Durham Research Online Deposited in DRO : 19

A new potential energy surface for the molecular ion He±H‡2 is used to predict microwave transitions that may be observable in environments such as circumstellar envelopes and planetary nebulae. For the vibrational ground state, transitions are predicted at wavelengths of 1215, 608, 405, 304, 244, 203, 175, 154, 137 and 124 mm. Key words: molecular processes ± ISM: molecules. 1 I N T R O D U C T I O N Chemical processes in the interstellar medium frequently involve molecular ions, especially in photodissociation regions such as circumstellar envelopes and planetary nebulae. Prominent species include CH, HCO and N2H . However, the simplest molecular ion, H‡2 , resists detection in the interstellar environment. Its lack of a dipole moment makes detection at infrared or radio frequencies dif®cult, although it does have a quadrupole spectrum that might be observable (Glinski, Schulz & Nuth 1997). However, the related ion He±H‡2 may also be present, and it has a large dipole moment that might make detection feasible even at relatively low densities. Bound He±H‡2 cannot be produced in collisions between He and H‡2 unless there is a third body present to remove the excess energy. This is unlikely in an interstellar environment, except perhaps in the inner regions of circumstellar envelopes. However, He±H‡2 can be formed in collisions between metastable He and neutral H2 by associative ionization, He ‡ H2 ! HeH‡2 ‡ e: …1† It is thus worthwhile to investigate the signatures by which He±H‡2 could be detected in interstellar space. To provide this information, rotation±vibration energy levels and microwave transitions calculated on a recently constructed potential energy surface (PES) are reported here. 2 C A L C U L AT I O N S Until recently, most theoretical studies on He±H‡2 used the potential energy surface calculated by McLaughlin & Thompson (1979, hereafter MT79) and subsequently ®tted to a functional form by Joseph & Sathyamurthy (1987). For example, Tennyson & Miller (1987) used this early surface to calculate energy levels from which the microwave and infrared spectra of He±H‡2 may be inferred. However, the MT79 surface is not very accurate, and SÏpirko & Kraemer (1995) and Falcetta & Siska (1996) have carried out improved calculations to remedy its more obvious de®ciencies. Unfortunately, even these improved surfaces have not proved adequate to explain the recent spectroscopic studies of neardissociation states of He±H‡2 carried out by Carrington et al. (1996). We have therefore calculated a new potential energy surface for He±H‡2 . The theoretical procedure is described in detail elsewhere (Meuwly & Hutson 1998). Interaction energies between He and H‡2 were calculated using a quantum chemical approach with a very extensive basis set of atomic orbitals. The method chosen [QCISD(T)] incorporates most of the electron correlation contributing to the binding between He and H‡2 . The calculations are performed on a grid of 378 intermolecular con®gurations. In He±H‡2 the three internal coordinates are the H ‡ 2 bond length r, the distance R from the helium atom to the centre of mass of H‡2 and the angle v between the two distance vectors. This Jacobi coordinate system is widely used in the study of intermolecular interactions. In neutral complexes the coupling between internal degrees of freedom and the intermolecular coordinates R and v is often very weak. Under these circumstances it is possible in a ®rst approximation to ®x r at the equilibrium separation of the monomer. This is not the case for He±H‡2 , so it was necessary to calculate the full threedimensional potential energy surface. The calculation of energy levels requires an analytical form for the potential surface. We ®tted the energies to a ̄exible functional form which takes into account the correct R long-range behaviour of the interaction (Meuwly & Hutson 1998). The ®tted potential V…R; r; v† was then used in the bound program (Hutson 1993) to calculate the rovibrational energies for the complete rotation± vibration Hamiltonian. The states of H‡2 and He±H ‡ 2 may be classi®ed as either ortho or para for total nuclear spin quantum numbers I ˆ 1 or 0 respectively. Ortho-H‡2 can occupy only odd rotational levels while para-H ‡ 2 can occupy only even levels. The ortho/para symmetry is conserved in the complex (apart from very small terms arising from the nuclear hyper®ne interaction). We ®nd that the potential energy surface for He±H‡2 supports 16 bound vibrational states of ortho symmetry and 14 states of para symmetry correlating with the v ˆ 0 level of H‡2 . The infrared bending and intermolecular stretching fundamentals lie at 642 and 716 cm respectively. The intramolecular stretch Mon. Not. R. Astron. Soc. 302, 790±792 (1999) q 1999 RAS *E-mail: [email protected] at U niersity of D uham on A uust 9, 2015 hp://m nras.oxjournals.org/ D ow nladed from (H‡2 v ˆ 1) lies slightly above the dissociation limit of the complex at about 1825 cm, redshifted by 370 cm from the free H‡2 monomer. The potential energy surface for H‡2 has pronounced minima at the two linear geometries, v ˆ 0± and 180±. Because these two minima are equivalent and separated by a high barrier, the low-lying states of the complex occur as pairs separated by small tunnelling splittings. In the calculations, the even tunnelling levels arise solely from para states of H‡2 , and the odd levels arise from ortho states. The overall energy level pattern is essentially that of a linear molecule, except that each level occurs in ortho and para modi®cations, and the two have slightly different rotational constants. All the microwave lines of He±H‡2 thus occur as closely spaced doublets. For the lower states, the splittings are too small to be resolved at current astronomical resolutions. The principal aim of the present paper is to report on spectroscopic transitions predicted in the microwave and far-infrared region. The most promising microwave transitions for interstellar observation are the pure rotational transitions in the lowest few vibrational states. The rotational constant of He±H‡2 is larger than those of most other species found in the interstellar medium. The lowest allowed (J ‡ 1 à J) rotational transitions for the ground state and the excited intermolecular stretching and bending state are given in Table 1. Further transition frequencies can be obtained from the authors upon request. Microwave and FIR transitions in He±H‡2 791 q 1999 RAS, MNRAS 302, 790±792 Table 1. Calculated rotational energy levels and line positions for the lowest few vibrational levels of He±H‡2 . The last line of each section gives the dipole moment of the vibrational state calculated for J ˆ 0. Bound state energies (cm) Allowed transitions …mm) J ortho para J ÿ J ortho para Ground state 0 ±1754.269 ±1754.251 1 ±1746.032 ±1746.014 1±