Example Carbon Monoxide, CO

The present CO fits are the most simple examples of how to use the programs SPFIT and SPCAT for fitting and predicting spectra. Two fits are presented, one with three parameters: the rotational constant B, and the quartic and sextic centrifugal distortion constants D and H. In the second fit, the octic centrifugal distortion constant L has been included in the fit additionally.

The first line contains the title and the date of the latest fit. In the second line it is indicated that there are 3 (or 4) parameters, 31 experimental lines, and a maximum of 4 iterations per fitting round. If the number of the parameters or lines is increased the respective number has to be changed in the parameter file. The program adjusts numbers that are too large. The third line indicates that parameters are labeled according to spinl.nam, that quantum numbers for a symmetric rotor are used, that the spin mulitplicity is one, that there is only one vibrational state with minimum and maximum K_a being 0 (after all, CO is a linear molecule), and that spin statistics can be ignored (weighting for even and odd states is the same !).

The experimental lines were summarized in the article "Sub-Doppler Measurements on the Rotational Transitions of Carbon Monoxide" by G. Winnewisser, S. P. Belov, Th. Klaus, and R. Schieder published in J. Mol. Spectrosc. 184 (1997) 468–472.

The following files are available:

• The line file co.lin is for both fits.
• The parameter file co_3.par without L.
• The parameter file co_4.par with L.
• co_3.fit and co_4.fit are the respective fit files.
• co_3.var and co_4.var are the respective variance/covariance files.
• The intensity file co.int is for both predictions.
• co_3.cat and co_4.cat contains the respective predictions.
• co_3.out and co_4.out are the auxiliary output files.
• co_3.mrg and co_4.mrg are the respective predictions with the experimental lines merged. The experimental lines are indicated by a minus sign in front of the tag number.
• co_3.log and co_4.log are the respective log files (showing which lines have been merged).

HINTS:

• The uncertainties attributed to the experimental transition frequencies are treated as absolute ones, not as relative ones. Changing their uncertainties by (e.g.) a factor of 100 causes the parameter uncertainties and the uncertainties of the predicted frequencies to change accordingly. Compare
  • CO_100.lin and co.lin
  • CO_100.fit and co_4.fit
  • CO_100.var and co_4.var
  • CO_100.cat and co_4.cat
  Obviously, there is no change in the parameter values etc. Clearly, this does make sense: if your transition frequencies are known less well, the resulting parameters and predictions are less reliable – irrespective of the residuals encountered between observed and calculated transition frequencies ! Of course, the weighted standard deviation of the fit should be close to 1.0 ideally. But in the real world there are many reasons for substantial deviations. E.g. if the line list is small compared to the number of prameters or if systematic deviations may be present the weighted standard deviation of the fit can be considerably smaller than 1.0. Systematic errors may be present, e.g., in Fourier transform infrared spectroscopy, the precision of the line frequencies is quite commonly better than the accuracy. Weighted standard deviations considerably larger than 1.0 may occur, e.g., if an important spectroscopic parameter is missing in the fit.
• No extension has to be specified to run the programs unless the file name differs from the default. In this case the non-default files have to be specified with the extension !
  E. g.: spfit co_4 co.lin