Advances in hydrogen molecular ions: H3+, H5+ and beyond

The H₃⁺ molecular ion is the simplest stable molecular ion of hydrogen. It is rapidly formed by collisions between H₂ and H₂⁺. Its role in the interstellar medium and the ionospheres of gas giant planets is now well established but careful studies of its spectra are providing valuable information on issues as diverse as the cosmic ray ionisation rate in different environments and wind speeds in planetary upper atmospheres. 

H₃⁺ is the electronically simplest stable polyatomic molecule and therefore provides a benchmark system for testing high accuracy ab initio methods. While impressive accuracy has been achieved, calculations on the isoelectronic H₂ molecule remain many orders of magnitude more accurate; this problem is not directly due to issues with the multi-dimensional nuclear motion problem, which is capable of high accuracy solution, but more due to treating various subtle effects in many dimensions. 

H₅⁺ may seem superficially similar to H₃⁺ but it is a fluxional molecule: one for which there is facile conversion between multiple equilibrium geometries leading to complicated and delocalised wave functions. H₅⁺, and indeed the higher hydrogen molecular ions, thus raise their particular issues especially in terms of predicting and interpreting their spectral signatures. Reactions between ionised and neutral hydrogenic species, such as H⁺ + H₂ or H₂⁺ + H₂, are of importance for studying hydrogen plasmas both on Earth and in the interstellar medium. These reactions also raise their own issues with fundamental physics. 

Modern experimental techniques, such as the ability to study atoms and molecules at extremely low temperatures, allow these processes to be studied with increasing detail, which raises new challenges for theory to address. The original discovery of H₃⁺ is now well over a century ago but there clearly remains a whole host of issues to be studied both using and involving the molecular ions of hydrogens.

Professor Jonathan Tennyson FRS, UCL, UK

Professor Jonathan Tennyson FRS, UCL, UK

Jonathan Tennyson is Massey Professor of Physics at University College London (UCL). After studying chemistry at the Universities of Cambridge and Sussex, he worked at the University of Nijmegen and Daresbury Laboratory before moving to UCL. He served as Head of UCL Physics and Astronomy from 2004 to 2011. His research focuses on high  accuracy calculations of molecular spectra and electron collisions. Highlights include the first assignment of a spectrum of H₃⁺ in the atmosphere of Jupiter based on precise quantum mechanical calculations. Since 2008 he has been a member of the HITRAN International Advisory Board and in 2011 he founded the ExoMol project dedicated to computing molecular line lists for exoplanetary and other atmospheres. This ExoMol database which is currently being extended to include data suitable for high resolution studies, photodissociation and the effects of line broadening for various atmospheres. He was elected a Fellow of The Royal Society in 2019.

The protonated hydrogen dimer, H₅⁺, is the smallest system including proton transfer, and of longstanding interest since its first laboratory observation in 1962. H₅⁺ and its isotopologues are the intermediate complexes in the deuterium fractionation reactions, and of central importance in molecular astrophysics. Recently, the IR spectra of H₅⁺/D₅⁺ and H₇⁺/D₇⁺ have been recorded revealing a rich vibrational dynamics of the cations, that present a challenge for the standard theoretical approaches. Although both of them are few-electron ions, which makes highly accurate electronic structure calculations tractable, the construction of ab initio-based potential energy and dipole moment surfaces has proved a hard task. In the same vein, the difficulties to treat the nuclear motion could also turn cumbersome as the dimensionality, floppiness and/or symmetry of the system increase. These systems are prototypical examples of studying large amplitude motions; as they are highly delocalised, interconverting between equivalent minima though rotation and proton transfer motions requiring state-of-the-art treatments. Recent advances in the vibrational spectroscopy of the H₅⁺ cations and beyond will be reported from full quantum spectral simulations, providing important information in a rigorous manner, and open perspectives for further future investigations.

Dr Rita Prosmiti, IFF-CSIC, Madrid, Spain

Dr Rita Prosmiti, IFF-CSIC, Madrid, Spain

Dr Prosmiti has more than 20 years of experience in Physics/Chemistry (Molecular, Quantum and Computational) research. Her interests are broad, constantly adapted to international advances, and focus on the study of structural, spectroscopic, dynamic and transport properties of molecular systems from the gas to condensed phases. Along her career, she has implemented and/or developed methods to treat ionic hydrogen clusters, van der Waals complexes, doped helium aggregates, and nanoconfined molecules in clathrate hydrates and fullerenes to study their formation, spectroscopy, predissociation and photofragmentation, and more recently she carried out computational simulations on aqueous solutions, with interest in weak interactions, for studying solvation/hydration effects. Dr Prosmiti's research work has been funded by the European Union, the Greek Ministry of Education, the Engineering and Physical Sciences Research Council (UK), the Community of Madrid and the Ministry of Education and Science of Spain. She has written more than 125 articles in scientific journals of international prestige (see at Google Scholar), and participated in more than 150 international conferences.

