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Infrared study of the 15N isotopic species of nitric oxide near 5.4 μm
JOURNAL
OF
MOLECULAR
Infrared
SPECTROSCOPY
76, 86- 103 (1979)
Study of the 15N Isotopic Species Oxide Near 5.4 pm
of Nitric
C. AMIOT Laboratoire de Physique Moliculaire et d’optique Atmosphtrique. Bririment 221 -Campus d’Orsay. 91405 Orsay. France AND
G. GUELACHVILI Laboratoire
d’lnfrarouge,
B&iment 350-Campus
d’orsay,
91405 Orsay, France
The 1-O and 2- 1 transitions of the rSNL60molecule have been investigated with a Fourier spectrometer (resolution 2.7 x 10e3cm-‘). The 1-O transition of the 15Nr70 and ‘sNL80 molecules have also been observed. A direct approach method was used to determine molecular constants from the observed data. The parameters A.,, and ye were calculated by combining the r4N160 and i5Ni60 results. Two spectral coincidences with r3CL60laser lines have been found. INTRODUCTION
The ordinary nitric oxide molecule 14N160 has been the subject of numerous investigations in the infrared and microwave regions of the spectrum. Only a few studies were made for the isotopic molecule 15N160. In the infrared region, the fundamental vibration-rotation band has been carefully studied by Keck and Hause (I), who observed the two “satellite” bands. As part of a study of the heaviest chemically stable isotopic molecule, 15N180, Griggs et al. (2) also reported the molecular constants of the 1-O transition of 15N160. The fundamental and first overtone bands were investigated by Olman et al. (3). The microwave region of the spectrum was first studied by Gallagher and Johnson (4). The molecular beam technique was employed by Meerts and Dymanus (5) to obtain extremely precise A doubling and hyerfine constants of the molecule. Lasers have been used by Dale et al. (6) to perform very high resolution measurements. Recently, opto-acoustic spectroscopy was employed by Pate1 and Kerl (7) in order to get accurate values of the A doubling in the 211,,zv = 0, 1 levels. In a previous paper (8) we reported a detailed analysis of the 1-O band of the molecule 14N160, and preliminary results were given for the spectra of the impurities 14N170, 14N180, and 15N160. In the present paper we report an accurate analysis of the 1-O and 2- 1 transitions obtained with an enriched sample of 15N160. The isotopic species 15N180 and 0022-2852/79/070086-18$02.00/0 Copyright
0 1979 by Academic
All rights of reproduction
Press,
Inc.
in any form reserved.
86
NITRIC OXIDE:
=N ISOTOPIC
SERIES
87
L
88
AMIOT AND GUELACHVILI
I i
I
I
NITRIC OXIDE:
=N ISOTOPIC
89
SERIES
15N1’0 9 present as impurities, have also been observed. The molecular constants of the ZI= 0, 1 levels of 15N*‘0 are reported for the first time. The present investigation was also intended as a means of obtaining an accurate determination of the parameters A.,, and ye. In the first part of this paper we shall briefly describe the experimental conditions used to obtain the spectra. The second part deals with the theoretical molecular model chosen for reducing the observational data. The results-observed wavenumbers and molecular constants -are presented in the third part. Finally, the results are discussed. EXPERIMENTAL
CONDITIONS
The spectra were obtained under vacuum with the “third generation” Fourier interferometer of the Laboratoire d’Infrarouge (9). The width of the apparatus function was equal to 2.7 x lo+ cm-’ (nonapodized). Three spectra corresponding to the three 15N1s0 gas pressures-0.045, 1.35, and 21.42 Tot-r-were recorded with a path length equal to 24.183 m. The 1-O band of CO was recorded simultaneously and used to determine the absolute calibration of the wavenumber scale. The wavenumbers of isolated and nonsaturated lines observed in the various calibrated spectra are reproducible within 6 x lop5 cm-‘. If one takes into account the uncertainty with which this standard is defined (IO), the absolute uncertainty for the spectral positions of the lines is of the order of t1.7 x lop4 cm-’ or 25 MHz. Figures 1 and 2 represent the Q branches recorded with, respectively, 0.045 and 1.35 Torr gas pressures. The low-J lines are shown in Fig. 1. It may be seen that the A doubling in the 2H3,2-211~,2Q-branch lines is resolved from J = 8.5. The 2H1,2-2111,2Q-branch lines are separated from J = 0.5 and show an incompletely resolved structure. The upper part of Fig. 1 below 1840.5 cm-’ TABLE
I
Matrix Elements of a *II State in a Parity Case (a) Basis Set
2$2
T+$+(B+A$X-1) -D[(X-1)2+X]+H[(X-1)3
SP.
242
++x
x =
(J+$p-l
.
Upper and lower signs
refer
to
e
and
f
levels respectively.
+x(3x-l)
90
AMIOT AND GUELACHVILI TABLE
II
15N’60: 1-O”
is repeated again in the lower part of Fig. 2. The higher gas pressure (1.35 Torr) used to record the spectrum allows the observation of weaker bands: 2-l of 15N160 and 1-O of 14N160, lsN1’O, and 15N180. The most remarkable feature consists in the partial resolution of the hyperfine structure in the Q branch. In the lower part of the figure the structure of the lines is shown by expanding the wavenumber scale by a factor of 5. The dominant hyperfine components in the Q
NITRIC OXIDE: 15N ISOTOPIC SERIES
91
TABLE II-Continued
a Observed 1O-5 cm-‘.
wavenumbers.
Calculated
wavenumbers
are shown
in parentheses. 0 - C given in
branch are those for which AF = AJ = 0. Due to the spin Z = l/i of atom, the 15N the hyperfine pattern consists of four lines, two of which are much lower in intensity than the other two. So the hyperfine structure looks like a doublet. In the other branches the hyperfine effect symmetrically broadens the lines. The intensity measurements and the calculation of hyperfine constants are under study and will soon be reported elsewhere (18). THEORY AND DATA REDUCTION
It is well known that the A-doubling effect splits the NO rotational lines into a doublet of components separated by low3 to 10T2 cm-l. In such cases, the spectra are Doppler limited. As a consequence, when the A doublets are partially resolved in the spectrum, an improvement of the observed wavenumbers has been obtained by two numerical treatments. First, we searched the true positions of the maxima of the lines by an iterative least-squares fit of the recorded profile to the sum of two components, each component having the spectral profile of an isolated,
92
AMIOT AND GUELACHVILI TABLE III
a Observed lo-$ cm-‘.
wavenumbers.
Calculated
wavenumbers
are shown in parentheses.
0 - C given in
well-resolved line of the spectrum. The least squares followed the minimum variance, linear unbiased estimates with the positions, heights, and widths of the spectral profiles as varied parameters. Second, the A-splitting measurements were improved by a smoothing of the curve representing the experimental A doubling as a function of the rotational quantum number J. This procedure allowed the evaluation of the wavenumbers of the A doublets even when they were not resolved in the spectra. These experimental data have been reduced to molecular constants by fitting the observed line positions to calculated ones obtained by diagonalizing the upperand lower-state Hamiltonians constructed with adjustable parameters. The Hamiltonian matrix elements of a 211state [parity case (a) basis set] are given in Table I. The definitions of the effective molecular parameters are those of Ref. (8). We used the set 0 defined in Ref. (8) since the main contributors to the A doubling are 2Zc- states. The 1-O and 2-l bands of 15N160 were processed simultaneously. A “branch weighting” was applied to the data (8). Due to the high correlation between the parameters A_,and y, the fits were done by constraining either AJ = 0 or y = 0 in the Hamiltonian matrix. The parameters pJ and qJ were not introduced in the model since they are barely significant and do not improve the quality of the fit.
NITRIC OXIDE: =N ISOTOPIC SERIES
93
TABLE IV ‘5N”O: 1-()a
a Observed 1O-5cm-‘.
wavenumbers.
Calculated
wavenumbers
are shown in parentheses.
For the calculation of the Dunham coefficients developed in the form A, = A, - q(u
the parameters
+ ‘/) + &(v
0 - C given in
A, and B, were
+ ‘h)‘,
B, = B, - CQ,(U+ %) + ,&,(u + %)2,
while only the first two terms, D, and (YD, were kept for the development of the D parameter. In the case of the isotopic species 15N”0 and 15N180, since only two levels (u = 0 and u = 1) were observed it was not possible to determine the parameters pi (i stands for 15N1’0 or 15N1*O). These were constrained to their calculated values using the isotope relations pi = p2pA and pi = p4& where PA and pB represent 14N160 values and p2 is the ratio of the reduced masses of r4Nr60 and of the isotope i. Also, since no satellite band was observed, the spin-orbit coupling constant Ai could not be obtained. It was then supposed that the equilibrium value A, was isotopically invariant. The parameters CX~ and C&were then calculated from the values of A or B for the levels v = 0 and 1 using the expressions CY;=A
(v = 0) - A
(21 = 1) + 2pA talc.,
CX;= B
(v = 0) - B
(u = 1) + 2/3, talc.
