# Fundamentals of Diatomic Molecular Spectroscopy

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results

#### 3.1. Angular Momentum Commutators

#### 3.1.1. Invariance for Unitary Transformations

#### 3.1.2. Invariance for Time Reversal or Reversal of Motion

#### 3.2. Diatomic Wave Function

#### 3.3. Selected Diatomic Spectra

## 4. Discussion and Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AM | Angular Momentum |

BESP | Boltzmann Equilibrium Spectrum Program |

CM | Classical Mechanics |

NMT | Nelder–Mead Temperature |

PGOPHER | Program for simulating rotational, vibrational, and electronic spectra, or |

“Program Gopher” | |

QM | Quantum Mechanics |

QMT | Quantum Mechanics Theory |

RAM | Reversed Angular Momentum |

WWE | Wigner–Witmer Eigenfunction |

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**Figure 1.**Computed spectrum of the ${A}^{2}\Sigma \to {X}^{2}\mathsf{\Pi}$ uv band of OH, T = 4 k K, (top) spectral resolutions of $\Delta \lambda =0.32$ nm ($\Delta \tilde{\nu}=$ 32 cm${}^{-1}$) and (bottom) idealized resolution for the stick spectrum $\Delta \lambda =0.002$ nm ($\Delta \tilde{\nu}=$ 0.2 cm${}^{-1}$) of the $\Delta \nu =0$ sequence (adapted from [6]).

**Figure 2.**C${}_{2}$ Swan ${d}^{3}{\mathsf{\Pi}}_{g}\to {a}^{3}{\mathsf{\Pi}}_{u}$ band $\Delta \nu =-1$ sequence, T = 8 kK, $\Delta \lambda =0.13$ nm ($\Delta \tilde{\nu}=$ 6 cm${}^{-1}$) (adapted from [6]).

**Figure 3.**C${}_{2}$ Swan ${d}^{3}{\mathsf{\Pi}}_{g}\to {a}^{3}{\mathsf{\Pi}}_{u}$ band $\Delta \nu =+1$ sequence, T = 8 kK, $\Delta \lambda =0.18$ nm ($\Delta \tilde{\nu}=$ 6 cm${}^{-1}$) (adapted from [6]).

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Parigger, C.G. Fundamentals of Diatomic Molecular Spectroscopy. *Foundations* **2021**, *1*, 208-216.
https://doi.org/10.3390/foundations1020016

**AMA Style**

Parigger CG. Fundamentals of Diatomic Molecular Spectroscopy. *Foundations*. 2021; 1(2):208-216.
https://doi.org/10.3390/foundations1020016

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Parigger, Christian G. 2021. "Fundamentals of Diatomic Molecular Spectroscopy" *Foundations* 1, no. 2: 208-216.
https://doi.org/10.3390/foundations1020016