OD radical up to v = 5 were performed by Rashid er al. (7). The isotopic species with I70 (170H and 170D) were studied by Carrington and Lucas (8) and the analysis of these spectra yields values for the l’0 magnetic hyperfine and electric quadrupole parameters. These magnetic measurements were recently extended in the 26- to 35-GHz region by Brown et al. (9). 1 Author to whom reprint requests should be sent. 0022-2852/81/0501%-23$02.00/O Copyright All rights
0 1981 by Academic of reproduction
Press,
in any form
Inc. reserved.
196
OD INFRARED
SPECTRUM
197
The hydroxyl radical was also the first radical to have been detected in the radiofrequency range in a molecular beam experiment. Extensive and very accurate measurements were performed by Dymanus and Meerts (10-13). Seventeen pure rotational laser transitions were reported in the 12- to 20-pm spectral range by Ducas et al. (14). A great number of papers have dealt with the derivation of a Hamiltonian capable of interpreting the accurate OH and OD microwave data and uv data. The contributions of Mizushima (25), Destombes et al. (Z6), Veseth (17), Brown et al. (9), Coxon (Z8), and Coxon et al. (19) are the most important ones. An extensive review of the microwave studies has been reported by Beaudet and Poynter (20). The hydroxyl radical is also involved in numerous combustion and flame processes which were studied in the uv spectral range through the AT + X*II band system (21). For the OD radical several analyses have been reported (22-28). However, the most reliable data and analysis for this transition have been derived by Coxon and his co-workers (18,27,28). In these last papers the 0- 1, O-O, I- 1, and 2-2 bands were carefully investigated by direct approach methods and “unique perturber approximation” outlined by Zare et al. (29,30). Other works concerned with the OD radical are gathered in Huber and Herzberg’s book (31). In the infrared part of the spectrum, the vibration-rotation spectrum between vibrational levels of the OH X*Il ground state was investigated by Maillard et al. (32 ) using Fourier Transform techniques. However, the OD radical had never been observed in this spectral region. A systematic investigation between 1 and 3 pm was then performed. In the present work we have observed the 2-0, 3-1, 4-2, and 5-3 bands and also some rotational lines of the 6-4, 3-0, and 4-l bands. In order to obtain a more reliable set of molecular constants we have performed a simultaneous analysis of our data and also of the uv and microwave spectroscopic data. The next section of this paper deals with the experimental aspects of the work, in particular the OD production. The effective Hamiltonians used in the direct approach method are then discussed. Finally the results are presented and the molecular constants are compared with those previously determined. II. EXPERIMENTAL
DETAILS
A high-temperature OD source with long-term stability is necessary for recording spectra with a Fourier technique. In the case of OH an oxyacetylene flame was employed by Maillard et al. (32). But, as deutered acetylene is not commonly available in large quantities we chose to use a deuterium-oxygen flame. Stoichiometric mixture ratios were adjusted for a total gas flow of 20 liters/h. As in previous experiments on OH the flame was imaged on a 4-mm diameter diaphragm to isolate a region of the outer cone giving the most intense OD emission with a rotational temperature of about 2500 K; that is much lower than in the oxyacetylene case. The high-resolution Fourier spectrometer (33,34) at the Meudon observatory was used to record the spectra. The apparatus has been put quite recently under vacuum, avoiding the parasitic absorption by H,O and CO, bands. The total spectral range from 3500 to 9000 cm-’ has been covered with
198
AMIOT,
MAILLARD,
AND CHAUVIL4.E
two records. A portion of the spectrum in the P branches of the 2-O to 6-4 bands is displayed in Fig. 1. The blending by D20 lines is very strong, particularly in the R branches, which are much less “clear” than the P branches. It is, however, worth noting that the signal-to-noise ratio is reduced compared with the similar OH spectrum due to the type of source used (32, Fig. 1). The observed linewidths are about 0.1 cm-‘. In the Av = 3 sequence the signal-to-noise ratio is poor due to the faintness of the bands and only some lines of the 3-O and 4- 1 bands are usable. The calibration of the spectra was performed by using residual H,O absorption lines (35) ensuring an absolute wavenumber accuracy better than 5 x 10e3 cm-‘. III. THEORY
The Hamiltonian for the interpretation of high-resolution spectra of diatomic molecules can be written, in the absence of external magnetic or electric fields, as
H,, includes the terms which are independent of rotation and in the Born-Oppenheimer approximation gives the vibronic term energy T, for the allowed vibrational states of the different electronic states. The term Hrot is the Hamiltonian describing the rotation of the nuclei. It has the form H,t
=
B(r)R2= -
h
87r2pr2
(J - L - S)Z,
where B(r) is the radial part of the rotational energy operator, p is the reduced mass, and r is the internuclear distance. The third term H, is related to the interactions between the orbital and spin motions of the electrons. This fine-structure Hamiltonian is composed of three parts H, = H,, + H,, + H,,. For all doublet states considered in this work the spin-spin interaction rigorously zero. The spin-orbit Hamiltonian H,, has the form:
H,, is
H,, = A(r)L.S,
where A(r) is the spin-orbit H,, is given by
coupling constant.
H,, = y(r)R.S
= y(r)(J
The spin-rotation
Hamiltonian
- L - S)vS,
where -y(r) is the spin-rotation constant. A basis set of Hund’s case (a) wavefunctions, eigenfunctions ofJ2,JZ, S2, S,, L, (eigenvalues J(J + l), Sz, S(S + l), 2, A) is used and noted 1211nvJ iI>, where R = 1A + IS ) . For a211 state the secular determinant to be solved is a 4 x 4 block and a 2 x 2 block for a 2Z state. When wavefunctions of well-defined parity, relative to reflection in the plane containing the internuclear axis, are introduced the dimensions of these blocks are divided by two. When interactions with other Born-Oppenheimer states (2IZ*and 21J)through the operators B(r)J,L, or [A(r)/2 + B(r)]L,S, are considered there is a removal of the degeneracy for the two 2 x 2 blocks. The small terms nondiagonal
OD INFRARED
SPECTRUM
8 --:
--f
-P --:
-8 --:
-0 --:
-B -_:
3
I
Q)
_:!
I
-4
199
200
AMIOT, MAILLARD,
AND CHAUVILLE
in S linking 211states through the operator H,, are neglected (36). We have adopted the notation e andf for the parity of each block (37). Rather than diagonalizing a large matrix with all the *F, *II, and *A states the Van Vleck transformation (38) is used in the “unique perturber approach” to keep one *II or one *C state only and to apply small corrections, due to the other electronic states, to the matrix elements of the Born-Oppenheimer state. The matrix elements are obtained by the methods outlined by Hougen (39), Zare et al. (SO), and Lefebvre-Brion (40). The matrix elements of the *II Hamiltonian are collected in Table I for this “unique perturber approximation.” The definitions of the elements are nearly analogous to those of Coxon (28), in particular higher-order terms for the A-doubling constants
TABLE I Hamiltonian Matrix Elements for OD X2H State in a Parity Case (a) Basis Set: Unique Perturber Approximation T
A
1,l
1
2,2
1
1,l
0.5
2.2
-0.5
AD 191 2,2 1.1 AH 2,2
6
0
Ii
L
o
192
0.25(3(z-1)2+2) q
1,l
z-l
2,2
ztl
1,2
-,0*5
1,l
-(z-1)2-z
9D
2,2 ’ -(2+1)2-z
q”
2 zzO.5
1,l
(z-1)3tz
(32-l)
2,2
(rt1)3tz
(32t1)
I,2
-(322tztl)
zO.5
1,l
(z-1)4tz(6z2-3zt2)
2,2
(z+l)4tz(6z2t5zt2) 4zzO.5
Y
to
2n Y,labe12to 3
-0.25
zoe5 J2(Jt1)2
(Jt0.5))
l-2
0.5 z”~
(-lk(Jt0.5))
191
0.5 z J(Jt1)
292
0.5(z+Zr
(Jt0.5))
132
0.5 z”~
(-l+
191
0.5 z J2(Jt1)2 0.5(zt2T(Jt0.5))J2(J+l)2
1.2
0.5 z”‘5(-1+(Jt0.5))J2(Jtl)i
1.1
-0.5
2.2
-0.5 0.5 zO.5 -0.5
J(Jt1)
-0.5
J(Jt1)
0.5 z”~
J(Jt1)
1.1
-0.5
J2(Jt1)2
YW 2.2
-0.5
J2(Jt1)2
f
J(J+l)
(JtO.5))5(5+1)
292
1.2
211$.
J(Jt1)
0.52
191
two the signs are given the lower is for
J(Jtl)
0.5(zt2r
0.5 zoe5 J2(Jt1)2
1.2 - Label 1 refers
z”~
191
YD 2.2
1
292
-0.25
(5t0.5))
2.2
192
(2 2tztl)
zO.~
0.5(lT
0.5(l+(Jt0.5))J2(Jt1)2
22,
-0.25(3(zt1)2tz)
-0.25
0.5(1?(&0.5))
pH 192
0.5(2-l) -0.5(2+1)
0.5 zO.5
1.2
292
pD 22,
1,2
1,2
192
P
z=(Jt0.5)2-1 levels,
=(J-0.5)(Jt1.5).
the upper for
e
levels.
When
OD INFRARED
201
SPECTRUM
p andq are obtained simply by an expansion inJ (J + 1). We have also constrained
the parameter o, to the value Ap/8B (U = 0). In analyzing the E.P.R. spectrum of OH X*II u = 0 Brown et al. (9) have recently developed a new effective Hamiltonian formalism using a formal tensor approach. The calculations are done within a single ‘II vibrational level, more precisely within the spin and rotational levels. The influence of the other electronic states is taken into account by operator techniques (41, 42). The corresponding matrix elements for this effective Hamiltonian are given in Table II. Although these matrix elements should be used since higher matrix elements are established in correct operator form we have also performed the calculations in the classical
TABLE II Hamiltonian Matrix Elements for OD X*Il State in a Parity Case (a) Basis Set: Effective Hamiltonian of Brown (41) T
A
AD
1,l
1
2,2
1 2,2 PO 1,2
1,l
2,2
1,l 232 192
H
L
?0.5(Jt0.5)(z+2)
0.5 -0.5
132
D
r0.5(Jt0.5)
191
1,l
B
2,2
232
229
AH
P
0.5 z -0.5
PH 2,2
(zt2)
1,2
(Jt0.5)
TO.5
(zt4)(J+0.5)3
i0.5
z”‘5(Jt0.5)3
z2 -(2+2) 2
9
zo.5 z z+2 _,0.5
qD
191
-z(ztl)
2,2
- (ztl)(zt4)
1,2
2zO*5(z+l)
191
z(z+l)(z+Z)
qH
(z+l)(z2+8zt8)
1,2
-zO.5(zt1)(3z+4)
191
-z(z+1)2
T(J+O.5)
1,2
+ 0.5 z”‘5
1,l
70.5 TO.5
(3zt4)(5+0.5)
I,2
i0.5
z”‘5(zt2)(Jt0.5)
2,2
-(z+l)
(z2t12i+16)
420.5(z+1)2
(z+Z)
YH
1,l
rz(JtD.5)3 T2(zt2)(Jt0.5)3
lO.5zo’5(zt4)(J+O.5)3
2rl T3
-1
,
label 2 to
two signs are quoted the lower is for
1,l
-0.5z -0.5(3zt4)
1,2
0.5
1,1
-Z-Z2
2,2
-2(ztl)(zt2)
211 i. f
0.5 z0.5
292
1,2 - Label 1 refers to
z(Jt0.5)
2,2
192
YD
(J+c\.5)
2,2
2,2
Y
(zt4) 2
2,2
1,2
2,2
1,2
l 0.25 z”‘5
zD.5(2+2)
0.5zO.5(z2+5z+4) z=(Jt0.5)2-1=(J-0,5)(J+1.5).
levels and the upper for
e
When levels.