AMIOT AND GUELACHVILI
94
TABLE
a Observed 1OP cm-‘.
wavenumbers.
The parameter
Calculated
wavenumbers
Bt was determined B’, = Y2B
V
(v =
are shown in parentheses.
by
0)- MB
(0= 1) + Pe talc.
Finally, the constrained numerical values in the reduction 15N180 data are given below (in cm-‘): 15Nl70
Aeff (v = 0) A, 103P.4 105PB
0 - C given in
123.13744 123.25191 -4.79 -1.83
of the 15N1’0 and
15Nl80
(46) (34) (23) (44)
123.13895 123.25191 -4.25 -1.74
(46) (34) (23) (44)
The uncertainties, equal to two standard deviations in units of the last digit, are obtained from those for 14N160 parameters.’ Also, due to the lack of lines with high J values, the accuracy of the calculations of the A-doubling parameter 1 It is supposed that when a parameter D is a linear combination of parameters d,, d,, . . , d, with standard deviations cl, (T*, . , (T, such that D = k,d, + k.& + . + k,,d,, then the standard deviation (TVis such that ai = kfc$ + k$o% + . . + k2.0-fn.
NITRIC OXIDE:
=N ISOTOPIC
TABLE
SERIES
95
VI
15N160: u = 0, 1, 2 Effective Molecular Constants (in cm-‘)*
0
123.135605
Aeff
(58)
1842.917717
(28)
3658.738596
(122)
122.895733
(58)
122.646142
(240)
B
1.6361951
(12)
1.6195494
(12)
1.6028761
(23)
Dx106
5.0931
(12)
5.1078
(10)
5.1229
(28)
px103
-11.2783
(30)
-11.2515
(32)
-11.2477
(116)
qXI06
-89.53
(18)
-87.75
(16)
-88.74
(242)
*Jeff
X104
1.6156
(10)
1.5659
(IO)
-11.8818
(72)
-11.6228
(70)
1.3597
(76)
1.3473
(17)
1.5211
(136)
(Y=O)
Y
eff"I03
-11.3894
(990)
(AJ=o)
cx102
633
input lines
* Quoted uncertainty The quantity -8
IS
: two
R.M.S.
=
1.6
1O-4
1.3355
cm
(235)
-I
standard deviations in units of the last digit.
often added to the parameter Aeff value when then
doubling is ignored. Here
-$
is not included in Aeff
.
9’ is not good. We chose to constrain the value of 4’ to the calculated one, that is, # = p4q. In our previous paper (8) we used the method outlined by Brown and Watson (II) to determine the parameters A.,, and ye. The apparent values of AJ and y, denoted A^; and Jo, permit us to obtain apparent equilibrium values AYe and x. The true constants AJe and -ye were obtained by the relation A:JP’ = &
-
C,Y,,
where the parameter C, = &/(A, - 28,) is calculated with AJ = 0 and y = 0 [see Appendix of Ref. (S)].
in view of the two fits
RESULTS
The observed wavenumbers resulting from the simultaneous analysis of the 1-O and 2- 1 bands of 15Nis0 are reported together with their differences from the calculated wavenumbers in Tables II and III. The data concerning the 1-O bands of 15N170 and 15N1*0 are given in Tables IV and V.
AMIOT AND GUELACHVILI TABLE VII 15N170: u = 0, 1 Effective Molecular Constants (in cm-l)* V=O
v=1
0
A
123.13744
eff
(461d
1816.766455
(88)
122.90102
(14)
B
1.5895337
(58)
1.5735982
(52)
Dx106
4.785
(18)
4.804
(14)
px103
-10.52
qx106
-03.465a
(11)
1.496
AJeffX104
-10.51
(12)
-81.1
(16)
1.453
(26)
(26)
(Y=O)
127
input lines
R.M.S. = 1.9 10-4 cm-'
: two
* Quoted uncertainty
standard deviations in units
of the last digit. and 9 constrained to calculated values from 14N161 a) A,ff constants [El and isotopic relations. P2 =O.q36982gg.
TABLE VIII 15N’80: u = 0, 1 Effective Molecular Constants (in cm-l)* v=o
\)0 A
v=1
1793.29200
0
123.13895
eff
(461a
122.905889
(46)
(80)
B
1.5482463
(24)
1.5329296
(24)
Dx106
4.5519
(58)
4.5671
(48)
px103
-10.600
qx106
-79.174a
(40)
1.459
AJ,ffX'04
-10.586
(40)
-78.63
(961
(13)
1.415
(13)
(Y=O) 149
input lines
* Quoted uncertainty
R.M.S. = 1.1 10-4 cm-'
: two
standard deviations in units of
the last digit.
a) A eff
and
4 constrained to calculated values from
constants [81 and isotopic relations.P'= -
0.91257984
14N160
97
NITRIC OXIDE: =N ISOTOPIC SERIES TABLE IX Dunham Coefficients
Ae( eff)
123.25191
aA
0.23404
For A, E, D (in cm-*): Verification of Isotopic Relations
(34) (61 )
oA calcd. @*XI0
3
flAxlo
3
-5.11
(23)
123.25189
(16)
123.25191
(34ja
123.25191
(341a
0.23015
(30)
0.22748
(59)
0.22456
(59)
0.22986
(61 )
0.22654
(6~)
0.22357
(61.)
-4.86
(14)
-4.79
(237
-4.25
(23)a
-4.93
(23)
-4.79
(23)
-4.25
(23)
calcd.
1.7049184
Be
(84)
Be c&cd. ffB
0.0175297(135)
czB calcd.
1.6445076
(28
)
1.5974790(101
1.6444945
(84)
1.5974795
0.0166181
(44)
0.0166060(135)
&X105
-2.09
(44)
-I.
BBX105
38
-1.94
)
I.5558829
(58
I .5558742
(84)
O.O158992(Il7)
0.0152819
(94)
O.OI5899I(l35)
0.0152820
(135)
(84)
(18)
-1.83
(44F
-1.74
(44F
(44)
-1.83
(44)
-1.74
(44)
)
calcd.
D&O6
5.4622
(88
1
D,x106
5.0857
(28)
4.7755
(90)
4.5443
(90)
5.0819
(88)
4.7954
(88)
4.5489
(88)
calcd. fYD”108
-1 .64
(75)
UDX108
-1.47
(47)
-1.90
(78)
-1.52
(75)
-1.50
(75)
-1.39
( 75 )
-1.30
(75)
calcd.
P2
1
isotope
i :
12: = paA, 8; = p2BA,
quoted uncertainty a)
constrained
0.96455906
: two
standard
B;
=
0.93698299
p2 Be
deviations
, CT;= ,03aB, in
units
Of
0.91257984
/j;=p4$,D;=p4D,,
the
last
CY;= p5a,
digit.
values.
The effective parameters v, Aerr, B, D, P, 4, 4 eff, and yett are reported in Table VI for the levels u = 0, 1, and 2 of 15N160. The results pertaining to the levels D = 0 and 2, = 1 of 15N1’0 are gathered in Table VII. The results for the same levels of 15Nls0 are given in Table VIII. From the previous constants a set of Dunham coefficients for the parameters A, B, and D has been deduced and is given in Table IX. Calculated values using isotopic relations are also included in this table. The results for 14Nls0 are given again since they are used for these calculations.
98
AMIOT AND GUELACHVILI TABLE X lsNIBO: Energy Values Relative to the Level D = *h, J = 0.5, e (-59.94323 cm-‘) "=,
V=O
”
V.,
i-l.illl4h _._..
