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Millimeter wave spectra of OPF3 in the vibrationally excited state v6 = 2
JOURNAL
OF MOLECULAR
Millimeter
SPECTROSCOPY
88,
126-132 (1981)
Wave Spectra of OPF, in the Vibrationally Excited State v6 = 2 JOHN
Physical Chemistry Department,
G. SMITH
The University, Newcastle
upon Tyne. England
Millimeter wave spectra have been recorded for the excited vibrational state ub:= 2 of OPFI. A full analysis of these spectra yields new rovibrational parameters and also the vibrational separation of the I = 0 and 1 = 2 levels, given by x,, = 16 134 2 390 MHz. The results are compared with the I+, = 1 state. INTRODUCTION
The microwave spectra of OPF, in some of its excited vibrational states have been reported previously (I, 2). In particular the us = 1 state has been discussed in detail. In this paper the 2)s = 2 excited states are examined. Formulae for the doubly excited states of a degenerate vibrational fundamental of a C3,. molecule have been discussed by several authors (3,4). While the theory is well known, there have been few attempts to record spectra in doubly excited states due to their lower population and hence the inherently weaker spectra associated with them. Extensive data are available for CH,CN in the uR = 2 states (5, 6). OPF, differs in that it is a near spherical top. EXPERIMENTAL
DETAILS
The sample of 0PF3 was purchased from Ozark-Mahoning Chemicals, Oklahoma. All millimeter wave spectra were recorded on the source-modulated spectrometer at Newcastle, the basis of which has been described elsewhere (7). All klystrons were phase locked to a standard crystal which was monitored against the BBC Droitwich transmission. Absolute accuracy is thought to be within 25 kHz at 100 GHz as judged by OCS measurements (8). All spectra were recorded at room temperature. THEORY
Perturbation formulae for doubly excited vibrational states have been given elsewhere (3, 4). While these are useful for appreciating the form of the spectrum and for preliminary fitting, they are not sufficiently accurate for final least-squares fitting and we have employed a matrix diagonalization of the appropriate hamiltonian (1) in order to obtain accurate rotational energies. The basis of this program has been described elsewhere (I) as have the required matrix elements (3).
0022-2852/81/070126-07$02.00/O Copyright
(B 1981 by Academic
AU rights of reproduction
Press, Inc.
in any form reserved.
126
MILLIMETER
WAVE SPECTRA OF OPFs
ASSIGNMENT
127
OF SPECTRUM
Initial assignments were based on the observation that for .Z” = 2 at 27.5 GHz, there are two lines at a frequency interval from the ground state which was approximately twice that of the u6 = 1 spectrum. The higher-frequency member of this pair was twice the intensity of the lower-frequency member and hence was tentatively assigned as the (I 1 = 2 component since it has the 1 degeneracy. In fact this assignment later proved erroneous and it is mentioned here to emphasize the dangers of using intensity data for spectral assignments. Measurements were also made of the millimeter wave spectra for successive J” between 6 and 13. A plot of v/2(.Z + 1) against (J + l)* for these transitions then yielded a series of near parallel lines for common k assignments. In particular the two most intense transitions near the centers of each .Z group lay on straight lines which could be extrapolated back to the two observed transitions at J” = 2. Hence they almost certainly included the k = 0 components for 1 = 0 and II 1 = 2. At this stage the .Z” = 17 spectrum at 165 GHz was recorded. At this .Z the lower-frequency part of the spectrum can clearly be seen to be composed of two series of transitions which show the spin statistical intensity pattern associated with three off-axis Z = l/2 nuclei in a CSa molecule. These two series could be related to the J” = 13 spectrum by the previously mentioned plots and, for the latter, trial k assignments were made. Plots of v vs k* then yielded a series of smooth curves depending on the particular k assignment chosen. These curves only had origins which coincided with the previous assignment of k = 0 for one choice of k assignment. For this particular choice, the spin statistical pattern showed quite clearly that, as mentioned previously, the early assignments of 1 = 0 and 1 = 2 were incorrect. Once the 1 = 0 components had been assigned, the lines which appear to high frequency of the k = 0,l = 2 line could only be due to higher k
FIG. 1. The J” = 13 spectrum for vg = 2 of OPF, at 128 GHz. The top trace is the experimental spectrum, the lower is a computer simulation.
JOHN G. SMITH
128
TABLE I Rotational Parameters Ground
Stare(Z)
AV/HHz.