202
AMIOT,
MAILLARD,
AND CHAUVILLE
“unique perturber approach” in order to compare our results with those of previous works. For the Y states the matrix elements of the Hamiltonian are given in Table III. The parameters T, B, D, y are effective parameters since the electronic perturbation parameters cannot be separated from the true mechanical constants. IV. DATA TREATMENT
In the previous reduction of the OH data a band-by-band treatment was adopted (32). In this work as in another analysis (43) a weighted, nonlinear, least-squares fitting routine is used to reduce the spectroscopic data. These input data are the wavenumbers that we have recorded in the infrared, the uv data of Clyne et al. (27), and the microwave transitions (4, 7, 10, II, 20). We have ignored the hyperfine structure of these transitions by considering only the gravity centers of the lines. The wavenumbers for these lines are then Z(2F + l)~ilX(2F + l), where oi is the hyperfine transition and the sum runs for AF = 0 transitions only. This is certainly an approximate value for the zero-field transition. The spectroscopic data were compared with the calculated differences of upper- and lower-state eigenvalues of the Hamiltonian matrix given in Tables I and III or Tables II and III. The initial values of the parameters used to evaluate the Hamiltonian matrix were taken from Coxon’s work. After diagonalization one obtains term values from which a first set of calculated transitions is derived. A comparison with the observed frequencies leads to corrections to the initial parameters. The whole set of data is then treated iteratively until convergence is achieved. The advantages of such computing procedures have been widely discussed (44, 45).
TABLE
III
Hamiltonian Matrix Elements for OD A%+ State in a Parity Case (a) Basis Set
1 T
(J - 0.5)
B
- (J - O.5)4
(J + D.5)4
- (J t 0.5)4
(J t 1.5)4
L
(J t 0.5)
-(J
- 0.5)*
(J t 0.5)
0.5
(J - 0.5)
0.5
(J t 1.5)
0.5
(J - 0.5)5(5+1)
0.5
(J t 1.5)5(5+1)
0.5
(J - 0.5)J2(Jt1)*
0.5
(J + 1.5)J2(Jt1)2
Y (J + 1.5)
(J t 0.5)*
D
YD -(J
t 0.5)*
(J + 1.5)2
(J - 0.5)3
(J + 0.5)3
H (J t 0.5)3
(J t 1.5)*
yH
LJpper line refers to
e
levels and lower line to
f
levels.
OD INFRARED
SPECTRUM
203
V. RESULTS
Least-squares fits of the data have been performed with the two *II Hamiltonian matrix elements quoted in Tables I and II. For each *II Hamiltonian two successive fits were made. A preliminary unweighted least-squares fit first provides adequate estimates for the weighting factors. These are taken equal to l/r?: if tij is the mean of the residuals for each vibration-rotation band or microwave transition. This first fit determines also the significant parameters. If a parameter is nonsignificant relative to one standard error its value is constrained, in the second weighted least-squares fit, to the last significant value in order of increasing vibrational quantum number. In this last fit the variance is calculated as: 1 &-‘,
=
Wi(U6 - Ui)’
i=1.n
n-m
where (~5, &. are the measured and calculated wavenumbers, n the number of wavenumbers, m the number of variable parameters, and wi the applied weights. If the values of wi are good estimates of the standard deviations of the distribution of measurement errors and if uh - c; are correct estimations of measurement errors, &-“,$ should fluctuate near unity. The constraint y=O was used, since it is well known that the parameters AD and y are nearly totally correlated. The derived molecular constants using the two approaches are collected in Tables IV and V. The 2, value is nearly equal to (1.040)’ in the two cases. It is worth noting that the value of AH (u = 0) from Table IV, increases from 0.121 x 1O-6 cm-’ when the first fit (unweighted and unconstrained) is performed to 0.221 10e6 cm-’ in the second fit. It may also be seen that the value of A, from Table IV does not show a smooth ZIvariation. In fact, centrifugal distortion terms and higher-order variation of A-doubling parameters show a smoother u dependence when Brown’s formalism is used. The observed wavenumbers for the 2-0, 3-1, 4-2, 5-3, 3-0, 4-l bands, together with the differences o-c between observed and calculated wavenumbers using Hamiltonian of Table II, are presented in Table VI. The few observed wavenumbers for the 6-4 band are also quoted in Table VI. The results for the uv bands are quite similar to those of Coxon et al. (27,28) and will not be reproduced here. The agreement between observed and calculated microwave transitions is given in Table VII. The residuals, of the order of a few MHz, are greater than the experimental uncertainty, especially for the M.B.E.R. results (10, II). This is due to our adopted approximate treatment for these transitions. The constants for the A*Z+ state do not depend significantly on the *II Hamiltonian used. Effective parameters are reported in Table VIII when Brown’s Hamiltonian is employed for the X*II state. In order to reduce the number of parameters for these X*II and A*X+ states a classical “Dunham-type” expansion of each parameter in powers of (v + l/2) has been performed. For the most accurately calculated parameters we give in Table IX the coefficients of ad hoc expansions
a
1
0.12553
P
brackets
Values
1400
=+x10
(IDX106
WI03
in
input
7.06
are
for
(17)
2632.To50
v=l
one
constants.
(17)
(15)
(56)
(37)
(77)
(12)
(47)
(30)
(35)
(30)
=
error,
freedom
standard
of
C-l.463
2.104
-10.597
-1.136
0.12237
[6.40]
1.9320
5.2978
9.607103
[1.21]
-1.65
-139.4343
Degrees
are
(12)
(25)
(12)
(22)
constrained
parentheses
uavenumbers.
-1.52
2.137
-10.966
-0.978
(II)
2.015
nx1oa
Lx1013
PDXlO5
(11)
5.3825
Dx104
(34)
(42)
(21)
2.14
9.883003
A&O7
B
(27)
(31)
-5.43
IO
CO1
-139.2157
A&04
A
v=o
in
1320. units
of
Standard
c-l.461
2.121
-10.2682
-1.054
0.11744
L6.401
1.8521
5.2222
9.334461
[1.21]
-3.55
-139.6203
5175.8434
v=2
( 2)
7632.2423
the
Last
deviation
(11)
(77)
(34)
(15)
(62)
= significant
a2
[-1.46i
1.901
-9.798
-0.765
0.112352
Lb.401
1.793
5.1526
( 9)
9.064067
[I.211
0.60
-139.8581
(41)
(20)
(32)
u=3
(31)
figure
(I.0311
(34)
(23)
(80)
(44)
(12)
(15)
(53)
(35)
(37)
2
. of
the
C-1 .46]
2.152
-9.562
-1.00
0.10837
Lh.401
1.587
5.0830
a.795619
Cl.213
-2.94
-139.9945
10001.894i
U=4
constant.
(61)
(27)
(16)
(55)
(24)
(21)
(58)
(31)
(44)
(17)
ODJXI 0 c u G 5 Molecular Constants (in cm-‘): % Hamiltonian ofTable I (U.P.A. Approximation)a
TABLE IV
Values
C-l.461
L2.301
-8.712
r_-1.501
0.10340
L6.401
0.88
4.9934
in
8.527887
Cl.211
0.72
-140.2081
12285.3421
v=5
square
(30)
(63)
(la)
(76)
(99)
(66)
(50)
(35)
a)
1400
-1.50
me
constrained
are
one
”
=
1
standard
of
the
deviation
c-1.461
2.139
-10.3002
cl.481
-1.631
0.11767
c6.401
1.8414
5.2119
9.330373
7.84
-7.178
-139.4517
in units
Standard
(17)
(14)
(59)
(36)
(73)
(11)
(461
(58)
(50)
(36)
v=2
(12)
1.757
Last
significant
? _) ^o L = (l.034)L figure
of
(31)
the
constant.
[-l&J]
Values
(66)
2.160
2.002
(13)
C-1.461
-9.228
in square
(251
(611
brackets
C-l.461
c2.311
Cl.481
(21)
(27)
[-I.441
-9.582
(18)
0.10577
L6.401
(161
[I.481
-1.49
0.10821
(7:) 1.21
(981
(251
(MO>
(56)
(37)
5.0085
8.524641
-9.876
(93)
(26)
1.617
(62)
(23)
5.0760
L6.403
(61)
8.791938
cl.481
-1.563
0.11401
(48)
(15)
5.1399
c6.403
(51)
9.060060
15.9
-5.874
-140.0113
12286.6976
v=5
(89)
(41)
(18)
(60
(11)
(44)
(70) (77)
(67)
7.44
(28)
7.08
(57)
-6.485
(38)
-6.236
(50)
(35)
-139.8253
7633.0729
< 5) (40)
(41)
-139.6606
v=4
of Table II (Brown
(19)
V--3
2rl Hamiltonian
10002.9713
V
(31)
(in cm-‘):
5176.3880
Constant
(30)
error
= 1314.
c-1.463
2.118
-10.632
cl.481
-1.668
0.12271
L6.401
1.9264
5.2881
9.602879
8.68
-7.523
-139.2702
2632.3780
of freedom
constants.
in parentheses
Degrees
(12)
(25)
2.139
input Lines.
IO
Values
qHxIO
qDX106
(46)
(II)
1.47
-10.993
pnx109
qx103
(74)
(21)
0.12567
p
-1.533
(38)
6.90
LX1013
PDX105
(12)
(12)
5.3719
2.002
(44)
Dx104
9.878587
B
(24)
(35)
(34)
Hxl08
8.85
-8.207
-139.0576
co1
AHHO
ADx103
A
7
v=o
OD X*fl 0 =Z u G 5 Molecular
TABLE
206
AMIOT,
MAILLARD,
AND CHAUVILLE
TABLE
VI
-6..
4:: 4::
-2:: -2.: -7:1 2: 13.5 -6.6 -..O -10.0 ::::: --Is., -12..
T,B,D, -..=
c K,t(vf My, i=O,n
where x represents any of the molecular constants and n is the degree of the polynomial. Correlations between parameters were ignored but a weighting according to uncertainties of Table V was applied. The term values for all the vibrational levels with 21s 5 for the ground state are collected in Table X. These data should be useful for predictions of microwave transitions to be measured in astrophysical observations. The absolute uncertainty of transition calculated in this manner is better than 150 MHz. A change in the ordering of the A-doubling levels e,fbetween theJ = 9.5 andJ = 10.5 rotational levels of theF,(211,,,) component may be noted. For the lower J values (~9.5) the e component has a smaller energy than thef. The reverse is true for J > 9.5. This phenomenon has been observed for all the vibrational levels studied. In the OH radical Brown et al. (9) observe such a change
OD INFRARED TABLE OD: J
P2e
3- 1
W-Continued
Vacuum Wavenumbers
o-c x 10’
R2e
207
SPECTRUM
O-C x IO’
and o--c Values (in cm-‘) Pie
o-c
3.6
-**.a
4::
-1.5 -8.6 -3.1
I:-:.
-2::: {:i.
-1% -1e.. o-c 103
-lt.2
-,.6
*:s
I
-7’:.
2:: 2: 2: -Il.0
I:9 f :i .
P2f
4:.
I.9
3:: C:! -;2
J
4:: 3:: :a:!
-5. 2”:: ::: 2.:.
-6:s
J
x 103
-_)7.3
2;::
O-C
Te
x 10’
O-C x 103
Plf
o-c x 103 LO.2
-;“,:: 2: -16.6 --8-o -3;9 -0.0
-2.1 --I.9 -0.0 ;::
0.6
0-C
5f
J
x 103 12.6
,::: 3,
-0
17-e -9.4
2:: ;p:i . 1.2 I.0
2:
3
-1:2 I:-: -0:0 -;:; .
in the ordering between J = 3.5 and J = 4.5 for the same 2111,2spin-orbit component. The constants determined in this work were also used to construct an R.K.R. potential energy curve for the ground state (4649). We used previously determined turning points and relative vibrational energies of the OH molecule (50) as additional constrained points of the potential energy function assuming that it is invariant by isotopic substitution. The results are presented in Table XI. The differences in the R,,, and R,,, values for the two spin-orbit components 2111,2and 2II3,2being small, a “mean” curve is given, obtained by using the T, B parameters of Table V as input data to the D.H.L. program. 2 By resolving the Schrodinger equation with the R.K.R. potential so determined the vibrational transitions are 2 The D.H.L. program (29, 30. 47) is a slightly modified version, for use on UNIVAC machines, of the original version available from Albritton (48) and usable directly on CDC machines.
208
AMIOT,
MAILLARD, TABLE
OD: 4-2
J
pze .71)1.01.3
zziz~ 471,:5722 4194.2925 4bb9.9525 .U..S,.Y
::5’ :%I-. :6”,:
LO.5
45b2.3744
16.5 19.5 20.5 21.5 22.5 23.5
J
4533.023R 4502.7318 ..7,.5299 4*39..041 .#1.4024 .3,2.5358 4337.8157 4352.2687 .2b5.901tB .228.,.50 4190.79,. .,52.0403
P2f
1.7 -1.9 -0.6 -:-:
2:,
-0.2 -0.T -1.3
-oz.P
r;i; 1:::
o-c
RZe
1n3
0.5 1.5
5:; 2X t::
VI-Continued
Vacuum Wavenumbers
o-c x
AND CHAUVILLE
I!