Hydrogen has played a very important role in the development of the physical sciences during the 20th century, and continues to do so into the next millennium. Although well-known from the citation of the 1932 Nobel Prize in Physics, it is probably not widely understood why the discovery of the allotropic forms of hydrogen was singled out as the most important consequence of Heisenberg’s quantum theory. In this talk, the dissociative recombination of H₃⁺ and D₅⁺ will be discussed. The former has been the subject of many experimental and theoretical investigations, whereas the latter has received far less attention. Molecular hydrogen in its ionised forms is continuously reinventing itself, in recent years not least by its presence in “hot Jupiter” exoplanets.

Professor Mats Larsson, Stockholm University, Sweden

Professor Mats Larsson, Stockholm University, Sweden

Mats Larsson is professor of physics at the Department of Physics, Stockholm University, and also director of the AlbaNova University Center, a joint enterprise between Stockholm University and the Royal Institute of Technology. He is member of the Royal Swedish Academy of Sciences and its physics class, which the awarding institution for the Nobel Prizes in Physics and Chemistry. He has a long affiliation with H₃⁺ and wrote the first proposal for an experiment with H₃⁺ in the storage ring CRYRING exactly 20 years ago. Needless to say, the situation concerning the recombination of H₃⁺ was also at that time in complete turmoil.

Exoplanet science is moving from object discoveries into characterisation and analysis. Transit spectroscopy has shown that exoplanet atmospheres form clouds which can be composed of minerals instead of water, and their phase curves indicate the presence of winds driven by the external, host-star irradiation. The large diversity of the more than 3000 exoplanets (of which a subclass resembles brown dwarfs) suggests that the atmospheres of these planets will differ considerably and so will their weather patterns and their chemical composition. Dr Helling will present results from 3D atmosphere simulations, providing insight into the complexity of exoplanet clouds, which are the precondition for lightning to occur. Lightning chemistry calculations show the strong feedback on the local chemistry, enabling the discussion of chemical lightning tracers. The occurrence of lightning is also linked to the ionisation of the atmospheres by external radiation. Dr Helling will present results that show that external radiation can cause the formation of a global but shallow ionosphere on brown dwarfs or of a deep but locally confined ionosphere on highly irradiated exoplanets. She will discuss the emergence of H₃⁺ resulting from Aurora on brown dwarfs.

Dr Christiane Helling, Centre for Exoplanet Science, University of St Andrews, UK

Dr Christiane Helling, Centre for Exoplanet Science, University of St Andrews, UK

Dr Christiane Helling is Reader in the School of Physics & Astronomy at the University of St Andrews and Director of the St Andrews Centre for Exoplanet Science. She was educated in Berlin, Germany, and previously worked for the European Space Agency. With support from the European Research Council, she established the LEAP (Life Electricity Atmospheres Planets) research group, following her interests in understanding atmospheres of extrasolar planets, the physics and chemistry of cloud formation and lightning, as well as their possible roles for the emergence of life. The headline of the Centre for Exoplanet Science, which combines expertise from astronomy/astrophysics, geosciences, biology, philosophy and social anthropology, summarises a key driver of her scientific endeavour: “Understanding how unusual Earth is may help humanity to appreciate how special it is.”

Earlier work on charge transfer in proton dihydrogen collisions demonstrated the decisive role of the seam connecting the ground and first excited potential energy surfaces of H₃⁺. This phenomenon stems from the difference in dissociation energy between H₂ and H₂⁺ exceeding that of ionisation potential between H₂ and H. While protons probe this connecting seam in a full collision, the photodissociation of H₃⁺ is actually probing it from within, as fragments depart from the classical turning point accessed via a vertical transition from the ground state potential well. Detailed experiments have been conducted for both reactions, making extensive use of three-dimensional imaging of dissociation products, that allows for the precise determination of vibrational distributions of reactants and products. While proton dihydrogen charge transfer leaves excited H₂⁺ products in specific vibrational distributions, photodissociation of hot H3⁺ in the near ultraviolet produces comparatively colder H₂⁺ products. Modelling the wavepacket dynamics along the repulsive potential surface is expected to account for the repopulation of the ground potential energy surface on its way to H₂ + H⁺ products. The role of the connecting seam will be emphasised and its importance for the astrophysically relevant H₂⁺ hydrogen charge transfer reaction underlined.