4811.7579(18)
B"lMH2
4594.2624(s)
AC
y/nHz
lq:I
/MHz
v6 =
/ (I)
4797.8(1.5)
(J=
DyK/kHz
0)
IB
4585.5350)
work)
1.07645*
0.968(4)
1.2971(7)
0.943(42) 1.0156(3)
"
1.2927(29) -4.53(l)
vJK/kHZ
1.038(z) 1.370(191 -14.30(4) 252(100)
y,'/kH=
-16.7(4)
/MHZ
16134(390)
rxxx2/kHz
-
1.834(17)
f24/kHr
*
(this
1.468(24)
yJ/kHr
X4$
2
-729.0(150)
l.ollg(l2)
(J#O)
" DJK/kHz
=
4589.8514(2)
-
O;/kHz
v6
4803.2(491
-710.0(52) 1.0758(6)
(rtpHz
O;/kHz
Obtained for OPF,
1.83* 2.2*
Constrained
at this value.
transitions for 1 = 2. Here too, there can be seen an intensity pattern, as can be seen in Fig. 1, though the transitions are not regularly spaced. Trial assignments at first proved incorrect as the /k 1 = 9 and 10 lines are in the opposite order to that expected from the rest of the transitions. Least-squares adjustments of the parameters to the frequencies were made using the diagonalization program to calculate the transition frequencies and further assignments were made on the basis of these parameters. The natural label for the rotational transitions of a Car molecule is k - 1. Unfortunately this is not convenient to use in this case and we have used Ik - 11S, where s is the sign of 1 (9). Unlike k - I, this gives a unique and readily understood label to each transition from which the rovibrational symmetry may be deduced by: symmetry
Ik - 11s = 3n
n =0,1,2,.
E symmetry
Ik - 11s # 3n
n = 0, 1, 2, . . . .
A,/A,
. . ,
A comparison of the observed and a calculated spectrum is shown in Fig. 1. Careful study of the observed and calculated spectra show that for 1 = 2, the I k - 11s = -3 A1A2 lines are split. Thus we have to include (k, 1 I Q%’ Ik + 2,l IF 4) matrix element in our hamiltonian. The coefficient of this matrix element is & and is as defined by Tarrago (3). Since these transitions are unfortunately blended with others we have not refined to them in the least squares. We have constrained& to the value suggested by trial plots of the J” = 13 spectrum and their comparison with the observed.
MILLIMETER
WAVE
SPECTRA
TABLE J"
2 : : : 3 7 1 7 1 7 7 1 30’ :t 10 10 :," 10 10 10 10 :o" :: 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 :: 11 11 11 11 12 12 12 12 12 12 12 12 12 12
(K-L)*S
0 0 1 0 -1 -2 3 -5 5 : -5 -6 -7 -a -9 7 a 9 a 7 6 5 4 3 2 1 -12 -11 -10 -9 11 10 9 a 1 6 5 4 3 2 9 8 7 6 5 " 3 2 1 -1 s: -6 -7 -a -9 -10 -11 -12 -13 12 11 10 9 a 1 6 5 4 0
SrAllDABO
085.
I
-2 0 0 0 2 2 2 2 2 2 2 2 -2 -2 -2 -2 0 0 0 0 0 0 0 0 0 0 2 2 2 2
27512.366 27513.012 36682.794 36683.098 36683.276 36683.519 36683.789 36684.162 73361.830 73362.415 73363.008 73366.763 73367.172 73367.639 73368.057 73368.543 100872.626 100871.529 looa69.aw 100867.275 100868.232 100869.116 100869.844 100870.755 100871.529 100872.278 100872.995 looaal.613 iooaao.812 100879.710 looa79.096 ilco39.858 110036.987 iloo3a.aal 110090.606 11co41.753 110042.a92 110043.684 110044.309 llCOP0.963 110045.298 llco34.asa 110035.975 llCO36.987 110037.960
2 2 2 2 2 2 -2 -2 -2 -7 -2 -2 -2 -2 -2 -2 0 0 0 0 0 0 0 0 0 0
llco3a.Sal 110039.777 llCO90.606 110091.402 11c002.205 110043.680 lloooa.394 110046.32a llCO46.991 110047.946 llOOU7.9Ub liooua.al2 lico49.3a7 1~0050.8~0 llC051.677 110052.760 119199.990 119202.906 119205.398 119207.020 119209.120 119210.560 119211.753 119212.680 119213.030 119214.785
-2 2" : 2 -"2 2 2 -: -2 1:
ESROB
01
AS
OBSLBVATICII
CALC.
BBiiOB I1
0.009 -0.084 -0.000 0.027 0.009 0.029 0.006 0.034 -0.037 -0.034 0.005 0.036 0.021 0.054 0.037 0.057
0.122 -0.116 -0.091 -0.068 -0.067 -0.180 -0.070 -0.060 -0.000 -0.021 0.021 0.028 -0.028 -0.099 O.lOU 0.055 0.076 0.219 0.035 0.065 -0.052 -0.152 -0.047 -0.105 -0.091 -0.03a -0.038 -0.029
0.200 0.200 0.050 0.050 0.050 0.050 0.050 0.050 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.400 0.400 0.000 0.200 0.200 0.200 0.300 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.400 o.aoo 0.900 0.400 0.200 0.200 0.400 0.400 0.400 0.200 0.400 0.200 0.400 0.200
-0.025 -0.000 -0.009 -0.009 0.031 0.071 0.096 0.041 0.019 0.078 -O.OBb -0.020 -0.011 0.068 0.059 0.085 -0.007 0.002 0.084 0.071 0.053 0.048 0.036 -0.023 -0.060 -0.061
0.400 0.200 0.400 0.200 0.200 0.900 0.400 0.200 0.200 0.400 0.400 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.20@ 0.200 0.200 0.200
a.001
01
129
II OBS.-
?RBG.
