# (J + 1/2) squared or J(J + 1) as functional for rotational terms in analysis of molecular spectra

## TL;DR

This paper evaluates two functionals, (J + 1/2)^2 and J(J + 1), for modeling rotational terms in diatomic molecular spectra, concluding that (J + 1/2)^2 is more appropriate based on theoretical and experimental evidence.

## Contribution

The study provides a comprehensive comparison of the two functionals, confirming that (J + 1/2)^2 better fits spectral data for diatomic molecules in the singlet-Sigma state.

## Key findings

- (J + 1/2)^2 is preferable for spectral analysis.
- Experimental spectra of HCl support the theoretical preference.
- The conclusion confirms Mulliken's 1930 statement.

## Abstract

The theoretical and experimental evidence regarding the use of (J + 1/2) squared and J(J + 1) as a functional in formulae for rotational term values in the spectral analysis of a diatomic molecule in electronic state singlet-Sigma is scrutinised. The infrared spectra of HCl serve as examples of the application of the two functionals. Tbe total evidence indicates that (J + 1/2) squared is preferable to J(J + 1) for the stated purpose, confirming Mulliken's statement in 1930.

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Source: https://tomesphere.com/paper/1905.01761