Rovibronic energy levels for triplet electronic states of molecular deuterium

TL;DR

This paper presents a comprehensive set of 1050 rovibronic energy levels for triplet states of molecular deuterium, derived through a novel statistical analysis method that improves accuracy and estimates uncertainties independently from original data.

Contribution

It introduces a new analysis method based on maximum likelihood and Rydberg-Ritz principles, providing more reliable energy levels and uncertainty estimates for D₂ triplet states.

Findings

Obtained 1050 energy levels for 35 triplet states of D₂.

Identified and removed 234 spurious wavenumber values from the dataset.

Discovered significant differences between new energy levels and previous literature values.

Abstract

An optimal set of 1050 rovibronic energy levels for 35 triplet electronic states of $D_2$ has been obtained by means of a statistical analysis of all available wavenumbers of triplet-triplet rovibronic transitions studied in emission, absorption, laser and anticrossing spectroscopic experiments of various authors. We used a new method of the analysis (Lavrov, Ryazanov, JETP Letters, 2005), which does not need any \it a priori \rm assumptions concerning the molecular structure being based on only two fundamental principles: maximum likelihood and Rydberg-Ritz. The method provides the opportunity to obtain the estimation of uncertainties of experimental wavenumbers independent from those presented in the original papers. 234 from 3822 published wavenumber values were found to be spurious, while the remaining set of the data may be divided into 19 subsets of uniformly precise data having close to normal distributions of random errors within the subsets. New wavenumber values of 125 questionable lines were measured in the present work (20-th subset). Optimal values of the rovibronic levels were obtained from the experimental data set consisting of 3713 wavenumber values (3588 old and 125 new). The unknown shift between levels of ortho- and para- deuterium was found by least squares analysis of the $a^3\Sigma_g^+$, $v = 0$, $N = 0 \div 18$ rovibronic levels with odd and even values of N. All the energy levels were obtained relative to the lowest vibro-rotational level ($v = 0$, N=0) of the $a^3\Sigma_g^+$ electronic state and presented in tabular form together with standard deviations (SD) of the semi-empirical determination. New energy level values differ significantly from those available in literature.