OF OPFI
MIT
PSIGAT
=
OBS.
0.34274
"AZ
130
JOHN G. SMITH TABLE II-Continued J” 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 11 13 13 13 13 13 13 13 13 13 13 13 13 11 13 13 13 13 13 13 13 13 l? 11 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14 14 14 14 14
(K-L)*S 10 9 8 7 6 5 ii 2 1 -14 -13 -12 -11 -10 -9 -a -7 -6 -5 13 12 11 10 9 a 7 6 5 4 3 0 11 10 9 a 7 6 5 4 3 2 1 0 -1 -2 -4 -5 -6 -7 -R -9 -10 -11 -12 -13 -14 -15 12 11 a 6 10 9 t 9 3 -5 -6 -a -10
L
2 2 2 2 2 2 2 2 2 2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 -2 2 2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 0 0 l-l 0 2 2 2 : 2 -2 -2 -2 -2
08s.
rrlcc.
119201.994 119203.203 179204.350 119205.398 119206.077 119207.120 119298.436 119209.350 115210.210 il92ll.080 119224.010 119222.570 119221.350 119220.532 119218.596 11921n.06e 119217.120 179217.808 119216.310 119215.530 lZE363.a63 12E367.572 12E370.753 128373.500 128375.661 128377.422 128379.030 128380.302 128381.335 i2E382.151 12E382.765 128383.693 12E36e.POO 128369.802 121371.096 12e372.358 12E373.500 12P374.682 128375.661 128376.797 128377.815 124378.714 [email protected] 126380.632 l2E3al.335 123382.151 12E383.693 126384.542 128385.376 128386.728 i2e385.949 l2E387.098 126387.030 l28390.070 i2E390.832 12E392.109 12L393.652 126395.566 137539.860 137538.220 137505.402 137598.980 137537.310 137538.668 137592.630 137543.610 i37544.82a 137545.a60 137553.060 137554.06e 137554.768 137555.620
OBS.-
CILLC.
BBBOR
-0.006 -0.006 -0.011 -0.059 -0.024 -0.076 -0.008 0.002 -0.002 0.039 0.102 0.027 -0.038 0.013 -0.087 -0.129 -0.154 -0.016 0.013
0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200
-0.000 -0.oa2 -0.096 -0.014 0.130 0.094 -0.000 0.04e 0.020 -0.012 -0.045 -0.070 0.034 -0.085 -0.049 -0.056 -0.034 -0.072 -0.019 -0.107 0.008 0.051 0.017 0.057 -0.199 0,053 0.061 0.029 0.073 0.046 -0.039 -0.190 -0.105 -0.110 0.059 -0.043 -0.017 0.029 0.157 -0.084 -0.055 -0.025 -0.019 -0.050 -0.086 0.081 -0.087 0.035 0.021 -0.021 0.017 0.202 -0.290
0.200 0.200 0.200 0.200 0.000 0.100 0.200 0.200 0.900 0.400 0.400 0.200 0.200 0.200 0.200 0.200 0.200 0.400 0.200 0.400 0.200 0.200 0.200 0.200 0.200 0.400 0.800 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.500
Ill OBS.
MILLIMETER
WAVE SPECTRA
TABLE .I” 14 14 14 :4" 14 14 14 15 :5 15 15 :: 15 15 15 15 :5' 15 15 15 15 15 15 :: 15 15 17 17 :7' 17 17 :: :7' :7' 17 17 17 11 17 17 17 17 :3 17 17 17 17 17 17 17 17 17
(K-I.)*S L -9 -7 -11 -12 -13 -lu -15 -16 14 13 12 B 6 5 P 3 2 13 9 B 4 3 2 1 -4 -5 -7 -12 -13 -15 -16 13 12 :i 9 B 6 1 15 19 13 12 11 10 9 B 7 6 5 4 3 1 -3 -4 -5 -6 -7 -11 -12 -15 -16
-2 -2 -2 1: -2 -2 -2 0 0 0 0" 0 0 0 0 : 2 2 2 2 -: -2 -2 -2 -2 -2 -2 0 0 0 0 0
n
0 0 2 2 2 2 : 2 2 2 2 2 2 2 2 -2 -2 -2 -2 -2 -2 -2 -2 -2
OBS.
OF OPF3
131
II-Continued PABC.
