Ro-vibrationally averaged molecular structure of benzene: Why almost the same bond lengths are observed for the CH and CD bonds?

Abstract Different from the well-established understanding that the C H bond length is longer than the C D bond length in the H(D)-isotopologues due to the anharmonicity of the potential, almost the same values of C H(D) bond lengths, derived from the experimental rotational constants, have been reported by Baba group for the cases of benzene, naphthalene, and anthracene H(D)-isotopologues. Taking benzene as an example, we show here that this unexpected, curious finding can be explained in terms of the ab initio stretching and bending potentials for each local mode. The explanation is based on the viewpoints that the experimental rotational constants correspond to the bond lengths projected onto each of the relevant principal-axis planes, and that on observation, we cannot distinguish the plus and minus bending angles in both out-of-plane ( L ⊥ ) and in-plane ( L ∥ ) bending local modes with respect to the C α H(D)α bond in [C5H(D)5Cα] H(D)α. The Cα H(D)α stretching local mode ( L str ) gives, as usual, longer Cα Hα than Cα Dα bond-lengths due to its anharmonicity. However, in both L ⊥ and L ∥ modes, the vibrationally averaged bond-length projected onto the principal axis is shorter for Cα Hα than for Cα Dα due to the larger averaged bending angle for the former bond. When we consider the projected bond-lengths, these antithetical factors, i.e., one in the L str mode against the others in L ⊥ and L ∥ modes, nearly cancel, resulting in almost the same C H and C D bond lengths as is experimentally reported. The vibrationally averaged structure of benzene in the zero-point vibration state is predicted to be non-flat for the peripheral C H bonds region, which is confirmed from the theoretical and experimental values of the inertial defect.