MOLECULAR PHYSICS, 1984, VOL. 51, NO. 4, 887-906 On the rovibrational levels of the H3 ÷ and H2D ÷ molecules by JONATHAN TENNYSON Science & Engineering Research Council, Daresbury Laboratory, Daresbury, Warrington WA4 4AD, England and BRIAN T. SUTCLIFFE Department of Chemistry, University of York, Heslington, York YO1 5DD, England (Received 18 ffuly 1983 ; accepted 11 October 1983) Variationally exact rovibrational levels for the H3+ and H2D ÷ molecules are calculated using a recently published accurate potential. Vibrational fundamentals are va1=3191 cm -1 and vE=2494 (2521.6) cm -1 for H3+ and vl=3000cm -1, v~=2184cm -x and v3=2310cm -1 for H~D +. For H3+ calculated ground state rotational constants are B0 = 43.51 (43-57) cm -1, Co = 20.59 (20-71) cm -1, D j ° = 0.04 (0.05) cm -1, Djn° = - 0.07 ( - 0.10) cm -1 and DK=0.04 (0-04)cm -1 (where experimental results are given in paren- thesis). An attempt is made to stabilize many vibrational states. We thus reassess the results of Carney and Porter. The implications for astrophysics, the interpretation of the infrared spectrum of H3+ near its dissociation limit and the unassigned spectrum of H,D + are discussed. 1. INTRODUCTION The H3 + molecular ion and its isotopic variants (HD~ +, H~D +, Ds+ etc.) are the simplest known polyatomic molecules from the point of view of electronic structure. The vibration-rotation spectra of these systems are of considerable consequence in astrophysics [1, 2]. H3 + and HD~ + have been the subject of extensive experimental investigation by Carrington et al. [3 ], who observed more than 26 000 transitions arising from molecules near their dissociation limit. These results are as yet unexplained. Infrared vibration-rotation spectra have been reported for H3 + by Oka [4] and for D3+ [5] and H2D+ [6] by Shy and co-workers. The H~D + spectrum remains unassigned. The simplicity of the systems means that it is possible to calculate ab initio and with high accuracy their rotation-vibration spectra, assuming that electronic and nuclear motions are separable. There are many highly accurate electronic potential energy surfaces available in the literature for these systems [7-11] and it is thus possible to concentrate on ab initio calculation of the vibration- rotation structure. The vibration-rotation spectra of these systems have been studied extensively by Carney and Porter [12-16] in a series of very detailed and careful papers. The potential energy surface used by these authors [9] was however variationally inferior to several [8, 10, 11] that are now available and they used one of a family of conventional methods of vibrational analysis based on the Eckart hamiltonian M.P. 2 F