137555.620 137555.620 137559.190 137559.959 137561.460 137562.960 137564.988 137567.340 146692.660 196697.480 146701.750 146713.090 196716.400 146717.610 146718.550 106719.180 146719.980 146699.710 196706.060 196707.310 116712.530 146713.670 146714.570 146715.730 146720.500 146721.430 146724.870 146728.970 146730.160 146739.350 146736.950 165029.012 165034.418 165038.500 165041.894 165090.713 165047.110 165050.791 165059.001 165028.159 165030.334 165032.144 165030.023 165035.856 165037.579 165039.272 165040.832 165042.364 165043.825 165005.269 165006.505 165047.868 165050.182 165059.950 165055.741 165056.881 165058.186 165061.997 165065.419 165065.919 165071.543 165075.280
OBS.-
CALC.
-0.191 -0.280 -0.047 -0.101 0.058 -0.085 -0.031 -0.031 0.351 -0.069 -0.089 0.033 0.058 O.OY6 0.012 -0.066 0.176 0.113 0.072 -0.093 0.101 0.123 -0.047 0.085 0.117 O.OBP 0.043 O.OPE -0.189 0.040 -0.012 -0.109 0.032 0.072 0.075 0.035 0.020 -0.014 -0.099 0.197 0.263 0.058 c.015 0.014 -0.011 0.015 -0.019 0.002 0.018 0.083 0.001 0.103 0.042 -0.173 0.155 0.134 0.028 -0.084 0.215 -0.187 -0.296 0.195
ERROR
TN
OBS.
0.500 0.500 0.200 0.200 0.200 0.200 0.200 0.200 0.300 0.300 0.300 0.300 0.300 0.500 0.500 0.500 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.500 0.500 0.300 0.300
The parameters employed in our final refinements require some comment. The I-doubling parameter, q f , was, surprisingly, not well determined by the present data and we have been forced to constrain it to the value obtained from u6 = l(2). Likewise, ~~~~~was constrained at the value obtained for the singly excited state. Unlike the latter, however, the 21~= 2 states give good information on the AI = +l, Ak = 72 resonance parameter, rf. This proved well determined and indeed essential for a good fit of the data. The separate distortion constants for the 1 = 0 and 1 = 2 components are given
132
JOHN G. SMITH
in Table I, where they are compared to the corresponding constants for u6 = 1. It is worth noting that the I/ 1 = 2 distortion constants are not very different from the r6 = 1 parameters as might be expected for what must be an essentially isolated and hence unperturbed level. The 1 = 0 parameters are, however, rather different. As with u6 = 1, some information is present on the value of the axial rotational constant. In this case the value obtained is constrained to fit both the 1 = 0 and 2 spectra and hence is some sort of average of those for the two states. Attempts to obtain separate A rotational constants were not successful. Perhaps for this reason the final value is rather different from that obtained for 06 = 1 and is appreciably less accurate. Of the remaining parameters, A 5 is similar to that obtained for the singly excited state. In particular the value of & obtained by using the experimental values of A and A< yields 0.1519(32) for us = 2 and 0.1480( 11) for u6 = 1 which is satisfactory and well within the error limits used in the force field calculations (I). qj differs by nearly a factor of three. There is no obvious explanation for this though it is possible that the effects of terms omitted from the hamiltonian are “mopped up” by this parameter. The two 1 dependent parameters 7:: and x,, are both well determined. The small size of the vibrational term, xII, is consistent with the nonappearance of obvious hot band structure in the low-resolution SpeCtrUtII of VS. The full set of parameters and those for uti = 1 are given in Table I. The fit to the observations is presented in Table II. In most cases the agreement is reasonable though there are one or two transitions which cannot be fitted to experimental accuracy. These small errors are presumably due to neglect of higher-order terms in the hamiltonian. ACKNOWLEDGMENTS The author wishes to thank Professor D. H. Whiffen and Dr. J. H. Carpenter for helpful discussions on this problem and Miss Janet Smith for initial attempts at assigning the spectra. RECEIVED:
October 24, 1980 REFERENCES
1. 2. 3. 4. 5. 6. 7.
J. G. SMITH, Mol. Phys. 32,621~645 (1976). T. AMANO AND R. H. SCHWENDEMAN,J. Chem. Phys. 68, 530-537 (1978). G. TARRAGO,J. Mol. Spectrosc. 34, 23-32 (1970). A. J. CARELESSAND H. W. KROTO,J. Mol. Spectrosc. 57, 189-197 (1975). A. BAUER,J. Mol. Spectrosc. 40, 183-206 (1971). A. BAUERAND S. MAES, J. Mol. Spectrosc. 40, 207-216 (1971). J. H. CARPENTER,J. D. COOPER,J. B. SIMPSON,J. G. SMITH, AND D. H. WHIFFEN,J. Phys. E. 7, 678-681 (1974). 8. N. W. LARSEN,B. P. WINNEWISSER,2. Naturforsch. A 29, 1213-1215 (1974). 9. D. H. WHIFFEN, private communication.
