Triatomic Spectral Database


2. Discussion of Centrifugal Distortion Analysis of F2O

Historically, the analysis of the Rotational and Centrifugal Distortion Constants for F2O has caused considerable difficulty. The first observations on F2O (Hilton et al. [61007] and Bransford et al. [60003]) were incorrectly interpreted and later Pierce et al. [63007] provided the correct assignments from a detailed centrifugal distortion analysis of new spectral measurements [61008] and [63007]. Although these results appeared consistent, Kirchhoff [72031] found that the 364,32-373,36 transition reported in [63007] at 29 473.73 MHz was erroneous. His conclusion was based on a detailed statistical analysis and several new measurements.

While examining Kirchhoff's calculations, provided to the author by W.H. Kirchhoff, it was noted that two of the resolved triplet (spin-rotation splitting) rotational lines reported by Pierce and DiCianni [63008] had been overlooked. Further, the questionable transitions of Hilton et al. assigned in [61007] were quite reasonably not included in the previous calculations. When the two new transitions, 242,23-233,20, at 17 257.86 MHz and 253,22-262,25 at 14 720.63 MHz, from [63008] were added to Kirchhoff s basic analysis, the fit substantially degraded with a standard deviation of 0.157 MHz versus 0.096 MHz without the two new transitions.

Following the procedure of successively eliminating one transition at a time as described by Kirchhoff [72031], three transitions were found which substantially degrade the fit, namely:

Transition Frequency σfit
(when excluded)
172,15-181,18 59 137.55 0.129 MHz
222,21-213,18 38 675.10 0.136 MHz
253,22-262,25 14 720.63 0.125 MHz

where σfit, is the standard deviation of the fit when each of the transitions is independently eliminated, as compared to σ = 0.157 when all are included.

When all three of these questionable transitions were simultaneously eliminated from the fit, the standard deviation dropped significantly to 0.070 MHz and all transitions in the fit exhibited reasonable statistical behavior. In addition, the predicted frequency for the 14 720 line was only 0.17 MHz higher than observed (t­test=0.5) while the 59 137 line was predicted 2.5 MHz higher than observed (t-test = 14.2) and the 38 675 line was predicted 1.1 MHz higher (t-test = 12.6). A calculation with only the latter two transitions (59.1 GHz and 38.6 GHz) eliminated appeared consistent. In the final analysis two of the low frequency lines from Hilton et al. were also included since they were in good agreement in all the fits which did not contain the questionable transitions.

The final results of this reanalysis are shown in table A.2.1 and compared to the results obtained with Kirchhoff's data set. In the upper part of the table all of the transitions excluded from the present analysis are given. The deviation found for the 172,25-181,18 of ~-2 MHz and ~-1 MHz deviation for the 222,21-213,18 suggest recording errors, i.e., the actual observed frequencies probably were 59 139.55 and 38 676.10, respectively. Note also the divergence between the present results and Kirchhoff's for the 364,32­373,35 line with Δν~-31 MHz versus Δν~+31 MHz. This is also indicated in comparing the Δν's and tν) results for the new transitions in the middle of table A.2.1. Although not added to the fit, the remaining lines from Hilton et al. [61007] in the 92 GHz to 104 GHz range appear to be assigned correctly by Pierce et al. [63007] based on the expected measurement uncertainty.

The difficulties encountered in the analysis of F2O are indicative of assigning spectral lines solely based on agreement with frequency predictions. Pierce et al. [63007] were forced to employ this method since Stark effect for lines with J>5 were unresolved. Thus, it is not surprising to find several transitions which are misassigned. Ideally, some additional measurements on F2O should be made in order to firmly establish the assignments and provide a centrifugal distortion analysis which results in better quality sextic parameters than presently obtainable. In the lower portion of table A.2.1 a list of predicted transitions is given. Observation of these transitions would remove any lingering doubts between the present analysis and those previously reported. Some additional confidence can be placed in the present results since the two new lines fit (17.2 GHz and 14.7 GHz) have been observed as triplets and are in good agreement with the spin-rotation analysis of Flygare [65011].

After this review was submitted a sample of F2O was obtained and new measurements were performed to resolve the questions relating to the analysis on F2O. The measurements shown in table A.2.2, were carried out in a parallel plate Stark-modulated spectrometer with fields up to about 3000 V/cm. Many of the observed transitions with J>30 occurred as K-doublets which assisted in the assignment. Several of the transitions predicted in table A.2.1. were measured and agreed well with the reanalysis described above. The molecular constants obtained by combining the new measurements with the data in The Microwave Spectrum of F2O are given in Rotational and Centrifugal Distortion Constants for F2O.

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