Rotation-vibrational states of H + 3 and the adiabatic approximation By Alexander Alijah 1 & Juergen Hinze 2 1 Departamento de Qu´ ımica, Universidade de Coimbra, 3004-535 Coimbra, Portugal 2 Fakult¨ at f¨ ur Chemie, Universit¨at Bielefeld, Postfach 100131, 33501 Bielefeld, Germany We discuss recent progress in the calculation and identification of rotation-vibra- tional states of H + 3 at intermediate energies up to 13000 cm −1 . Our calculations are based on the potential energy surface of Cencek et al., which is of sub micro-hartree accuracy. As this surface includes diagonal adiabatic and relativistic corrections to the fixed nuclei electronic energies, the remaining discrepancies between our calcu- lated and experimental data should be due to the neglect of non-adiabatic coupling to excited electronic states in the calculations. To account for this, our calculated energy values were adjusted empirically by a simple correction formula. Founded on our understanding of the adiabatic approximation we suggest two new approaches to account for the off diagonal adiabatic correction, which should work, however they have not been tested yet for H + 3 . Theoretical predictions made for the above- barrier energy region of recent experimental interest are accurate to 0.35 cm −1 or better. Keywords: H + 3 , rotation-vibrational states, adiabatic approximation, adiabatic corrections, non-adiabatic corrections 1. Introduction There appears to be no need to explicate here the importance of H + 3 and its rotation- vibrational states in astrophysics. The role it plays in planetary atmospheres, dense and diffuse interstellar clouds or even in the early development of our universe will surely be discussed and presented in great detail in this issue by those, who are experts in these fields. The focus of our presentation will be the description and analysis of an accurate and precise calculation of the rotation-vibrational states of H + 3 , the most simple triatomic molecule. This is done with the aim to extrapolate guidelines from our experience, which should be useful for similar ab initio calcu- lations of the rotation-vibrational states of other triatomic or even more complex molecules in the future. We apologize for not reviewing the many other earlier ab initio calculations of the rotation-vibrational states of H + 3 , as this has been done in the past, and by other authors of this issue, e.g. Kutzelnigg & Jaquet (2006), Tennyson et al. (2006). At the same time we are grateful for the highly, sub micro-hartree, accurate potential energy surface of H + 3 , which resulted from an extensive electronic structure calcu- lation, with the imaginative explicit inclusion of electron correlation, by Cencek et Article submitted to Royal Society T E X Paper