4866..92. .BRO.,929 489..,O,tl 4906.4905 4917.R934 492fi.2373 4937.5559 .94b.7,,5 4952.8503 4950.8939 .9b3.7321 .96,..,hS .9b9.087I3 .9,,.202CI 49, I .?983 4970.1139 496,.R285 4964.268R 4959.4531 4953.394e 49.0.0833 *93,.5,30 .92,.1,,9
o-c
R2f
II-l3
and o-c
2.3 15.2 -,.,
3-z . -85.6 -1.4 -3.0 .
4i.i 0.1
--b.* -10.0 3.3
o-c
o-c
Pl2
x lo3 4796.
25.2
,177
4774.bSb5 l 752.1703 4728.0465
Z%. . izz7: 4b52.4707
4b25.2174 l 59?.ob39
.568.0200 4s38.1ob9 4507.3118
4475rbSC,5
4443.1455 4409.7922 4375.bO52 4340.b028 l 30*.79t2 .2(r8.2103 6230.8031 .,92.bb.1) 4 153.7.86 411*.1035
Plf
4853.4870 4870.1761 U)S5.5832
-13.9 . -5’: .t **.t. 183-b 9.b y-:. -0.b -2.7 f:t -1.4 -4.3 -3 .? 2.: -7:0 -‘2:“, 2.2
o-c
0.8 48(rb.51.0 4t3a0.7929
,780.9000
-7.1
‘2: s:a
13.5 14.5 15.5 16.5 17.5 18.5 19.5 20.5
4760.902b l 739.7oe2 471?.*605 4694.lJBP ebb.?sab' . m.t.7.y.e.7: . 4562.0145 y3',.gw?*" . 4.71.03bl 4438.87b9 6605.0329 .371.9256 l 337.3b52 4301.5bbt 4265.1513
::.: 73:5
t:'~.~z . 4151.1e.87
;:; .
::3 6.5 2: 1::: 11.5 12.5
..1
:E%.s% 49*,:9039 4928.346,
1;::
-%-z .
4953.0132 495R.9902
1.2
+a . ::: . 3.5" --I.8 -3.2
t~;.~%. 49b9.9e55 4971.2e.25 4971.3461 4970.2395 49b?.AROb 49b4.2BTI 4959..!a,P 4953.3701
-12.9 -1::: 4.b -,3.5 -11.0 -b.O -,a.2 9.1
Rle
.79e.o2,e 4774.5813 .752.1025 1728.b4bS 4704.1953 .678.,973 l e52..707 lb2b.2820 l 597.1824 .5wl.**23 4538.2958 .507.53,6
-12-B
-2b .8 -2b.6
23.; 14.2 -3.3 -28.1 -5.5 ,":T ti:: -3.5 -0.6
--;3:: 22.9
-1::: 7.1
-..2
2:5
-,‘,:t
-4.0 -s$t
49bb.bISb
l PoP.JUI l97O.B.03 497l.1175 4970.1319 4967.89b5 l 96e..o,+
2:; 2:: 7.5 8.5 1.5
-2&i 10.0 9..
If'X . 12.5
-lb.3
:t.: . 20.5
l9n.e317
5:'s" 2315
6920.0114 l9lb.911(1
%f
J y-:
4.4
:tz.t~~ .
o-c
J
x 103 *as3.sboo 4n?o.l933 .8t?5.5032 l 99.bBW 4912.4695 : ,f:X ycl3.w& . :'Gi.km,: . 4957.2754 7:4 t'g',.zp7: I _:y; 9.1 *9b9:2320 : -,5.6 0.0 t,';z.z0; 49b9:9WS
::; -2.5 -10.9
O-C x 103
4923.9Wb ~~~.as~ . 4950.w71 4957.4022 l JL2.6*95
x 103
x 103
x 103
Values (in cm-‘)
*9b7.822.5 *PbI.3I29
.9w.sma ~953.5054 mt.g32t . l 928.0062 .9.6.9323
:-: 2:5 3.5 4.5
10.5 "9.5 . II.5 ::.: 14:s L5.5 L6.5 L7.5 ‘8.5 19.5
1-z.: 3b:6
:v:: _
22:5 23.5
recalculated to better than 0.18 cm-’ and the B, values to better than 23 x low5 cm-‘. With this method it is possible also to calculate D, and H, values. They are compared to our fitted parameters in Table XII. The agreement between the values is good although the R.K.R. calculated parameters are always slightly larger than the derived parameters of Tables IV and V. VI. DISCUSSION
A comparison of the results obtained with the two 211 Hamiltonians will be presented first. Then our values for the molecular constants are compared with the previously reported ones. The expected relations between the parameters of a 211 state expressed in the “unique perturber approximation” and in Brown’s formalism have been given by this author (42, Table III) and more specifically in the case where the constraint Yno = 0 is applied. For example the following relation exists between the vibrational terms:
OD INFRARED
209
SPECTRUM
TABLE VI-Continued OD: 5-3 Vacuum Wavenumbers J
o-c
Pze
103
x
o.= 1.5 2.5 3.7 4.5
5.5 6.5
7.5 Ft.5 a.5
.609.2>02 .5e9.a&v31 4569.0624 4547.3r6. .524.6559 4500.6637 4.76.0.02 4450.2183 4423.3699 4395.5681 4366.6236 4337.1230 4306.5105 4274.9810 4242.5609 4209.2930 4175.1897
p2f
J 0 .5 L.5
4bOY.2502
2.5 3.‘;
4569.64PJ 456~~.980A 45.1.273H 4524.5031 4500.6655 4415.812. 4449.9493 4423.0814 4395.23RO 4366.4307 4336.6960 430b.fl38.
9.5 5.5 6.5 7.5 8.5 7.5 10.5 11.5 12.5 13.5 14.5 15.5
4274.4636 4P42.04’62 4208.7069 4,7.**45,
L6.5 I -P .S IR.5
-21.2 -7.4 -5.0 -7.1 11.0 . -ii 5.2 6.6 2.5 4.9 -5.1 -0.9 -15.9 7.0
o-c x 103
-_(
.-a _.. .
$2 3.1 7.3 -7.6 -5.2 2.3
I.2
4::: -1.3 0.0
-1Jil
lb.7 -5.5 4.0
o-c
Rze x
b.2 26.5 10.3 15.9 29.6 8qO -6.4 26.0 3.1
. 4716.9976 .730.692S 4741.6065 4751.0624 4760.474J 47hB.2572 4774.877b 4780.3947 47w.7711 4767.9Wl 4790.02bb 47w.n773 4790.52b. 4786.9622 4766.1740 4782.1512
o-c
R2f
x 103 -14.0 -9.4
4692.3529 4706.1b29 4719.0392 4730.9506 4741 .es91 4751.7310 4760.5719 4768.3475 4774.9700 4780.5039 4784.e.771 4708.086e 4790.1179 4790.9560
:;p9.;;;1 .
o-c
Pll?
5.7 .
-1:s -K-f. -13.9
.b24.0:*3'4603.2197 4561.3i7tl .55R.z!r)9f! 4534.5465 4509.7540 4.84.Ol50 4.57.3ee 4429.0053 4.01.35RH 4372.072. 4341.8413 4310.7C59 .27.5.*,29 4746.0758 4P12.4732 417tt.0.54 4142.602b
L
1;::
x
x 4623.9606 4603.1405 4561.2641 :S~~;~~ . 4509.7540 44h4.0371 4457.4229 44 29.9074 4401.5032 4372.2103 4342.044. 4311.0189 4279.1272
.695.7560 4710.b266 472e.1403 4730.4266 4747.4266 4757.1651 4765.6636 4772.9252 4770.9130 .?83*6A03 4787.2037 47cI9.4900 4790.5367 0790.1402 .760.6957 .78b.l97C 4781.2402 4777.0159
o-c
Plf
4246.4156 4212.6154 4178.4412 4143.2433
2
-0.5 5.7 -9.1 r-23.3 . ;7.b 12.9 12.5 4.7 4.7 1.6 -6.2 1.3
o-c
Rle
x lo3 4biW.6428
xxz::
4786.2000 1782.1529
103
and o-c Values (in cm-‘)
Rlf
103
J
103 ,,.5
5.0
1.5 2.5
-3.1 21.6 -30.6 -?5.. -31.0 -13.0
3.5 4.5 5.5 6.5 7.5 8.5 4.5 0.5 1.5 2.5 3.5 4.5 5.5 a.5 F.5 e.5
2.6 -7.0
O-C
J
x lo3 0.5 I.5
4b79.7,02
9.5 6.1 19.5 A.3 -0.5 -10.1 -6.3 -3.3 2.2 1.7 1.7 6.6 ll3.0
-17.9 -4.0
4695.hllb 9710.6280
:;g.:.$f . 4747.4266 4757.139, .7bS.b,122 4rr2.83Rb .??R.(‘;‘?O 4703.5b07 4767.1010 y;.ya; . 4790.2855 .786.@09') .7Rb.I242 47RP.ltJ22 677b.977,
-7.6 -36.7
::5: a.5
4(A,” - 0,7 - 2B; - q;)
The superscript 7~is relative to the unique perturber case and the tilded parameters are related to Brown’s approach. From our T values (which are in fact differences of T: or e’,, between two vibrational levels) quoted in Table IV one must be able to calculate the parameters given in Table V. The results are quoted below for the four vibrational levels from v = 1 to v = 5 (all values are in cm-‘): 1
2
3
4
5
U.P.A.
2632.1050 (30)
5175.8434 (2)
7632.2423 (31)
10001.8941 (17)
12285.3421 (35)
T
2632.3803
5176.3904
7633.0580
10002.9815
12286.6972
2632.3780 (30)
5176.3880 (5)
7633.0729 (31)
10002.9713 (19)
12286.6976 (37)
V
T
talc form. (1)
T Table V
210
AMIOT, MAILLARD, TABLE OD:
3-O
AND CHAUVILLE
VI-Continued
Vacuum Wavenumbers
and o--c Values (in cm-‘)
U.P.A. stands for “unique perturber approximation.” The agreement between the values of Table V and those calculated formula (1) is good. For the rotational constant B, Brown et al. (42) give the relation
using
As before the comparison using Bg and q; constants of Table IV to calculate l!?,, by formula (2) are summarized below (all values are in cm-’ except ((B;- 8,,)/2) which are given in lop4 cm-‘):
OD INFRARED
211
SPECTRUM
TABLE VII OD Microwave Transitions and o-c Values (in MHz)
_
F
Y _
0
_ 1 _ I
_ 4
I =
TABLE VIII OD Molecular Constants for A?%+ (in cm-‘): Spectroscopic 0
v
32487.1370
T
a
Data Form Coxon (18)” 2
1
(17)
(36)
34701.6591
(41)
36812.8839
9.043523
(46)
8.721484
(51)
a.398740
(88)
x
lo4
5.77498
(13)
5.7272
(12)
5.6914
(34)
H
x
a 10
1.797
(12)
1.5839
(82)
1.096
(38)
L
x
10'2
1.293
(39)
0.12017
(23)
D
Y YD yH
a)
0.11718
x
IO5
-1.471
(61)
-1.30
x
109
2.80
(40)
C2.683
Quoted the
uncertainty
Last
Values
digit. in
square
equal Hamiltonian brackets
L1.2451
[!.245]
to
one of
sre
(10)
(61) (19)
-1.59 c2.681
standard Table
0.11262
(36)
deviation
II.
constrained
constants.
in
units
of
212
AMIOT, MAILLARD,
AND CHALJVILLE
TABLE IX “Dunham-Type”
Coefficients for the PII
States of OD (in cm-‘; p, q in MHz)
V
0
1
2
3
4
5
B::
9.883003 (42)
9.607103 (47)
9.334461 (41)
9.064067 (53)
8.795619 (58)
8.527887 (99)
B”, talc form. (2)
9.877520
9.601804
9.329312
9.059168
8.790838
8.523530
L Table V
9.878587 (44)
9.602879 (46)
9.330373 (44)
9.060060 (51)
8.791938 (61)
8.524641 (98)
5.33
5.37
5.30
4.46
5.50
5.55
B; -
2
I&,,
It appears that a systematic difference occurs between the B values calculated by formula (2) and those reported in Table V. This difference, nearly equal to 20;, as shown by the last line of the above Table, arises because in the U.P.A. approximation matrix elements of R2 are used while Brown uses W, i.e., formula (2) given in Ref. (42) is not quite correct. For the other rotational constants D, H, and L the agreement is good between the two sets. For the spin-orbit constant the following relation must hold:
xi,,,= (A;
- 0;)
P:
2(A; - 0:: - 2B; - 4;) 1 ’
The comparison between calculated values by this formula and constants Table V is given below (all values are in cm-l):
of
TABLE X OD XW
Energy Values Relative to the Level u = 0, n = 3/2, J = 0.5, e
u=3
v=2
f
e J
112
312
l/Z
l/2
312
312
l/2
v=5
v=4
l/2
l/2
312
3/z
311
J
f
e
f
e J
f
e 112
312
112
3/z
J
L
1 213
214
AMIOT, MAILLARD,
AND CHAUVILLE
TABLE XI OD X*Il: Vibrational Terms, Rotational Constants, V
”
ohs
=
Gv+Yoo cm
V
CCilC-v
-1
x
103cm
a”
ohs -1
cm
and R.K.R. Turning Pointsa
aY - 0”
-1
x IO
5
T
R. M1l-l
talc -1 cnl
i
0
1351.2423
19
9.878587
-1.6
0.894184
1.061863
1
3983.6139
56
9.602879
6.6
0.047362
1.141786
2
6527.6303
80
9.330373
14.4
0.818776
1.204321
3
8984.2610
100
9.060059
21.3
0.797547
1.260430
4
11354.2146
128
0.791930
23.0
0.780556
1.313324
10.4
0.766396
1.364523
5
13637.9397
174
t
8.524641
E
a)
Reduced the
V
AZ
mass
p
coefficients
=
1.70877. of
Table
yoo V
1.5493
. The
9"
cm-'. are
2
1
0
=
The
taken
Gy from
are
calculated
Table
3
with
V.
