Hydrogen halides HBr/DBr/TBr and HI/DI/TI: Born-Oppenheimer rovibrational spectrum

Abstract

The full bound rovibrational spectra E ( ν , L ) for the ground electronic state X 1 Σ + of the hydrogen bromine HBr and hydrogen iodine HI is calculated in the Born-Oppenheimer approximation. As a starting point an analytical expression for the potential energy curve V(R), valid in the entire domain R ∈ [ 0 , ∞ ) , is obtained in the form of a two-point Padé approximant that correctly reproduces the asymptotic behavior for small R → 0 and large R → ∞ internuclear distances. Remaining free parameters are fixed by making a fit with the experimental RKR points. In a second stage, the rovibrational spectra E ( ν , L ) is obtained by solving the nuclear Schröodinger equation with nuclear interaction V(R). It was found that the potential energy curve for the ground electronic state X 1 Σ + supports a total of 798/748 rovibrational states with maximal vibrational/rotational quantum numbers v max = 19 / 17 and L max = 65 / 66 for hydrogen halides HBr/HI, respectively. Through a simple modification in the nuclear Schröodinger equation, the bound rovibrational spectra E ( ν , L ) is obtained for the isotopological species with deuterium (D) and tritium (T) content: DBr/TBr (1575/2329 states in total with ν max = 27 / 34 and L max = 92 / 112 ) and DI/TI (1485/2207 states in total with ν max = 25 / 31 and L max = 93 / 114 ).