Vibrational spectroscopy of H2He+ and D2He+
Graphical abstract
Introduction
H2He+ is a fundamental open-shell molecular system consisting of two protons, one -particle, and three electrons. To the best of our knowledge it was first detected, in 1925, in a mass spectrum by Hogness and Lunn [1]. This molecular ion, as well as larger complexes of the He-solvated series , have been unambiguously observed by mass-spectrometric means in a drift tube [2] and in He-droplet experiments [3].
As the H2He+ molecular ion is composed of the only elements abundantly available at the very beginning of the universe, it might have been formed at the earliest stages of chemical evolution. Most importantly, it must have played a crucial role as the intermediate in the fundamental inelastic or reactive collisions between ions and He atoms, as well as in the collision between the first molecule of the primordial universe, the HeH+ ion, detected recently [4] in the hot gas of the planetary nebula NGC 7027, and hydrogen atoms. Therefore, the detailed knowledge of at least the potential energy surface (PES) of H2He+ [5], [6] is of fundamental importance for astronomy (the excited electronic states of H2He+ are well separated from the ground state). Due to the presence of two H atoms, the molecular ion has two nuclear-spin isomers, ortho- and para-H2He+ (a similar statement holds for D2He+).
The PES of H2He+ has been explored experimentally by numerous reactive scattering experiments through the reaction + He and its isotopic variants [7], [8], [9], [10], [11], where v is the vibrational quantum number. Due to its endothermicity of 0.806 eV [7], the reaction exhibits strong enhancement upon vibrational excitation.
Experimental investigations of the (ro)vibrational bound states of H2He+ via spectroscopy are extremely sparse. The only investigation available up to date, due to Carrington and co-workers [12], [13], is an unusual one, in which a mass-selected and highly-excited beam of H2He+ ions was subjected to microwave radiation. Those ions very close to the dissociation limit were subsequently dissociated by an electric field and the fragments counted as a function of the excitation frequency. Several microwave and millimeter-wave transitions have been observed for H2He+ [13]; in particular, a para transition close to 21.8 GHz and an ortho transition at 15.2 GHz, exhibiting fine- and hyperfine substructure. As the states involved in these transitions are close to the dissociation limit, the interpretation of these spectra provided a considerable challenge for first-principles computations [6].
Scattering and photodissociation simulations on the related PESs, as well as bound rovibrational states and transitions between these states in the ground electronic state of H2He+ have all been calculated with increasing accuracy during the last decades [6], [12], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25]. In the most recent work [6], high-level ab initio computations were used to construct two very similar analytical PESs, accurately including the important long-range part of the interaction between and He. Both PESs feature a global minimum with an equilibrium dissociation energy of cm−1 at the linear H–H–He configuration. One of these PESs, called FCI, is heavily utilized during the present study. In Ref. [6], computations of the bound states on these PESs were executed with two different variational techniques, one utilizing the DVR3D code [26] and the other a coupled-channels variational method (CCVM) [27]. Both yielded the lowest bound state at cm−1, which corresponds to a dissociation energy of cm−1 for para-H2He+ and cm−1 for ortho-H2He+ (the latter is higher by about 58 cm−1 due to dissociation into , see also Table 1, where j is the quantum number associated with the rotation of the diatomic unit). The PES of H2He+() is thus characterized by a relatively deep well and allows the ion to harbour more than a dozen vibrational states and hundreds of bound rovibrational states with total angular momenta up to , where J is the quantum number corresponding to the overall rotation of the molecular ion. In another study, a plethora of rovibrational resonances [28] with widely different lifetimes were found beyond the dissociation limit, though utilizing a different, less sophisticated PES [29]. All the bound states essentially correspond to strongly coupled –He stretching and bending motions, while the H–H stretch motion is expected to be around 1800 cm−1, which is just below the dissociation limit of ortho-H2He+. The high quality of the recent first-principles computations facilitate reliable assignment suggestions [6], in particular for the near-dissociation spectra measured some 20 years ago [13]. Since the dissociation energy is in the infrared range probed by our experiments, one must address the question whether the spectral features observed can be interpreted as those belonging to a semirigid linear molecule or require sophisticated variational treatments whereby rigidity of the molecular ion is not assumed.
