On the calculation and interpretation of centrifugal distortion constants: A statistical basis for model testing: The calculation of the force field

170

150

a b s t r a c tStimulated by recent THz measurements of the methanol spectrum in one of our laboratories, undertaken in support of NASA programs related to the Herschel Space Observatory (HSO) and the Atacama Large Millimeter Array (ALMA), we have carried out a global analysis of available microwave and high-resolution infrared data for the first three torsional states (m t = 0, 1, 2), and for J values up to 30. This global fit of approximately 5600 frequency measurements and 19 000 Fourier transform far infrared (FTFIR) wavenumber measurements to 119 parameters reaches the estimated experimental measurement accuracy for the FTFIR transitions, and about twice the estimated experimental measurement accuracy for the microwave, submillimeter-wave, and terahertz transitions. The present fit is essentially a continuation of our earlier work, but we have greatly expanded our previous data set and have added a large number of new torsion-rotation interaction terms to the Hamiltonian in our previously used computer program. The results, together with a number of calculated (but unmeasured) transitions, including their line strength, estimated uncertainty, and lower state energy, are made available in the supplementary material as a database formatted to be useful for astronomical searches. Some discussion of several open spectroscopic problems, e.g., (i) an improved notation for the numerous parameters in the torsion-rotation Hamiltonian, (ii) possible causes of the failure to fit frequency measurements to the estimated measurement uncertainty, and (iii) pitfalls to be avoided when intercomparing apparently identical parameters from the internal axis method and the rho axis method are also given.

Section: Methanol Thz Data Basementioning

confidence: 99%

Torsion–rotation global analysis of the first three torsional states (νt=0, 1, 2) and terahertz database for methanol

Fisher

Lees

et al. 2008

170

150

“…e Measurement uncertainties assigned to the various types of transitions (type B, k=1 [32]). a Order of the Hamiltonian term in the notation of Ref.…”

Section: List Of Tablesmentioning

confidence: 99%

“…95 percent confidence levels or expanded uncertainty with coverage factor k = 2) and were estimated from the variance-covariance matrix as described in Ref. [32].…”

Section: Ch 3 Oh Line Listmentioning

confidence: 99%

See 1 more Smart Citation

Millimeter wave and terahertz spectra and global fit of torsion–rotation transitions in the ground, first and second excited torsional states of 13 CH 3 OH methanol

Lees

Hao

et al. 2014

“…(For examples of previous similar uses of such synthetic data, see Refs. (3,4,7).) In particular, a set of synthetic data for the three bands of Fig.…”

Section: Model Bad Systemmentioning

confidence: 99%

A method for merging the results of separate least-squares fits and testing for systematic errors

Albritton¹,

Schmeltekopf²,

Zare

1977

144

A method is presented for merging the results of separate least-squares fits to obtain the most precise, single values for each of the molecular constants of a spectroscopic system. The output molecular constants and accompanying variance-covariance matrices from each of the separate fits are taken together as input to a correlated least-squares fit, which then yields the desired merged single values. The method is applied to a X-r8 diatomic model band system using well-defined synthetic data as an example. Other currently used, multistate methods of obtaining molecular constants for a spectroscopic system are special cases of the method described here. For the nonlinear least-squares fits required for multiplet states, the merge method is particularly advantageous. The properties of the merged values of the molecular constants and their standard errors are examined with regard to forming confidence limits for these estimates and it is shown that, in most spectroscopic applications, the confidence limits have their usual meaning. Furthermore, it is similarly shown that the confidence limits for the variance of the merged fit provide a simple and convenient test for the presence of relative systematic errors between the separate least-squares results being merged. Although the method is illustrated here by merged separate band-by-band results, it also can be applied to any type of spectroscopic results.