5
4
- 139.2157 - 139.4343 - 139.6203 - 139.8581 - 139.9945 - 140.2081 (31) (32) (37) (35) (44) (50)
Al, - 139.0507 - 139.2681 - 139.4499 - 139.6878 - 139.8269 - 140.0381 talc. (3) AZ,1 - 139.0576 - 139.2702 - 139.4517 - 139.6606 - 139.8253 - 140.0113 Table V (34) (40) (36) (50) (56) (35) The value of o; is constrained at -0.22 cm-’ for all v. The A,,,, constants, which are much better defined in Brown’s formalism, follow the relation: &,, = A 6, -t PIT
B: + (1/2)qF A,“-o;-2B;-q;
V
0
1
2
Afi,
-5.43 (27)
-1.65 (30)
-3.55 (20)
A,,, talc. (4)
-88.53
-75.82
-72.88
A,,,
-82.07
-75.23
(50)
(35)
(4)
*
The results are quoted below where all constraints
Table V
must
are in 10m4cm-l: 3
4
5
-2.94 (31)
0.72 (66)
-65.10
-63.43
- 56.75
-71.78
-64.85
-62.36
-58.74
(38)
(57)
(70)
(130)
0.60 (35)
OD INFRARED
215
SPECTRUM
TABLE XII Comparison of D,., H,. Observed and Calculated Using the R.K.R. Method (all Parameters
in cm ‘Y’
D
”
x
0
1
2
3
4
5
a)
10
D 4
x
5.3719
(12)
5.3825
(111
5.2881
(111
5.2978
(12)
5.2119
(11)
5.2222
(
5.1399
(15)
5.1526
(15)
5.0760
(23) (21)
5.0085
(71)
4.9934
(76)
given
Dabs in
and Table
IO
4
x
5.3863
5.3053
5.2293
9)
5.0830
For
H
talc
5.1592
5.0959
5.0402
Hobs V,
the
the
x
2.002
(12)
2.015
(111
1.9264
(73)
1.9320
(77)
1.8414
168)
1.8521
(62)
1.757
(12)
1.793
(12)
1.9476
(2.5)
1.21
(16)
0.88
(18)
line
to
those
a
2.0287
(24)
refers
10
2.0955
1.617
Line
ca1c
2.1456
1.587
first
second
10
H 8
1.8412
1.6317
to of
the Table
results IV.
The variation of this constant with the vibrational quantum number u is smooth in Brown’s approximation. In comparing the parameters of Tables IV and V it is worth noting that the “unique perturber approximation” constants p: and 9: are identical to those of Brown et al. (42). The higher-order constants p. and qD have also the same order of magnitude in the two approaches. More reliable determinations of these and higher-order A-doubling parameters will be obtained only by M.B.E.R. or microwave works like those of Meerts et al. (12), Coxon (19) or Brown et al. (9) performed on the OH radical. The molecular constants obtained in the “unique perturber approximation” and quoted in Table IV, can be compared with the results of the uv study of Coxon (18). They concern the only previously reported molecular constants of the ground state for the vibrational levels u = 0, 1,2. The results are summarized in Table XIII. The agreement is good within three standard deviations except for L” and 4:. Obviously, these constants have been defined with opposite signs in the two analyses. In our work the parameter pH was found to be nonsignificant and constrained to a zero value while Coxon constrained it to the value 1.33 x lo+’ cm-’ for all vibrational levels. A more marked difference appears in the vibrational term values quoted below (in cm-l) (relative to the v = 0 vibrational term value).
(25)
(21)
5.3742
1.935
1040”
(19)
(36)
-10.934
-2.034
103Q"
106s;
0"
1o"Q
*)
a)
0
the
l-l
are
(12)
(25)
(12)
1.295
(22)
band
of
*2z+
constrained
error
.-o-2221
i-9.631
-2.117
-10.643
Cl.331
0.12240
c-4.521
(27) (17)
-139.446
(31)
2.065 c-5.191
(111 (34)
5.3307
9.60889
COXON
-
XIII
units
(25)
(22)
(79)
(60)
( 6)
(14)
(28)
(17)
A'n.
1.9320
5.2970
9.607103
of
the
L -0.2201
c-14.61
2.104
-10.597
CO!
-1.136
0.12237
-1.65
-139.4343
2.455
5.276
[-0.219)
c-9.631
L-2.201
-10.206
Cl.331
[1.30]
0.11694
c-4.681
.?39.644
(58)
(94)
of
(13)
(74)
(53)
(10)
L'81
digit
COXON
9.3346
significant
(17)
(15)
(56)
(37)
(30)
(35)
(77)
(12)
(47)
IV
c-5.193
(in cm-‘)a
work
last
Table
This
Constants
c6.401
1
Molecular
constants.
in
[~I*
of OD PII
(11)
(42)
standard
for
: one
L-O.2201
-15.2
2.137
-10.966
CO3
-0.978
5.12553
-5.43
brackets
from
7.06
2.015
5.3825
IV
work
9.883003
Table
This
-139.2157
uncertainty
square
Results
in
Quoted
c-0.223:
(160)
(95)
(47)
1.283
1.33
105pg
109p;;
-9.63
(46)
P"
0.12661
L-4.361
( 4)
.139.230
A II
104Ai
(59)
-5.19
10'31.
?08H”
Cl?)
[=I
9.88310
COXON
8”
”
Comparison
TABLE
This
t6.401
I.8521
5.2222
9.334461
Table
the
IV
work
constant.
c-0.22Ol
L-14.61
2.121
-10.2682
CO1
-1.054
0.11744
-3.55
-139.6203
2
Values
(11)
(77)
(34)
(15)
(20)
(32)
(62)
( 9)
(41)
OD INFRARED SPECTRUM
1
2
3
2632.12 2632.105
5176.20 5175.843
7632.0 7632.242
2214.54 2214.523
4326.10 4325.750
6333.3
V
X’Il
217
ATi.+
The first line refers to Coxon’s results (18) and the second one to our work. The differences come from the necessary use in Coxon’s work of older data on the 2-0, 2- 1, 3- 1, 3-2, and 3-3 bands which are clearly subject to large systematic errors. ACKNOWLEDGMENTS C. Amiot is indebted to Dr. J. M. Brown for helpful correspondence and for making his YI Hamiltonian matrix elements available to him. The authors are grateful to the Referee for many valuable comments on the manuscript.
RECEIVED:
July 7, 1980 REFERENCES
1. H. WEAVER, D. R. W. WILLIAMS, N. H. DIETER,AND W. T. LUM, Narure 208, 29-31 (1965). 2. K. M. EVENSON, J. S. WELLS, AND H. E. RADFORD,Phys. Rev. Leit. 25, 199-202 (1970). 3. E. HERBST AND W. KLEMPERER,Astrophys. J. 185, 505-533 (1973). 4. G. C. DOUSMANIS, T. M. SANDERS,AND C. H. TOWNES, Phys. Rev. 100, 1735-1754 (195% 5. H. E. RADFORD,Phys. Rev. 122, 114-130 (1961). 6. H. E. RADFORD.Phys. Rev. 126, 1035-1045 (1962). 7. M. H. RASHID, K. P. LEE, AND K. V. L. N. SASTRY,J. Mol. Spectrosc. 68, 299-306 (1977).
A. CARRINGTONAND N. J. D. LUCAS, Proc. Roy. Sot. London A 314, 567-583 (1970). J. M. BROWN, M. KAISE, C. M. L. KERR, AND D. J. MILTON, Mol. Phys. 36, 553-582 (1978). W. L. MEERTSAND A. DYMANUS, Astrophys. J. 180, L93-95 (1973). W. L. MEERTSAND A. DYNAMUS, Cannd. J. Phys. 53, 2123-2141 (1975). 12. W. L. MEERTS,J.-P. BEKOOY, AND A. DYMANUS, Mol. Phys. 37, 425-439 (1979).
8. 9. 10. II.
13. W. L. MEERTS,Chem. Phys. Lett. 46, 24-28 (1977). 14. T. W. DUCAS,L. D. GEOFFRION,R. M. OSGOOD,ANDA. JAVAN.Appl. Phys. Lett. 21,42-44( 1972). 15. M. MIZUSHIMA,Phys. Rev. A 5, 143-157 (1972). 16. J. L. DESTOMBES,C. MARLIERE,AND F. ROHARD,J. Mol. Spectrosc. 67, 93-116 (1977). J. L. DESTOMBES,ThL?se d’Etat, Lille, 1978. 17. L. VESETH,J. Mol. Spectrosc. 63, 180-192 (1976). 18. J. A. COXON.J. Mol. Spectrosc. 58, l-28 (1975). 19. J. A. COXON, K. V. L. N. SASTRY,J. A. AUSTIN, AND D. H. LEVY, Canad. J. Phys. 57, 619634 (1979). 20. R. A. BEAUDETAND R. L. POYNTER,J. Phys. Chem. Ref. Data, No. 1, 311-362 (1978). 21, G. H. DIEKEAND H. M. CROSSWHITE,J. Quant. Spectrosc. Radiat. Transfer 2, 97-199 (1962). 22. M. G. SASTRY,Indian J. Phys. 15, 27-51 (1941). 23. H. OURA AND M. MIMOMIYA,Proc. Phys. Math. Sot. (Japan) 25, 335-342 (1943). 24. H. OURA, Low Temperature Sci. 6, 41-43 (1951). 25. R. ENGLEMAN.J. Quant. Specfrosc. Radiat. Transfer 12, 1347-1350 (1972). 26. A. E. DOUGLAS,Canad. J. Phys. 52, 318-323 (1974). 27. M. A. A. CLYNE, J. A. COXON, AND A. R. WOON FAT, J. Mol. Spectrosc. 46, 146-170 (1973).
