Rotational transitions of HF that are important as a wavenumber standard have been analyzed by simultaneous fitting of the reported rotational and vibrational-rotational transitions plus rotational measurements of the present study with the non-Born-Oppenheimer effective Hamiltonian expressed with the optimal parameters, i.e., the determinable clusters of the expansion coefficients of the correction functions for the breakdown of the Born-Oppenheimer approximation. Since the spectral fit is made with the analytical solution of the Schrödinger equation, one can easily reproduce the fitting procedure. This is the first example of the non-Born-Oppenheimer analysis of a single isotopologue with physically meaningful parameters based on the traditional concept of the molecular constants. Fitting of a data set for HF has generated 15 independent parameter values that include 4 determinable clusters of the expansion coefficients. These 15 parameters are sufficient to generate 41 Yij coefficients and 72 rotational constants, which provide comprehensive sets of molecular constants of HF.

Analytic expressions for Born–Oppenheimer corrections to Dunham’s Yij with optimal fitting parameters, i.e., determinable clusters of expansion coefficients, are applied in analysis of data of reported vibrational–rotational and rotational transitions of HCl. In this method of analysis the choices of a set of fitting parameters and also a corresponding set of Yij that connects the fitting parameters with the term values are unique. A layered structure for empirical parameters Δij is revealed. All spectral lines of four isotopomers of HCl are simultaneously fitted to a single set of molecular constants well within the experimental errors. The approach thus provides a better fit of smaller standard deviations with fewer number of adjustable parameters than from other methods of analysis. The determined values for the coefficients of adiabatic effects s1H and s1Cl reveal the wobble-stretch term to be unimportant in the adiabatic correction for HCl.

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a b s t r a c tIn total, 626 vibrational-rotational spectral lines of the Dv = 1 transitions of 13 C 32 S up to band v = 5-4 have been measured with a Fourier-transform spectrometer at resolution 0.010 cm À1 . To calibrate accurately the spectral lines, a separate observation of the vibrational-rotational bands of 12 C 32 S was made with simultaneous recording of the N 2 O spectrum in absorption, to serve as wavenumber standards, with dual sample cells at resolution 0.008 cm À1 . The spectral wavenumbers of 12 C 32 S in turn become calibration standards. All present vibrational-rotational spectra of 13 C 32 S and 12 C 32 S, the reported vibrationalrotational spectra of 12 C 32 S, 12 C 33 S, 12 C 34 S, and 13 C 32 S, and the reported rotational spectra of 12 C 32 S, 12 C 33 S, 12 C 34 S, 12 C 36 S, 13 C 32 S, 13 C 33 S and 13 C 34 S were subjected to a global multi-isotopologue analysis, which reduced them to molecular parameters in a single set. The wavenumbers of 3974 spectral lines, in total, comprising data of seven isotopologues were fitted with 22 isotopically invariant, traditional molecular parameters in a single set. As the normalized standard deviation is 1.38, the obtained fit is satisfactory. To facilitate the calculation of spectral wavenumbers, the values of the Dunham coefficients of 42 Y ij for each of 12 the spectra of the latter five isotopologues are not yet reported, were back-calculated with uncertainties using the evaluated 22 molecular parameters. The physical significance of the conventional treatments of the adiabatic and nonadiabatic corrections for D 01 C and D 01 S is discussed.