E
1.5 2.5 3.5 4.5 5.5 6.5 7.5 0.5 9.5 10.5 11.5 12.5 13.5 14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5 23.5 24.5 25.5 26.5 27.5 23.5 29.5 30.5 31.5 32.5 33.5 34.5 35.5 36.5 37.5 39.5 39.5 40.5 41.5 42.5
124.85029 133.14259 144.75098 159.67466 177.91260 193.46355 224.32607 252.49951 283.97900 318.76552 356.85536 398.24762 442.93824 490.92503 542.20512 596.77551 654.6330t 715.77452 780.19648 M47.89545 319.86779 993.10978 1070.61758 1151.38724 1235.41473 1322.6959) 1413.22650 1507.00221 1604.01861 1704.27116 1807.75524 1914.46616 2024.39911 2137.54918 2253.91140 2373.48067 249b.25192 2622.21958 2751.37957 2883.72332 3019.24928 3157.94778
4.83543 12.89931) 24.18857 39.70620 56.45112 77.42322 101.62237 129.04339 159.70104 193.53004 231.69504 271.01562 314.57129 361.35141 411.35535 464.58229 521.03134 530.70149 643.59161 703.70043 779.02657 951.56950 927.32457 1006.29296 1088.47174 1173.95890 1262.45132 1354.24970 1449.24660 1547.44294 1649.93487 1753.41941 1861.19341 1972.15357 2086.29646 2203.61849 2324.1159tJ 2447.79477 2574.62111 2704.62071 2837.77924 2974.03220
1.5 2.5 3.5 4.5 ::: 7.5 a.5 1::: 11.5 12.5 13.5 14.5 15.5 lb.5
124.85032 133.14270 144.75125 159.67520 177.91354 193.46505 224.32831 252.50168 293.99332 318.77124 356.96321 399.25687 442.94969 490.93395 542.22191 596.79528 654.65623 715.90140 780.2274rJ 847.93072 918.90775 933.15475 1071.6679Y 1151.44320 1235.476b7 1322.76414 1413.30137 1517.08402 1604.107tb 1704.3677t 1807.85971 1914.57979 2024.52019 2137.L79Ol 2254.05026 2373.62835 2496.40960 2622.38723 2751.55637 2383.91154 3019.44717 3159.157bl
3753.27503 3791.39659 3802.76597 3817.38239 3935.24484 3856.35211 3980.70290 3908.29523 3939.12776 3373.19824 4010.50455 4051.04436 4094.81515 4141.81429 4192.03894 4245.49617 4302.15287 4362.03584 4425.13172 4491.43704 4560.94823 4633.66157
l”47.02104 ~.._
_
4.85932 12.93256 24.23413 38.76295 56.51892 77.50132 101.71180 129.14833 159.31129 193.70036 230.81518 271.15531 314.72024 361.50936 411.52177 464.75729 521.21440 580.83230 643.79934 709.90576 779.23368 351.797O1, 327.54924 1006.52343 1039.70769 1174.0>991 1262.69796 1354.49316 1449.50127 1547.70151 1649.03705 1753.69489 1861.4b189 1972.42475 ZOY6.57OOb 2203.99422 2324.3934Y 2443.Ob395 2574.90161 2704.90225 283Y.Ot155 2374.37504
1967.61353 1975.92052 1937.3095') 2002.079bb 2020.12999 2041.45927 2066.06606 2033.94874 2125.10547 2159.53425 2197.23287 2233.19899 2282.43006 2329.92341 2380.b7b20 2434.18546 2491.94807 2552.46090 2616.22027 2693.22299 2753.46537 2926.94368 2903.65410 2983.59272 30t6.75549 3153.13823 3242.73ta8 3335.54t94 3431.5640b 3531.78370 3633.20127 3738.91205 3947.61123 3953.59394 4074.7551t 4193.03932 4314.59274 4439.25863 l(jt'7.09212 4694.05773 4832.17970 4969.44235
__~~_3783.27506
if63.69804 3671.58847 3682.65130 3696.87665 3714.26382 3734.81327 375'3.52461 3735.39761 3915.43133 3849.62739 3884.98341 3924.49956 3967.17526 4013.00386 4062.00260 4114.15263 4163.45896 4227.92053 4299.53612 4354.30442 4422.22396 4493.29316
3791.39670 3902.76624 j917.39291 3'935.24575 3356.35357 3830.70497 3908.29336 3939.13196 3973.20378 4010.51169 4051.0533s 4094.82628 4141.82782 4192.05518 4245.50541 43oi.i7142 4362.06201 4425.16193 4491.47141 4560.98718 4633.70543
1947.8o791 1855.78355 186b.96622 1881.33777 1898.90411 1919.bt,510 1943.t20bO 1370.77039 2001.11422 2034.t5177 2071.38265 2111.30642 2154.42254 2200.73037 2250.22320 2302.91820 2359.79645 2417.96288 24Y0.11634 2545.55554 2614.17904 2C35.33530 27b0.97261 2339.13915 2920.48294 3005.0018t 3092.b33t.3 3193.55585 3277.58595 3374.79121 3475.1337t 3573.t5560 3635.32854 3795.15427 3905.12937 4024.2501t 4143.51290 4265.913b7 4391.44840 4520.11290 4651.90279 4786.81359
3663.7109i _._~... 3671.62264 3682.69174 c696.93305 3714.33146 3734.89179 3759.C1384 3785.49736 1815.54204 j949.74752 3835.11337 3924.63909 3967.32409 4013.16771 406i.16917 4114.72761
19t7.tl35t 1975.92063 1937.3097b 2002.081119 2020.13091 2041.4t073 20bt.Ot925 2093.95194 2125.10969 2159.53332 2197.24005 2238.20303 2282.44124 2329.93701 2380.t9252 2434.70473 2491.97073 2552.48708 ZClb.25')50 2tY3.2j749 2753.50445 2926.93767 29'13.70333 2933.t4743 30tt.91t13 3153.2051'1 3242.31019 3335.t27Ot 3431.b5123 3530.37835 3t,33.303t3 3733.92242 3547.72971 3359.7212'3 4074.99130 4193.23512 4314.74747 4439.42301 4jt7.2jt'52 4t99.24237 4932.37503 43t?.t4333
i:; 2.5 7.5
_ ;::
$:i 9:5 10.5 11.5 12.5 13.5 14.5 15.5 16.5 li.5 18.5 19.5 20.5 21.5 22.5
1847.O7247 1947.93X4 1855.92372 18t7.Ollb7 1881.39433 1839.97175 1919.743t,3 1943.70933 1970.97014 2?)01.22427 2034.7719) 2071.512tO 2111.445Y3 2154.57133 2201.39917 2250.39572 2393.03313 23jY.37948 2418.05371 24Y0.314t5 2545.7tlOO 2614.33135 2tYt.ZQ412 27t1.197b4 2339.37OOt 2320.71341 3095.24357 3092.94029 3133.30712 3277.84153 3375.04080 3475.402Ut 3579.92231 3635.53539 3795.42t37 310Y.404tO 41324.527tb 4143.7924'3 42t,t.13433 4391.73103 4520.33b77 4t52.187tO 4797.0>303
11.5 1.5 2.5 ::: 5.5 t.1 1.3 9.5 9.5 lCl.5 11.5 12.1, 13.5 14.5 11.5 1 t,.5
17.5 Id.5 19.5 2'1.5 21.5 22.5 23.5 24.j 2j.5 2t.5 27.j 23.5 29.1, 30.j 31.5 32.5 :i:: 35.3 3t.5 37.5 33.5 39.5 43.1, 41.j '(2.j
99
NITRIC OXIDE: =N ISOTOPIC SERIES TABLE XI 15N*‘0: Energy Values Relative to the Level R = M, J = 0.5, e (-59.99003 cm-‘)
TABLE XII 15N’80: Energy Values Relative to the Level n = M, I = 0.5, e (-60.03214 cm-‘)
The calculated energy values relative to the lower level with s1 = y2, J = 0.5, e are given in Tables X, XI, and XII for the 15N160, 15N1’0, and 15Nls0 molecules. The constants AJe and ye are given in Table XIII with all the data necessary for their evaluation. Finally, some previously unreported spectral coincidences between 15N160 absorption lines and 13P60 laser lines measured by Johns et al. (12) are given below: Spectral Coincidences 13Cl60
laser transition ll-lOP(9) 11-10 P(8)
m laser (in cm-‘) (12)
1814.565 (3) 1818.171 (3)
with 13P60 Laser Lines NO transition P’kf(8.5) REj’(7.5)
15N160 lsN’sO
@NO (in cm-l) 1814.56152 1818.17702
100
AMIOT AND GUELACHVILI TABLE XIII Determination 1
I
4& lo *Je 14N160
15N160
Y,
of A,,, -ye (in cm-‘)
I
1
I
106 (pv
104 (I
*Je
c
lo2 ce
1.7668
(22)
-5.73
(18)
-12.454
(24)
2.95
(20)
1.4186
(45)
1.6404
(12)
-4.96
(IO)
-12.0110
(58)
2.586
(50)
1.3657
(16)
= -12.5(16)10-3cm-1
Quoted uncertainty
-2.5
lO-5
cm-'
<
AJe < 8.5 IO-~,"-'
equal two standard deviations in units of the last digit.
