Optimal values of rovibronic energy levels for triplet electronic states of molecular deuterium

TL;DR

This paper presents a statistically optimized set of 1050 rovibronic energy levels for triplet states of molecular deuterium, derived from extensive spectroscopic data using a novel analysis method that minimizes assumptions and estimates uncertainties.

Contribution

The study introduces a new analysis method for rovibronic energy levels that does not rely on prior assumptions and improves uncertainty estimates, providing a comprehensive and accurate energy level dataset for D₂.

Findings

Identified and removed spurious data points from the spectroscopic dataset.

Derived new energy levels that significantly differ from previous literature values.

Estimated uncertainties and shifts between ortho- and para-deuterium energy levels.

Abstract

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 priory \rm assumptions concerning the molecular structure being based on only two fundamental principles: Rydberg-Ritz and maximum likelihood. The method provides the opportunity to obtain the RMS estimates for uncertainties of the experimental wavenumbers independent from those presented in original papers. 234 from 3822 published wavenumber values were found to be spurious, while the remaining set of the data may be divided into 20 subsets (samples) of uniformly precise data having close to normal distributions of random errors within the samples. New experimental wavenumber values of 125 questionable lines were obtained in the present work. 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 the standard deviations of the empirical determination. New energy level values differ significantly from those available in literature.