Title: Ro-vibrationally averaged molecular structure of benzene: Why almost the same bond lengths are observed for the C H and C D bonds?
Abstract: Different from the well-established understanding that the CH bond length is longer than the CD bond length in the H(D)-isotopologues due to the anharmonicity of the potential, almost the same values of CH(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 CαH(D)α bond in [C5H(D)5Cα]H(D)α. The CαH(D)α stretching local mode (Lstr) gives, as usual, longer CαHα than CαDα 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 CαHα than for CαDα 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 Lstr mode against the others in L⊥ and L∥ modes, nearly cancel, resulting in almost the same CH and CD 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 CH bonds region, which is confirmed from the theoretical and experimental values of the inertial defect.