OF MOLECULAR
Millimeter
SPECTROSCOPY
88,
126-132 (1981)
Wave Spectra of OPF, in the Vibrationally Excited State v6 = 2 JOHN
Physical Chemistry Department,
G. SMITH
The University, Newcastle
upon Tyne. England
Millimeter wave spectra have been recorded for the excited vibrational state ub:= 2 of OPFI. A full analysis of these spectra yields new rovibrational parameters and also the vibrational separation of the I = 0 and 1 = 2 levels, given by x,, = 16 134 2 390 MHz. The results are compared with the I+, = 1 state. INTRODUCTION
The microwave spectra of OPF, in some of its excited vibrational states have been reported previously (I, 2). In particular the us = 1 state has been discussed in detail. In this paper the 2)s = 2 excited states are examined. Formulae for the doubly excited states of a degenerate vibrational fundamental of a C3,. molecule have been discussed by several authors (3,4). While the theory is well known, there have been few attempts to record spectra in doubly excited states due to their lower population and hence the inherently weaker spectra associated with them. Extensive data are available for CH,CN in the uR = 2 states (5, 6). OPF, differs in that it is a near spherical top. EXPERIMENTAL
DETAILS
The sample of 0PF3 was purchased from Ozark-Mahoning Chemicals, Oklahoma. All millimeter wave spectra were recorded on the source-modulated spectrometer at Newcastle, the basis of which has been described elsewhere (7). All klystrons were phase locked to a standard crystal which was monitored against the BBC Droitwich transmission. Absolute accuracy is thought to be within 25 kHz at 100 GHz as judged by OCS measurements (8). All spectra were recorded at room temperature. THEORY
Perturbation formulae for doubly excited vibrational states have been given elsewhere (3, 4). While these are useful for appreciating the form of the spectrum and for preliminary fitting, they are not sufficiently accurate for final least-squares fitting and we have employed a matrix diagonalization of the appropriate hamiltonian (1) in order to obtain accurate rotational energies. The basis of this program has been described elsewhere (I) as have the required matrix elements (3).
0022-2852/81/070126-07$02.00/O Copyright
(B 1981 by Academic
AU rights of reproduction
Press, Inc.
in any form reserved.
126
MILLIMETER
WAVE SPECTRA OF OPFs
ASSIGNMENT
127
OF SPECTRUM
Initial assignments were based on the observation that for .Z” = 2 at 27.5 GHz, there are two lines at a frequency interval from the ground state which was approximately twice that of the u6 = 1 spectrum. The higher-frequency member of this pair was twice the intensity of the lower-frequency member and hence was tentatively assigned as the (I 1 = 2 component since it has the 1 degeneracy. In fact this assignment later proved erroneous and it is mentioned here to emphasize the dangers of using intensity data for spectral assignments. Measurements were also made of the millimeter wave spectra for successive J” between 6 and 13. A plot of v/2(.Z + 1) against (J + l)* for these transitions then yielded a series of near parallel lines for common k assignments. In particular the two most intense transitions near the centers of each .Z group lay on straight lines which could be extrapolated back to the two observed transitions at J” = 2. Hence they almost certainly included the k = 0 components for 1 = 0 and II 1 = 2. At this stage the .Z” = 17 spectrum at 165 GHz was recorded. At this .Z the lower-frequency part of the spectrum can clearly be seen to be composed of two series of transitions which show the spin statistical intensity pattern associated with three off-axis Z = l/2 nuclei in a CSa molecule. These two series could be related to the J” = 13 spectrum by the previously mentioned plots and, for the latter, trial k assignments were made. Plots of v vs k* then yielded a series of smooth curves depending on the particular k assignment chosen. These curves only had origins which coincided with the previous assignment of k = 0 for one choice of k assignment. For this particular choice, the spin statistical pattern showed quite clearly that, as mentioned previously, the early assignments of 1 = 0 and 1 = 2 were incorrect. Once the 1 = 0 components had been assigned, the lines which appear to high frequency of the k = 0,l = 2 line could only be due to higher k
FIG. 1. The J” = 13 spectrum for vg = 2 of OPF, at 128 GHz. The top trace is the experimental spectrum, the lower is a computer simulation.
JOHN G. SMITH
128
TABLE I Rotational Parameters Ground
Stare(Z)
AV/HHz.
