Accuracy of Morse and Morse-like oscillators for diatomic molecular interaction: A comparative study

Abstract

This study aims at comprehensively evaluating and comparing the goodness-of-fit of several potential energy curves (PECs), which are Morse, Manning-Rosen, Rosen-Morse and Modified-Rosen-Morse oscillators, to the corresponding experimental Rydberg-Klein-Rees (RKR) or RKR-style data of diatomic molecules. In this work, we also determined vibrational energies of the diatomics based on Bohr-Sommerfeld quantization rule. The goodness-of-fit to RKR data of 34 electronic states of 17 diatomics and the accuracy of the calculated vibrational energies were compared for the four oscillators and reported simultaneously for the first time in this study. These results showed that some oscillators demonstrated better goodness-of-fit than the others. Overall, the (Modified)-Rosen-Morse oscillators generated more accurate vibrational levels for most molecules studied, while Manning-Rosen oscillator was generally better for molecules in their excited electronic states. Although all oscillators performed well for more classical molecules, the Morse oscillator was superior to the other three in describing the ground states of 12C16O and 28Si32S. Particularly, it reproduced all 38 observed experimental ground state vibrational levels of 12C16O with error below 0.79% and even accurately predicted four states unobserved experimentally.