Professor Xavier Urbain, Université catholique de Louvain, Belgium

Professor Xavier Urbain, Université catholique de Louvain, Belgium

Xavier Urbain is a Senior Research Fellow of the FRS-FNRS and a professor at the Université catholique de Louvain, where he teaches atomic physics at the bachelor and master level.

Trained as both an experimental and a theoretical physicist, Xavier focuses his research on collisional and radiative processes at play in astrophysical and technical plasmas, with special emphasis on the reactivity of small ionic systems. He specialized in merged and crossed beam experiments involving electrons, atoms and ions, and is active in several laboratories (UCLouvain, Columbia University, MPI for Nuclear Physics). He also conducts experiments with ultrafast lasers by bringing equipment to laser facilities (CEA Saclay, CELIA Bordeaux).

Xavier has pioneered several methods allowing absolute determination of cross sections for collision- or photon-induced processes, and various approaches to multiple fragment detection. Differential measurements obtained by high resolution momentum imaging provide additional insight into the dynamics, which regularly challenge common views.

Analysis of infrared absorption line profiles of H₃⁺ toward stars in the ~300 pc diameter central molecular zone (CMZ) of the galaxy show that most of the front half of the CMZ is filled with a few million solar masses of warm diffuse gas. The variation of the velocity profiles of the H₃⁺ lines across the CMZ demonstrate that this gas is moving radially outward from the centre at speeds of up to ~140 km/s. This is consistent with past interpretations of high velocity molecular gas observed at cm wavelengths in the galactic centre as arising in an expanding ring of gas at the outer edge of the CMZ. The characteristic time scale (r/vmax) of the expanding gas is roughly one million years, significantly less than the ages of the three clusters of hot and massive stars located near the centre, whose stellar winds and supernovae must contribute to powering the radial expansion of the diffuse gas. The observed velocities are significantly less than those found in the winds of massive stars and in supernova ejecta, suggesting that the ejected gas from stars and supernovae is impeded by the CMZ’s gas and decelerated by the gravity of its stars.

Dr Thomas R Geballe, Gemini Observatory, USA

Dr Thomas R Geballe, Gemini Observatory, USA

Dr Geballe obtained a PhD in physics in 1974 under Professor Charles Townes at U C Berkeley. Following postdoctoral fellowships at Berkeley and Leiden, and a Carnegie Fellowship at Hale Observatories in Pasadena, he became a staff astronomer at the United Kingdom Infrared Telescope in 1981. He was Astronomer-in-charge, Associate Director, and Head of Operations at UKIRT from 1987 until 1998, when he joined Gemini. Among his research interests are the Galactic center, the late stages of stellar evolution, H₃⁺ as a probe of interstellar gas, the composition of interstellar dust, the surfaces, atmospheres, and aurorae of solar system objects, and brown dwarfs.

Cosmic rays are mysterious particles mostly atomic nuclei with extremely high energy from 106 eV (MeV) to 1021 eV (Zev). Their energy spectra for many nuclei are known in detail from the measurements on the earth. To measure cosmic rays in the galaxy, however, we need a chemical method using spectroscopy. H₃⁺, trihydrium, provides the ideal probe for this purpose because of (1) its ubiquity, (2) simple chemistry, and (3) concise spectrum. For about 30 years from the classic paper by Spitzer & Tomasko (1968) when H⁺ was used as the probe, the cosmic ray ionisation rate of H₂ was thought to be on the order of ζ  ~ 10-17 s-1 and uniform throughout the galaxy. When in 1997 H₃⁺ was discovered in diffuse clouds and in the galactic centre (GC), however, this picture has gone down the drain. It is now established that ζ in diffuse clouds is 10 times higher than in dense clouds and ζ in the central molecular zone of the GC is 1000 times higher. The uniformity of cosmic ray energy density throughout the galaxy which was once thought to be reasonable because of its high penetrability has been completely negated.

Professor Emeritus Takeshi Oka FRS, Enrico Fermi Institute and University of Chicago, USA

Professor Emeritus Takeshi Oka FRS, Enrico Fermi Institute and University of Chicago, USA

Oka received his BS degree in Chemistry from the University of Tokyo in 1955 and a PhD for his work on microwave spectroscopy on formaldehyde in Professor Shimoda's lab in Physics of the same University in 1960. He was then a postdoctoral fellow at the National Research Council of Canada, later Herzberg Institute of Astrophysics. He joined the University of Chicago in 1981 jointly affiliated to the Department of Chemistry and the Department of Astronomy and Astrophysics. He joined the Enrico Fermi Institute in 1993. He became a professor emeritus in 2003. His research interests are in the areas of high-resolution spectroscopy and astrophysics of molecular ions, in particular, H₃⁺ near the Galactic centre.