DISCUSSION
The accuracy and the consistency of our results will be discussed first. Then a comparison of the wavenumbers and constants obtained in recent investigations will be presented. From Table VI it is seen that the 15N160 parameters for the 2, = 2 level are much more poorly defined than those for the r = 0 and o = 1 levels. However, the root-mean-squares of the differences between the observed and calculated wavenumbers is only 1.6 x 10e4 cm-’ or 4.8 MHz with 633 spectral lines. For 15N170, the rms given in Table VII is slightly increased to 1.9 x lop4 cm-’ (5.7 MHz) but the agreement is a little better in the case of 15N1s0 (1.1 x lop4 cm-’ or 3.3 MHz). The consistency of the results can be appreciated by examining Table IX. The constant A, is seen to be isotopically invariant from the accurate 14N160 and 15N160 results. This is an a posteriori justification of the admitted hypothesis to derive the A (v = 0) values for the isotopic species 15N1’0 and 15N180. Because the parameters (Y* and PA are well predicted by the isotopic relations, we have performed a weighted least-squares fit with both the A, values. The derived constants are (in cm-‘) A, = 123.25193 (32), (YA= 0.23422 (50), PA = -5.06 (20) x 10e3. The uncertainties for (Y~and PA are very slightly increased, indicating that the isotopic relations are only approached. This is also obvious from the other calculated values reported in Table IX. The calculated values of parameters A, and ye given in Table XIII are defined with different accuracy. Although the parameter ye is consistent with our preliminary determination (8), the parameter A,, is not accurately evaluated. The calculated value is very near zero, but the uncertainty is large, 2 1.7 x lop5 cm-‘. The theoretical values obtained by the formula of Veseth (13) and Merer (14) give, respectively, -4.9 x 10e5 and -4.5 x 10m5cm-l for the value ofA,. A better determination of A.,, can be obtained only by the study of several enriched gas samples, particularly the heaviest isotopic species 15N180. We compare our measured wavenumbers only with recently reported values. Three lines of the 2113,3-2113,2 1-O subband have been measured with laser mag-
101
NITRIC OXIDE: =N ISOTOPIC SERIES TABLE XIV 15N1@O: Comparison of Y, A, B, D Molecular Effective Constants (in cm-‘) R.M.DALE
et al
P. KRISTIANSEN
C61 1842.9195
(y = 0)
123.1404(28)
123.141244(58!
(8)
i842.9l7717(283
123.1419(14)
122.8986(16)
lZ2.901358(58:
1.636191(30)
BO
This work
121
1.63613?(14:
l.63619,1(1;)
1.619642(30)
1.6195494(12)
106xD0
5.095
(16)
5.0931 (12)
lo6 x D,
5.108 (18)
5.1078 (10)
B1
Quoted uncertainty digit.
: two standard
deviations in units of the last
netic resonance techniques by Dale et al. (6). As may be noted from the comparison given below, the two sets of results are in excellent agreement.
R (1.5)
Q (1.5)
P (2.5)
Dale et al. (6)
This work*
1850.9696 (8) 1842.7629 (9) 1834.4698 (57)
1850.97027 (17) 1842.76326 (17) 1834.47090 (17)
* Mean of e-e and f-fobserved wavenumbers.
The molecular constants, without the A-doubling ones, are compared in Table XIV with the results of Dale et al. (6) and those of Kristiansen (25). Dale et al. combined their own measurements with those of Keck and Hause (I), while Kristiansen obtained accurate ground-state constants by mixing microwave and infrared data. The agreement among the three sets of results is good. Kristiansen’s B, value is a little different because, in this parameter, part of the A-doubling constants is certainly included. We turn now to discuss the A-doubling parameters p and q. For the level 2, = 2 no precise value was given for 15N160. Since the isotopic relations are well verified it is, however, possible to calculate accurate parameters from the measurements of Pine et al. (16) for the level 2) = 2 of 14N160. The comparison is presented below (values in cm-‘). From Pine et al. (16) lO$ 1064 Note. Quoted uncertainty:
- 11.2462 (20) -85.46 (17)
This work -11.2477 (116) -88.74 (242)
two standard deviations in units of the last digit.
102
AMIOT AND GUELACHVILI TABLE XV 15N’60: Ground-State
A-Doubling Constants
MEERTS-DYMANUS
11.275280 (52) (54)
87.721
KRISTIANSEN
This work
CSI
[>I
11.271908 (6)
11.2783 (30)
88.73
89.53
(6)
(18)
Quoted uncertainties:two standard deviations in units of the last digit.
If we constrain the 4 value to -85.46 x lo+ cm-l in our parametersexcept the p parameter-change very slightly; to - 11.2377 x 10e3 cm-‘. For the u = 1 level the most recent reported by Pate1 et al. (7). The agreement with our values within the stated uncertainties. Pate1 et al. (7)
This work
11.20 (13) 67 (27)
- 11.2515 (32) -87.75 (16)
103Pl
lO%, Note. Quoted uncertainty:
calculations, the p becomes equal values have been (in cm-l) is good
two standard deviations in units of the last digit.
Accurate values for the ground-state
A-doubling constants have been reported.
TABLE XVI 15N1*O:Comparison of Effective Molecular Constants (in cm-l)a
This work
?.M.DALE etal[$*
v1+o
A0 Al
1793.2917
(42)
793.29200
(46)
123.56
(54)
123.13895
(46)b
123.32
(54)
122.905889
(80)
1.548304
(130)
1.5482463
(24)
1.532981
(130)
1.5329296
(24)
106 x Do
4.66
(10)
4.5519
(58)
JO6 x D1
4.67
(IO)
4.5671
(48)
EO Bl
* Data
of
Griggs
et
al Quoted incertainty
a1.121.
: two
standard deviations in
units of the last digit. b) Constrained value (see text).
NITRIC OXIDE: 15N ISOTOPIC SERIES
103
A comparison between the various determinations is presented in Table XV. It is worthwhile to clarify the definition of the parameters as given below: This work -P -4
Gallagher et al. (4) 2P,
-
4q,
Meerts et al. (5)
Kristiansen (15)
4(% - a,)
PK - %K qIi
4%
2a7
For example we have -p = pK - 4qK, wherep is our definition, andp, and qK those from Kristiansen. From Table XV it is shown that, although very close to one another, none of the reported constants agree within the claimed uncertainties except our p value and that of Meerts. Small differences can occur because the data are different or because different theoretical models are used to reduce the wavenumbers to molecular constants. Finally, Dale et al. (6), using the observational data of Griggs et al. (2) and their own observations, obtained a set of constants for the levels 21= 0 and v = 1 of 15Ni80. A comparison with our values is given in Table XVI. ACKNOWLEDGMENT The authors are grateful to Dr. R. Bacis for many valuable comments RECEIVED:
on the manuscript.
July 24, 1978 REFERENCES
I. D. B. KECK AND C. D. HAUSE, J. Mol. Specfrosc. 26, 163-174 (1968). 2. J. L. GRIGGS, K. N~RAHARI RAO, J. H. JONES, AND R. M. POTTER,J. Mol. Spectrosc.
22,
383-401 (1%7). 3. M. D. OLMAN, M. D. MCNELIS, AND C. D. HAUSE, J. Mol. Specfrosc. 14, 62-78 (1964). 4. J. J. GALLAGHERAND C. M. JOHNSON,Whys. Rev. 103, 1727-1737 (1956). 5. W. L. MEERTSAND A. DYMANUS,J. Mol. Spectrosc. 44, 320-346 (1972). 6. R. M. DALE, J. W. C. JOHNS, A. R. W. MCKELLAR, AND M. RIGGIN, J. Mol. Spectrosc. 67, 440-458 (1977). 7. C. K. N. PATELAND R. J. KERL, Opt. Commun. 24, 294-296 (1978). 8. C. AMIOT, R. BACIS, AND G. GUELACHVILI,Canad. J. Phys. 56, 251-265 (1978). 9. G. GUELACHVILI,Appl. Opt. 17, 1322-1326 (1978). IO. G. GUELACHVILI,J. Mol. Spectrosc., in press. II. J. M. BROWN AND J. K. G. WATSON, J. Mol. Spectrosc. 65, 65-74 (1977). 12. J. W. C. JOHNS,A. R. W. MCKELLAR, AND D. WEITZ, J. Mol. Spectrosc. 51, 539-545 (1974). 13. L. VESETH,J. Mol. Spectrosc. 38, 228-242 (1971). 14. A. J. MERER,Mol. Phys. 23, 309-315 (1972). 15. P. KRISTIANSEN,J. Mol. Spectrosc. 66, 177-184 (1977). 16. A. S. PINE, J. W. C. JOHNS,AND A. G. ROBIETTE,J. Mol. Spectrosc. 74, 52-69 (1979). 17. W. L. MEERTS,Chem. Phys. 14,421-425 (1976). 18. C. AMIOT, R. BACIS, G. GUELACHVILI,J. Mol. Spectrosc., in press.
