Determination of the electronic-vibrational-rotational terms of diatomic molecules from measured wave numbers

Abstract

A method is proposed for determining the electronic-vibrational-rotational (rovibronic) terms of diatomic molecules from experimental data on the wave numbers of the rovibronic spectral lines. In contrast to the currently available methods, the proposed method is based only on the Rydberg-Ritz combination principle. It is demonstrated that a correlation between the sets of magnitudes of the rovibronic terms and the wave numbers of the observed spectral lines appears when the spectrum involves three or more electronic-vibrational states related in pairs by radiative transitions. Unlike the traditional methods, the proposed approach (i) does not require additional assumptions regarding the molecular structure; (ii) does not employ intermediate parameters, such as molecular constants in the traditional methods; (iii) makes it possible, within the one-step optimization procedure, to use all the available experimental data obtained for several sets of bands by different authors and in different experiments; (iv) permits one to select effectively experimental data, reject outliers and blunders, correct the identification of the rovibronic spectral lines, and analyze the consistency of different data sets in the interactive mode; and (v) provides a means for determining not only the optimum magnitudes of the rovibronic terms but also their errors associated with the amount and quality of the available experimental data. A necessary condition for the implementation of the new method is the preliminary identification of the lines revealed in the rovibronic spectra under investigation, i.e., the assignment of the observed spectral lines to particular rovibronic transitions. This requires the use of conventional procedures for analyzing the molecular spectra.