218
AMIOT,
MAILLARD,
AND CHAUVILLE
28. J. A. COXON AND R. E. HAMMERSLEY,J. Mol. Spectrosc. 58, 29-38 (1975). 29. R. N. ZARE, A. L. SCHMELTEKOPF,W. J. HARROP, AND D. L. ALBITTRON, .I. Mol. Spectrosc. 46, 37-66 (1973). 30. R. N. ZARE, A. L. SCHMELTEKOPF,D. L. ALBRITTON, AND W. J. HARROP, .I. Mol. Spectrosc. 48, 174- 180 (1973). 31. K. P. HUBER AND G. HERZBERG, “Molecular Spectra and Molecular Structure. IV. Constants of Diatomic Molecules,” Van Nostrand-Reinhold, Princeton, N. J., 1979. 32. J.-P. MAILLARD, J. CHAUVILLE, AND A. W. MANTZ, J. Mol. Spectrosc. 61, 120-141 (1976). Vol. 3, I. A. U. (G. Contopoulos, Ed.), Reidel, 33. J.-P. MAILLARD, “Highlights of Astronomy” Dordrecht , 1973. 34. J.-P. MAILLARD, Thesis, Orsay, 1974. 35. J.-M. FLAUD, C. CAMY-PEYRET, G. GUELACHVILI,AND C. AMIOT, Mol. Phys. 26,825-855 (1973). 36. I. KOVACS, “Rotational Structure in the Spectra of Diatomic Molecules” American Elsevier, New York, 1969. 37. J. M. BROWN. J. T. HOUGEN, K. P. HUBER, J. W. C. JOHNS, I. KOPP, H. LEFEBVRE-BRION, A. J. MERER, D. A. RAMSAY, J. ROSTAS, AND R. N. ZARE,J. Mol. Spectrosc. 55,500-502 (1975). 38. J. H. VAN VLECK, Phys. Rev. 33, 467-506 (1929). 39. J. T. HOUGEN, “The Calculation of Rotational Energy Levels and Rotational Line Intensities in Diatomic Molecules,” Nat. Bur. Stand., U. S. Monogr. No. 115 (1970). 40. H. LEFEBVRE-BRION,in “Atoms, Molecules and Lasers,” pp. 411-448, Intern. Energy Agency, Vienna, 1974. 41. J. M. BROWN, private communication. 42. J. M. BROWN, E. A. COLBOURN, J. K. G. WATSON, AND F. D. WAYNE, .I. Mol. Spectrosc. 74, 294-318 (1979). 43. C. AMIOT, R. BACIS, AND G. GUELACHVILI, Canad. J. Phys. 56, 251-265 (1978). C. AMIOT AND G. GUELACHVILI, J. Mol. Spectrosc. 76, 86-103 (1979). 44. A. J. KOTLAR, R. W. FIELD, J. I. STEINFELD, AND J. A. COXON, J. Mol. Spectrosc. 80, 86108 (1980). 45. D. L. ALBRITTON, A. L. SCHMELTEKOPF,AND R. N. ZARE, in “Molecular Spectroscopy, Modern Research,” Vol. II (K. Narahari Rao, Ed.), pp. l-67, Academic Press, New York, 1976. 46. R. RYDBERG, Z. Phys. 73, 376-385 (1931); 80, 514-524 (1933). 0. KLEIN, Z. Phys. 76, 226-235 (1932). A. L. G. REES, Proc. Phys. Sot. London 59, 998-1010 (1947). 47. J. T. HOUGEN AND B.\OLSON, Private communication.
48. D. L. ALBRITTON,Private communication. 49. R. N. ZARE, J. Chem. Phys. 40, 1934-1945 (1964). 50. R. J. FALLON, I. TOBIAS, AND J. T. VANDERSLICE,J. Chem. Phys. 34, 167-168
(1961).
OF
MOLECULAR
SPECTROSCOPY
87, 196-218 (1981)
Fourier Spectroscopy of the OD Infrared Spectrum. Merge of Electronic, Vibration-Rotation, and Microwave Spectroscopic Data C. AMIOT~ Laboratoire
de Physique Molkculaire et d’optique Atmosphkrique, Campus d’orsay, 91405 Orsay Cedex, France
B&iment 221
I
AND
J.-P. MAILLARD Observatoire
de Meudon,
Laboratoire
AND
J. CHAUVILLE
du Telescope
Infrarouge,
92190Meudon, France
The OD infrared spectrum, emitted in a flame of deuterium and oxygen, has been recorded for the first time in the 2-pm spectral range with a Fourier Transform spectrometer. A simultaneous fit of the ir 2-0, 3- 1, 4-2, 5-3, 3-0, 4-l vibration-rotation bands, of the uv data (O-O, l-l, 2-2, O-l bands of the A%+ + XV transition) and of the microwave data, gives accurate molecular constants for the ground-state vibrational levels up to v = 5. The classical “unique perturber approach” and the effective Hamiltonian of Brown for W states, have been successively used for the reduction ofthe spectroscopic data. I. INTRODUCTION
The hydroxyl radical has been intensively studied because it is involved in a wide variety of chemical and physical systems. It has been detected in interstellar gas clouds by radio-astronomy (I ) and it is commonly observed in astrophysical sources, some of which are masers (2). The short-lived transient OH plays an important role in the chemistry of the interstellar clouds (3). Numerous investigations were performed in different spectral regions. The hydroxyl radical was the first short-lived molecule to be investigated in the microwave region. Dousmanis ef al. (4) detected the transitions between A-doublet components of both spin components (Q2, J = 2.5 to 5.5 and 2113,2,J = 5.5 to 8.5) in the spectra of the OD, 160H, and ‘*OH molecules located in the 7.5-40-GHz region. The gas-phase E.P.R. spectra of OD and OH were observed by Radford (5,6). Magnetic moments generated by spin-uncoupling were strong enough to allow the observation of transitions involving the 2111,2component. Accurate E.P.R. measurements of the OD radical up to v = 5 were performed by Rashid er al. (7). The isotopic species with I70 (170H and 170D) were studied by Carrington and Lucas (8) and the analysis of these spectra yields values for the l’0 magnetic hyperfine and electric quadrupole parameters. These magnetic measurements were recently extended in the 26- to 35-GHz region by Brown et al. (9). 1 Author to whom reprint requests should be sent. 0022-2852/81/0501%-23$02.00/O Copyright All rights
0 1981 by Academic of reproduction
Press,
in any form
Inc. reserved.
196
OD INFRARED
SPECTRUM
197
The hydroxyl radical was also the first radical to have been detected in the radiofrequency range in a molecular beam experiment. Extensive and very accurate measurements were performed by Dymanus and Meerts (10-13). Seventeen pure rotational laser transitions were reported in the 12- to 20-pm spectral range by Ducas et al. (14). A great number of papers have dealt with the derivation of a Hamiltonian capable of interpreting the accurate OH and OD microwave data and uv data. The contributions of Mizushima (25), Destombes et al. (Z6), Veseth (17), Brown et al. (9), Coxon (Z8), and Coxon et al. (19) are the most important ones. An extensive review of the microwave studies has been reported by Beaudet and Poynter (20). The hydroxyl radical is also involved in numerous combustion and flame processes which were studied in the uv spectral range through the AT + X*II band system (21). For the OD radical several analyses have been reported (22-28). However, the most reliable data and analysis for this transition have been derived by Coxon and his co-workers (18,27,28). In these last papers the 0- 1, O-O, I- 1, and 2-2 bands were carefully investigated by direct approach methods and “unique perturber approximation” outlined by Zare et al. (29,30). Other works concerned with the OD radical are gathered in Huber and Herzberg’s book (31). In the infrared part of the spectrum, the vibration-rotation spectrum between vibrational levels of the OH X*Il ground state was investigated by Maillard et al. (32 ) using Fourier Transform techniques. However, the OD radical had never been observed in this spectral region. A systematic investigation between 1 and 3 pm was then performed. In the present work we have observed the 2-0, 3-1, 4-2, and 5-3 bands and also some rotational lines of the 6-4, 3-0, and 4-l bands. In order to obtain a more reliable set of molecular constants we have performed a simultaneous analysis of our data and also of the uv and microwave spectroscopic data. The next section of this paper deals with the experimental aspects of the work, in particular the OD production. The effective Hamiltonians used in the direct approach method are then discussed. Finally the results are presented and the molecular constants are compared with those previously determined. II. EXPERIMENTAL
DETAILS
A high-temperature OD source with long-term stability is necessary for recording spectra with a Fourier technique. In the case of OH an oxyacetylene flame was employed by Maillard et al. (32). But, as deutered acetylene is not commonly available in large quantities we chose to use a deuterium-oxygen flame. Stoichiometric mixture ratios were adjusted for a total gas flow of 20 liters/h. As in previous experiments on OH the flame was imaged on a 4-mm diameter diaphragm to isolate a region of the outer cone giving the most intense OD emission with a rotational temperature of about 2500 K; that is much lower than in the oxyacetylene case. The high-resolution Fourier spectrometer (33,34) at the Meudon observatory was used to record the spectra. The apparatus has been put quite recently under vacuum, avoiding the parasitic absorption by H,O and CO, bands. The total spectral range from 3500 to 9000 cm-’ has been covered with
198
AMIOT,
MAILLARD,
AND CHAUVIL4.E
two records. A portion of the spectrum in the P branches of the 2-O to 6-4 bands is displayed in Fig. 1. The blending by D20 lines is very strong, particularly in the R branches, which are much less “clear” than the P branches. It is, however, worth noting that the signal-to-noise ratio is reduced compared with the similar OH spectrum due to the type of source used (32, Fig. 1). The observed linewidths are about 0.1 cm-‘. In the Av = 3 sequence the signal-to-noise ratio is poor due to the faintness of the bands and only some lines of the 3-O and 4- 1 bands are usable. The calibration of the spectra was performed by using residual H,O absorption lines (35) ensuring an absolute wavenumber accuracy better than 5 x 10e3 cm-‘. III. THEORY
The Hamiltonian for the interpretation of high-resolution spectra of diatomic molecules can be written, in the absence of external magnetic or electric fields, as
H,, includes the terms which are independent of rotation and in the Born-Oppenheimer approximation gives the vibronic term energy T, for the allowed vibrational states of the different electronic states. The term Hrot is the Hamiltonian describing the rotation of the nuclei. It has the form H,t
=
B(r)R2= -
h
87r2pr2
(J - L - S)Z,
where B(r) is the radial part of the rotational energy operator, p is the reduced mass, and r is the internuclear distance. The third term H, is related to the interactions between the orbital and spin motions of the electrons. This fine-structure Hamiltonian is composed of three parts H, = H,, + H,, + H,,. For all doublet states considered in this work the spin-spin interaction rigorously zero. The spin-orbit Hamiltonian H,, has the form:
H,, is
H,, = A(r)L.S,
where A(r) is the spin-orbit H,, is given by
coupling constant.
H,, = y(r)R.S
= y(r)(J
The spin-rotation
Hamiltonian
- L - S)vS,
where -y(r) is the spin-rotation constant. A basis set of Hund’s case (a) wavefunctions, eigenfunctions ofJ2,JZ, S2, S,, L, (eigenvalues J(J + l), Sz, S(S + l), 2, A) is used and noted 1211nvJ iI>, where R = 1A + IS ) . For a211 state the secular determinant to be solved is a 4 x 4 block and a 2 x 2 block for a 2Z state. When wavefunctions of well-defined parity, relative to reflection in the plane containing the internuclear axis, are introduced the dimensions of these blocks are divided by two. When interactions with other Born-Oppenheimer states (2IZ*and 21J)through the operators B(r)J,L, or [A(r)/2 + B(r)]L,S, are considered there is a removal of the degeneracy for the two 2 x 2 blocks. The small terms nondiagonal
OD INFRARED
SPECTRUM
8 --:
--f
-P --:
-8 --:
-0 --:
-B -_:
3
I
Q)
_:!
I
-4
199
200
AMIOT, MAILLARD,
AND CHAUVILLE
in S linking 211states through the operator H,, are neglected (36). We have adopted the notation e andf for the parity of each block (37). Rather than diagonalizing a large matrix with all the *F, *II, and *A states the Van Vleck transformation (38) is used in the “unique perturber approach” to keep one *II or one *C state only and to apply small corrections, due to the other electronic states, to the matrix elements of the Born-Oppenheimer state. The matrix elements are obtained by the methods outlined by Hougen (39), Zare et al. (SO), and Lefebvre-Brion (40). The matrix elements of the *II Hamiltonian are collected in Table I for this “unique perturber approximation.” The definitions of the elements are nearly analogous to those of Coxon (28), in particular higher-order terms for the A-doubling constants
TABLE I Hamiltonian Matrix Elements for OD X2H State in a Parity Case (a) Basis Set: Unique Perturber Approximation T
A
1,l
1
2,2
1
1,l
0.5
2.2
-0.5
AD 191 2,2 1.1 AH 2,2
6
0
Ii
L
o
192
0.25(3(z-1)2+2) q
1,l
z-l
2,2
ztl
1,2
-,0*5
1,l
-(z-1)2-z
9D
2,2 ’ -(2+1)2-z
q”
2 zzO.5
1,l
(z-1)3tz
(32-l)
2,2
(rt1)3tz
(32t1)
I,2
-(322tztl)
zO.5
1,l
(z-1)4tz(6z2-3zt2)
2,2
(z+l)4tz(6z2t5zt2) 4zzO.5
Y
to
2n Y,labe12to 3
-0.25
zoe5 J2(Jt1)2
(Jt0.5))
l-2
0.5 z”~
(-lk(Jt0.5))
191
0.5 z J(Jt1)
292
0.5(z+Zr
(Jt0.5))
132
0.5 z”~
(-l+
191
0.5 z J2(Jt1)2 0.5(zt2T(Jt0.5))J2(J+l)2
1.2
0.5 z”‘5(-1+(Jt0.5))J2(Jtl)i
1.1
-0.5
2.2
-0.5 0.5 zO.5 -0.5
J(Jt1)
-0.5
J(Jt1)
0.5 z”~
J(Jt1)
1.1
-0.5
J2(Jt1)2
YW 2.2
-0.5
J2(Jt1)2
f
J(J+l)
(JtO.5))5(5+1)
292
1.2
211$.
