Introduction

Preface

This guide teaches the first steps into rotational (and vibrational spectroscopy) based on the three tools

LLWP to explore and assign the lines in the spectrum to quantum numbers
SPFIT to fit the assignments to an effective Hamiltonian
SPCAT to create predictions from that effective Hamiltonian

There are plenty of other codes in use (see the PROSPE webpage by Zbigniew Kisiel for an excellent overview) and the optimal software stack can vary heavily depending on your science case and personal taste.

The guide focusses on the art of finding and assigning patterns in the spectra and less on the theory. Of course, the required theory will be introduced but there are a lot of books that give a much more complete description. Some recommended books are

P. Bernath: "Spectra of Atoms and Molecules"
G. Herzberg: "Molecular Spectra and Molecular Structure", I-III
P. R. Bunker/P. Jensen: "Fundamentals of Molecular Symmetry"
W. Gordy/R. L. Cook: "Microwave Molecular Spectra"
C. H. Townes/A. L. Schawlow: "Microwave Spectroscopy"

Lastly, this course is heavily based on my PhD thesis. Especially chapters 4. Analysis Process and Software and 5. Spectroscopy of Vibrationally Excited COMs are worth reading in this context. Please also refer to the thesis for further information and a full list of references.

Introduction

Rotational spectroscopy is an extremely accurate and versatile tool. Some of its many use cases are identifying and quantifying samples in space or in the laboratory, determining molecular structures and other properties (e.g., moments of inertia, dipole moments, vibrational energy separations, barriers to large amplitude motions, …), as well as examining fundamental physics.

This guide will teach you to assign the rotational (and rovibrational) fingerprints of a molecule which unambiguously identify it (similar to a human fingerprint). The rotational fingerprint of a molecule is the set of its rotational transitions. As is known from the rules of quantum mechanics, molecules possess distinct energy levels for their rotational, vibrational, and electronic states. These energy levels are characteristic of the geometry of the molecule, its force field, and its electronic structure, respectively. Consequently, the transitions between the molecular energy levels are distinct and characteristic to the molecule.

Typically, the rotational transitions of a molecule are found in the microwave (1-30 GHz), millimeter-wavelength (30-300 GHz), and sub-millimeter-wavelength (300 GHz-30 THz) regions. A great advantage of the rotational spectrum is the atmospheric transparency in that region which makes it possible to use Earth-based telescopes to study distant regions in space.

The opacity of Earth’s atmosphere for different frequencies (upper scale) or wavelengths (lower scale). Rotational transitions fall into the radio window of the atmosphere and can therefore be observed from Earth. For frequencies above 300 GHz, the opacity reaches up to 100% requiring observations to be either performed at very high altitudes (e.g., ALMA) or above the troposphere (e.g., with SOFIA, the Herschel Space Observatory, JWST, or the here shown Compton Gamma Ray Observatory and Hubble Space Telescope). Figure adapted from NASA.

While the first molecule detected in space, CH$^+$, was found via electronic transitions in the UV and visible regions, most astronomical detections of molecules since then have been made using radio telescopes. The vast majority of recent detections were made with three single-dish telescopes: The Institut de Radioastronomie Millimétrique (IRAM) 30m telescope, the Green Bank 100m Telescope (GBT), and the Yebes 40m telescope. The latter two are located at altitudes of 818m and 931m with the highest observable frequencies at 116 GHz and 90 GHz, respectively. In contrast, the IRAM 30m telescope covers frequencies up to 375 GHz and is located at an altitude of 2850m. The telescopes measure the EM radiation emitted by regions in space, which can then be searched for molecular fingerprints. Once a molecule is found, appropriate models of its spectral characteristics can be used to infer the prevalent physical properties of the astronomical source which is invaluable to astronomers in understanding and modelling these regions.

Prerequisites