To the best of our knowledge, no experimental (ro)vibrational spectroscopic data, apart from those already mentioned [12], [13], are available for this molecule and its isotopologues, despite its potential astronomical relevance. To improve our knowledge about the structure and dynamics of the H2He+ and D2He+ systems, we need to obtain high-resolution rovibrational and rotational spectra of these elusive molecules, preferentially yielding their fundamental transitions and beyond. On our path to generate this knowledge, we present here the first low-resolution vibrational fingerprints of H2He+ and D2He+, obtained by using a combination of a 4 K cryogenic ion trap apparatus [30] and the widely tunable free electron laser at the FELIX facility [31]. Furthermore, we present accurate variational calculations of the rovibrational states and transitions of H2He+ and D2He+, based on the three-dimensional FCI potential surface described in Ref. [6], as well as second-order vibrational perturbation theory (VPT2) [32], [33], [34] calculations based on the linear H–H–He equilibrium structure.
As to the structure of the rest of this paper, the experimental details are given in Section 2, while the rovibrational eigenstate calculations are described in Section 3. Sections 4 and 5 summarize the spectral results obtained during this study for H2He+ and D2He+, respectively, as well as a comparison of the experimental results with their computational counterparts, aiding the understanding of all the experimental features. Finally, in Section 6, we sketch a path how to obtain high-resolution spectra for the two ions investigated. The approach outlined is similar to that taken recently for the proton–helium cations [35], [36], [37]. Section 6 also contains a summary of the results of this study.
Section snippets
Experimental setup
The experimental setup employed during this study is elucidated using the scheme shown in Fig. 1. The central part of this experiment is a 22-pole ion trapping machine, called FELION [30], which is nearly identical to the one described in detail in Ref. [38]. Molecular ions are produced in an external storage ion source. In this source, electrons with small kinetic energy ( 20 eV) are used to ionize (and also fragment) the precursor gas. After mass selection in a linear quadrupole mass filter,
Preliminaries
In its ground electronic state H2He+ may be considered as a semi-rigid open-shell molecular ion with a linear equilibrium structure of point-group symmetry. Nevertheless, especially in its higher rovibrational states, we may also consider H2He+ as a more or less floppy Van der Waals complex that tunnels between two equivalent linear equilibrium structures with He on either side of the subunit and assign it to the permutation-inversion symmetry group , also called
Low-resolution spectroscopy of H2He+
The experimental spectrum obtained for H2He+ is shown in Fig. 6, together with a simulated spectrum based on the line lists from the variational calculations. The D2FOPI and CCVM calculations yield indistinguishable spectra. As we used n-H2 as a precursor in the ion source, we assume that its ratio of 3:1 is transferred to the ratio of H2He+ generated in the ion trap. At the cryogenic conditions of the experiment all transitions originate from the lowest quantum levels of -H2He+. At
Low-resolution spectroscopy of D2He+
The spectrum measured for D2He+ is shown in Fig. 7, again in combination with the spectrum simulated with the theoretically calculated line lists. Here again, for the same reason, only the CCVM spectrum is shown. We assume the -ratio of D2He+ to be 2:1, while only the lowest , 1, 2, and 3 levels are substantially populated at an assumed rotational temperature of 15 K. Due to the lower wavenumbers of the fundamental vibrational modes and the correspondingly lower zero-point energy, the PES
Conclusions and outlook
Using a combination of a cryogenic ion trap machine with a highly tunable and powerful pulsed IR source a number of IR vibrational modes of the fundamental molecules H2He+ and D2He+ have been identified experimentally at low resolution. The measurements are supplemented with high-level ab initio electronic structure and first-principles nuclear-motion computations of the rovibrational states and transitions for both ions. Unfortunately, due to the detection via multi-photon dissociation, not
CRediT authorship contribution statement
Oskar Asvany: Investigation, Formal analysis, Writing - original draft. Stephan Schlemmer: Funding acquisition, Writing - review & editing. Ad van der Avoird: Investigation, Formal analysis, Writing - original draft. Tamás Szidarovszky: Investigation, Formal analysis, Writing - original draft. Attila G. Császár: Investigation, Formal analysis, Writing - original draft.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
We acknowledge the support of Radboud University and of the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), providing the required beam time at the FELIX Laboratory. We highly appreciate the skillful assistance of the FELIX staff. The research leading to the results presented has been supported by the project CALIPSOplus under the Grant Agreement 730872 from the EU Framework Programme for Research and Innovation HORIZON 2020. The German co-authors have been supported by the
References (62)
- et al.