J(Jt1)
0.52
191
two the signs are given the lower is for
J(Jtl)
0.5(zt2r
0.5 zoe5 J2(Jt1)2
1.2 - Label 1 refers
z”~
191
YD 2.2
1
292
-0.25
(5t0.5))
2.2
192
(2 2tztl)
zO.~
0.5(lT
0.5(l+(Jt0.5))J2(Jt1)2
22,
-0.25(3(zt1)2tz)
-0.25
0.5(1?(&0.5))
pH 192
0.5(2-l) -0.5(2+1)
0.5 zO.5
1.2
292
pD 22,
1,2
1,2
192
P
z=(Jt0.5)2-1 levels,
=(J-0.5)(Jt1.5).
the upper for
e
levels.
When
OD INFRARED
201
SPECTRUM
p andq are obtained simply by an expansion inJ (J + 1). We have also constrained
the parameter o, to the value Ap/8B (U = 0). In analyzing the E.P.R. spectrum of OH X*II u = 0 Brown et al. (9) have recently developed a new effective Hamiltonian formalism using a formal tensor approach. The calculations are done within a single ‘II vibrational level, more precisely within the spin and rotational levels. The influence of the other electronic states is taken into account by operator techniques (41, 42). The corresponding matrix elements for this effective Hamiltonian are given in Table II. Although these matrix elements should be used since higher matrix elements are established in correct operator form we have also performed the calculations in the classical
TABLE II Hamiltonian Matrix Elements for OD X*Il State in a Parity Case (a) Basis Set: Effective Hamiltonian of Brown (41) T
A
AD
1,l
1
2,2
1 2,2 PO 1,2
1,l
2,2
1,l 232 192
H
L
?0.5(Jt0.5)(z+2)
0.5 -0.5
132
D
r0.5(Jt0.5)
191
1,l
B
2,2
232
229
AH
P
0.5 z -0.5
PH 2,2
(zt2)
1,2
(Jt0.5)
TO.5
(zt4)(J+0.5)3
i0.5
z”‘5(Jt0.5)3
z2 -(2+2) 2
9
zo.5 z z+2 _,0.5
qD
191
-z(ztl)
2,2
- (ztl)(zt4)
1,2
2zO*5(z+l)
191
z(z+l)(z+Z)
qH
(z+l)(z2+8zt8)
1,2
-zO.5(zt1)(3z+4)
191
-z(z+1)2
T(J+O.5)
1,2
+ 0.5 z”‘5
1,l
70.5 TO.5
(3zt4)(5+0.5)
I,2
i0.5
z”‘5(zt2)(Jt0.5)
2,2
-(z+l)
(z2t12i+16)
420.5(z+1)2
(z+Z)
YH
1,l
rz(JtD.5)3 T2(zt2)(Jt0.5)3
lO.5zo’5(zt4)(J+O.5)3
2rl T3
-1
,
label 2 to
two signs are quoted the lower is for
1,l
-0.5z -0.5(3zt4)
1,2
0.5
1,1
-Z-Z2
2,2
-2(ztl)(zt2)
211 i. f
0.5 z0.5
292
1,2 - Label 1 refers to
z(Jt0.5)
2,2
192
YD
(J+c\.5)
2,2
2,2
Y
(zt4) 2
2,2
1,2
2,2
1,2
l 0.25 z”‘5
zD.5(2+2)
0.5zO.5(z2+5z+4) z=(Jt0.5)2-1=(J-0,5)(J+1.5).
levels and the upper for
e
When levels.
202
AMIOT,
MAILLARD,
AND CHAUVILLE
“unique perturber approach” in order to compare our results with those of previous works. For the Y states the matrix elements of the Hamiltonian are given in Table III. The parameters T, B, D, y are effective parameters since the electronic perturbation parameters cannot be separated from the true mechanical constants. IV. DATA TREATMENT
In the previous reduction of the OH data a band-by-band treatment was adopted (32). In this work as in another analysis (43) a weighted, nonlinear, least-squares fitting routine is used to reduce the spectroscopic data. These input data are the wavenumbers that we have recorded in the infrared, the uv data of Clyne et al. (27), and the microwave transitions (4, 7, 10, II, 20). We have ignored the hyperfine structure of these transitions by considering only the gravity centers of the lines. The wavenumbers for these lines are then Z(2F + l)~ilX(2F + l), where oi is the hyperfine transition and the sum runs for AF = 0 transitions only. This is certainly an approximate value for the zero-field transition. The spectroscopic data were compared with the calculated differences of upper- and lower-state eigenvalues of the Hamiltonian matrix given in Tables I and III or Tables II and III. The initial values of the parameters used to evaluate the Hamiltonian matrix were taken from Coxon’s work. After diagonalization one obtains term values from which a first set of calculated transitions is derived. A comparison with the observed frequencies leads to corrections to the initial parameters. The whole set of data is then treated iteratively until convergence is achieved. The advantages of such computing procedures have been widely discussed (44, 45).
TABLE
III
Hamiltonian Matrix Elements for OD A%+ State in a Parity Case (a) Basis Set
1 T
(J - 0.5)
B
- (J - O.5)4
(J + D.5)4
- (J t 0.5)4
(J t 1.5)4
L
(J t 0.5)
-(J
- 0.5)*
(J t 0.5)
0.5
(J - 0.5)
0.5
(J t 1.5)
0.5
(J - 0.5)5(5+1)
0.5
(J t 1.5)5(5+1)
0.5
(J - 0.5)J2(Jt1)*
0.5
(J + 1.5)J2(Jt1)2
Y (J + 1.5)
(J t 0.5)*
D
YD -(J
t 0.5)*
(J + 1.5)2
(J - 0.5)3
(J + 0.5)3
H (J t 0.5)3
(J t 1.5)*
yH
LJpper line refers to
e
levels and lower line to
f
levels.
OD INFRARED
SPECTRUM
203
V. RESULTS
Least-squares fits of the data have been performed with the two *II Hamiltonian matrix elements quoted in Tables I and II. For each *II Hamiltonian two successive fits were made. A preliminary unweighted least-squares fit first provides adequate estimates for the weighting factors. These are taken equal to l/r?: if tij is the mean of the residuals for each vibration-rotation band or microwave transition. This first fit determines also the significant parameters. If a parameter is nonsignificant relative to one standard error its value is constrained, in the second weighted least-squares fit, to the last significant value in order of increasing vibrational quantum number. In this last fit the variance is calculated as: 1 &-‘,
=
Wi(U6 - Ui)’
i=1.n
n-m
where (~5, &. are the measured and calculated wavenumbers, n the number of wavenumbers, m the number of variable parameters, and wi the applied weights. If the values of wi are good estimates of the standard deviations of the distribution of measurement errors and if uh - c; are correct estimations of measurement errors, &-“,$ should fluctuate near unity. The constraint y=O was used, since it is well known that the parameters AD and y are nearly totally correlated. The derived molecular constants using the two approaches are collected in Tables IV and V. The 2, value is nearly equal to (1.040)’ in the two cases. It is worth noting that the value of AH (u = 0) from Table IV, increases from 0.121 x 1O-6 cm-’ when the first fit (unweighted and unconstrained) is performed to 0.221 10e6 cm-’ in the second fit. It may also be seen that the value of A, from Table IV does not show a smooth ZIvariation. In fact, centrifugal distortion terms and higher-order variation of A-doubling parameters show a smoother u dependence when Brown’s formalism is used. The observed wavenumbers for the 2-0, 3-1, 4-2, 5-3, 3-0, 4-l bands, together with the differences o-c between observed and calculated wavenumbers using Hamiltonian of Table II, are presented in Table VI. The few observed wavenumbers for the 6-4 band are also quoted in Table VI. The results for the uv bands are quite similar to those of Coxon et al. (27,28) and will not be reproduced here. The agreement between observed and calculated microwave transitions is given in Table VII. The residuals, of the order of a few MHz, are greater than the experimental uncertainty, especially for the M.B.E.R. results (10, II). This is due to our adopted approximate treatment for these transitions. The constants for the A*Z+ state do not depend significantly on the *II Hamiltonian used. Effective parameters are reported in Table VIII when Brown’s Hamiltonian is employed for the X*II state. In order to reduce the number of parameters for these X*II and A*X+ states a classical “Dunham-type” expansion of each parameter in powers of (v + l/2) has been performed. For the most accurately calculated parameters we give in Table IX the coefficients of ad hoc expansions
a
1
0.12553
P
brackets
Values
1400
=+x10
(IDX106
WI03
in
input
7.06
are
for
(17)
2632.To50
v=l
one
constants.
(17)
(15)
(56)
(37)
(77)
(12)
(47)
(30)
(35)
(30)
=
error,
freedom
standard
of
C-l.463
2.104
-10.597
-1.136
0.12237
[6.40]
1.9320
5.2978
9.607103
[1.21]
-1.65
-139.4343
Degrees
are
(12)
(25)
(12)
(22)
constrained
parentheses
uavenumbers.
-1.52
2.137
-10.966
-0.978
(II)
2.015
nx1oa
Lx1013
PDXlO5
(11)
5.3825
Dx104
(34)
(42)
(21)
2.14
9.883003
A&O7
B
(27)
(31)
-5.43
IO
CO1
-139.2157
A&04
A
v=o
in
1320. units
of
Standard
c-l.461
2.121
-10.2682
-1.054
0.11744
L6.401
1.8521
5.2222
9.334461
[1.21]
-3.55
-139.6203
5175.8434
v=2
( 2)
7632.2423
the
Last
deviation
(11)
(77)
(34)
(15)
(62)
= significant
a2
[-1.46i
1.901
-9.798
-0.765
0.112352
Lb.401
1.793
5.1526
( 9)
9.064067
[I.211
0.60
-139.8581
(41)
(20)
(32)
u=3
(31)
figure
(I.0311
(34)
(23)
(80)
(44)
(12)
(15)
(53)
(35)
(37)
2
. of
the
C-1 .46]
2.152
-9.562
-1.00
0.10837
Lh.401
1.587
5.0830
a.795619
Cl.213
-2.94
-139.9945
10001.894i
U=4
constant.
(61)
(27)
(16)
(55)
(24)
(21)
(58)
(31)
(44)
(17)
ODJXI 0 c u G 5 Molecular Constants (in cm-‘): % Hamiltonian ofTable I (U.P.A. Approximation)a
TABLE IV
Values
C-l.461
L2.301
-8.712
r_-1.501
0.10340
L6.401
0.88
4.9934
in
8.527887
Cl.211
0.72
-140.2081
12285.3421
v=5
square
(30)
(63)
(la)
(76)
(99)
(66)
(50)
(35)
a)
1400
-1.50
me
constrained
are
one
”
=
1
standard
of
the
deviation
c-1.461
2.139
-10.3002
cl.481
-1.631
0.11767
c6.401
1.8414
5.2119
9.330373
7.84
-7.178
-139.4517
in units
Standard
(17)
(14)
(59)
(36)
(73)
(11)
(461
(58)
(50)
(36)
v=2
(12)
1.757
Last
significant
? _) ^o L = (l.034)L figure
of
(31)
the
constant.
[-l&J]
Values
(66)
2.160
2.002
(13)
C-1.461
-9.228
in square
(251
(611
brackets
C-l.461
c2.311
Cl.481
(21)
(27)
[-I.441
-9.582
(18)
0.10577
L6.401
(161
[I.481
-1.49
0.10821
(7:) 1.21
(981
(251
(MO>
(56)
(37)
5.0085
8.524641
-9.876
(93)
(26)
1.617
(62)
(23)
5.0760
L6.403
(61)
8.791938
cl.481
-1.563
0.11401
(48)
(15)
5.1399
c6.403
(51)
9.060060
15.9
-5.874
-140.0113
12286.6976
v=5
(89)
(41)
(18)
(60
(11)
(44)
(70) (77)
(67)
7.44
(28)
7.08
(57)
-6.485
(38)
-6.236
(50)
(35)
-139.8253
7633.0729
< 5) (40)
(41)
-139.6606
v=4
of Table II (Brown
(19)
V--3
2rl Hamiltonian
10002.9713
V
(31)
(in cm-‘):
5176.3880
Constant
(30)
error
= 1314.
c-1.463
2.118
-10.632
cl.481
-1.668
0.12271
L6.401
1.9264
5.2881
9.602879
8.68
-7.523
-139.2702
2632.3780
of freedom
constants.
in parentheses
Degrees
(12)
(25)
2.139
input Lines.
