Uncertainty of the potential curve minimum for diatomic molecules extrapolated from Dunham type coefficients

Abstract

In the traditional description of electronic states of diatomic molecules by means of molecular constants or Dunham coefficients, one of the important fitting parameters is the value of the zero point energy – the minimum of the potential curve or the energy of the lowest vibrational-rotational level – E00. Their values are almost always the result of an extrapolation and it may be difficult to estimate their uncertainties, because they are connected not only with the uncertainty of the experimental data, but also with the distribution of experimentally observed energy levels and the particular realization of set of Dunham coefficients. This paper presents a comprehensive analysis based on Monte Carlo simulations, which aims to demonstrate the influence of all these factors on the uncertainty of the extrapolated minimum of the potential energy curve U(Re) and the value of E00. The very good extrapolation properties of the Dunham coefficients are quantitatively confirmed and it is shown that for a proper estimate of the uncertainties, the ambiguity in the composition of the Dunham coefficients should be taken into account.