OF
MOLECULAR
Infrared
SPECTROSCOPY
76, 86- 103 (1979)
Study of the 15N Isotopic Species Oxide Near 5.4 pm
of Nitric
C. AMIOT Laboratoire de Physique Moliculaire et d’optique Atmosphtrique. Bririment 221 -Campus d’Orsay. 91405 Orsay. France AND
G. GUELACHVILI Laboratoire
d’lnfrarouge,
B&iment 350-Campus
d’orsay,
91405 Orsay, France
The 1-O and 2- 1 transitions of the rSNL60molecule have been investigated with a Fourier spectrometer (resolution 2.7 x 10e3cm-‘). The 1-O transition of the 15Nr70 and ‘sNL80 molecules have also been observed. A direct approach method was used to determine molecular constants from the observed data. The parameters A.,, and ye were calculated by combining the r4N160 and i5Ni60 results. Two spectral coincidences with r3CL60laser lines have been found. INTRODUCTION
The ordinary nitric oxide molecule 14N160 has been the subject of numerous investigations in the infrared and microwave regions of the spectrum. Only a few studies were made for the isotopic molecule 15N160. In the infrared region, the fundamental vibration-rotation band has been carefully studied by Keck and Hause (I), who observed the two “satellite” bands. As part of a study of the heaviest chemically stable isotopic molecule, 15N180, Griggs et al. (2) also reported the molecular constants of the 1-O transition of 15N160. The fundamental and first overtone bands were investigated by Olman et al. (3). The microwave region of the spectrum was first studied by Gallagher and Johnson (4). The molecular beam technique was employed by Meerts and Dymanus (5) to obtain extremely precise A doubling and hyerfine constants of the molecule. Lasers have been used by Dale et al. (6) to perform very high resolution measurements. Recently, opto-acoustic spectroscopy was employed by Pate1 and Kerl (7) in order to get accurate values of the A doubling in the 211,,zv = 0, 1 levels. In a previous paper (8) we reported a detailed analysis of the 1-O band of the molecule 14N160, and preliminary results were given for the spectra of the impurities 14N170, 14N180, and 15N160. In the present paper we report an accurate analysis of the 1-O and 2- 1 transitions obtained with an enriched sample of 15N160. The isotopic species 15N180 and 0022-2852/79/070086-18$02.00/0 Copyright
0 1979 by Academic
All rights of reproduction
Press,
Inc.
in any form reserved.
86
NITRIC OXIDE:
=N ISOTOPIC
SERIES
87
L
88
AMIOT AND GUELACHVILI
I i
I
I
NITRIC OXIDE:
=N ISOTOPIC
89
SERIES
15N1’0 9 present as impurities, have also been observed. The molecular constants of the ZI= 0, 1 levels of 15N*‘0 are reported for the first time. The present investigation was also intended as a means of obtaining an accurate determination of the parameters A.,, and ye. In the first part of this paper we shall briefly describe the experimental conditions used to obtain the spectra. The second part deals with the theoretical molecular model chosen for reducing the observational data. The results-observed wavenumbers and molecular constants -are presented in the third part. Finally, the results are discussed. EXPERIMENTAL
CONDITIONS
The spectra were obtained under vacuum with the “third generation” Fourier interferometer of the Laboratoire d’Infrarouge (9). The width of the apparatus function was equal to 2.7 x lo+ cm-’ (nonapodized). Three spectra corresponding to the three 15N1s0 gas pressures-0.045, 1.35, and 21.42 Tot-r-were recorded with a path length equal to 24.183 m. The 1-O band of CO was recorded simultaneously and used to determine the absolute calibration of the wavenumber scale. The wavenumbers of isolated and nonsaturated lines observed in the various calibrated spectra are reproducible within 6 x lop5 cm-‘. If one takes into account the uncertainty with which this standard is defined (IO), the absolute uncertainty for the spectral positions of the lines is of the order of t1.7 x lop4 cm-’ or 25 MHz. Figures 1 and 2 represent the Q branches recorded with, respectively, 0.045 and 1.35 Torr gas pressures. The low-J lines are shown in Fig. 1. It may be seen that the A doubling in the 2H3,2-211~,2Q-branch lines is resolved from J = 8.5. The 2H1,2-2111,2Q-branch lines are separated from J = 0.5 and show an incompletely resolved structure. The upper part of Fig. 1 below 1840.5 cm-’ TABLE
I
Matrix Elements of a *II State in a Parity Case (a) Basis Set
2$2
T+$+(B+A$X-1) -D[(X-1)2+X]+H[(X-1)3
SP.
242
++x
x =
(J+$p-l
.
Upper and lower signs
refer
to
e
and
f
levels respectively.
+x(3x-l)
90
AMIOT AND GUELACHVILI TABLE
II
15N’60: 1-O”
is repeated again in the lower part of Fig. 2. The higher gas pressure (1.35 Torr) used to record the spectrum allows the observation of weaker bands: 2-l of 15N160 and 1-O of 14N160, lsN1’O, and 15N180. The most remarkable feature consists in the partial resolution of the hyperfine structure in the Q branch. In the lower part of the figure the structure of the lines is shown by expanding the wavenumber scale by a factor of 5. The dominant hyperfine components in the Q
NITRIC OXIDE: 15N ISOTOPIC SERIES
91
TABLE II-Continued
a Observed 1O-5 cm-‘.
wavenumbers.
Calculated
wavenumbers
are shown
in parentheses. 0 - C given in
branch are those for which AF = AJ = 0. Due to the spin Z = l/i of atom, the 15N the hyperfine pattern consists of four lines, two of which are much lower in intensity than the other two. So the hyperfine structure looks like a doublet. In the other branches the hyperfine effect symmetrically broadens the lines. The intensity measurements and the calculation of hyperfine constants are under study and will soon be reported elsewhere (18). THEORY AND DATA REDUCTION
It is well known that the A-doubling effect splits the NO rotational lines into a doublet of components separated by low3 to 10T2 cm-l. In such cases, the spectra are Doppler limited. As a consequence, when the A doublets are partially resolved in the spectrum, an improvement of the observed wavenumbers has been obtained by two numerical treatments. First, we searched the true positions of the maxima of the lines by an iterative least-squares fit of the recorded profile to the sum of two components, each component having the spectral profile of an isolated,
92
AMIOT AND GUELACHVILI TABLE III
a Observed lo-$ cm-‘.
wavenumbers.
Calculated
wavenumbers
are shown in parentheses.
0 - C given in
well-resolved line of the spectrum. The least squares followed the minimum variance, linear unbiased estimates with the positions, heights, and widths of the spectral profiles as varied parameters. Second, the A-splitting measurements were improved by a smoothing of the curve representing the experimental A doubling as a function of the rotational quantum number J. This procedure allowed the evaluation of the wavenumbers of the A doublets even when they were not resolved in the spectra. These experimental data have been reduced to molecular constants by fitting the observed line positions to calculated ones obtained by diagonalizing the upperand lower-state Hamiltonians constructed with adjustable parameters. The Hamiltonian matrix elements of a 211state [parity case (a) basis set] are given in Table I. The definitions of the effective molecular parameters are those of Ref. (8). We used the set 0 defined in Ref. (8) since the main contributors to the A doubling are 2Zc- states. The 1-O and 2-l bands of 15N160 were processed simultaneously. A “branch weighting” was applied to the data (8). Due to the high correlation between the parameters A_,and y, the fits were done by constraining either AJ = 0 or y = 0 in the Hamiltonian matrix. The parameters pJ and qJ were not introduced in the model since they are barely significant and do not improve the quality of the fit.
NITRIC OXIDE: =N ISOTOPIC SERIES
93
TABLE IV ‘5N”O: 1-()a
a Observed 1O-5cm-‘.
wavenumbers.
Calculated
wavenumbers
are shown in parentheses.
For the calculation of the Dunham coefficients developed in the form A, = A, - q(u
the parameters
+ ‘/) + &(v
0 - C given in
A, and B, were
+ ‘h)‘,
B, = B, - CQ,(U+ %) + ,&,(u + %)2,
while only the first two terms, D, and (YD, were kept for the development of the D parameter. In the case of the isotopic species 15N”0 and 15N180, since only two levels (u = 0 and u = 1) were observed it was not possible to determine the parameters pi (i stands for 15N1’0 or 15N1*O). These were constrained to their calculated values using the isotope relations pi = p2pA and pi = p4& where PA and pB represent 14N160 values and p2 is the ratio of the reduced masses of r4Nr60 and of the isotope i. Also, since no satellite band was observed, the spin-orbit coupling constant Ai could not be obtained. It was then supposed that the equilibrium value A, was isotopically invariant. The parameters CX~ and C&were then calculated from the values of A or B for the levels v = 0 and 1 using the expressions CY;=A
(v = 0) - A
(21 = 1) + 2pA talc.,
CX;= B
(v = 0) - B
(u = 1) + 2/3, talc.