At the low temperatures (~10 K) and high densities (~100,000 H2 molecules per cc) of molecular cloud cores and protostellar envelopes, a large amount of molecular species (in particular molecules containing C and O) freeze-out onto dust grain surfaces. It is in these regions that the deuteration of H₃⁺ becomes very efficient, with a sharp abundance increase of H₂D+ and D₂H⁺. The multi-deuterated forms of H₃⁺ participate in an active chemistry: (i) their collision with neutral species produces deuterated molecules such as the commonly observed N₂D⁺, DCO⁺ and multi-deuterated NH₃; (ii) their dissociative electronic recombination increases the D/H atomic ratio by several orders of magnitude above the D cosmic abundance, thus allowing deuteration of molecules (eg CH₃OH and H₂O) on the surface of dust grains. Deuterated molecules are the main diagnostic tools of dense and cold interstellar clouds, where the first steps toward star and protoplanetary disk formation take place. Recent observations of deuterated molecules will be presented and discussed in view of astrochemical models inclusive of spin-state chemistry. Models assuming complete scrambling to calculate branching ratio tables for reactions between chemical species that include protons and/or deuterons will be compared to models that assume non-scrambling, and with observations.

Professor Paola Caselli, Max Planck Institute for Extraterrestrial Physics, Garching, Germany

Professor Paola Caselli, Max Planck Institute for Extraterrestrial Physics, Garching, Germany

Paola Caselli studied Astronomy at the University of Bologna, where she graduated in 1990. In 1994 she obtained the PhD in Astrophysics at the University of Bologna, after spending nine months as visiting student at the Ohio State University with Professor Eric Herbst and two years at the Harvard Smithsonian Center for Astrophysics (CfA) as a pre-doctoral fellow with Professor Phil Myers. After a Postdoctoral Fellowship at CfA, in 1996 she became Researcher at the Arcetri Astrophysical Observatory in Florence, where she remained until 2005. In 2006 and 2007 she was Visiting Scholar in the Department of Astronomy, Harvard University, and in 2007 she became Professor of Astronomy at the School of Physics and Astronomy, University of Leeds. Since 2014, she is Director of the Centre for Astrochemical Studies at the Max-Planck-Institute for Extraterrestrial Physics and Honorary Professor at the Ludwig Maximilian University of Munich.

As the main infrared emitter of the ionosphere of hydrogen atmospheres, H₃⁺ is an ideal probe for these evanescent atmospheric layers. Ionospheres are transition layers between the deeper atmosphere and outer space. As such, they are of particular importance to understand the energetic processes at work from above and below. H₃⁺ controls the temperature of the ionosphere, by ensuring an energy balance between the infrared radiative emission and the energy input from external or internal sources. The source of heating are twofold: UV and external particle precipitation, with all the aeronomy reactions induced, and gravity waves dissipation from internal sources. Understanding the balance between these different processes is an active research field in astrophysics, for giant planets and exoplanets. The spatial variability of these phenomena is inherent to their sources: auroral precipitations, wave activity related to the dynamics, or even meteoroids. The ability to obtain high spatial resolution images in H₃⁺ emission from ground-based telescopes is therefore of high interest for 3D models of thermal global circulation models, in association with other observational techniques (UV observations, radio occultation). Mapping H₃⁺ emissions on giant planets will ultimately address the question of the coupling between the magnetosphere and the ionosphere.

Dr Pierre Drossart, LESIA, Observatoire de Paris, Meudon, France

Dr Pierre Drossart, LESIA, Observatoire de Paris, Meudon, France

Pierre Drossart has devoted his research activity to planetology, in the field of the atmosphere of giant and terrestrial planets through infrared spectroscopy. From ground-based infrared spectroscopy on CFHT/FTS instrument, he has obtained many results on the spectroscopy of Jupiter, including the first spectroscopic detection of H3+ on Jupiter. He has participated in many planetary space missions for infrared imaging spectrometer (Galileo/NIMS, IKS/Phobos, Cassini/VIMS, OMEGA/Mars Express, VIRTIS/Venus Express, VIRTIS/Rosetta). He is currently involved in the future ARIEL mission of European Space Agency (ESA) in the infrared spectrometer devoted to exoplanets' transit spectroscopy.

He has been head of department at LESIA (Laboratoire d'Études Spatiales et d'Instrumentation en Astrophysique) in France from 2010 to 2018.