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.

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.

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.

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.

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.

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.

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.

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.

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.