IO
Values
qHxIO
qDX106
(46)
(II)
1.47
-10.993
pnx109
qx103
(74)
(21)
0.12567
p
-1.533
(38)
6.90
LX1013
PDX105
(12)
(12)
5.3719
2.002
(44)
Dx104
9.878587
B
(24)
(35)
(34)
Hxl08
8.85
-8.207
-139.0576
co1
AHHO
ADx103
A
7
v=o
OD X*fl 0 =Z u G 5 Molecular
TABLE
206
AMIOT,
MAILLARD,
AND CHAUVILLE
TABLE
VI
-6..
4:: 4::
-2:: -2.: -7:1 2: 13.5 -6.6 -..O -10.0 ::::: --Is., -12..
T,B,D, -..=
c K,t(vf My, i=O,n
where x represents any of the molecular constants and n is the degree of the polynomial. Correlations between parameters were ignored but a weighting according to uncertainties of Table V was applied. The term values for all the vibrational levels with 21s 5 for the ground state are collected in Table X. These data should be useful for predictions of microwave transitions to be measured in astrophysical observations. The absolute uncertainty of transition calculated in this manner is better than 150 MHz. A change in the ordering of the A-doubling levels e,fbetween theJ = 9.5 andJ = 10.5 rotational levels of theF,(211,,,) component may be noted. For the lower J values (~9.5) the e component has a smaller energy than thef. The reverse is true for J > 9.5. This phenomenon has been observed for all the vibrational levels studied. In the OH radical Brown et al. (9) observe such a change
OD INFRARED TABLE OD: J
P2e
3- 1
W-Continued
Vacuum Wavenumbers
o-c x 10’
R2e
207
SPECTRUM
O-C x IO’
and o--c Values (in cm-‘) Pie
o-c
3.6
-**.a
4::
-1.5 -8.6 -3.1
I:-:.
-2::: {:i.
-1% -1e.. o-c 103
-lt.2
-,.6
*:s
I
-7’:.
2:: 2: 2: -Il.0
I:9 f :i .
P2f
4:.
I.9
3:: C:! -;2
J
4:: 3:: :a:!
-5. 2”:: ::: 2.:.
-6:s
J
x 103
-_)7.3
2;::
O-C
Te
x 10’
O-C x 103
Plf
o-c x 103 LO.2
-;“,:: 2: -16.6 --8-o -3;9 -0.0
-2.1 --I.9 -0.0 ;::
0.6
0-C
5f
J
x 103 12.6
,::: 3,
-0
17-e -9.4
2:: ;p:i . 1.2 I.0
2:
3
-1:2 I:-: -0:0 -;:; .
in the ordering between J = 3.5 and J = 4.5 for the same 2111,2spin-orbit component. The constants determined in this work were also used to construct an R.K.R. potential energy curve for the ground state (4649). We used previously determined turning points and relative vibrational energies of the OH molecule (50) as additional constrained points of the potential energy function assuming that it is invariant by isotopic substitution. The results are presented in Table XI. The differences in the R,,, and R,,, values for the two spin-orbit components 2111,2and 2II3,2being small, a “mean” curve is given, obtained by using the T, B parameters of Table V as input data to the D.H.L. program. 2 By resolving the Schrodinger equation with the R.K.R. potential so determined the vibrational transitions are 2 The D.H.L. program (29, 30. 47) is a slightly modified version, for use on UNIVAC machines, of the original version available from Albritton (48) and usable directly on CDC machines.
208
AMIOT,
MAILLARD, TABLE
OD: 4-2
J
pze .71)1.01.3
zziz~ 471,:5722 4194.2925 4bb9.9525 .U..S,.Y
::5’ :%I-. :6”,:
LO.5
45b2.3744
16.5 19.5 20.5 21.5 22.5 23.5
J
4533.023R 4502.7318 ..7,.5299 4*39..041 .#1.4024 .3,2.5358 4337.8157 4352.2687 .2b5.901tB .228.,.50 4190.79,. .,52.0403
P2f
1.7 -1.9 -0.6 -:-:
2:,
-0.2 -0.T -1.3
-oz.P
r;i; 1:::
o-c
RZe
1n3
0.5 1.5
5:; 2X t::
VI-Continued
Vacuum Wavenumbers
o-c x
AND CHAUVILLE
I!
4866..92. .BRO.,929 489..,O,tl 4906.4905 4917.R934 492fi.2373 4937.5559 .94b.7,,5 4952.8503 4950.8939 .9b3.7321 .96,..,hS .9b9.087I3 .9,,.202CI 49, I .?983 4970.1139 496,.R285 4964.268R 4959.4531 4953.394e 49.0.0833 *93,.5,30 .92,.1,,9
o-c
R2f
II-l3
and o-c
2.3 15.2 -,.,
3-z . -85.6 -1.4 -3.0 .
4i.i 0.1
--b.* -10.0 3.3
o-c
o-c
Pl2
x lo3 4796.
25.2
,177
4774.bSb5 l 752.1703 4728.0465
Z%. . izz7: 4b52.4707
4b25.2174 l 59?.ob39
.568.0200 4s38.1ob9 4507.3118
4475rbSC,5
4443.1455 4409.7922 4375.bO52 4340.b028 l 30*.79t2 .2(r8.2103 6230.8031 .,92.bb.1) 4 153.7.86 411*.1035
Plf
4853.4870 4870.1761 U)S5.5832
-13.9 . -5’: .t **.t. 183-b 9.b y-:. -0.b -2.7 f:t -1.4 -4.3 -3 .? 2.: -7:0 -‘2:“, 2.2
o-c
0.8 48(rb.51.0 4t3a0.7929
,780.9000
-7.1
‘2: s:a
13.5 14.5 15.5 16.5 17.5 18.5 19.5 20.5
4760.902b l 739.7oe2 471?.*605 4694.lJBP ebb.?sab' . m.t.7.y.e.7: . 4562.0145 y3',.gw?*" . 4.71.03bl 4438.87b9 6605.0329 .371.9256 l 337.3b52 4301.5bbt 4265.1513
::.: 73:5
t:'~.~z . 4151.1e.87
;:; .
::3 6.5 2: 1::: 11.5 12.5
..1
:E%.s% 49*,:9039 4928.346,
1;::
-%-z .
4953.0132 495R.9902
1.2
+a . ::: . 3.5" --I.8 -3.2
t~;.~%. 49b9.9e55 4971.2e.25 4971.3461 4970.2395 49b?.AROb 49b4.2BTI 4959..!a,P 4953.3701
-12.9 -1::: 4.b -,3.5 -11.0 -b.O -,a.2 9.1
Rle
.79e.o2,e 4774.5813 .752.1025 1728.b4bS 4704.1953 .678.,973 l e52..707 lb2b.2820 l 597.1824 .5wl.**23 4538.2958 .507.53,6
-12-B
-2b .8 -2b.6
23.; 14.2 -3.3 -28.1 -5.5 ,":T ti:: -3.5 -0.6
--;3:: 22.9
-1::: 7.1
-..2
2:5
-,‘,:t
-4.0 -s$t
49bb.bISb
l PoP.JUI l97O.B.03 497l.1175 4970.1319 4967.89b5 l 96e..o,+
2:; 2:: 7.5 8.5 1.5
-2&i 10.0 9..
If'X . 12.5
-lb.3
:t.: . 20.5
l9n.e317
5:'s" 2315
6920.0114 l9lb.911(1
%f
J y-:
4.4
:tz.t~~ .
o-c
J
x 103 *as3.sboo 4n?o.l933 .8t?5.5032 l 99.bBW 4912.4695 : ,f:X ycl3.w& . :'Gi.km,: . 4957.2754 7:4 t'g',.zp7: I _:y; 9.1 *9b9:2320 : -,5.6 0.0 t,';z.z0; 49b9:9WS
::; -2.5 -10.9
O-C x 103
4923.9Wb ~~~.as~ . 4950.w71 4957.4022 l JL2.6*95
x 103
x 103
x 103
Values (in cm-‘)
*9b7.822.5 *PbI.3I29
.9w.sma ~953.5054 mt.g32t . l 928.0062 .9.6.9323
:-: 2:5 3.5 4.5
10.5 "9.5 . II.5 ::.: 14:s L5.5 L6.5 L7.5 ‘8.5 19.5
1-z.: 3b:6
:v:: _
22:5 23.5
recalculated to better than 0.18 cm-’ and the B, values to better than 23 x low5 cm-‘. With this method it is possible also to calculate D, and H, values. They are compared to our fitted parameters in Table XII. The agreement between the values is good although the R.K.R. calculated parameters are always slightly larger than the derived parameters of Tables IV and V. VI. DISCUSSION
A comparison of the results obtained with the two 211 Hamiltonians will be presented first. Then our values for the molecular constants are compared with the previously reported ones. The expected relations between the parameters of a 211 state expressed in the “unique perturber approximation” and in Brown’s formalism have been given by this author (42, Table III) and more specifically in the case where the constraint Yno = 0 is applied. For example the following relation exists between the vibrational terms:
OD INFRARED
209
SPECTRUM
TABLE VI-Continued OD: 5-3 Vacuum Wavenumbers J
o-c
Pze
103
x
o.= 1.5 2.5 3.7 4.5
5.5 6.5
7.5 Ft.5 a.5
.609.2>02 .5e9.a&v31 4569.0624 4547.3r6. .524.6559 4500.6637 4.76.0.02 4450.2183 4423.3699 4395.5681 4366.6236 4337.1230 4306.5105 4274.9810 4242.5609 4209.2930 4175.1897
p2f
J 0 .5 L.5
4bOY.2502
2.5 3.‘;
4569.64PJ 456~~.980A 45.1.273H 4524.5031 4500.6655 4415.812. 4449.9493 4423.0814 4395.23RO 4366.4307 4336.6960 430b.fl38.
9.5 5.5 6.5 7.5 8.5 7.5 10.5 11.5 12.5 13.5 14.5 15.5
4274.4636 4P42.04’62 4208.7069 4,7.**45,
L6.5 I -P .S IR.5
-21.2 -7.4 -5.0 -7.1 11.0 . -ii 5.2 6.6 2.5 4.9 -5.1 -0.9 -15.9 7.0
o-c x 103
-_(
.-a _.. .
$2 3.1 7.3 -7.6 -5.2 2.3
I.2
4::: -1.3 0.0
-1Jil
lb.7 -5.5 4.0
o-c
Rze x
b.2 26.5 10.3 15.9 29.6 8qO -6.4 26.0 3.1
. 4716.9976 .730.692S 4741.6065 4751.0624 4760.474J 47hB.2572 4774.877b 4780.3947 47w.7711 4767.9Wl 4790.02bb 47w.n773 4790.52b. 4786.9622 4766.1740 4782.1512
o-c
R2f
x 103 -14.0 -9.4
4692.3529 4706.1b29 4719.0392 4730.9506 4741 .es91 4751.7310 4760.5719 4768.3475 4774.9700 4780.5039 4784.e.771 4708.086e 4790.1179 4790.9560
:;p9.;;;1 .
o-c
Pll?
5.7 .
