On the rovibrational levels of the H₃⁺ and H₂D⁺ molecules

Abstract

Variationally exact rovibrational levels for the H₃ ⁺ and H₂D⁺ molecules are calculated using a recently published accurate potential. Vibrational fundamentals are v _{A 1} = 3191 cm^-1 and v_E = 2494 (2521·6) cm^-1 for H₃ ⁺ and v ₁ = 3000 cm^-1, v ₂ = 2184 cm^-1 and v ₃ = 2310 cm^-1 for H₂D⁺. For H₃ ⁺ calculated ground state rotational constants are B ₀ = 43·51 (43·57) cm^-1, C ₀ = 20·59 (20·71) cm^-1, D_J ⁰ = 0·04 (0·05) cm^-1, D_{J K} ⁰ = -0·07 (-0·10) cm^-1 and D_K = 0·04 (0·04) cm^-1 (where experimental results are given in parenthesis). 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 H₂D⁺ are discussed.