A b i n i t i o molecular orbital calculations on HBr−2: Geometry, frequencies, and enthalpy changes

Abstract

HBr−2 has D∞h symmetry at both the second-order (MP2) and third-order (MP3) Mo/ller–Plesset perturbation levels of theory with the extended basis sets, whereas the Hartree–Fock level of theory predicts that it has C∞v symmetry. A potential energy map is calculated with the MP2 method as a function of two parameters, i.e., the distance of two Br atoms and the displacement of H from the center of them. Two-dimensional vibration analysis is performed by using this potential energy map. The calculated ν1 is 200 cm−1 and the ν3 is 837 cm−1 in HBr−2, and those in DBr−2 are 199 and 569 cm−1, respectively. Thus the ratio of the asymmetric vibration (ν3)H/(ν3)D is 1.47, being somewhat greater than the value of √2 expected for a harmonic oscillator. The enthalpy changes (ΔH°) in the reaction of Br− with an HBr molecule are determined by both the MP3 total energy changes and the thermal energy changes between the reactants and the product. The calculated enthalpy change of −21.2 kcal/mol is in good agreement with the experimental one (−21 kcal/mol) recently observed by Caldwell and Kebarle. These calculated data on HBr−2, which will provide us with a useful guide for future measurements of gas-phase vibrational spectra, are compared with those on HCl−2 and HF−2.