-1:s -K-f. -13.9
.b24.0:*3'4603.2197 4561.3i7tl .55R.z!r)9f! 4534.5465 4509.7540 4.84.Ol50 4.57.3ee 4429.0053 4.01.35RH 4372.072. 4341.8413 4310.7C59 .27.5.*,29 4746.0758 4P12.4732 417tt.0.54 4142.602b
L
1;::
x
x 4623.9606 4603.1405 4561.2641 :S~~;~~ . 4509.7540 44h4.0371 4457.4229 44 29.9074 4401.5032 4372.2103 4342.044. 4311.0189 4279.1272
.695.7560 4710.b266 472e.1403 4730.4266 4747.4266 4757.1651 4765.6636 4772.9252 4770.9130 .?83*6A03 4787.2037 47cI9.4900 4790.5367 0790.1402 .760.6957 .78b.l97C 4781.2402 4777.0159
o-c
Plf
4246.4156 4212.6154 4178.4412 4143.2433
2
-0.5 5.7 -9.1 r-23.3 . ;7.b 12.9 12.5 4.7 4.7 1.6 -6.2 1.3
o-c
Rle
x lo3 4biW.6428
xxz::
4786.2000 1782.1529
103
and o-c Values (in cm-‘)
Rlf
103
J
103 ,,.5
5.0
1.5 2.5
-3.1 21.6 -30.6 -?5.. -31.0 -13.0
3.5 4.5 5.5 6.5 7.5 8.5 4.5 0.5 1.5 2.5 3.5 4.5 5.5 a.5 F.5 e.5
2.6 -7.0
O-C
J
x lo3 0.5 I.5
4b79.7,02
9.5 6.1 19.5 A.3 -0.5 -10.1 -6.3 -3.3 2.2 1.7 1.7 6.6 ll3.0
-17.9 -4.0
4695.hllb 9710.6280
:;g.:.$f . 4747.4266 4757.139, .7bS.b,122 4rr2.83Rb .??R.(‘;‘?O 4703.5b07 4767.1010 y;.ya; . 4790.2855 .786.@09') .7Rb.I242 47RP.ltJ22 677b.977,
-7.6 -36.7
::5: a.5
4(A,” - 0,7 - 2B; - q;)
The superscript 7~is relative to the unique perturber case and the tilded parameters are related to Brown’s approach. From our T values (which are in fact differences of T: or e’,, between two vibrational levels) quoted in Table IV one must be able to calculate the parameters given in Table V. The results are quoted below for the four vibrational levels from v = 1 to v = 5 (all values are in cm-‘): 1
2
3
4
5
U.P.A.
2632.1050 (30)
5175.8434 (2)
7632.2423 (31)
10001.8941 (17)
12285.3421 (35)
T
2632.3803
5176.3904
7633.0580
10002.9815
12286.6972
2632.3780 (30)
5176.3880 (5)
7633.0729 (31)
10002.9713 (19)
12286.6976 (37)
V
T
talc form. (1)
T Table V
210
AMIOT, MAILLARD, TABLE OD:
3-O
AND CHAUVILLE
VI-Continued
Vacuum Wavenumbers
and o--c Values (in cm-‘)
U.P.A. stands for “unique perturber approximation.” The agreement between the values of Table V and those calculated formula (1) is good. For the rotational constant B, Brown et al. (42) give the relation
using
As before the comparison using Bg and q; constants of Table IV to calculate l!?,, by formula (2) are summarized below (all values are in cm-’ except ((B;- 8,,)/2) which are given in lop4 cm-‘):
OD INFRARED
211
SPECTRUM
TABLE VII OD Microwave Transitions and o-c Values (in MHz)
_
F
Y _
0
_ 1 _ I
_ 4
I =
TABLE VIII OD Molecular Constants for A?%+ (in cm-‘): Spectroscopic 0
v
32487.1370
T
a
Data Form Coxon (18)” 2
1
(17)
(36)
34701.6591
(41)
36812.8839
9.043523
(46)
8.721484
(51)
a.398740
(88)
x
lo4
5.77498
(13)
5.7272
(12)
5.6914
(34)
H
x
a 10
1.797
(12)
1.5839
(82)
1.096
(38)
L
x
10'2
1.293
(39)
0.12017
(23)
D
Y YD yH
a)
0.11718
x
IO5
-1.471
(61)
-1.30
x
109
2.80
(40)
C2.683
Quoted the
uncertainty
Last
Values
digit. in
square
equal Hamiltonian brackets
L1.2451
[!.245]
to
one of
sre
(10)
(61) (19)
-1.59 c2.681
standard Table
0.11262
(36)
deviation
II.
constrained
constants.
in
units
of
212
AMIOT, MAILLARD,
AND CHALJVILLE
TABLE IX “Dunham-Type”
Coefficients for the PII
States of OD (in cm-‘; p, q in MHz)
V
0
1
2
3
4
5
B::
9.883003 (42)
9.607103 (47)
9.334461 (41)
9.064067 (53)
8.795619 (58)
8.527887 (99)
B”, talc form. (2)
9.877520
9.601804
9.329312
9.059168
8.790838
8.523530
L Table V
9.878587 (44)
9.602879 (46)
9.330373 (44)
9.060060 (51)
8.791938 (61)
8.524641 (98)
5.33
5.37
5.30
4.46
5.50
5.55
B; -
2
I&,,
It appears that a systematic difference occurs between the B values calculated by formula (2) and those reported in Table V. This difference, nearly equal to 20;, as shown by the last line of the above Table, arises because in the U.P.A. approximation matrix elements of R2 are used while Brown uses W, i.e., formula (2) given in Ref. (42) is not quite correct. For the other rotational constants D, H, and L the agreement is good between the two sets. For the spin-orbit constant the following relation must hold:
xi,,,= (A;
- 0;)
P:
2(A; - 0:: - 2B; - 4;) 1 ’
The comparison between calculated values by this formula and constants Table V is given below (all values are in cm-l):
of
TABLE X OD XW
Energy Values Relative to the Level u = 0, n = 3/2, J = 0.5, e
u=3
v=2
f
e J
112
312
l/Z
l/2
312
312
l/2
v=5
v=4
l/2
l/2
312
3/z
311
J
f
e
f
e J
f
e 112
312
112
3/z
J
L
1 213
214
AMIOT, MAILLARD,
AND CHAUVILLE
TABLE XI OD X*Il: Vibrational Terms, Rotational Constants, V
”
ohs
=
Gv+Yoo cm
V
CCilC-v
-1
x
103cm
a”
ohs -1
cm
and R.K.R. Turning Pointsa
aY - 0”
-1
x IO
5
T
R. M1l-l
talc -1 cnl
i
0
1351.2423
19
9.878587
-1.6
0.894184
1.061863
1
3983.6139
56
9.602879
6.6
0.047362
1.141786
2
6527.6303
80
9.330373
14.4
0.818776
1.204321
3
8984.2610
100
9.060059
21.3
0.797547
1.260430
4
11354.2146
128
0.791930
23.0
0.780556
1.313324
10.4
0.766396
1.364523
5
13637.9397
174
t
8.524641
E
a)
Reduced the
V
AZ
mass
p
coefficients
=
1.70877. of
Table
yoo V
1.5493
. The
9"
cm-'. are
2
1
0
=
The
taken
Gy from
are
calculated
Table
3
with
V.
5
4
- 139.2157 - 139.4343 - 139.6203 - 139.8581 - 139.9945 - 140.2081 (31) (32) (37) (35) (44) (50)
Al, - 139.0507 - 139.2681 - 139.4499 - 139.6878 - 139.8269 - 140.0381 talc. (3) AZ,1 - 139.0576 - 139.2702 - 139.4517 - 139.6606 - 139.8253 - 140.0113 Table V (34) (40) (36) (50) (56) (35) The value of o; is constrained at -0.22 cm-’ for all v. The A,,,, constants, which are much better defined in Brown’s formalism, follow the relation: &,, = A 6, -t PIT
B: + (1/2)qF A,“-o;-2B;-q;
V
0
1
2
Afi,
-5.43 (27)
-1.65 (30)
-3.55 (20)
A,,, talc. (4)
-88.53
-75.82
-72.88
A,,,
-82.07
-75.23
(50)
(35)
(4)
*
The results are quoted below where all constraints
Table V
must
are in 10m4cm-l: 3
4
5
-2.94 (31)
0.72 (66)
-65.10
-63.43
- 56.75
-71.78
-64.85
-62.36
-58.74
(38)
(57)
(70)
(130)
0.60 (35)
OD INFRARED
215
SPECTRUM
TABLE XII Comparison of D,., H,. Observed and Calculated Using the R.K.R. Method (all Parameters
in cm ‘Y’
D
”
x
0
1
2
3
4
5
a)
10
D 4
x
5.3719
(12)
5.3825
(111
5.2881
(111
5.2978
(12)
5.2119
(11)
5.2222
(
5.1399
(15)
5.1526
(15)
5.0760
(23) (21)
5.0085
(71)
4.9934
(76)
given
Dabs in
and Table
IO
4
x
5.3863
5.3053
5.2293
9)
5.0830
For
H
talc
5.1592
5.0959
5.0402
Hobs V,
the
the
x
2.002
(12)
2.015
(111
1.9264
(73)
1.9320
(77)
1.8414
168)
1.8521
(62)
1.757
(12)
1.793
(12)
1.9476
(2.5)
1.21
(16)
0.88
(18)
line
to
those
a
2.0287
(24)
refers
10
2.0955
1.617
Line
ca1c
2.1456
1.587
first
second
10
H 8
1.8412
1.6317
to of
the Table
results IV.
The variation of this constant with the vibrational quantum number u is smooth in Brown’s approximation. In comparing the parameters of Tables IV and V it is worth noting that the “unique perturber approximation” constants p: and 9: are identical to those of Brown et al. (42). The higher-order constants p. and qD have also the same order of magnitude in the two approaches. More reliable determinations of these and higher-order A-doubling parameters will be obtained only by M.B.E.R. or microwave works like those of Meerts et al. (12), Coxon (19) or Brown et al. (9) performed on the OH radical. The molecular constants obtained in the “unique perturber approximation” and quoted in Table IV, can be compared with the results of the uv study of Coxon (18). They concern the only previously reported molecular constants of the ground state for the vibrational levels u = 0, 1,2. The results are summarized in Table XIII. The agreement is good within three standard deviations except for L” and 4:. Obviously, these constants have been defined with opposite signs in the two analyses. In our work the parameter pH was found to be nonsignificant and constrained to a zero value while Coxon constrained it to the value 1.33 x lo+’ cm-’ for all vibrational levels. A more marked difference appears in the vibrational term values quoted below (in cm-l) (relative to the v = 0 vibrational term value).
(25)
(21)
5.3742
1.935
1040”
(19)
(36)
-10.934
-2.034
103Q"
106s;
0"
1o"Q
*)
a)
0
the
l-l
are
(12)
(25)
(12)
1.295
(22)
band
of
*2z+
constrained
error
.-o-2221
i-9.631
-2.117
-10.643
Cl.331
0.12240
c-4.521
(27) (17)
-139.446
(31)
2.065 c-5.191
(111 (34)
5.3307
9.60889
COXON
-
XIII
units
(25)
(22)
(79)
(60)
( 6)
(14)
(28)
(17)
A'n.
1.9320
5.2970
9.607103
of
the
L -0.2201
c-14.61
2.104
-10.597
CO!
-1.136
0.12237
-1.65
-139.4343
2.455
5.276
[-0.219)
c-9.631
L-2.201
-10.206
Cl.331
[1.30]
0.11694
c-4.681
.?39.644
(58)
(94)
of
(13)
(74)
(53)
(10)
L'81
digit
COXON
9.3346
significant
(17)
(15)
(56)
(37)
(30)
(35)
(77)
(12)
(47)
IV
c-5.193
(in cm-‘)a
work
last
Table
This
Constants
c6.401
1
Molecular
constants.
in
[~I*
of OD PII
(11)
(42)
standard
for
: one
L-O.2201
-15.2
2.137
-10.966
CO3
-0.978
5.12553
-5.43
brackets
from
7.06
2.015
5.3825
IV
work
9.883003
Table
This
-139.2157
uncertainty
square
Results
in
Quoted
c-0.223:
(160)
(95)
(47)
1.283
1.33
105pg
109p;;
-9.63
(46)
P"
0.12661
L-4.361
( 4)
.139.230
A II
104Ai
(59)
-5.19
10'31.
?08H”
Cl?)
[=I
9.88310
COXON
8”
”
Comparison
TABLE
This
t6.401
I.8521
5.2222
9.334461
Table
the
IV
work
constant.
c-0.22Ol
L-14.61
2.121
-10.2682
CO1
-1.054
0.11744
-3.55
-139.6203
2
Values
(11)
(77)
(34)
(15)
(20)
(32)
(62)
( 9)
(41)
OD INFRARED SPECTRUM
1
2
3
2632.12 2632.105
5176.20 5175.843
7632.0 7632.242
2214.54 2214.523
4326.10 4325.750
6333.3
V
X’Il
217
ATi.+
The first line refers to Coxon’s results (18) and the second one to our work. The differences come from the necessary use in Coxon’s work of older data on the 2-0, 2- 1, 3- 1, 3-2, and 3-3 bands which are clearly subject to large systematic errors. ACKNOWLEDGMENTS C. Amiot is indebted to Dr. J. M. Brown for helpful correspondence and for making his YI Hamiltonian matrix elements available to him. The authors are grateful to the Referee for many valuable comments on the manuscript.
RECEIVED:
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