4811.7579(18)
B"lMH2
4594.2624(s)
AC
y/nHz
lq:I
/MHz
v6 =
/ (I)
4797.8(1.5)
(J=
DyK/kHz
0)
IB
4585.5350)
work)
1.07645*
0.968(4)
1.2971(7)
0.943(42) 1.0156(3)
"
1.2927(29) -4.53(l)
vJK/kHZ
1.038(z) 1.370(191 -14.30(4) 252(100)
y,'/kH=
-16.7(4)
/MHZ
16134(390)
rxxx2/kHz
-
1.834(17)
f24/kHr
*
(this
1.468(24)
yJ/kHr
X4$
2
-729.0(150)
l.ollg(l2)
(J#O)
" DJK/kHz
=
4589.8514(2)
-
O;/kHz
v6
4803.2(491
-710.0(52) 1.0758(6)
(rtpHz
O;/kHz
Obtained for OPF,
1.83* 2.2*
Constrained
at this value.
transitions for 1 = 2. Here too, there can be seen an intensity pattern, as can be seen in Fig. 1, though the transitions are not regularly spaced. Trial assignments at first proved incorrect as the /k 1 = 9 and 10 lines are in the opposite order to that expected from the rest of the transitions. Least-squares adjustments of the parameters to the frequencies were made using the diagonalization program to calculate the transition frequencies and further assignments were made on the basis of these parameters. The natural label for the rotational transitions of a Car molecule is k - 1. Unfortunately this is not convenient to use in this case and we have used Ik - 11S, where s is the sign of 1 (9). Unlike k - I, this gives a unique and readily understood label to each transition from which the rovibrational symmetry may be deduced by: symmetry
Ik - 11s = 3n
n =0,1,2,.
E symmetry
Ik - 11s # 3n
n = 0, 1, 2, . . . .
A,/A,
. . ,
A comparison of the observed and a calculated spectrum is shown in Fig. 1. Careful study of the observed and calculated spectra show that for 1 = 2, the I k - 11s = -3 A1A2 lines are split. Thus we have to include (k, 1 I Q%’ Ik + 2,l IF 4) matrix element in our hamiltonian. The coefficient of this matrix element is & and is as defined by Tarrago (3). Since these transitions are unfortunately blended with others we have not refined to them in the least squares. We have constrained& to the value suggested by trial plots of the J” = 13 spectrum and their comparison with the observed.
MILLIMETER
WAVE
SPECTRA
TABLE J"
2 : : : 3 7 1 7 1 7 7 1 30’ :t 10 10 :," 10 10 10 10 :o" :: 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 :: 11 11 11 11 12 12 12 12 12 12 12 12 12 12
(K-L)*S
0 0 1 0 -1 -2 3 -5 5 : -5 -6 -7 -a -9 7 a 9 a 7 6 5 4 3 2 1 -12 -11 -10 -9 11 10 9 a 1 6 5 4 3 2 9 8 7 6 5 " 3 2 1 -1 s: -6 -7 -a -9 -10 -11 -12 -13 12 11 10 9 a 1 6 5 4 0
SrAllDABO
085.
I
-2 0 0 0 2 2 2 2 2 2 2 2 -2 -2 -2 -2 0 0 0 0 0 0 0 0 0 0 2 2 2 2
27512.366 27513.012 36682.794 36683.098 36683.276 36683.519 36683.789 36684.162 73361.830 73362.415 73363.008 73366.763 73367.172 73367.639 73368.057 73368.543 100872.626 100871.529 looa69.aw 100867.275 100868.232 100869.116 100869.844 100870.755 100871.529 100872.278 100872.995 looaal.613 iooaao.812 100879.710 looa79.096 ilco39.858 110036.987 iloo3a.aal 110090.606 11co41.753 110042.a92 110043.684 110044.309 llCOP0.963 110045.298 llco34.asa 110035.975 llCO36.987 110037.960
2 2 2 2 2 2 -2 -2 -2 -7 -2 -2 -2 -2 -2 -2 0 0 0 0 0 0 0 0 0 0
llco3a.Sal 110039.777 llCO90.606 110091.402 11c002.205 110043.680 lloooa.394 110046.32a llCO46.991 110047.946 llOOU7.9Ub liooua.al2 lico49.3a7 1~0050.8~0 llC051.677 110052.760 119199.990 119202.906 119205.398 119207.020 119209.120 119210.560 119211.753 119212.680 119213.030 119214.785
-2 2" : 2 -"2 2 2 -: -2 1:
ESROB
01
AS
OBSLBVATICII
CALC.
BBiiOB I1
0.009 -0.084 -0.000 0.027 0.009 0.029 0.006 0.034 -0.037 -0.034 0.005 0.036 0.021 0.054 0.037 0.057
0.122 -0.116 -0.091 -0.068 -0.067 -0.180 -0.070 -0.060 -0.000 -0.021 0.021 0.028 -0.028 -0.099 O.lOU 0.055 0.076 0.219 0.035 0.065 -0.052 -0.152 -0.047 -0.105 -0.091 -0.03a -0.038 -0.029
0.200 0.200 0.050 0.050 0.050 0.050 0.050 0.050 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.400 0.400 0.000 0.200 0.200 0.200 0.300 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.400 o.aoo 0.900 0.400 0.200 0.200 0.400 0.400 0.400 0.200 0.400 0.200 0.400 0.200
-0.025 -0.000 -0.009 -0.009 0.031 0.071 0.096 0.041 0.019 0.078 -O.OBb -0.020 -0.011 0.068 0.059 0.085 -0.007 0.002 0.084 0.071 0.053 0.048 0.036 -0.023 -0.060 -0.061
0.400 0.200 0.400 0.200 0.200 0.900 0.400 0.200 0.200 0.400 0.400 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.20@ 0.200 0.200 0.200
a.001
01
129
II OBS.-
?RBG.
