Ro-vibrationally averaged dipole moments of linear triatomic molecules

Abstract

We discuss here which of the dipole moment components of a linear triatomic molecule (of type A–B–A or A–B–C) will vanish, and which can be observed with non-zero values. We aim to resolve some confusion arisen in connection with the relationship between vibrationally averaged structures and the values of components of the electric dipole moment μ. We have previously demonstrated that a linear triatomic molecule, whose equilibrium structure is linear, will necessarily be observed as being bent on ro-vibrational average (see J. Mol. Spectrosc., 343 (2018) 54–61, and references therein). Accordingly, the b-axis component μb attains a non-zero value. However, it is ‘integrated away’ when the rotation of the molecule about the a axis is considered; the a axis coincides with the molecular axis at the linear geometry. Therefore, for triatomic molecules of type A–B–C, with A ≠ C, only the a-axis component μa survives to be observed in Stark experiments, and an A–B–A linear molecule such as CO2 shows zero permanent dipole moment on observation. Numerical checks of these assertions were successfully done for the linear molecules CO2 and HCO+ using wavefunctions and dipole moment functions determined ab initio. The 〈μa〉0 value thus calculated for the vibrational ground state of X∼1Σ+ HCO+ is 3.933 D, which is in good agreement with experimental value of 3.922(31) D. The non-zero 〈μb〉0 value, derived theoretically and experimentally for CO2, provides further evidence that this linear molecule shows a bent average structure on observation. Strategies for comparing experimental and calculated dipole moment values are suggested.