AMIOT AND GUELACHVILI
94
TABLE
a Observed 1OP cm-‘.
wavenumbers.
The parameter
Calculated
wavenumbers
Bt was determined B’, = Y2B
V
(v =
are shown in parentheses.
by
0)- MB
(0= 1) + Pe talc.
Finally, the constrained numerical values in the reduction 15N180 data are given below (in cm-‘): 15Nl70
Aeff (v = 0) A, 103P.4 105PB
0 - C given in
123.13744 123.25191 -4.79 -1.83
of the 15N1’0 and
15Nl80
(46) (34) (23) (44)
123.13895 123.25191 -4.25 -1.74
(46) (34) (23) (44)
The uncertainties, equal to two standard deviations in units of the last digit, are obtained from those for 14N160 parameters.’ Also, due to the lack of lines with high J values, the accuracy of the calculations of the A-doubling parameter 1 It is supposed that when a parameter D is a linear combination of parameters d,, d,, . . , d, with standard deviations cl, (T*, . , (T, such that D = k,d, + k.& + . + k,,d,, then the standard deviation (TVis such that ai = kfc$ + k$o% + . . + k2.0-fn.
NITRIC OXIDE:
=N ISOTOPIC
TABLE
SERIES
95
VI
15N160: u = 0, 1, 2 Effective Molecular Constants (in cm-‘)*
0
123.135605
Aeff
(58)
1842.917717
(28)
3658.738596
(122)
122.895733
(58)
122.646142
(240)
B
1.6361951
(12)
1.6195494
(12)
1.6028761
(23)
Dx106
5.0931
(12)
5.1078
(10)
5.1229
(28)
px103
-11.2783
(30)
-11.2515
(32)
-11.2477
(116)
qXI06
-89.53
(18)
-87.75
(16)
-88.74
(242)
*Jeff
X104
1.6156
(10)
1.5659
(IO)
-11.8818
(72)
-11.6228
(70)
1.3597
(76)
1.3473
(17)
1.5211
(136)
(Y=O)
Y
eff"I03
-11.3894
(990)
(AJ=o)
cx102
633
input lines
* Quoted uncertainty The quantity -8
IS
: two
R.M.S.
=
1.6
1O-4
1.3355
cm
(235)
-I
standard deviations in units of the last digit.
often added to the parameter Aeff value when then
doubling is ignored. Here
-$
is not included in Aeff
.
9’ is not good. We chose to constrain the value of 4’ to the calculated one, that is, # = p4q. In our previous paper (8) we used the method outlined by Brown and Watson (II) to determine the parameters A.,, and ye. The apparent values of AJ and y, denoted A^; and Jo, permit us to obtain apparent equilibrium values AYe and x. The true constants AJe and -ye were obtained by the relation A:JP’ = &
-
C,Y,,
where the parameter C, = &/(A, - 28,) is calculated with AJ = 0 and y = 0 [see Appendix of Ref. (S)].
in view of the two fits
RESULTS
The observed wavenumbers resulting from the simultaneous analysis of the 1-O and 2- 1 bands of 15Nis0 are reported together with their differences from the calculated wavenumbers in Tables II and III. The data concerning the 1-O bands of 15N170 and 15N1*0 are given in Tables IV and V.
AMIOT AND GUELACHVILI TABLE VII 15N170: u = 0, 1 Effective Molecular Constants (in cm-l)* V=O
v=1
0
A
123.13744
eff
(461d
1816.766455
(88)
122.90102
(14)
B
1.5895337
(58)
1.5735982
(52)
Dx106
4.785
(18)
4.804
(14)
px103
-10.52
qx106
-03.465a
(11)
1.496
AJeffX104
-10.51
(12)
-81.1
(16)
1.453
(26)
(26)
(Y=O)
127
input lines
R.M.S. = 1.9 10-4 cm-'
: two
* Quoted uncertainty
standard deviations in units
of the last digit. and 9 constrained to calculated values from 14N161 a) A,ff constants [El and isotopic relations. P2 =O.q36982gg.
TABLE VIII 15N’80: u = 0, 1 Effective Molecular Constants (in cm-l)* v=o
\)0 A
v=1
1793.29200
0
123.13895
eff
(461a
122.905889
(46)
(80)
B
1.5482463
(24)
1.5329296
(24)
Dx106
4.5519
(58)
4.5671
(48)
px103
-10.600
qx106
-79.174a
(40)
1.459
AJ,ffX'04
-10.586
(40)
-78.63
(961
(13)
1.415
(13)
(Y=O) 149
input lines
* Quoted uncertainty
R.M.S. = 1.1 10-4 cm-'
: two
standard deviations in units of
the last digit.
a) A eff
and
4 constrained to calculated values from
constants [81 and isotopic relations.P'= -
0.91257984
14N160
97
NITRIC OXIDE: =N ISOTOPIC SERIES TABLE IX Dunham Coefficients
Ae( eff)
123.25191
aA
0.23404
For A, E, D (in cm-*): Verification of Isotopic Relations
(34) (61 )
oA calcd. @*XI0
3
flAxlo
3
-5.11
(23)
123.25189
(16)
123.25191
(34ja
123.25191
(341a
0.23015
(30)
0.22748
(59)
0.22456
(59)
0.22986
(61 )
0.22654
(6~)
0.22357
(61.)
-4.86
(14)
-4.79
(237
-4.25
(23)a
-4.93
(23)
-4.79
(23)
-4.25
(23)
calcd.
1.7049184
Be
(84)
Be c&cd. ffB
0.0175297(135)
czB calcd.
1.6445076
(28
)
1.5974790(101
1.6444945
(84)
1.5974795
0.0166181
(44)
0.0166060(135)
&X105
-2.09
(44)
-I.
BBX105
38
-1.94
)
I.5558829
(58
I .5558742
(84)
O.O158992(Il7)
0.0152819
(94)
O.OI5899I(l35)
0.0152820
(135)
(84)
(18)
-1.83
(44F
-1.74
(44F
(44)
-1.83
(44)
-1.74
(44)
)
calcd.
D&O6
5.4622
(88
1
D,x106
5.0857
(28)
4.7755
(90)
4.5443
(90)
5.0819
(88)
4.7954
(88)
4.5489
(88)
calcd. fYD”108
-1 .64
(75)
UDX108
-1.47
(47)
-1.90
(78)
-1.52
(75)
-1.50
(75)
-1.39
( 75 )
-1.30
(75)
calcd.
P2
1
isotope
i :
12: = paA, 8; = p2BA,
quoted uncertainty a)
constrained
0.96455906
: two
standard
B;
=
0.93698299
p2 Be
deviations
, CT;= ,03aB, in
units
Of
0.91257984
/j;=p4$,D;=p4D,,
the
last
CY;= p5a,
digit.
values.
The effective parameters v, Aerr, B, D, P, 4, 4 eff, and yett are reported in Table VI for the levels u = 0, 1, and 2 of 15N160. The results pertaining to the levels D = 0 and 2, = 1 of 15N1’0 are gathered in Table VII. The results for the same levels of 15Nls0 are given in Table VIII. From the previous constants a set of Dunham coefficients for the parameters A, B, and D has been deduced and is given in Table IX. Calculated values using isotopic relations are also included in this table. The results for 14Nls0 are given again since they are used for these calculations.
98
AMIOT AND GUELACHVILI TABLE X lsNIBO: Energy Values Relative to the Level D = *h, J = 0.5, e (-59.94323 cm-‘) "=,
V=O
”
V.,
i-l.illl4h _._..