OF OPFI
MIT
PSIGAT
=
OBS.
0.34274
"AZ
130
JOHN G. SMITH TABLE II-Continued J” 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 11 13 13 13 13 13 13 13 13 13 13 13 13 11 13 13 13 13 13 13 13 13 l? 11 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14 14 14 14 14
(K-L)*S 10 9 8 7 6 5 ii 2 1 -14 -13 -12 -11 -10 -9 -a -7 -6 -5 13 12 11 10 9 a 7 6 5 4 3 0 11 10 9 a 7 6 5 4 3 2 1 0 -1 -2 -4 -5 -6 -7 -R -9 -10 -11 -12 -13 -14 -15 12 11 a 6 10 9 t 9 3 -5 -6 -a -10
L
2 2 2 2 2 2 2 2 2 2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 -2 2 2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 0 0 l-l 0 2 2 2 : 2 -2 -2 -2 -2
08s.
rrlcc.
119201.994 119203.203 179204.350 119205.398 119206.077 119207.120 119298.436 119209.350 115210.210 il92ll.080 119224.010 119222.570 119221.350 119220.532 119218.596 11921n.06e 119217.120 179217.808 119216.310 119215.530 lZE363.a63 12E367.572 12E370.753 128373.500 128375.661 128377.422 128379.030 128380.302 128381.335 i2E382.151 12E382.765 128383.693 12E36e.POO 128369.802 121371.096 12e372.358 12E373.500 12P374.682 128375.661 128376.797 128377.815 124378.714 [email protected] 126380.632 l2E3al.335 123382.151 12E383.693 126384.542 128385.376 128386.728 i2e385.949 l2E387.098 126387.030 l28390.070 i2E390.832 12E392.109 12L393.652 126395.566 137539.860 137538.220 137505.402 137598.980 137537.310 137538.668 137592.630 137543.610 i37544.82a 137545.a60 137553.060 137554.06e 137554.768 137555.620
OBS.-
CILLC.
BBBOR
-0.006 -0.006 -0.011 -0.059 -0.024 -0.076 -0.008 0.002 -0.002 0.039 0.102 0.027 -0.038 0.013 -0.087 -0.129 -0.154 -0.016 0.013
0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200
-0.000 -0.oa2 -0.096 -0.014 0.130 0.094 -0.000 0.04e 0.020 -0.012 -0.045 -0.070 0.034 -0.085 -0.049 -0.056 -0.034 -0.072 -0.019 -0.107 0.008 0.051 0.017 0.057 -0.199 0,053 0.061 0.029 0.073 0.046 -0.039 -0.190 -0.105 -0.110 0.059 -0.043 -0.017 0.029 0.157 -0.084 -0.055 -0.025 -0.019 -0.050 -0.086 0.081 -0.087 0.035 0.021 -0.021 0.017 0.202 -0.290
0.200 0.200 0.200 0.200 0.000 0.100 0.200 0.200 0.900 0.400 0.400 0.200 0.200 0.200 0.200 0.200 0.200 0.400 0.200 0.400 0.200 0.200 0.200 0.200 0.200 0.400 0.800 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.500
Ill OBS.
MILLIMETER
WAVE SPECTRA
TABLE .I” 14 14 14 :4" 14 14 14 15 :5 15 15 :: 15 15 15 15 :5' 15 15 15 15 15 15 :: 15 15 17 17 :7' 17 17 :: :7' :7' 17 17 17 11 17 17 17 17 :3 17 17 17 17 17 17 17 17 17
(K-I.)*S L -9 -7 -11 -12 -13 -lu -15 -16 14 13 12 B 6 5 P 3 2 13 9 B 4 3 2 1 -4 -5 -7 -12 -13 -15 -16 13 12 :i 9 B 6 1 15 19 13 12 11 10 9 B 7 6 5 4 3 1 -3 -4 -5 -6 -7 -11 -12 -15 -16
-2 -2 -2 1: -2 -2 -2 0 0 0 0" 0 0 0 0 : 2 2 2 2 -: -2 -2 -2 -2 -2 -2 0 0 0 0 0
n
0 0 2 2 2 2 : 2 2 2 2 2 2 2 2 -2 -2 -2 -2 -2 -2 -2 -2 -2
OBS.
OF OPF3
131
II-Continued PABC.
