Vibrational Bound States of the He 2 Ne + Cation † Jose´ Zu´ niga,* ,‡ Adolfo Bastida,* ,‡ Alberto Requena,* ,‡ Nadine Halberstadt,* ,§ J. Alberto Beswick,* ,§ and Kenneth C. Janda* ,| Departamento de Quı ´mica Fı ´sica, UniVersidad de Murcia, 3010 Murcia, Spain, Laboratoire Collisions, Agre´gats, Re´actiVite´, IRSAMC, UniVersite´ de Toulouse, UPS, and CNRS, UMR5589, F-31062 Toulouse, France, and Department of Chemistry and Institute of Surface and Interface Science, UniVersity of California at IrVine, IrVine, California 92697-2025 ReceiVed: May 29, 2009; ReVised Manuscript ReceiVed: September 4, 2009 The vibrational bound states of the He 2 Ne + complex have been determined using a potential energy surface previously published by Seong et al. [J. Chem. Phys. 2004, 120, 7456]. The calculation was performed by sequential diagonalization-truncation techniques in a discrete variable representation using Radau hyper- spherical coordinates. There are 52 bound levels. The ground state has an energy of 605.3 cm -1 above the absolute minimum and lies about half way to dissociation. The evaporation energy of one He atom is equal to 866.1 cm -1 . Only four levels have energies below the classical energy for dissociation, and all the other 48 states are bound by the zero-point energy of the HeNe + fragment. The implications of the properties of the eigenvalue spectrum and of the corresponding wave functions on the vibrational relaxation dynamics and infrared spectra of He N Ne + clusters is discussed. Introduction The He N D + cluster ions, where D is an atomic or molecular dopant, are very interesting because they represent a simple example of gas phase “solvation” of an ion, and they are amenable to experimental study. They also constitute ideal model systems for dynamical studies in a novel medium, helium nanodroplets, which provide a homogeneous, superfluid, and extremely cold environment for spectroscopic and dynamical studies of molecular species. The final stage of many experi- ments is the electron-impact ionization of the doped cluster. This leads to a violent fragmentation of the droplet and a distribution of He N D + , n , N, that is surprisingly difficult to predict even in the relatively simple case where the dopant is a single rare gas atom. 1–5 The relative stability of small mixed rare gas cluster ions of the type He n Rg + has been examined by Murrell et al., 6 Seong et al., 7 and Brindle et al. 8 The first element of this series, HeNe + , has been extensively studied because of its relevance to the Ne + ion mobility in helium. 9 Its electronic structure is particularly interesting since the ionization energy of helium is only 2.99 eV higher than that of neon. This difference is small enough to induce a partial delocalization of the charge from the neon to the helium atom, resulting in weak covalent bonding. For instance, with the potentials used in the present work the (He-Ne) + dissociation energy is D e ) 0.669 eV (5397 cm -1 ). Unexpectedly, the mass spectra of the He N Ne + species do not show any structure, whereas the helium and argon ones do. Diffusion Monte Carlo simulations 8 have shown that this absence of shell structure is due to important zero-point effects resulting in very diffuse wave functions and a smooth variation of the incremental bonding energy with the number of helium atoms. The ion is also very interesting. It is the ionic core in the He N Ne + series, the additional helium atoms being mainly bound by electrostatic interaction to this core. Its second helium is bound by 0.127 eV (1026 cm -1 ). This value is relatively large relative to pure electrostatic bonding and may be at least partially responsible for the fact that fragments are more prevalent in experimental data than in ref 8. Ab initio calculations of Seong et al. 7 for the He 2 Ne + complex have yielded an asymmetric collinear (He-Ne-He) + geometry with a small barrier between two equivalent minima. Because of its practical interest, as well as its peculiar potential energy surface, we have undertaken a study of its bound states which could be useful for experiments trying to identify its presence or its vibrational relaxation rates. Vibrational relaxation is expected to play an important role in the dissociation of helium droplets once the charge has been localized on the neon atom, and the two main candidates to relax energy are HeNe + and He 2 Ne + . In this paper, we present the calculation of all vibrational states of the He 2 Ne + complex for total angular momentum zero. The theoretical treatment of these types of wide amplitude floppy systems relies heavily on the choice of internal coordinates. Orthogonal coordinates are particularly useful because the kinetic energy operators are easy to evaluate, and this facilitates the calculation of the corresponding differential matrix elements. This issue has been discussed in great detail by Aquilanti and co-workers. 10–13 The hyperspherical versions of these coordinates are particularly interesting for systems such as He 2 Ne + with two identical light atoms and a third heavier atom. In this work we have used Radau hyperspherical coordinates. The potential energy surface is given by a diatomics-in- molecule (DIM) model based on ab initio calculations for He 2 Ne + and the best available potentials for He 2 and HeNe dimers, as discussed in detail in ref 7. This potential has been previously used for diffusion Monte Carlo calculations of † Part of the “Vincenzo Aquilanti Festschrift”. * To whom correspondence should be addressed. E-mail: zuniga@um.es; bastida@um.es; requena@um.es; nhalbers@irsamc.ups-tlse.fr; beswick@ irsamc.ups-tlse.fr; kcjanda@uci.edu. ‡ Universidad de Murcia. § Universite´ de Toulouse. | University of California at Irvine. J. Phys. Chem. A 2009, 113, 14896–14903 14896 10.1021/jp905043t  2009 American Chemical Society Published on Web 10/07/2009