A global potential energy surface for H3+

Reactions of H2, HD, and D2 with H2+, HD+, and D2+: Product-Channel Branching Ratios and Simple Models

We present measurements of the product-channel branching ratios of the reactions (i) HD+ + HD forming H2D+ + D (38.1(30)%) and HD2+ + H (61.9(30)%), (ii) HD+ + D2 forming HD2+ + D (61.4(35)%) and D3+ + H (38.6(35)%), and (iii) D2+ + HD forming HD2++ D (60.5(20)%) and D3+ + H (39.5(20)%) at collision energies Ecoll near zero, i.e., below kB × 1 K. These branching ratios are compared with branching ratios predicted using three simple models: a combinatorial model (M1), a model (M2) describing the reactions as H-, H+-, D-, and D+-transfer processes, and a statistical model (M3) that relates the reaction rate coefficients to the translational and rovibrational state densities of the HnD3-n+ + H/D (n = 0, 1, 2 or 3) product channels. The experimental data are incompatible with the predictions of models M1 and M2 and reveal that the branching ratios exhibit clear correlations with the product state densities.

Three states global fittings with improved long range: singlet and triplet states of H

Full dimensional analytical fits of the coupled potential energy surfaces for the three lower singlet and triplet adiabatic states of H are developed, providing analytic derivatives and non-adiabatic coupling matrix elements. The fits are highly accurate and include an improved description of the long range interactions, including new terms for the description of the long range in the diatomic fits and the atom-diatom dissociation channels. The fits are based on the DIM formalism including three body terms in Hamiltonian matrix elements, each of them obeying S₂ permutational symmetry, where the positive charge is placed in either of the three hydrogen atoms, but the full system obeys S₃ permutational symmetry, invariant under all permutations of the nuclei. The ab initio points used in the fitting are obtained from a complete basis set extrapolation, made for all electronic states. Total root mean square errors of the fits are 27 and 12 cm^-1, for the singlet and triplet states, respectively. The errors in the channels are lower than 2 cm^-1 and 6 cm^-1 for the H + H and H⁺ + H₂ channels respectively. The new fits have been used to calculate the rovibrational bound states of the lowest singlet and lowest triplet states showing very good agreement with previous calculations in the literature.

Near-resonant effects in the quantum dynamics of the H + H2 + → H2 + H+ charge transfer reaction and isotopic variants

The non-adiabatic quantum dynamics of the H + H₂ ⁺ → H₂ + H⁺ charge transfer reactions, and some isotopic variants, is studied with an accurate wave packet method. A recently developed 3 × 3 diabatic potential model is used, which is based on very accurate ab initio calculations and includes the long-range interactions for ground and excited states. It is found that for initial H₂ ⁺(v = 0), the quasi-degenerate H₂(v' = 4) non-reactive charge transfer product is enhanced, producing an increase in the reaction probability and cross section. It becomes the dominant channel from collision energies above 0.2 eV, producing a ratio between v' = 4 and the rest of v's, which that increase up to 1 eV. The H + H₂ ⁺ → H₂ ⁺ + H exchange reaction channel is nearly negligible, while the reactive and non-reactive charge transfer reaction channels are of the same order, except that corresponding to H₂(v' = 4), and the two charge transfer processes compete below 0.2 eV. This enhancement is expected to play an important vibrational and isotopic effect that needs to be evaluated. For the three proton case, the problem of the permutation symmetry is discussed when using reactant Jacobi coordinates.

The H2+ + HD reaction at low collision energies: H3+/H2D+ branching ratio and product-kinetic-energy distributions

The fully state-selected reactions between H2+ molecules in the X+ 2Σg+(v+ = 0, N+ = 0) state and HD molecules in the X 1Σg+(v = 0, J = 0) state forming H3+ + D and H2D+ + H have been studied at collision energies Ecoll between 0 and kB·30 K with a resolution of about 75 mK at the lowest energies. H2 molecules in a supersonic beam were prepared in Rydberg-Stark states with principal quantum number n = 27 and merged with a supersonic beam of ground-state HD molecules using a curved surface-electrode Rydberg-Stark decelerator and deflector. The reaction between H2+ and HD was studied within the orbit of the Rydberg electron to avoid heating of the ions by stray electric fields. The reaction was observed for well-defined and adjustable time intervals, called reaction-observation windows, between two electric-field pulses. The first pulse swept all ions away from the reaction volume and its falling edge defined the beginning of the reaction-observation window. The second pulse extracted the product ions toward a charged-particle detector located at the end of a time-of-flight tube and its rising edge defined the end of the reaction-observation window. Monitoring and analysing the time-of-flight distributions of the H3+ and H2D+ products in dependence of the duration of the reaction-observation window enabled us to obtain information on the kinetic-energy distribution of the product ions and determine branching ratios of the H3+ + D and H2D+ + H reaction channels. The mean product-kinetic-energy release is 0.46(5) eV, representing 27(3)% of the available energy, and the H3+ + D product branching ratio is 0.225(20). The relative reaction rates correspond closely to Langevin capture rates down to the lowest energies probed experimentally (≈kB·50 mK).

General mathematical formulation of scattering processes in atom-diatomic collisions in the RmatReact methodology

Accurately modelling cold and ultracold reactive collisions occurring over deep potential wells, such as [Formula: see text], requires the development of new theoretical and computational methodologies. One potentially useful framework is the R-matrix method adopted widely for electron-molecule collisions which has more recently been applied to non-reactive heavy-particle collisions such as Ar-Ar. The existing treatment of non-reactive elastic and inelastic scattering needs to be substantially extended to enable modelling of reactive collisions: this is the subject of this paper. Herein, we develop the general mathematical formulation for non-reactive elastic and inelastic scattering, photoassociation, photodissociation, charge exchange and reactive scattering using the R-matrix method. Of particular note is that the inner region, of central importance to calculable R-matrix methodologies, must be finite in all scattering coordinates rather than a single scattering coordinate as for non-reactive scattering. This article is part of a discussion meeting issue 'Advances in hydrogen molecular ions: H₃⁺, H₅⁺ and beyond'.

Non-adiabatic effects in the H3+ spectrum

The effect of non-adiabatic coupling on the computed rovibrational energy levels amounts to about 2 cm-1 for H3+ and must be included in high-accuracy calculations. Different strategies to obtain the corresponding energy shifts are reviewed in the article. A promising way is to introduce effective vibrational reduced masses that depend on the nuclear configuration. A new empirical method that uses the stockholder atoms-in-molecules approach to this effect is presented and applied to H3+. Furthermore, a highly accurate potential energy surface for the D3+ isotopologue, which includes relativistic and leading quantum electrodynamic terms, is constructed and used to analyse the observed rovibrational frequencies for this molecule. Accurate band origins are obtained that improve existing data. This article is part of a discussion meeting issue 'Advances in hydrogen molecular ions: H3+, H5+ and beyond'.

Hydrogen molecular ions: H3+, H5+ and beyond

Three decades after the spectroscopic detection of H3+ in space, the inspiring developments in physics, chemistry and astronomy of Hn+ (n = 3, 5, 7) systems, which led to this Royal Society Discussion Meeting, are reviewed, the present state of the art as represented by the meeting surveyed and future lines of research considered. This article is part of a discussion meeting issue 'Advances in hydrogen molecular ions: H3+, H5+ and beyond'.