137555.620 137555.620 137559.190 137559.959 137561.460 137562.960 137564.988 137567.340 146692.660 196697.480 146701.750 146713.090 196716.400 146717.610 146718.550 106719.180 146719.980 146699.710 196706.060 196707.310 116712.530 146713.670 146714.570 146715.730 146720.500 146721.430 146724.870 146728.970 146730.160 146739.350 146736.950 165029.012 165034.418 165038.500 165041.894 165090.713 165047.110 165050.791 165059.001 165028.159 165030.334 165032.144 165030.023 165035.856 165037.579 165039.272 165040.832 165042.364 165043.825 165005.269 165006.505 165047.868 165050.182 165059.950 165055.741 165056.881 165058.186 165061.997 165065.419 165065.919 165071.543 165075.280
OBS.-
CALC.
-0.191 -0.280 -0.047 -0.101 0.058 -0.085 -0.031 -0.031 0.351 -0.069 -0.089 0.033 0.058 O.OY6 0.012 -0.066 0.176 0.113 0.072 -0.093 0.101 0.123 -0.047 0.085 0.117 O.OBP 0.043 O.OPE -0.189 0.040 -0.012 -0.109 0.032 0.072 0.075 0.035 0.020 -0.014 -0.099 0.197 0.263 0.058 c.015 0.014 -0.011 0.015 -0.019 0.002 0.018 0.083 0.001 0.103 0.042 -0.173 0.155 0.134 0.028 -0.084 0.215 -0.187 -0.296 0.195
ERROR
TN
OBS.
0.500 0.500 0.200 0.200 0.200 0.200 0.200 0.200 0.300 0.300 0.300 0.300 0.300 0.500 0.500 0.500 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.500 0.500 0.300 0.300
The parameters employed in our final refinements require some comment. The I-doubling parameter, q f , was, surprisingly, not well determined by the present data and we have been forced to constrain it to the value obtained from u6 = l(2). Likewise, ~~~~~was constrained at the value obtained for the singly excited state. Unlike the latter, however, the 21~= 2 states give good information on the AI = +l, Ak = 72 resonance parameter, rf. This proved well determined and indeed essential for a good fit of the data. The separate distortion constants for the 1 = 0 and 1 = 2 components are given
132
JOHN G. SMITH
in Table I, where they are compared to the corresponding constants for u6 = 1. It is worth noting that the I/ 1 = 2 distortion constants are not very different from the r6 = 1 parameters as might be expected for what must be an essentially isolated and hence unperturbed level. The 1 = 0 parameters are, however, rather different. As with u6 = 1, some information is present on the value of the axial rotational constant. In this case the value obtained is constrained to fit both the 1 = 0 and 2 spectra and hence is some sort of average of those for the two states. Attempts to obtain separate A rotational constants were not successful. Perhaps for this reason the final value is rather different from that obtained for 06 = 1 and is appreciably less accurate. Of the remaining parameters, A 5 is similar to that obtained for the singly excited state. In particular the value of & obtained by using the experimental values of A and A< yields 0.1519(32) for us = 2 and 0.1480( 11) for u6 = 1 which is satisfactory and well within the error limits used in the force field calculations (I). qj differs by nearly a factor of three. There is no obvious explanation for this though it is possible that the effects of terms omitted from the hamiltonian are “mopped up” by this parameter. The two 1 dependent parameters 7:: and x,, are both well determined. The small size of the vibrational term, xII, is consistent with the nonappearance of obvious hot band structure in the low-resolution SpeCtrUtII of VS. The full set of parameters and those for uti = 1 are given in Table I. The fit to the observations is presented in Table II. In most cases the agreement is reasonable though there are one or two transitions which cannot be fitted to experimental accuracy. These small errors are presumably due to neglect of higher-order terms in the hamiltonian. ACKNOWLEDGMENTS The author wishes to thank Professor D. H. Whiffen and Dr. J. H. Carpenter for helpful discussions on this problem and Miss Janet Smith for initial attempts at assigning the spectra. RECEIVED:
October 24, 1980 REFERENCES
1. 2. 3. 4. 5. 6. 7.
J. G. SMITH, Mol. Phys. 32,621~645 (1976). T. AMANO AND R. H. SCHWENDEMAN,J. Chem. Phys. 68, 530-537 (1978). G. TARRAGO,J. Mol. Spectrosc. 34, 23-32 (1970). A. J. CARELESSAND H. W. KROTO,J. Mol. Spectrosc. 57, 189-197 (1975). A. BAUER,J. Mol. Spectrosc. 40, 183-206 (1971). A. BAUERAND S. MAES, J. Mol. Spectrosc. 40, 207-216 (1971). J. H. CARPENTER,J. D. COOPER,J. B. SIMPSON,J. G. SMITH, AND D. H. WHIFFEN,J. Phys. E. 7, 678-681 (1974). 8. N. W. LARSEN,B. P. WINNEWISSER,2. Naturforsch. A 29, 1213-1215 (1974). 9. D. H. WHIFFEN, private communication.