Observation of a microwave spectrum of the long-range He… complex
Chem. Phys. Lett.
(1996) - et al.
Ab initio predicted rotation-vibration energy levels of
J. Mol. Spectrosc.
(1995) - et al.
Ab initio calculated rotation–vibration linestrengths for
J. Mol. Spectrosc.
(1997) - et al.
Revisiting the potential energy surface for the He + HeH+ + H reaction at the full configuration interaction level
Chem. Phys. Lett.
(2009) - et al.
DVR3D: a program suite for the calculation of rotation-vibration spectra of triatomic molecules
Comput. Phys. Commun.
(2004) - et al.
The free-electron-laser user facility FELIX
Infrared Phys. Technol.
(1995) - et al.
A systematic study of molecular vibrational anharmonicity and vibration-rotation interaction by self-consistent-field higher derivative methods. Linear polyatomic molecules
Chem. Phys.
(1990) - et al.
The labeling of parity doublet levels in linear molecules
J. Mol. Spectrosc.
(1975) The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices
J. Comput. Phys.
(1975)- et al.
Numerical simulations of kinetic ion temperature in a cryogenic linear multipole trap
Int. J. Mass Spectrom.
(2009)
The ionization of hydrogen by electron impact as interpreted by positive ray analysis
Phys. Rev.
Formation of helium cluster ions () and () in a very low temperature drift tube
Z. Phys. D
Cationic complexes of hydrogen with helium
ChemPhysChem
Astrophysical detection of the helium hydride ion HeH+
Nature
The electronic structure of
Int. J. Quant. Chem. Quant. Chem. Symp.
Near dissociation states for –He on MRCI and FCI potential energy surfaces
Phys. Chem. Chem. Phys.
A pulsed-field ionization photoelectron secondary ion coincidence study of the + He proton transfer reaction
J. Chem. Phys.
Photoionization study of ion–molecule reactions in mixtures of hydrogen and rare gases
J. Chem. Phys.
He + ion-molecule reaction: A comparison between experimental and quantum-mechanical results
Phys. Rev. A
The effects of collision energy and vibrational excitation on + He reactions
J. Chem. Phys.
Collinear reactive scattering of state-selected + He HeH+ + H: A method for probing dynamical resonances
J. Chem. Phys.
Microwave and millimeter-wave spectrum of the He… long-range complex
J. Chem. Phys.
Predicted vibration–rotation levels of H2He+ and its isotopomers
J. Chem. Phys.
Radiative association of
J. Chem. Phys.
The potential energy surface and near-dissociation states of He-
J. Chem. Phys.
Predictions of microwave and far-infrared transitions in
Mon. Not. Royal Astron. Soc.
The He + HeH+ + H reaction: Ab initio studies of the potential energy surface, benchmark time-independent quantum dynamics in an extended energy range and comparison with experiments
J. Chem. Phys.
Photodissociation dynamics of weakly bound in intense light fields
Phys. Rev. A
Full-dimensional simulation of the laser-induced alignment dynamics of H2He+
Mol. Phys.
A general variational approach for computing rovibrational resonances of polyatomic molecules. Application to the weakly bound H2He+ and H2CO systems
J. Chem. Phys.
Rovibrational resonances in H2He+
J. Chem. Theory Comput.
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