E
1.5 2.5 3.5 4.5 5.5 6.5 7.5 0.5 9.5 10.5 11.5 12.5 13.5 14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5 23.5 24.5 25.5 26.5 27.5 23.5 29.5 30.5 31.5 32.5 33.5 34.5 35.5 36.5 37.5 39.5 39.5 40.5 41.5 42.5
124.85029 133.14259 144.75098 159.67466 177.91260 193.46355 224.32607 252.49951 283.97900 318.76552 356.85536 398.24762 442.93824 490.92503 542.20512 596.77551 654.6330t 715.77452 780.19648 M47.89545 319.86779 993.10978 1070.61758 1151.38724 1235.41473 1322.6959) 1413.22650 1507.00221 1604.01861 1704.27116 1807.75524 1914.46616 2024.39911 2137.54918 2253.91140 2373.48067 249b.25192 2622.21958 2751.37957 2883.72332 3019.24928 3157.94778
4.83543 12.89931) 24.18857 39.70620 56.45112 77.42322 101.62237 129.04339 159.70104 193.53004 231.69504 271.01562 314.57129 361.35141 411.35535 464.58229 521.03134 530.70149 643.59161 703.70043 779.02657 951.56950 927.32457 1006.29296 1088.47174 1173.95890 1262.45132 1354.24970 1449.24660 1547.44294 1649.93487 1753.41941 1861.19341 1972.15357 2086.29646 2203.61849 2324.1159tJ 2447.79477 2574.62111 2704.62071 2837.77924 2974.03220
1.5 2.5 3.5 4.5 ::: 7.5 a.5 1::: 11.5 12.5 13.5 14.5 15.5 lb.5
124.85032 133.14270 144.75125 159.67520 177.91354 193.46505 224.32831 252.50168 293.99332 318.77124 356.96321 399.25687 442.94969 490.93395 542.22191 596.79528 654.65623 715.90140 780.2274rJ 847.93072 918.90775 933.15475 1071.6679Y 1151.44320 1235.476b7 1322.76414 1413.30137 1517.08402 1604.107tb 1704.3677t 1807.85971 1914.57979 2024.52019 2137.L79Ol 2254.05026 2373.62835 2496.40960 2622.38723 2751.55637 2383.91154 3019.44717 3159.157bl
3753.27503 3791.39659 3802.76597 3817.38239 3935.24484 3856.35211 3980.70290 3908.29523 3939.12776 3373.19824 4010.50455 4051.04436 4094.81515 4141.81429 4192.03894 4245.49617 4302.15287 4362.03584 4425.13172 4491.43704 4560.94823 4633.66157
l”47.02104 ~.._
_
4.85932 12.93256 24.23413 38.76295 56.51892 77.50132 101.71180 129.14833 159.31129 193.70036 230.81518 271.15531 314.72024 361.50936 411.52177 464.75729 521.21440 580.83230 643.79934 709.90576 779.23368 351.797O1, 327.54924 1006.52343 1039.70769 1174.0>991 1262.69796 1354.49316 1449.50127 1547.70151 1649.03705 1753.69489 1861.4b189 1972.42475 ZOY6.57OOb 2203.99422 2324.3934Y 2443.Ob395 2574.90161 2704.90225 283Y.Ot155 2374.37504
1967.61353 1975.92052 1937.3095') 2002.079bb 2020.12999 2041.45927 2066.06606 2033.94874 2125.10547 2159.53425 2197.23287 2233.19899 2282.43006 2329.92341 2380.b7b20 2434.18546 2491.94807 2552.46090 2616.22027 2693.22299 2753.46537 2926.94368 2903.65410 2983.59272 30t6.75549 3153.13823 3242.73ta8 3335.54t94 3431.5640b 3531.78370 3633.20127 3738.91205 3947.61123 3953.59394 4074.7551t 4193.03932 4314.59274 4439.25863 l(jt'7.09212 4694.05773 4832.17970 4969.44235
__~~_3783.27506
if63.69804 3671.58847 3682.65130 3696.87665 3714.26382 3734.81327 375'3.52461 3735.39761 3915.43133 3849.62739 3884.98341 3924.49956 3967.17526 4013.00386 4062.00260 4114.15263 4163.45896 4227.92053 4299.53612 4354.30442 4422.22396 4493.29316
3791.39670 3902.76624 j917.39291 3'935.24575 3356.35357 3830.70497 3908.29336 3939.13196 3973.20378 4010.51169 4051.0533s 4094.82628 4141.82782 4192.05518 4245.50541 43oi.i7142 4362.06201 4425.16193 4491.47141 4560.98718 4633.70543
1947.8o791 1855.78355 186b.96622 1881.33777 1898.90411 1919.bt,510 1943.t20bO 1370.77039 2001.11422 2034.t5177 2071.38265 2111.30642 2154.42254 2200.73037 2250.22320 2302.91820 2359.79645 2417.96288 24Y0.11634 2545.55554 2614.17904 2C35.33530 27b0.97261 2339.13915 2920.48294 3005.0018t 3092.b33t.3 3193.55585 3277.58595 3374.79121 3475.1337t 3573.t5560 3635.32854 3795.15427 3905.12937 4024.2501t 4143.51290 4265.913b7 4391.44840 4520.11290 4651.90279 4786.81359
3663.7109i _._~... 3671.62264 3682.69174 c696.93305 3714.33146 3734.89179 3759.C1384 3785.49736 1815.54204 j949.74752 3835.11337 3924.63909 3967.32409 4013.16771 406i.16917 4114.72761
19t7.tl35t 1975.92063 1937.3097b 2002.081119 2020.13091 2041.4t073 20bt.Ot925 2093.95194 2125.10969 2159.53332 2197.24005 2238.20303 2282.44124 2329.93701 2380.t9252 2434.70473 2491.97073 2552.48708 ZClb.25')50 2tY3.2j749 2753.50445 2926.93767 29'13.70333 2933.t4743 30tt.91t13 3153.2051'1 3242.31019 3335.t27Ot 3431.b5123 3530.37835 3t,33.303t3 3733.92242 3547.72971 3359.7212'3 4074.99130 4193.23512 4314.74747 4439.42301 4jt7.2jt'52 4t99.24237 4932.37503 43t?.t4333
i:; 2.5 7.5
_ ;::
$:i 9:5 10.5 11.5 12.5 13.5 14.5 15.5 16.5 li.5 18.5 19.5 20.5 21.5 22.5
1847.O7247 1947.93X4 1855.92372 18t7.Ollb7 1881.39433 1839.97175 1919.743t,3 1943.70933 1970.97014 2?)01.22427 2034.7719) 2071.512tO 2111.445Y3 2154.57133 2201.39917 2250.39572 2393.03313 23jY.37948 2418.05371 24Y0.314t5 2545.7tlOO 2614.33135 2tYt.ZQ412 27t1.197b4 2339.37OOt 2320.71341 3095.24357 3092.94029 3133.30712 3277.84153 3375.04080 3475.402Ut 3579.92231 3635.53539 3795.42t37 310Y.404tO 41324.527tb 4143.7924'3 42t,t.13433 4391.73103 4520.33b77 4t52.187tO 4797.0>303
11.5 1.5 2.5 ::: 5.5 t.1 1.3 9.5 9.5 lCl.5 11.5 12.1, 13.5 14.5 11.5 1 t,.5
17.5 Id.5 19.5 2'1.5 21.5 22.5 23.5 24.j 2j.5 2t.5 27.j 23.5 29.1, 30.j 31.5 32.5 :i:: 35.3 3t.5 37.5 33.5 39.5 43.1, 41.j '(2.j
99
NITRIC OXIDE: =N ISOTOPIC SERIES TABLE XI 15N*‘0: Energy Values Relative to the Level R = M, J = 0.5, e (-59.99003 cm-‘)
TABLE XII 15N’80: Energy Values Relative to the Level n = M, I = 0.5, e (-60.03214 cm-‘)
The calculated energy values relative to the lower level with s1 = y2, J = 0.5, e are given in Tables X, XI, and XII for the 15N160, 15N1’0, and 15Nls0 molecules. The constants AJe and ye are given in Table XIII with all the data necessary for their evaluation. Finally, some previously unreported spectral coincidences between 15N160 absorption lines and 13P60 laser lines measured by Johns et al. (12) are given below: Spectral Coincidences 13Cl60
laser transition ll-lOP(9) 11-10 P(8)
m laser (in cm-‘) (12)
1814.565 (3) 1818.171 (3)
with 13P60 Laser Lines NO transition P’kf(8.5) REj’(7.5)
15N160 lsN’sO
@NO (in cm-l) 1814.56152 1818.17702
100
AMIOT AND GUELACHVILI TABLE XIII Determination 1
I
4& lo *Je 14N160
15N160
Y,
of A,,, -ye (in cm-‘)
I
1
I
106 (pv
104 (I
*Je
c
lo2 ce
1.7668
(22)
-5.73
(18)
-12.454
(24)
2.95
(20)
1.4186
(45)
1.6404
(12)
-4.96
(IO)
-12.0110
(58)
2.586
(50)
1.3657
(16)
= -12.5(16)10-3cm-1
Quoted uncertainty
-2.5
lO-5
cm-'
<
AJe < 8.5 IO-~,"-'
equal two standard deviations in units of the last digit.
