First-principles computations and experimental measurements of transition energies are carried out for vibrational overtone lines of the triatomic hydrogen ion H3+ corresponding to floppy vibrations high above the barrier to linearity. Action spectroscopy is improved to detect extremely weak visible-light spectral lines on cold trapped H3+ ions. A highly accurate potential surface is obtained from variational calculations using explicitly correlated Gaussian wave function expansions. After nonadiabatic corrections, the floppy H3+ vibrational spectrum is reproduced at the 0.1\,\,cm-1 level up to 16\,600\,\,cm-1.

In this study we consider Born-Oppenheimer coupled equations with the aim of deriving a single approximated Born-Oppenheimer-type equation which contains the effect of the nonadiabatic coupling terms. The derivation is done for a situation where N (⩾2) adiabatic surfaces, including the ground-state surface, have a degeneracy along a single line (e.g., conical intersection). The new equation can be considered as an extended version of the Born-Oppenheimer approximation. Although derived for a nongeneral case, the extension to a general case is also discussed. As special cases we treat, in the present paper, the two-state system and, in the following paper, the three-state system.

Calibration-quality ab initio adiabatic potential energy surfaces (PES) have been determined for all isotopologues of the molecular ion ${\mathrm{H}}_3^{+}$ . The underlying Born–Oppenheimer electronic structure computations used optimized explicitly correlated shifted Gaussian functions. The surfaces include diagonal Born–Oppenheimer corrections computed from the accurate electronic wave functions. A fit to the 41 655 ab initio points is presented which gives a standard deviation better than 0.1 cm⁻¹ when restricted to the points up to 6000 cm⁻¹ above the first dissociation asymptote. Nuclear motion calculations utilizing this PES, called GLH3P, and an exact kinetic energy operator given in orthogonal internal coordinates are presented. The ro-vibrational transition frequencies for ${\mathrm{H}}_3^{+}$ , H₂D⁺, and ${\mathrm{HD}}_2^{+}$ are compared with high resolution measurements. The most sophisticated and complete procedure employed to compute ro-vibrational energy levels, which makes explicit allowance for the inclusion of non-adiabatic effects, reproduces all the known ro-vibrational levels of the ${\mathrm{H}}_3^{+}$ isotopologues considered to better than 0.2 cm⁻¹. This represents a significant (order-of-magnitude) improvement compared to previous studies of transitions in the visible. Careful treatment of linear geometries is important for high frequency transitions and leads to new assignments for some of the previously observed lines. Prospects for further investigations of non-adiabatic effects in the ${\mathrm{H}}_3^{+}$ isotopologues are discussed. In short, the paper presents (a) an extremely accurate global potential energy surface of ${\mathrm{H}}_3^{+}$ resulting from high accuracy ab initio computations and global fit, (b) very accurate nuclear motion calculations of all available experimental line data up to 16 000 cm⁻¹, and (c) results suggest that we can predict accurately the lines of ${\mathrm{H}}_3^{+}$ towards dissociation and thus facilitate their experimental observation.

The authors present diabatic and adiabatic potential energy surfaces for the three lowest electronic singlet states of H3+. The modeling of the surfaces is based on the multi-sheeted double many-body expansion method which consists of dressing the various matrix elements of the diatomics-in-molecules potential matrix with three-body terms. The avoided crossing between the two lowest states and the conical intersection between the second and the third state are accurately represented by construction.