Introduction

Preface

This guide introduces the fundamentals of rotational (and vibrational) spectroscopy using three tools:

There are plenty of other codes in use (see Zbigniew Kisiel's PROSPE webpage for an excellent overview) and the optimal software stack can vary significantly depending on your scientific objectives and personal preferences.

The guide focuses on finding and assigning patterns in the spectra rather than on theory. The required theory will, of course, be introduced, but there are many books that provide a much more comprehensive description. Some recommended books are

Lastly, this course draws heavily on my scientific publications and my PhD thesis. In particular, chapters 4. Analysis Process and Software and 5. Spectroscopy of Vibrationally Excited COMs of the latter are worth reading in this context. Please refer to my PhD thesis for further information and a full list of references.

Introduction

Rotational spectroscopy is an extremely accurate and versatile tool. Its many use cases include identifying and quantifying samples in space or in the laboratory, determining molecular structures and other properties (e.g. moments of inertia, dipole moments and vibrational energy separations), and examining fundamental physics.

This course will teach you how to assign a molecule's rotational (and rovibrational) fingerprints, which can be used to identify it unambiguously - in a similar way to how human fingerprints are used for identification. The rotational fingerprint of a molecule is the set of its rotational transitions. According to the rules of quantum mechanics, molecules possess distinct energy levels for their rotational, vibrational and electronic states. These energy levels are characteristic of the molecule's geometry, force field and electronic structure, respectively. Consequently, the transitions between molecular energy levels are distinct and characteristic of the molecule.

The rotational transitions of a molecule are typically found in the microwave (1–30 GHz), millimetre-wavelength (30–300 GHz) and submillimetre-wavelength (300 GHz–30 THz) regions. One advantage of the rotational spectrum is atmospheric transparency in these regions, 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 within the radio window of the atmosphere and can therefore be observed from Earth. For frequencies above 300 GHz, the opacity reaches up to 100%, so observations must be performed either at very high altitudes (e.g., ALMA) or above the troposphere (e.g., with SOFIA, the Herschel Space Observatory, JWST, or the Compton Gamma Ray Observatory and Hubble Space Telescope shown here). Figure adapted from NASA.

While the first molecule detected in space, CH, was found via electronic transitions in the ultraviolet (UV) and visible regions of the electromagnetic spectrum, most subsequent astronomical detections of molecules have been made using radio telescopes. The vast majority of recent detections were made using three single-dish telescopes: the 30 m telescope of the Institut de Radioastronomie Millimétrique (IRAM), the 100 m Green Bank Telescope (GBT), and the 40 m Yebes telescope. The latter two are located at altitudes of 818 m and 931 m, with the highest observable frequencies being 116 GHz and 90 GHz, respectively. By contrast, the IRAM 30 m telescope covers frequencies up to 375 GHz and is located at an altitude of 2,850 m. These telescopes measure the electromagnetic (EM) radiation emitted by regions in space, which can then be searched for molecular fingerprints. Once a molecule is identified, models of its spectral characteristics can be used to infer the physical properties of the astronomical source, providing astronomers with invaluable information for understanding and modelling these regions.

Prerequisites