DISCUSSION
The accuracy and the consistency of our results will be discussed first. Then a comparison of the wavenumbers and constants obtained in recent investigations will be presented. From Table VI it is seen that the 15N160 parameters for the 2, = 2 level are much more poorly defined than those for the r = 0 and o = 1 levels. However, the root-mean-squares of the differences between the observed and calculated wavenumbers is only 1.6 x 10e4 cm-’ or 4.8 MHz with 633 spectral lines. For 15N170, the rms given in Table VII is slightly increased to 1.9 x lop4 cm-’ (5.7 MHz) but the agreement is a little better in the case of 15N1s0 (1.1 x lop4 cm-’ or 3.3 MHz). The consistency of the results can be appreciated by examining Table IX. The constant A, is seen to be isotopically invariant from the accurate 14N160 and 15N160 results. This is an a posteriori justification of the admitted hypothesis to derive the A (v = 0) values for the isotopic species 15N1’0 and 15N180. Because the parameters (Y* and PA are well predicted by the isotopic relations, we have performed a weighted least-squares fit with both the A, values. The derived constants are (in cm-‘) A, = 123.25193 (32), (YA= 0.23422 (50), PA = -5.06 (20) x 10e3. The uncertainties for (Y~and PA are very slightly increased, indicating that the isotopic relations are only approached. This is also obvious from the other calculated values reported in Table IX. The calculated values of parameters A, and ye given in Table XIII are defined with different accuracy. Although the parameter ye is consistent with our preliminary determination (8), the parameter A,, is not accurately evaluated. The calculated value is very near zero, but the uncertainty is large, 2 1.7 x lop5 cm-‘. The theoretical values obtained by the formula of Veseth (13) and Merer (14) give, respectively, -4.9 x 10e5 and -4.5 x 10m5cm-l for the value ofA,. A better determination of A.,, can be obtained only by the study of several enriched gas samples, particularly the heaviest isotopic species 15N180. We compare our measured wavenumbers only with recently reported values. Three lines of the 2113,3-2113,2 1-O subband have been measured with laser mag-
101
NITRIC OXIDE: =N ISOTOPIC SERIES TABLE XIV 15N1@O: Comparison of Y, A, B, D Molecular Effective Constants (in cm-‘) R.M.DALE
et al
P. KRISTIANSEN
C61 1842.9195
(y = 0)
123.1404(28)
123.141244(58!
(8)
i842.9l7717(283
123.1419(14)
122.8986(16)
lZ2.901358(58:
1.636191(30)
BO
This work
121
1.63613?(14:
l.63619,1(1;)
1.619642(30)
1.6195494(12)
106xD0
5.095
(16)
5.0931 (12)
lo6 x D,
5.108 (18)
5.1078 (10)
B1
Quoted uncertainty digit.
: two standard
deviations in units of the last
netic resonance techniques by Dale et al. (6). As may be noted from the comparison given below, the two sets of results are in excellent agreement.
R (1.5)
Q (1.5)
P (2.5)
Dale et al. (6)
This work*
1850.9696 (8) 1842.7629 (9) 1834.4698 (57)
1850.97027 (17) 1842.76326 (17) 1834.47090 (17)
* Mean of e-e and f-fobserved wavenumbers.
The molecular constants, without the A-doubling ones, are compared in Table XIV with the results of Dale et al. (6) and those of Kristiansen (25). Dale et al. combined their own measurements with those of Keck and Hause (I), while Kristiansen obtained accurate ground-state constants by mixing microwave and infrared data. The agreement among the three sets of results is good. Kristiansen’s B, value is a little different because, in this parameter, part of the A-doubling constants is certainly included. We turn now to discuss the A-doubling parameters p and q. For the level 2, = 2 no precise value was given for 15N160. Since the isotopic relations are well verified it is, however, possible to calculate accurate parameters from the measurements of Pine et al. (16) for the level 2) = 2 of 14N160. The comparison is presented below (values in cm-‘). From Pine et al. (16) lO$ 1064 Note. Quoted uncertainty:
- 11.2462 (20) -85.46 (17)
This work -11.2477 (116) -88.74 (242)
two standard deviations in units of the last digit.
102
AMIOT AND GUELACHVILI TABLE XV 15N’60: Ground-State
A-Doubling Constants
MEERTS-DYMANUS
11.275280 (52) (54)
87.721
KRISTIANSEN
This work
CSI
[>I
11.271908 (6)
11.2783 (30)
88.73
89.53
(6)
(18)
Quoted uncertainties:two standard deviations in units of the last digit.
If we constrain the 4 value to -85.46 x lo+ cm-l in our parametersexcept the p parameter-change very slightly; to - 11.2377 x 10e3 cm-‘. For the u = 1 level the most recent reported by Pate1 et al. (7). The agreement with our values within the stated uncertainties. Pate1 et al. (7)
This work
11.20 (13) 67 (27)
- 11.2515 (32) -87.75 (16)
103Pl
lO%, Note. Quoted uncertainty:
calculations, the p becomes equal values have been (in cm-l) is good
two standard deviations in units of the last digit.
Accurate values for the ground-state
A-doubling constants have been reported.
TABLE XVI 15N1*O:Comparison of Effective Molecular Constants (in cm-l)a
This work
?.M.DALE etal[$*
v1+o
A0 Al
1793.2917
(42)
793.29200
(46)
123.56
(54)
123.13895
(46)b
123.32
(54)
122.905889
(80)
1.548304
(130)
1.5482463
(24)
1.532981
(130)
1.5329296
(24)
106 x Do
4.66
(10)
4.5519
(58)
JO6 x D1
4.67
(IO)
4.5671
(48)
EO Bl
* Data
of
Griggs
et
al Quoted incertainty
a1.121.
: two
standard deviations in
units of the last digit. b) Constrained value (see text).
NITRIC OXIDE: 15N ISOTOPIC SERIES
103
A comparison between the various determinations is presented in Table XV. It is worthwhile to clarify the definition of the parameters as given below: This work -P -4
Gallagher et al. (4) 2P,
-
4q,
Meerts et al. (5)
Kristiansen (15)
4(% - a,)
PK - %K qIi
4%
2a7
For example we have -p = pK - 4qK, wherep is our definition, andp, and qK those from Kristiansen. From Table XV it is shown that, although very close to one another, none of the reported constants agree within the claimed uncertainties except our p value and that of Meerts. Small differences can occur because the data are different or because different theoretical models are used to reduce the wavenumbers to molecular constants. Finally, Dale et al. (6), using the observational data of Griggs et al. (2) and their own observations, obtained a set of constants for the levels 21= 0 and v = 1 of 15Ni80. A comparison with our values is given in Table XVI. ACKNOWLEDGMENT The authors are grateful to Dr. R. Bacis for many valuable comments RECEIVED:
on the manuscript.
July 24, 1978 REFERENCES
I. D. B. KECK AND C. D. HAUSE, J. Mol. Specfrosc. 26, 163-174 (1968). 2. J. L. GRIGGS, K. N~RAHARI RAO, J. H. JONES, AND R. M. POTTER,J. Mol. Spectrosc.
22,
383-401 (1%7). 3. M. D. OLMAN, M. D. MCNELIS, AND C. D. HAUSE, J. Mol. Specfrosc. 14, 62-78 (1964). 4. J. J. GALLAGHERAND C. M. JOHNSON,Whys. Rev. 103, 1727-1737 (1956). 5. W. L. MEERTSAND A. DYMANUS,J. Mol. Spectrosc. 44, 320-346 (1972). 6. R. M. DALE, J. W. C. JOHNS, A. R. W. MCKELLAR, AND M. RIGGIN, J. Mol. Spectrosc. 67, 440-458 (1977). 7. C. K. N. PATELAND R. J. KERL, Opt. Commun. 24, 294-296 (1978). 8. C. AMIOT, R. BACIS, AND G. GUELACHVILI,Canad. J. Phys. 56, 251-265 (1978). 9. G. GUELACHVILI,Appl. Opt. 17, 1322-1326 (1978). IO. G. GUELACHVILI,J. Mol. Spectrosc., in press. II. J. M. BROWN AND J. K. G. WATSON, J. Mol. Spectrosc. 65, 65-74 (1977). 12. J. W. C. JOHNS,A. R. W. MCKELLAR, AND D. WEITZ, J. Mol. Spectrosc. 51, 539-545 (1974). 13. L. VESETH,J. Mol. Spectrosc. 38, 228-242 (1971). 14. A. J. MERER,Mol. Phys. 23, 309-315 (1972). 15. P. KRISTIANSEN,J. Mol. Spectrosc. 66, 177-184 (1977). 16. A. S. PINE, J. W. C. JOHNS,AND A. G. ROBIETTE,J. Mol. Spectrosc. 74, 52-69 (1979). 17. W. L. MEERTS,Chem. Phys. 14,421-425 (1976). 18. C. AMIOT, R. BACIS, G. GUELACHVILI,J. Mol. Spectrosc., in press.