First-principles simulations of vibrational states and spectra for H5(+) and D5(+) clusters using multiconfiguration time-dependent Hartree approach

The Role of Tunneling in the Spectra of H5+ and D5+ up to 7300 cm-1

The spectra for H₅⁺ and D₅⁺ are extended to cover the region between 4830 and 7300 cm^-1. These spectra are obtained using mass-selected photodissociation spectroscopy. To understand the nature of the states that are accessed by the transitions in this and prior studies, we develop a four-dimensional model Hamiltonian. This Hamiltonian is expressed in terms of the two outer H₂ stretches, the displacement of the shared proton from the center of mass of these two H₂ groups, and the distance between the H₂ groups. This choice is motivated by the large oscillator strength associated with the shared proton stretch and the fact that the spectral regions that have been probed correspond to zero, one, and two quanta of excitation in the H₂ stretches. This model is analyzed using an adiabatic separation of the H₂ stretches from the other two vibrations and includes the non-adiabatic couplings between H₂ stretch states with the same total number of quanta of excitation in the H₂ stretches. Based on the analysis of the energies and wave functions obtained from this model, we find that when there are one or more quanta of excitation in the H₂ stretches the states come in pairs that reflect tunneling doublets. The states accessed by the transitions in the spectrum with the largest intensity are assigned to the members of the doublets with requisite symmetry that are localized on the lowest-energy adiabat for a given level of H₂ excitation.

The smallest proton-bound dimer H5+: theoretical progress

The protonated hydrogen dimer, H5+, is the smallest system including proton transfer, and has been of long-standing interest since its first laboratory observation in 1962. H5+ and its isotopologues are the intermediate complexes in deuterium fractionation reactions, and are of central importance in molecular astrophysics. The recently recorded infrared spectra of both H5+ and D5+ reveal a rich vibrational dynamics of the cations, which presents a challenge for standard theoretical approaches. Although H5+ is a four-electron ion, 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 in treating the nuclear motion could also become cumbersome due to their high dimensionality, floppiness and/or symmetry. These systems are prototypical examples for studying large-amplitude motions, as they are highly delocalized, interconverting between equivalent minima through internal rotation and proton transfer motions requiring state-of-the-art treatments. Recent advances in the computational vibrational spectroscopy of the H5+ cation and its isotopologues are reported from full quantum spectral simulations, providing important information in a rigorous manner, and open perspectives for further future investigations. This article is part of a discussion meeting issue 'Advances in hydrogen molecular ions: H3+, H5+ and beyond'.

Communication: Infrared photodissociation spectroscopy of the H6+ cation in the gas phase

The H₆⁺ cation was generated in a pulsed-discharge supersonic expansion of hydrogen and mass-selected in a time-of-flight spectrometer. Its vibrational spectrum was measured in the region of 2050-4550 cm^-1 using infrared photodissociation with a tunable OPO/OPA laser system. The H₆⁺ photodissociates, producing H₅⁺, H₄⁺, and H₃⁺ fragments; each of these fragment channels has a different spectrum. Computational studies identify two low-lying isomers described in previous work, whose energies were evaluated at the CCSD(T)/cc-pVTZ//MP2/cc-pVTZ level of theory. A D_2d species having an H₂⁺ cation bridging between two perpendicular H₂ molecules is the global minimum structure. A C_s structure with an H₃⁺ core ion bound to both H₂ and an H atom lies 4.0 kcal mol^-1 higher in energy. Anharmonic vibrational spectra were computed for each of these isomers with second-order vibrational perturbation theory (VPT2) in combination with density functional theory at the B2PLYP/cc-pVTZ level. The comparison between experimental and predicted spectra confirms the presence of both the D_2d and C_s structures and explains the spectra in different fragmentation channels. Although we find reasonable agreement between the experiment and the spectra predicted by VPT2 computations, a more sophisticated computational approach is needed to better understand this complex system.

Probing the Relationship Between Large-Amplitude Motions in H5(+) and Proton Exchange Between H3(+) and H2

Understanding the spectroscopy and dynamics of H5(+) is central in gaining insights into the H3(+) + H2 → H5(+) → H2 + H3(+) proton transfer reaction. This molecular ion exhibits large-amplitude vibrations, which allow for the transfer of a proton between H3(+) and H2 even in its ground vibrational state. With vibrational excitation, the number of open channels for permutations of protons increase. In this work, the minimized energy path variant of diffusion Monte Carlo is used to investigate how the energetically accessible proton permutations evolve as H5(+) is dissociated into H3(+) + H2. Two mechanisms for proton permutation are investigated. The first is the proton hop, which correlates to large-amplitude vibrations of the central proton in H5(+). The second is the exchange of a pair of hydrogen atoms between H3(+) and H2. This mechanism requires several proton hops along with a 120° rotation of H3(+) within the H5(+) molecular ion. This analysis shows that while there is a narrow region of configuration space over which both isomerization processes are energetically accessible, full permutation of the five protons in H5(+) more likely occurs through a stepwise mechanism. Such full permutation of the protons becomes accessible when the shared proton stretch is excited to the vpt = 2 or 3 excited state. The effects of deuteration and rotational excitation of the H2 and H3(+) products are also investigated. Deuteration inhibits permutation of protons, while rotational excitation has only a small impact on these processes.

Theoretical predictions on the role of the internal H3(+) rotation in the IR spectra of the H5(+) and D5(+) cations

The IR spectra of the H5(+) and D5(+) cations in the mid- and far-IR spectral regions have been recently reported by experimentalists. These spectra show very rich vibrational patterns representing a challenge for state-of-the-art theoretical methods to provide definitive interpretations of them. Using a full-dimensional quantum anharmonic treatment, within the MCTDH approach, together with ab initio potential and dipole moment surfaces, the predominant features in the spectra are assigned, completing an important part in previous theoretical and experimental comparisons. The internal rotation of the H3(+) unit by exciting the H3(+)-H2 stretching mode is found to correspond to the new calculated features at 1182, 1876, and 2139 cm(-1) of the H5(+) spectrum, leading to a consistent assignment with the experimental spectra. In the calculated spectra of both H5(+) and D5(+) clusters, the progressions in the H3(+)-H2 stretch of the shared proton and the in- and out-of- plane H3(+) rotation are demonstrated to be the main features. Such states are expected to play a central role in the low temperature hydrogen/deuterium proton hop/exchange H3(+) + H2 reactions.